GENESYS V8. Synthesis I: Classic Filter Synthesis. Eagleware Corporation 635 Pinnacle Court Norcross, GA Copyright

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1 GENESYS V8 Synthesis I: Classic Filter Synthesis Copyright Eagleware Corporation 635 Pinnacle Court Norcross, GA Phone: (678) FAX: (678) Printed in the USA

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3 TABLE OF CONTENTS Introduction xi GENESYS and Synthesis Programs xi FILTER xii A/FILTER xiii M/FILTER xiv Chapter 1:FILTER Operation First Example Units Modifying a Design Noise-BW N-help Output Defaults Writing Superstar Files Q Defaults ExitingFILTERToWindows Using SuperStar and Filter Together Using Other GENESYS Supported Tools Chapter 2:FILTER Types Monotonic or Elliptic Minimum Inductor All-pole Lowpass Minimum Capacitor All-pole Lowpass Minimum Inductor All-pole Highpass Minimum Capacitor All-pole Highpass Minimum Inductor All-pole Bandpass Minimum Capacitor All-pole Bandpass Coupled All-pole Bandpass Filter Types Mixed Coupling Reactors Top C Coupled All-pole Bandpass Top L Coupled All-pole Bandpass Shunt C Coupled All-pole Bandpass Tubular All-pole Bandpass Blinchikoff 4th Order Flat Delay All-pole Bandpass Symmetry Preserving All-pole Bandpass SymmetricTransform Symmetric TransformLimitations FullTransformAll-poleBandstop Minimum Inductor Elliptic Lowpass Minimum Capacitor Elliptic Lowpass Minimum Inductor Elliptic Highpass Minimum Capacitor Elliptic Highpass

4 iv Table of Contents Full Transform Elliptic Bandpass Minimum Inductor ( Zig Zag ) Elliptic Bandpass Elliptic Bandstop Chapter 3:FILTER Examples Example 1 - Transmission Line resonators Example 2 - Bessel Crystal Filter Example 3 - Filter Symmetry Example 4 - Creating a Unique Lowpass Prototype Example 5 - Designing a Bandpass Filter From the New Prototype Chapter 4 :A/FILTER Operation First Example Units Modifying a Design Noise-BW & N-Help Output Defaults Component Defaults Preferences Chapter5:A/FILTERTypes Lowpass All Pole Minimum Inductor Lowpass All Pole Minimum Capacitor Lowpass All Pole Single Feedback Lowpass All Pole Multiple Feedback Lowpass All Pole Low Sensitivity Lowpass All Pole VCVS Lowpass All Pole State Variable (biquad) Lowpass Elliptic Minimum Capacitor Lowpass Elliptic VCVS Lowpass Elliptic State Variable Highpass All Pole Minimum Inductor Highpass All Pole Minimum Capacitor Highpass All Pole Single Feedback Highpass All Pole Multiple Feedback Highpass All Pole Low Sensitivity Highpass All Pole VCVS HighpassAll Pole State Variable Highpass Elliptic Minimum Inductor Highpass Elliptic VCVS Highpass Elliptic State Variable Bandpass All Pole Top C Bandpass All Pole Top L

5 Table of Contents v Bandpass All Pole Multiple Feedback Bandpass All Pole Multiple Feedback Max Gain Bandpass All Pole Dual Amplifier Bandpass All Pole Dual Amplifier Max Gain Bandpass All Pole Low Sensitivity Bandpass All Pole State Variable Bandpass Elliptic VCVS Bandpass Elliptic State Variable Bandstop All Pole VCVS Bandstop All Pole State Variable ComparisonTable Chapter 6:A/FILTER Examples Example 1 - Lowpass Minimum Inductor Example 2 - Lowpass Minimum Capacitor Example 3 - Lowpass Single Feedback Example 4 - Lowpass Multiple Feedback Example 5 - Bandpass Maximum Gain Dual Amplifier 100 Chapter 7:M/FILTER Menus Overview of rhe M/FILTER Screen Using the Procedure Flowchart File Menu Type Menu Schematic Menu Layout Menu Utilities Menu Setup Menu LayoutWindow Tuning Parameters Chapter 8:M/FILTER Operation Entering Parameters Using SuperStar with M/FILTER Electrical or Physical? Writing DXF/Gerber Files Selecting Output Options Chapter 9:M/FILTER Types Filter Shapes And Processes Filter Physical Size Filter Examples Edge Coupled Bandpass Hairpin Bandpass

6 vi Table of Contents Stepped-Z Lowpass Stepped-Z Bandpass Combline Bandpass Interdigital Bandpass Elliptic Lowpass Elliptic Bandpass End Coupled Bandpass Stub Lowpass Stub Highpass Edge Coupled Bandstop Chapter 10: M/FILTER Error Messages Appendix A:Filter Shapes Butterworth Chebyshev Bessel Blinchikoff Flat Delay Bandpass Singly-Equalized Delay Singly-Terminated Cauer-Chebyshev User Filters ObservingG Values Prototype Files Included Prototype Files Linear Phase Equiripple Error Transitional Gaussian Singly-terminated Cauer-chebyshev Bessel Passband Elliptic Stopband Prototype File Selection Assistance N-Help Appendix B: Noise Bandwidth General Case Noise Bandwidth Example Frequency Range And Step Size Appendix C : File Formats Appendix D: GIC Transform Fundamentals Appendix E:Training Appendix F:References

7 Introduction GENERAL INFORMATION For system requirements, installation, and setup information, refer to the GENESYS SIMULATION manual. This SYNTHESIS manual describes Eagleware s classic filter synthesis programs, FILTER, A/FILTER, and M/FILTER. (S/FILTER is in a separate manual). GENESYS AND SYNTHESIS PROGRAMS The synthesis programs are launched from the SuperStar Professional simulator. This enhances the integration of the synthesis and simulation process. GENESYS synthesis programs also support the simulator Touchstone from HP/EEsof, generic Berkeley SPICE 2 and SPICE 3 formats and specific SPICE based simulators. Although very slow, SPICE based simulation provides a rich set of output data unavailable in linear and harmonic balance simulators such as bias simulation, oscillator starting time analysis and filter transient analysis. The synthesis programs write text and SCHEMAX files for SuperStar and text files for Touchstone and SPICE. Thus a schematic environment for both Touchstone and SPICE simulation is provided by writing SCHEMAX files from the synthesis programs. The use of GENESYS programs with Touchstone and SPICE simulators is described in more detail in the Reference manual.

8 xii Introduction A/FILTER and FILTER have a Place in EQUATE block checkbox in the Component Setup dialog. If this box is checked, the component quality factors and op-amp parameters are placed in the SuperStar EQUATE block. This allows easy group (gang) tuning of components, and allows easy sensitivity analysis with respect to part quality. FILTER FILTER makes designing L-C filters a snap. With GENESYS you can simulate the filter performance, customize or optimize the filter and check the effects of parasitics. The following chapters are devoted to FILTER: FILTER Operation Chapter 1 FILTER Types Chapter 2 FILTER Examples Chapter 3 Filter Shapes Appendix A Noise Bandwidth Appendix B Chapter 1 provides the basic information required to design all the filters built into FILTER. Chapter 2 and Appendix A are designed for further clarification and reference. They discuss the filter topologies and response shapes. They may be read rather quickly and referred to later when designing certain filters. Chapter 3 provides additional ideas and tips on filter design and the use of FILTER and SuperStar Professional to modify, optimize and customize filter designs. Appendix B (Noise Bandwidth) discusses the effective noise bandwidth of filters. FILTER automatically integrates the S-parameter data file of any filter analyzed by

9 Introduction xiii SuperStar to determine the effective noise bandwidth of the filter. FEATURE OVERVIEW FILTER synthesizes many L-C filter types suitable for a wide range of applications. Principle features include: 20 filter topologies. Topology choices provide for practical realizations and specific application needs A wide range of transfer approximations (amplitude and delay response shapes) Effective noise bandwidth calculation Writing SuperStar circuit or schematic files. A/FILTER A/FILTER makes designing active filters fast and easy. A/FILTER also includes EQUALIZE for active equalizer synthesis. With a GENESYS simulator, you can simulate the filter performance, customize or optimize the filter, and check the effects of parasitic reactances or finite op-amp parameters, such as unity gain bandwidth. The following chapters are devoted to A/FILTER: A/FILTER Operation Chapter 4 A/FILTER Types Chapter 5 A/FILTER Examples Chapter 6 GIC Transform FundamentalsAppendix D Chapter 4 introduces program operation with a quick example and describes unique A/FILTER features. For information on filter shape approximations or noise bandwidth calculations are given in Appendix A and B. Chapter 5 discusses the filter types designed by A/FIL- TER. The topologies are discussed, and the benefits of

10 xiv Introduction each is given. This chapter can be read rather quickly, and used as a reference when selecting a filter type. In Chapter 6, additional ideas and tips on filter design and the use of A/FILTER and SuperStar to modify optimize and customize filter designs are given. FEATURE OVERVIEW A/FILTER synthesizes many filter types suitable for a wide range of applications. Principle features include: Over 30 filter topologies. Choices provide for practical realization of specific application needs. Many types allow specification of passband gain. A wide range of transfer approximations (amplitude, phase and delay response shapes). Effective noise bandwidth calculation Writing SuperStar circuit or schematic files. M/FILTER M/FILTER is the GENESYS synthesis program which designs microwave distributed filters. SPICE simulation poorly supports distributed circuits and Touchstone does not include the models required for certain popular microwave filters, so the preferred GENESYS simulator for use with M/FILTER is SuperStar Professional. A feature of M/FILTER is the ability to absorb discontinuties during synthesis. Independent SuperStar response calculation verifies the synthesis process. The following chapters are devoted to M/FILTER: M/FILTER Menus Chapter 7 M/FILTER Operation Chapter 8 M/FILTER Types Chapter 9 M/FILTER Error Messages Chapter 10

11 Introduction xv The book HF Filter Design and Computer Simulation also includes additional information on filter theory, elements and a variety of practical microwave filter structures. FEATURE OVERVIEW The principal features of M/FILTER include: Lowpass, highpass, bandstop and a wide range of bandpass filter types Five different implementation processes including simple electrical, microstrip, stripline, slabline and coaxial. Automatically writes SuperStar.SCH and.ckt files Automatically displays layout or schematic on screen Allows specification of units, size and cross hairs for final board layout

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13 Chapter 1 FILTER Operation FILTER is launched by starting GENESYS and then selecting FILTER from the Synthesis menu (top of the screen). The FILTER main window and menu appear. The screen should look like the sample screen figure. Input fields appear on the bottom section of the screen. The top part contains the schematic and values of the filter Figure 1-1 Sample FILTER screen.

14 2 FILTER Operation being designed. At any time you may press F1 for help on theinput at thecursorlocation, orpressalt-f1 (hold down the Alt key and press F1) forgeneralhelp. The cursor is initially located on the order input field. You may press the arrow keys to move between and edit input fields. To automatically continue to the next input field, press the Tab or Enter key. To go to the previous input field, press Shift-Tab. Optionally, the left mouse button may be used to select a radio button or to move the cursor. When the cursor is on an input field you may type in a new value for that field. As you change an input, the output will automatically update. FIRST EXAMPLE Try an example. The design will be a 7th order lowpass filter with a.25 db passband ripple Chebyshev response. The cutoff frequency is 70 MHz and the characteristic impedance is 50 ohms. First, press Alt-T to access the topology menu. Select the change type item. A new subwindow will appear. This window will contain three sets of radio buttons. Use the up and down arrow keys or the left mouse button to change thehighlightedradiobuttonineachsection,andusethe Tab or Enter key to move between sections. Make these selections: Lowpass, All-pole, and Minimum Capacitor. Select the Close button to continue (press Enter when it is highlighted. Next, the shape subwindow appears. Select the Chebyshev button. Choose the Close button to continue. Additional help about shapes can be obtained before closing the window by pressing F1 (help). You may then use PgUp and PgDn or the scroll bar to move between help pages. Press Escape to exit the help window. The additional information in this section pertains to filters which have unequal input and output impedances, such as even order

15 FILTER Operation 3 Chebyshev and singly-terminated filters. More about this is given in Appendix A. The cursor will now be located on the main window at the order prompt. Enter 7. (Filters up to 21st order may be designed for most types.) The suggested range area of the screen gives you a reminder of the range for an input. Next enter the passband ripple: FILTER directly computes the lowpass prototype G values for popular response shapes and does not use tables for these shapes, so any passband ripple greater than zero and less than 3 db may be chosen. This is true even for elliptic Cauer-Chebyshev filters. The cutoff frequency of all-pole filters, such as Butterworth, is normally defined as the 3 db attenuation frequency. The cutoff of filters with ripple in the passband, such as Chebyshev, is often defined as the ripple value. FILTER allows the user to specify the attenuation, A a,of the cutoff frequency for Butterworth and Chebyshev filters. For these filters, A a is prompted. For normally defined cutoff attenuation, enter A a equal to the ripple for Chebyshev filters, and A a equal to db for Butterworth filters. For this example, enter 0.25 at the A a prompt. Next, for Butterworth and Chebyshev filters, FILTER prompts for F ca, the desired cutoff frequency. FILTER then computes and displays the cutoff frequency at the normally defined cutoff attenuation. This value is used by the FILTER program during the design process. For filter response shapes other than Butterworth and Chebyshev, the prompts for A a and F ca are skipped, and the program prompts for F c. Enter 70 at the F ca prompt in this example.

16 4 FILTER Operation Finally the input impedance Rin is requested. Enter 50. After entering the input impedance, FILTER will compute and display the output impedance. In the case of odd order Chebyshev filters, the output impedance is equal to the input impedance. For even order Chebyshev filters, the output impedance will be greater or less than the input impedance, depending on the subtype selected. FILTER automatically calculates and displays the correct impedance. Certain filter types allow specifying the output impedance independent of the input impedance. For these filters, FILTER requests the desired output impedance. The results on the screen should be similar to the screen shown earlier in this chapter. OTHER DATA Also displayed on the lower right portion of the screen is the summation of the lowpass prototype g values of the filter just designed. This quantity may be used to estimate the insertion loss, L o, and group delay, D o, of the filter at frequencies well removed from the cutoff. These estimated parameters are also displayed. UNITS The units used in FILTER are the same units used in SuperStar. They are: Resistance...ohms Inductance...nanohenries Capacitance...picofarads Frequency...Megahertz

17 FILTER Operation 5 MODIFYING A DESIGN FILTER remembers the selections previously made, so modifying a design is easy. This is true even if FILTER is exited. For a permanent record, the filter design may be saved to a *.fi$ file (a setup file, not a circuit file) using the file menu options save, save as, and open. NOISE-BW FILTERcanbeusedtocalculatetheeffectivenoisebandwidth of lowpass and bandpass filters. This is done by integrating the amplitude response of any filter analyzed by the SuperStar Professional program. This offers the advantage of being unrestricted to theoretical ideal response types. Even the effects of finite component Q or approximate bandpass transforms are taken into account. Using FILTER to calculate filter effective noise bandwidth is discussed in Appendix B. N-HELP See Appendix A for information on N-Help. OUTPUT DEFAULTS When FILTER writes a SuperStar Professional text or schematic file, FILTER specifies in the OUTPUT block of the SuperStar Professional file what output data is to be displayed. The data specified by FILTER may be changed by the user by pressing Alt-S to choose the Setup menu. Select the circuit file default item. Up to four lines of graphical data (GPH and SMH) or one line of tabular data (DSP or PRI) may be specified. The rules for use of these codes is identical to their use in SuperStar Professional. Please refer to the description of these codes in the Element Reference chapter of the SIMULATION manual. Select Close to return to the main FILTER window. The normal form of an OUTPUT block line is

18 6 FILTER Operation GPH S Once changed in FILTER, these output options are used to write a text or shematic file until new output data is specified. The output data format may also be manually edited in SuperStar but this does not effect the output data format written the next time by FILTER. WRITING SuperStar FILES FILTER automatically writes SuperStar Professional circuit text files (.CKT) or schematic files (.SCH) for SCHE- MAX. SuperStar Professional then computes and displays the frequency responses of that filter. SuperStar Professional is used to tune or optimize the filter, test the effect of component Q, test the results with standard values, compute and display the group delay or investigate effects of component tolerances. To write a SuperStar circuit file, press F8, or select Write.CKT file from the file menu. Then enter the desired filename using the file dialog box. FILTER automatically uses the extension.ckt unless a different extension is entered. To write a schematic file for SCHEMAX, select Write.SCH file from the file menu. After writing the.ckt or.sch file you may select to launch SuperStar Professional or return to FILTER. The.CKT files written by FILTER are ASCII files. SCHE- MAX.SCH files are binary and should not be opened or viewed in a text editor. Q DEFAULTS When FILTER designs filters it assumes infinite component Q unless otherwise specified. The effects of finite component Q are readily observed by analyzing filters with SuperStar Professional. When FILTER writes a file, the default component Q is one million.

19 FILTER Operation 7 The component Q used for writing files may be changed by selecting the Components option from the Setup menu. The effective Q of resonators (inductor and capacitor combinations) is given by: 1 Qr = Q Q l c For example, an inductor Q of 120 and capacitor Q of 600 results in a resonator Q of 100. FILTER writes all capacitors with equal Q and all inductors with equal Q. They may be independently specified once in SuperStar Professional. Once the default Qs are changed, they remain in effect until they are changed again, or a new filter setup file (*.FI$) is loaded. EXITING FILTER TO WINDOWS FILTER can be exited by selecting the Exit option from the File menu. Alternatively, programs may be closed by pressing Alt-F4. USING SuperStar AND FILTER TOGETHER After FILTER has written the SuperStar Professional circuit file it prompts for the next desired action: Return to FILTER Automatically run SuperStar If Run SuperStar Professional is chosen, FILTER causes the following to occur: FILTER terminates, SuperStar Professional runs, the last circuit file written by FILTER is loaded, SuperStar Professional analyzes that circuit and you are given control of SuperStar. This provides a fast and convenient environment for designing, simulating and customizing filters.

20 8 FILTER Operation USING OTHER GENESYS SUPPORTED TOOLS SPICE is useful for determining the time-domain response of filters. Using FILTER with other GENESYS supported simulators is described in the GENESYS SIMULATION manual. This description includes an example time-domain response.

21 Chapter 2 FILTER Types Filter type specifies whether the filter is lowpass, highpass, bandpass or bandstop. Type also specifies elliptic or all-pole. Each of these generic types may have alternate forms. For example, the lowpass type, can have a series inductor first (minimum capacitor) or a shunt capacitor first (minimum inductor). Schematics of the 20 filter topologies designed by FILTER are given on the following pages. The values of the elements in these filters determine the response shape. Response shapes, such as Butterworth and Cauer-Chebyshev are discussed in Appendix A. All-pole filters have monotonically increasing attenuation in the stopbands with increasing frequency from the passband. All zeros of transmission occur at DC or infinite frequencies. The elliptic transfer function has one or more zeros at finite frequencies. For a given number of inductors, this type of filter has superior performance in some respects to all-pole filters. Selectivity is improved at the expense of ultimate attenuation and complexity. The elliptic functions used in FILTER are of the Cauer- Chebyshev type. This is further discussed in Appendix A. The minimum order for Cauer-Chebyshev filters is three.

22 10 FILTER Types MONOTONIC OR ELLIPTIC When do you choose a monotonic stopband filter and when an elliptic filter? For a given number of inductors, the elliptic filter will give better selectivity. For a given number of components, the monotonic filter will generally give better selectivity. The elliptic filter is less advantageous when high stopband attenuation is required. The elliptic filter frequency response sensitivity to component tolerances may be greater, and tuning may be more difficult. Table 2-1 gives some examples of selectivity of 0.25 db passband ripple Chebyshev and Cauer-Chebyshev lowpass filters. Each filter has a cutoff frequency of 1 MHz. The db column numbers in the table are the frequencies in MHz where the stopband attenuation has reached the specified level of 40 or 70 db. Also given in the table are the number of inductors and the number of total components in each order filter. Table 2-1 Selectivity in 0.25dB Ripple 1 MHz lowpass filters Order Components Inductors 40 db 70 db All-Pole Chebyshev 6th MHz 2.82 MHz 7th MHz 2.25 MHz Elliptic Cauer-Chebyshev 4th MHz 3.88 MHz 5th MHz 2.32 MHz 6th MHz 1.70 MHz 7th MHz 1.40 MHz

23 FILTER Types 11 MINIMUM INDUCTOR ALL-POLE LOWPASS MINIMUM CAPACITOR ALL-POLE LOWPASS L1 L1 L nh nh 6510 nh C pf C pf C pf C pf 3rd Order 4th Order L1 L2 L1 L nh 8209 nh 8824 nh nh C pf C pf C pf 3rd Order 4th Order All-pole lowpass minimum inductor (top) and minimum capacitor (bottom) filters. Minimum inductor and minimum capacitor subtypes are the lowpass options. Because inductors are usually larger, more expensive and have lower Q, minimum inductance filters are normally the first choice. For even order, both types have an equal number of inductors and capacitors, so subtype choice is less significant. Both types are open to ground and pass DC. However, at frequencies well into cutoff, a series inductor becomes a high impedance and a shunt capacitor becomes a low impedance. This may affect the selection in some applications, such as diplexers or in active interstage coupling networks where stability may be a factor.

24 12 FILTER Types MINIMUM INDUCTOR ALL-POLE HIGHPASS MINIMUM CAPACITOR ALL-POLE HIGHPASS C1 C2 C1 C pf L nh 3086 pf 2871 pf L nh 1798 pf L nh 3rd Order 4th Order C1 C1 C pf 2437 pf 3891 pf L1 L2 L1 L nh 7714 nh 7177 nh 4495 nh 3rd Order 4th Order All-pole highpass minimum inductor (top) and minimum capacitor (bottom) filters. Minimum inductor and minimum capacitor refer to the relative number of inductors or capacitors in the odd order highpass filter, and not the lowpass prototype. Many of the same factors affect the selection of Highpass subtype as in the lowpass filter case. However, unlike the lowpass case, DC coupling to ground is effected by the selection.

25 FILTER Types 13 MINIMUM INDUCTOR ALL-POLE BANDPASS L2 C2 L nh nh C pf pf L nh C pf 3rd Order L2 C2 L4 C4 L nh nh C pf pf L nh 21.7 nh C pf pf 4th Order Minimum inductor is a full transform to bandpass of the minimum inductor lowpass filter. Each series L in the lowpass prototype becomes a series L-C network, and each shunt C in the lowpass prototype becomes a parallel L-C network. Therefore the minimum inductor and minimum capacitor bandpass filters have an equal number of inductors and capacitors for even and odd order. This filter type is most useful for wide bandwidth (>30%) filters. For narrower bandwidths, consider using a coupled filter type.

26 14 FILTER Types MINIMUM CAPACITOR ALL-POLE BANDPASS L1 C1 L3 C nh pf L nh 1642 nh C pf pf 3rd Order L1 C1 L3 C nh pf L nh 2818 nh C pf pf L nh C pf 4th Order The all-pole bandpass minimum capacitor type is a direct transform of the all-pole lowpass minimum capacitor type. Each series L in the lowpass prototype becomes a series L-C network, and each shunt C in the lowpass prototype becomes a parallel L-C network. This filter type is similar to the minimum inductor type but has a series resonator first. This filter type is most useful for wide bandwidth (>30%) filters. For narrower bandwidths, consider using a coupled filter type.

27 FILTER Types 15 COUPLED ALL-POLE BANDPASS FILTER TYPES The minimum inductor and minimum capacitor bandpass subtypes have the disadvantage that for narrow bandwidths, or even moderate bandwidths, the values of the elements in the series and shunt branches are very different from each other. This makes practical construction of the inductors very difficult. The shunt inductors tend smaller and the series inductors tend larger for narrower bandwidths. For this reason, the minimum inductor and minimum capacitor bandpass subtypes are more useful for wider bandwidths, particularly at higher center frequencies where parasitics are often a greater problem. Therefore for narrow bandwidths, the top capacitor (top C), top inductor (top L), shunt capacitor (shunt C) and tubular coupled bandpass subtypes are frequently used. All resonators are of the same type (series or parallel), so component values are closer in value to each other. These narrow bandwidth filters also provide for input and output matching via the end coupling reactors. These filters are excellent choices for filters with bandwidths less than 20%, and are useful for bandwidths of up to 30%. The passband shape, bandwidth and center frequency will increase in error for larger bandwidths. The routines in FILTER apply the Cohn lowpass to bandpass accuracy enhancements for these topologies [2]. Also, for wider bandwidths, the stopband and skirts of these topologies become asymmetric. For the top-c bandpass filter, the stopband and skirt above the passband suffer. For the shunt-c, top-l and tubular topologies the stopband and skirt below the passband suffer. As the bandwidth is narrowed, the symmetry of these filters improves, and as the bandwidth is widened, the symmetry of the response worsens.

28 16 FILTER Types For wider bandwidths, the order requirement determined by the N-Help routine in FILTER is pessimistic on one side or the other for these subtypes. Often, selectivity is more important on one side than another, and the subtype choice can be made accordingly. Otherwise, a higher order, a narrower bandwidth or the full transform filters must be used. Sample responses are shown on the following pages to illustrate this issue. MIXED COUPLING REACTORS If selectivity is almost adequate, the trick of changing a coupling capacitor to an inductor can improve selectivity on one side at the expensive of the selectivity on the other side. An example of this transform is given in Chapter 3. This technique may also be used to change the DC coupling or stopband impedance characteristics of these filters. Eagleware sometimes receives requests to include approximate transform bandpass filters with mixed coupling elements, such as alternating capacitors and inductors. These filter types were not included for a specific reason. Approximate transform bandpass filters designed without the Cohn correction mentioned earlier are limited to an upper bandwidth limit of 2-5% percent, otherwise the resulting response has a significant frequency shift. Bandpass filters designed with practical inductor Q s are limited to bandwidths greater than 2-5% percent. Therefore, in general, there is no acceptable bandwidth for accurate design of this type of practical bandpass filters without the Cohn correction. Unfortunately the Cohn correction only applies to like coupling elements. The problem is not that a solution does not exist. The problem is that the closed formulas are not known. These filters can be designed by converting a coupling element type and using tuning or optimization techniques.

29 FILTER Types 17 TOP C COUPLED ALL-POLE BANDPASS C1 C3 C pf L1 220 nh C pf 248 pf L2 220 nh pf C pf 2nd order filter schematic and typical (5th order) response. The top-c bandpass filter subtype consists of shunt parallel resonant L-C circuits coupled via series capacitors. This type of filter is an approximate transform, with decreasing accuracy for increasing bandwidths. It is most accurate (and useful) for bandwidths of less than 30%. This type is very practical since all inductors are the same value, and that value can be specified by the user. Optionally, by choosing an inductor value just inside the given limit, the input and output coupling capacitors will become large enough so that they may be eliminated from the design.

30 18 FILTER Types TOP L COUPLED ALL-POLE BANDPASS L nh L nh C pf L3 692 nh L nh C pf L nh 2nd order filter schematic and typical (5th order) response. The top-l bandpass filter subtype consists of shunt parallel resonant L-C circuits coupled via series inductors. This type of filter is an approximate transform, with decreasing accuracy for increasing bandwidths. It is most accurate (and useful) for bandwidths of less than 30%. This type is very practical since all capacitors are the same value, and that value can be specified by the user. Optionally, by choosing a capacitor value just inside the given limit, the input and output coupling inductors will become small enough so that they may be eliminated from the design.

31 FILTER Types 19 SHUNT C COUPLED ALL-POLE BANDPASS L1 C2 L2 C4 330 nh pf C pf C pf 330 nh pf C pf 2nd order filter schematic and typical (5th order) response. The shunt-c coupled bandpass filter consists of series resonant L-C circuits, coupled via shunt capacitors. Like the top-c and top-l transforms, the shunt-c transform is also an approximate bandpass transform. It is most accurate (and useful) for bandwidths of less than 30%. This type is very practical since all inductors are the same value, and that value can be specified by the user. By choosing an inductor value just inside the given limit, the input and output coupling capacitors will become small enough so that they may be eliminated from the design.

32 20 FILTER Types TUBULAR ALL-POLE BANDPASS L1 C3 L2 FILTER C pf 470 nh C pf pf C pf 470 nh C pf 2nd order filter schematic and typical (5th order) response. The tubular bandpass filter is a derivative of the shunt-c coupled bandpass created by converting internal capacitor tee networks into equivalent pi networks. It is an approximate bandpass transform and is most accurate (and useful) for bandwidths of less than 30%. This type is often used as a basis for coaxial tubular filters. By choosing an inductor value just inside the given limit, the input and output coupling capacitors will become small enough so that they may be eliminated from the design.

33 FILTER Types 21 BLINCHIKOFF 4TH ORDER FLAT DELAY ALL-POLE BANDPASS L1 C1 L2 C3 L nh pf C pf 192 nh pf L nh nh C pf C pf The Blinchikoff 4th order wideband bandpass filter is unique in that it has constant delay through the passband[1]. It is a special class of filter whose properties were synthesized directly as a bandpass filter. This avoids the normal destruction of lowpass prototype phase properties during the transform to bandpass. The Blinchikoff bandpass filters are available for 30 to 70% bandwidth. Blinchikoff filters are further discussed in Appendix A.

34 22 FILTER Types SYMMETRY PRESERVING ALL-POLE BANDPASS It is well known that the Top-C coupled bandpass filter has poor symmetry for bandwidths exceeding 5% to 10%. Carassa proved[4] that the ratio of the number of transmission zeros in a filter at infinite frequency to the number at DC must be approximately 3:1 if the filter is to exhibit good delay and arithmetic amplitude symmetry for wide bandwidth. Unfortunately, none of the published lowpass to bandpass transforms result in a filter topology needed for symmetry. This is true for even the conventional bandpass transform, which has a multiplicity ratio of 1:1, and therefore has greater low side selectivity. It is feasible to manually modify the topology of a bandpass filter to achieve a multiplicity of 3:1. However, it is then necessary to numerically determine the required new component values. Many workers have contributed much to the art of symmetric filters. Szentirmai[5][6] developed methods for synthesizing symmetric bandpass filters. This approach developed a characteristic function which resulted in specified bandpass filter performance. Hummel[7] developed 2nd and 4th order bandpass filters with desirable phase characteristics. Blinchikoff and Savetman[8] carried forward Hummel s work and developed a class of wideband flat delay bandpass filters, and this work is the basis of the Blinchikoff filter designed in FILTER. Each of these works consider the bandpass directly to avoid undesirable lowpass to bandpass transformation effects. Consequently, network synthesis techniques are required to realize the filter. Eagleware has developed a general lowpass to bandpass transform with good symmetry attributes, which can be applied to filters of arbitrary degree and which uses simple closed form formulas to determine component values.

35 FILTER Types 23 SYMMETRIC TRANSFORM CONVENTIONAL SYMMETRIC TRANSFORM N=2 N=3 N=4 N=5 The all-pole lowpass to bandpass transform which satisfies these conditions is presented next. We will refer to this transform as the symmetric transform. On the left of the figure above are the topologies of conventional bandpass filters for orders two through five. We use the convention that bandpass filter order is equal to the order of the lowpass prototype from which it is developed. While not rigorous, the convention is broadly used. Shown above are the topologies of the symmetric bandpass filters of corresponding order. The symmetric bandpass filter topology results when the first and then every other shunt parallel resonator is replaced with a series resonator. The parallel to series resonator conversion is based on impedance inverters as published by Cohn[9]. It can be shown that the multiplicity ratio of these symmetric transform filters for even order is 3:1 and asymptotically approaches 3:1 with increasing odd order. The remaining task is therefore to find a process for determining compo-

36 24 FILTER Types nent values. An approximate solution is known and is the technique utilized in the symmetric transform incorporated in the FILTER program. Shown on the above figure are the amplitude and delay responses for a conventional 6th order 0.1 db ripple Chebyshev bandpass filter with 45% arithmetic bandwidth

37 FILTER Types 25 centered at 100 MHz, and for 6th order 0.1 db ripple Chebyshev symmetric transform bandpass filters designed by FILTER for 15%, 30%, 45%, 60% and 75% bandwidths. (The 75% filter was tuned somewhat in SuperStar). The results illustrate marvelous symmetry. SYMMETRIC TRANSFORM LIMITATIONS The approximate method used to compute component values limits the practical bandwidth. Depending on the acceptable levels of center frequency error, ripple or response error, and return loss, bandwidths to 40% or 50% are generally practical. If some error in the response is acceptable, for certain lowpass prototypes, or if optimization is employed, greater bandwidths may be specified. For wider bandwidth the passband is not equi-ripple, but the response is improved by tuning the resonator inductors or capacitors. The 75% bandwidth filter shown above required tuning of the resonators using SuperStar. For even wider bandwidths, some element values may be negative. The bandwidth at which this occurs is a function of the lowpass prototype selected. Prototypes with a large variation in G values, such as is the case with controlled phase prototypes, may be restricted to 20% or less bandwidth. It may be possible to extend the bandwidth before negative values result by reversing the order of the G-values. The delay preserving attributes of the symmetric transform is not as desirable as the symmetry attributes. The practical lower BW limit is similar to the conventional bandpass filter. As the bandwidth decreases, the ratio of the inductors in the series and shunt branches becomes extreme. For bandwidths below approximately 5% to 10%, the symmetry of the top-c coupled and the shunt-c

38 26 FILTER Types coupled bandpass filters is generally acceptable, and these filters are preferred.

39 FILTER Types 27 FULL TRANSFORM ALL-POLE BANDSTOP C pf L nh L nh 99.5 MHz L nh C pf C pf 99.5 MHz 99.5 MHz The bandstop filter is a full transform from the lowpass prototype. The input section is a shunt series resonant L-C network. The next branch is a series parallel resonant L-C network. This form is automatically chosen for the bandstop filter, so a subtype selection is not necessary.

40 28 FILTER Types MINIMUM INDUCTOR ELLIPTIC LOWPASS MINIMUM CAPACITOR ELLIPTIC LOWPASS C2 C pf pf L1 986 nh MHz L nh pf C3 Minimum Inductor L nh L nh L nh C pf C pf MHz Minimum Capacitor There are two elliptic lowpass filter subtypes in FILTER, minimum inductor and minimum capacitor. The minimum inductor subtype has a shunt capacitor for the input branch. The next branch is a series parallel resonant L-C. For odd order filters, the output branch is a shunt capacitor. For even order filters, the output branch is not a resonant network. It is a series inductor. The minimum capacitor elliptic lowpass has a series inductor for the input branch. The second branch is a shunt series L-C network. For odd order, the output branch is a series inductor. For even order, the output branch is just a shunt capacitor.

41 FILTER Types 29 MINIMUM INDUCTOR ELLIPTIC HIGHPASS MINIMUM CAPACITOR ELLIPTIC HIGHPASS C1 C3 300 pf L nh pf L nh C pf MHz Minimum Inductor C1 L nh pf L nh MHz C pf L nh Minimum Capacitor There are two elliptic lowpass subtypes in FILTER, minimum inductor and minimum capacitor. The minimum inductor subtype has a series capacitor in the input branch and has the minimum number of inductors. The next branch is a series L-C to ground. For odd order, the output branch is a series capacitor. For even order, the output branch is an inductor to ground. The minimum capacitor has a shunt inductor in the input branch and has the minimum number of capacitors. The next branch is a parallel L-C series branch. For odd order, the output branch is an inductor to ground. For even order, the output branch is a series capacitor. Notice the DC passing and bypassing characteristics of the elliptic highpass are different for minimum inductor and minimum capacitor.

42 30 FILTER Types FULL TRANSFORM ELLIPTIC BANDPASS C2 C pf pf L5 C5 L nh C pf L nh MHz L nh MHz L nh 327 nh C pf pf This type is a full bandpass transform of the minimum inductor elliptic lowpass prototype. Each shunt capacitor is transformed into a shunt parallel resonant L-C. Each series parallel resonant L-C is transformed into a pair of series parallel resonant L-C networks. The output series inductor of the even order lowpass prototype is transformed into a series branch series resonant L-C network. This filter has the same disadvantages as the all-pole full transform bandpass filter. This filter has the additional problem of stray capacity at the common node of the series branch parallel resonant network pair may be a problem.

43 FILTER Types 31 MINIMUM INDUCTOR ( ZIG ZAG ) ELLIPTIC BANDPASS C3 C pf L4 C6 L nh pf C pf L nh MHz L nh C pf nh C pf pf MHz An elliptic bandpass filter that reduces these problems is the minimum inductor subtype. It is a marvelous filter in that no other bandpass filter with the same number or fewer inductors can achieve the selectivity performance of this design. It is based on the work of R. Saal and E. Ulbrich[3]. When constructed with precision capacitors, tuning is accomplished by simply adjusting the zero frequencies with the inductors. The fact that this filter has not enjoyed wider use is clearly understood by anyone who has manually calculated the values for even one design. Theschematicfora4thorderfilterisshownabove.

44 32 FILTER Types ELLIPTIC BANDSTOP C2 C3 C pf pf pf L1 375 nh L2 9.7 nh L nh L nh L nh MHz MHz 99.5 MHz C pf C pf 99.5 MHz 99.5 MHz The elliptic bandstop filter input branch is a series L-C to ground. The next branch is series and consists of a cascade of parallel L-C networks. For odd order, the output branch is a series L-C to ground. For even order, the output branch is series and consists of one parallel L-C.

45 Chapter 3 FILTER Examples In this chapter, useful tricks and filter customization using SuperStar Professional are illustrated with various examples. These examples demonstrate SuperStar Professional and FILTER operation and interaction using text circuit files. EXAMPLE 1 - TRANSMISSION LINE RESONATORS A 5th order 0.25 db Chebyshev 860 to 900 MHz bandpass TC filter is designed and then converted to a top-c coupled transmission line resonator filter with similar performance characteristics. The original L-C design is done in FILTER and the modification in SuperStar. First start SuperStar and then launch FILTER from the Shell menu. Enter data into the FILTER input cells as illustrated in Figure 3-1. The final values in the schematic should be readable on your screen. If not, the view zoom may be controlled using the M, +, - and scroll buttons. Next, select Write.CKT File from the FILTER File menu, enter a filename and select Run SuperStar. FILTER terminates and SuperStar Professional runs and displays responses of the L-C filter. Press F8 to examine the circuit file in the SuperStar editor, as shown in Table 3-1. Your component Q and output formats may be different.

46 34 FILTER Examples Figure 3-1 Sample Filter Screen Next, the inductor-capacitor pairs from a node to ground are converted to shorted quarter-wavelength transmission line stubs. The characteristic impedance of the lines are defined by [14] Zo = π ωl 4 where ω is 2 π times the resonant frequency of the substituted L-C pair. The frequency of the first three L-C pairs are , and respectively. The element values are symmetric so the other resonator frequencies are the mirror image of these. The electrical length of each line is 90 degrees at the resonant frequency. The inductance in each case in 8.67 nh so the resulting stubline impedances are , and ohms respectively.

47 FILTER Examples 35 Table 3-1 CIRCUIT CAP 1 2 C= Q=1E6 C1 IND 2 0 L=8.67 Q=1E6 L1 CAP 2 0 C=3.001 Q=1E6 C2 CAP 2 3 C= Q=1E6 C3 IND 3 0 L=8.67 Q=1E6 L2 CAP 3 0 C=3.553 Q=1E6 C4 CAP 3 4 C=0.1 Q=1E6 C5 IND 4 0 L=8.67 Q=1E6 L3 CAP 4 0 C=3.579 Q=1E6 C6 CAP 4 5 C=0.1 Q=1E6 C7 IND 5 0 L=8.67 Q=1E6 L4 CAP 5 0 C=3.553 Q=1E6 C8 CAP 5 6 C= Q=1E6 C9 IND 6 0 L=8.67 Q=1E6 L5 CAP 6 0 C=3.001 Q=1E6 C10 CAP 6 7 C= Q=1E6 C11 DEF2P 1 7 FILTER WINDOW FILTER(50,50) GPH S GPH S GPH S GPH DLY FREQ SWP This conversion procedure is approximate so the frequency at which each line is 90 degrees long is optimized in SuperStar to equalize the insertion loss ripple and the return loss. Original L-C filter responses are given on the left in the Figure 3-2 and the responses of the converted filter before (solid) and after optimization (dashed) are also given. The following circuit file after conversion and optimization is given in Table 3-2.

48 36 FILTER Examples Figure 3-2 Original L-C filter responses (left) and responses of the converted filter before (solid) and after optimization (dashed) Table 3-2 Circuit file after conversion and optimization CIRCUIT CAP 1 2 C= TLE 2 0 Zo= L=90 F=? CAP 2 3 C= TLE 3 0 Zo= L=90 F=? CAP 3 4 C=0.1 TLE 4 0 Zo= L=90 F=? CAP 4 5 C=0.1 TLE 5 0 Zo= L=90 F=? CAP 5 6 C= TLE 6 0 Zo= L=90 F=? CAP 6 7 C= DEF2P 1 7 FILTER WINDOW FILTER(50,50) GPH S GPH S FREQ SWP

49 FILTER Examples 37 EXAMPLE 2 - BESSEL CRYSTAL FILTER The shunt-c coupled bandpass filter topology is similar to ladder crystal bandpass filters. Since the shunt-c filter allows specifying the series inductance, designing ladder crystal filters is straightforward. A 5th order Bessel filter with a center frequency of MHz, a bandwidth of 500 Hz and 600 ohms terminating impedance is designed using a crystal with the following parameters: R s = 20 ohms L m = 32 millihenries (32E6 nh) Co= 2.4 pf Cm resonates with Lm at the crystal series frequency. Use FILTER to design the shunt-c coupled bandpass, specifying 32E6 nh for the inductor, and then write the SuperStar file. Each series inductor-capacitor pair is converted to a crystal XTL model. The circuit file is shown in Table 3-3. Figure 3-3

50 38 FILTER Examples Table 3-3 CIRCUIT CAP 1 0 C=5.916 XTL 1 2 Rs=20 Lm=3.2E+7 Cm= E- 3 Co=2.4 CAP 2 0 C=52.31 XTL 2 3 Rs=20 Lm=3.2E+7 Cm= E-3 Co=2.4 CAP 3 0 C=112.3 XTL 3 4 Rs=20 Lm=3.2E+7 Cm= E-3 Co=2.4 CAP 4 0 C=166.3 XTL 4 5 Rs=20 Lm=3.2E+7 Cm= E-3 Co=2.4 CAP 5 0 C=278.7 XTL 5 6 Rs=20 Lm=3.2E+7 Cm= E-3 Co=2.4 CAP 6 0 C=104.1 DEF2P 1 6 FILTER WINDOW FILTER(600,600) GPH S GPH S GPH S GPH DLY 0 2E6 FREQ SWP The 2.4 pf crystal parallel capacitance causes the high side selectivity to be greater. This places an upper limit on the bandwidth of this type of ladder crystal filter. Placing an inductor in parallel with the crystal to resonate out C o may allow a wider bandwidth. EXAMPLE 3 - FILTER SYMMETRY Some filter applications require amplitude and delay arithmetic symmetry about the center frequency. For narrow band filters, this is approximately realized by most transforms. However, for wider bandwidths, symmetry frequently suffers. This is further discussed in the chapter EQUALIZATION. In this example, the symmetry of an elliptic filter is significantly improved. First design a 4th order elliptic minimum-inductor (zigzag) bandpass filter with F l =50MHz,F u = 90 MHz, 0.177

51 FILTER Examples 39 db passband ripple,a min = 45 db, type C equal termination and 50 ohms terminating impedance. Define the output block to display the data shown in Figure 3-4 and change the frequency sweep to SWP Results in Figure 3-4 show greater low-side selectivity, and higher low-side group delay. As it turns out, the reason for Figure 3-4

52 40 FILTER Examples this is too many transmission zeros at DC in relation to the number of transmission zeros at infinity. The number of zeros at DC can be reduced by one by converting the first shunt inductor (55.46 nh) to a series inductor. The parallel nh inductor and 50 ohm source resistance are converted to the series equivalent via the relations: R s 2 RX o p = R + X 2 2 o p X s = R 2 RX o p 2 2 o + Xp R s, 13.1 ohms, is the new input impedance of the filter. X s is the reactance of the series inductor and is used to calculate a series inductance of 50.1 nh. The modified file with? s added to optimize components and with an OPT block is given in Table 3-4. Notice for the optimization, the number of frequency points has been reduced to 41, to decrease optimization time. Table 3-4 CIRCUIT IND 1 2 L=?50.1 CAP 2 0 C=?94.12 CAP 2 3 C=?26.94 IND 3 4 L=?146.2 CAP 3 4 C=?9.36 IND 4 7 L=?92.81 CAP 7 0 C=?249.5 CAP 4 0 C=?86.68 IND 4 5 L=?199.7 CAP 5 6 C=?30.56 DEF2P 1 6 FILTER WINDOW FILTER(13,50) GPH S GPH S GPH DLY FREQ SWP OPT 0 20 S21<-50 W21= S21<-50 W21= S21>-.177

53 FILTER Examples 41 After several rounds, optimization was stopped and the FREQ block was modified for 101 frequencies to obtain a smooth plot. Notice the greatly improved amplitude and delay symmetry. The input resistance is only 13 ohms. A 1:4 broadband transformer could be used at the input, or the input resistance can be changed to 50 ohms, and the response re-optimized. The resulting bandwidth is somewhat wider when this is done. EXAMPLE 4 - CREATING A UNIQUE LOWPASS PROTOTYPE In this example, a class of lowpass prototype G values is made. It s desired to have a filter type with Bessel passband characteristics (flat delay and improved selectivity). Use FILTER to design a 6th order lowpass Bessel filter with 1 ohm input and output impedance and a cutoff of 1 MHz. Then modify the file, adding a capacitor in parallel with the second and fourth elements, both series inductors. The intent is to add zeros in the stopband, and modify all values in an attempt to retain nearly flat delay in the passband. The form of the prototype is identical to a 6th order elliptic. Starting capacitor values are small (100 pf) so as not to destroy the Bessel characteristic at the start. The optimize goals are flat delay (DLY%), at least 50 db of attenuation from 3 to 3.6 MHz and at least 70 db of attenuation above 3.6 MHz. To achieve the stopband requirements, the optimizer might make the passband very narrow; an easy way out. However, decreasing the bandwidth increases delay, making it more difficult to flatten the delay. The optimizer is therefore forced to maintain passband bandwidth.

54 42 FILTER Examples Figure 3-5 The results are very gratifying. The original and 25 round pattern search response is shown in Figure 3-5. The file, after optimization, is shown in Table 3-5. Table 3-5 CIRCUIT CAP 1 0 C=? IND 1 2 L=? CAP 1 2 C=? CAP 2 0 C=? IND 2 3 L=? CAP 2 3 C=? CAP 3 0 C=? IND 3 4 L=? DEF2P 1 4 FILTER WINDOW FILTER(1,1) GPH S GPH S GPH DLY FREQ SWP OPT DLY% WDL= S21<-50 W21=1E S21<-70 W21=1E4

55 FILTER Examples 43 EXAMPLE 5 - DESIGNING A BANDPASS FILTER FROM THE NEW PROTOTYPE There are several advantages to creating a lowpass prototype when designing a unique filter. The prototype, once developed, can be used over and over to design lowpass, bandpass, etc., filters with different frequencies and bandwidths or terminating impedances. Also, there are far fewer parts in the prototype than a bandpass filter, so optimization is faster and can be done on higher orders. The elliptic lowpass prototype developed in Example 5 was for 1 ohm and 1 MHz. To be used as a standard prototype, the frequency must be normalized to 1 radian/sec. This is accomplished by multiplying each inductor and capacitor by 2* *1E6. The resulting prototype values are: G(0)=1 G(1)=0.136 G(2)= G(3)=0.441 G(4)=0.660 G(5)= G(6)=0.842 G(7)=1.047 G(8)=2.459 G(9)=1 Figure 3-6

56 44 FILTER Examples Run FILTER and design a to MHz elliptic full transform bandpass with the User File selection in the Shape option of the Topology menu. Once User File is selected, you are asked to specify a filename for holding the above data which is entered in the format described in Appendix A. Use 50 ohm terminating impedances. The results are shown in Figure 3-6. The file was modified to include delay output. There is some slope in the delay. This can be removed by optimization.

57 Chapter 4 A/FILTER Operation A /FILTER is launched by starting GENESYS and then selecting A/FILTER from the Synthesis menu (top of the screen). The main A/FILTER screen looks like the sample screen in Figure 4-1. Input fields appear on the bottom section of the screen. The top part contains the schematic and values of the filter being designed. At any time, press F1 for help on the input at the cursor location. The cursor is initially located on the order input field. Press the arrow keys to move between and edit input fields. To automatically continue to the next input field, press the Tab or Enter key. To go to the previous field, press Shift-Tab. Optionally, the left mouse button may be used to select a radio button or to move the cursor. When the cursor is on an input field you may type in a new value for that field. After changing an input parameter, the component values on the schematic will automatically update. FIRST EXAMPLE The first design example will be a Single Feedback 7th order lowpass filter with a 0.25 db passband ripple Chebyshev response. The cutoff frequency is 10 khz, and the filter will have +2dB gain in the passband.

58 46 A/FILTER Operation Figure 4-1 Sample A/FILTER Screen First, select Alt-T, or click on Topology to access the topology menu. Selecting the Type item causes a new window to appear. This window will contain three sets of radio buttons, labeled Types, Poles, and Topologies. The types box specifies what type of filter you are designing. The poles box contains selections for elliptic and all-pole response realizations. The topologies box contains different filter schematic realizations of the current type, each with differing benefits. Use the up and down arrow keys or the left mouse button to change the highlighted radio button in each selection, and use the Tab or Enter key to move between sections. Make these selections: Lowpass, All-Pole, and Single Feedback. Select the OK button to continue (press Enter when it is highlighted). Next, the Shape subwindow appears. This defines the shape approximation type for the filter. Select the Chebyshev button. Help on the shapes can be obtained before

59 A/FILTER Operation 47 closing the window by pressing F1 (HELP). Use PgUp and PgDn or the scroll bar to move between help pages. Press Escape to exit the help window. Choose the OK button to continue. Filters which have unequal input and output impedances, such as even order Chebyshev and singly-terminated filters, are covered in detail in Appendix A. The cursor is now located on the main window at the order prompt. Enter 7. Filters up to 21st order may be designed for most types. The suggested range at the bottom of the screen gives a reminder of the valid range for the currently selected input. Next enter the passband ripple: A/FILTER directly computes the lowpass prototype G values for popular response shapes and does not use tables for these shapes, so any real value less than 3 db may be chosen for the passband ripple. This is true even for elliptic Cauer-Chebyshev filters. The cutoff frequency of all-pole filters, such as Butterworth, is normally defined as the 3 db attenuation frequency. The cutoff of filters with ripple in the passband, such as Chebyshev, is often defined as the ripple value. A/FILTER allows specification of the attenuation, A a,at the cutoff frequency for Butterworth and Chebyshev filters. For normally defined cutoff attenuation, enter A a equal to the ripple value for Chebyshev filters, and 3.01 db for Butterworth filters. For this example, enter 0.25 at the A a prompt. Next, for Butterworth and Chebyshev filters, A/FILTER prompts for F ca, the desired frequency at which the specified cutoff attenuation A a will occur. A/FILTER then computes and displays the cutoff frequency at the normally

60 48 A/FILTER Operation defined cutoff attenuation. This value is used by A/FIL- TER during the design process. For filter response shapes other than Butterworth and Chebyshev, the prompts for A a and F ca are skipped, and the program prompts for F c. Enter 0.01 at the F ca prompt for this example, to indicate a cutoff of 0.01 MHz (10 khz). The Std R input is the desired value for the selectable resistors in the current filter. Std C is the desired value of capacitance. Certain filter types allow the user to specify one or more part values. When this is the case, A/FILTER prompts for the value. This can be any valid part value. Not all of the part values are selectable. Some filter types allow selection of all resistors, whereas some do not allow any freedom. This is discussed in further detail in Chapter 5. For this example, enter (10 kω) for the resistor value, and (10000 pf) for capacitor value. The schematic of the filter just designed is shown on the screen. OTHER DATA Also displayed on the lower right portion of the screen is the summation of the lowpass prototype G values of the filter just designed. This quantity may be used to estimate the insertion loss, Lo, and group delay, Do, of the filter at frequencies well within the passband. These estimated parameters are also displayed. UNITS The units used in A/FILTER are the same units used in SuperStar. They are: Resistance...ohms Capacitance...picofarads

61 A/FILTER Operation 49 Frequency...megahertz MODIFYING A DESIGN A/FILTER remembers the selections made, so modifying a design is easy. This is true even if A/FILTER is exited. For a permanent record, the design can be saved to a *.AF$ file (a setup file, not a circuit file) using the file menu options save, and save as. NOISE-BW & N-HELP Please refer to Chapter 1 for coverage of these topics. OUTPUT DEFAULTS When A/FILTER writes a SuperStar circuit file, it includes output data specifications. The data used by A/FILTER can be specified by selecting the Output Block option from the Setup menu. Up to four different output parameters can be selected. The only restriction is that output options 2 and 4 must coincide with the formats of 1 and 3, respectively. That is, if output 1 is a polar plot and output 2 is used, it also must be a polar plot. There are 4 buttons at the top of the screen labeled 1 to 4. Begin by choosing the button whose number corresponds to the plot to be changed. This is done by using the arrow keys to select the desired option, or by clicking the option with the left mouse button. Next, choose the form in which to display the output data. The options are displayed in the Types box. They are: NONE GPH SMH POL Display no output for this option number Graph of selected data vs. frequency Smith Chart output Polar chart output

62 50 A/FILTER Operation LOG DSP Diplays GPH using log frequency scale Displays a window with numeric data The Options box contains circuit parameters available for output display. Choose the parameter that should be displayed in the selected format. Finally, if either GPH or POL is chosen as the output type, the display range information at the bottom of the screen must be filled in. The Minimum and Maximum boxes contain the upper and lower display values for the GPH option. The POL box is the desired radius for a polar plot. Another output number can be selected to add more output displays, or select Close to accept the settings. Since A/FILTER saves the settings after each exit, these settings become the default until they are changed again. Please refer to the FILTER manual for information on writing SuperStar files. COMPONENT DEFAULTS A/FILTER allows specification of capacitor Q and operational amplifier characteristics. SuperStar then uses these values in the determination of the filter response. To view or change these values, select Components from the Setup menu. Several input boxes are displayed. The first is the desired value for capacitor Q. A new value can be specified, or simply press Enter or one of the vertical arrow keys to move to another field. The op-amp parameters allow A/FILTER to model virtually any real amplifier by knowing critical operating parameters. The Input Resistance is the series DC input resistance of the amplifier. The Output Resistance is the apparent DC output resistance. GDC is the DC open-loop gain, and the 0 db frequency is the frequency in MHz at which the amplifier s characteristic curve yields a maxi-

63 A/FILTER Operation 51 mum gain of 0 db. Typical amplifier parameters are available from online help in A/FILTER. PREFERENCES Most of the filter topologies designed by A/FILTER use a minimum number of components, and do not match to a specified source or load termination. For this reason, the transmission and reflection parameters may behave erratically unless a matching buffer is added at either end. For instance, the Minimum Inductor and Minimum Capacitor types assume a near zero source termination, and near infinite load resistance. Unless low or high values are specified for the source and load terminations (A/FILTER default) the source sees a mismatch and voltage follower buffers must be added on each port. These buffers add a shunt resistance equal to the source resistance on the source side of the input buffer. A/FILTER does not do this by default, but it can be enabled by selecting the Preferences option from the Setup menu. Two options are available. They are: Z o matching buffer...matching buffer (follower) with resistance equal to the specified port termination resistance. Voltage follower...voltage follower with no matching resistor. These can be placed on either port, or not used at all. Some filter types have no gain built inherently into their structure. If no gain is allowed in a filter that has been designed but voltage followers are used, A/FILTER can add feedback resistors to these followers in an attempt to provide the requested gain. The preferences box contains four other options to customize the way that A/FILTER selects sections during the filter design process. They are:

64 52 A/FILTER Operation Allow third order sections Distribute Gain Use simple first order section Reverse order of poles A/FILTER can design a three pole section using a single op-amp. This is useful since it can eliminate parts from a design, but it does not allow gain. It can, however, be used to simplify the overall filter design for orders greater than two. The section has a high sensitivity to component tolerances, since one element can tune three poles simultaneously. The three pole section allows specification of a single value for all resistors. This provides a greater component flexibility than the two pole section, but does not allow gain. Check the Allow Third Order Sections box if the three pole section should be used in designs. When a filter contains more than one section which can provide gain, A/FILTER can distribute the required gain evenly among them. This can lessen the strain on each op-amp, and in some cases allow a lower bandwidth amplifier to be used. Check the Distribute Gain box to have the overall gain distributed through the allowed sections. In odd order filters not using the three pole section, a single inverting amplifier is used to realize the extra pole. This can add an extra gain section, but it adds parts to a design. However, buffering capability is present in the more complex circuit, so a voltage follower on the output is not normally required. Check the Use Simple First Order Section box for A/FILTER to use a single RC section rather than an additional op-amp pole. By default, A/FILTER places all pole pairs first in the filter cascade. For the real pole to be placed first, or for the pole pairs to be reversed, check the Reverse Order of Poles box. This may be desirable in low-noise design, since most of the gain occurs in the first section with the poles reversed.

65 A/FILTER Operation 53 Even 0dB gain filters will generally amplify the signal in some stages while attenuating it in others, so use this option with caution. When this option is on, the amplifying sections will be first, so the input level must be much smaller to avoid saturating the op-amps in the first stages. For more details on gain levels in individual sections, see Chapter 5.

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67 Chapter 5 A/FILTER Types Filter type specifies whether the filter is lowpass, highpass, bandpass, or bandstop. For each type, A/FIL- TER offers several available topologies. Each of these has different options and benefits, depending on the application need. Schematics and descriptions of the topologies designed by A/FILTER are given on the following pages. Please refer to Appendix A for a discussion of filter transfer approximations (shapes).

68 56 A/FILTER Types LOWPASS ALL POLE MINIMUM INDUCTOR C1 FILTER 4700 pf C pf R ohm C pf Q ohm R1 C pf Q2 R ohm R3? ohm The minimum inductor type is a direct element transformation of an LC minimum inductor filter using the 1/s transform. This topology is particularly useful when low sensitivity is needed. See Appendix E for a complete description of the transform types. This filter is insensitive enough to component tolerances that tuning is not usually needed. However, the cutoff frequency is tuned by adjusting the grounded resistor (R3) in each D element (see Appendix E). Thisfiltertypeallowstheusertochooseavalueforall specifiable capacitors and resistors. For equal termination filters (e.g. Butterworth and odd-order Chebyshev), all capacitors have the same value. Gain is not available in this type. In fact, there is an inherent loss of 6dB.

69 A/FILTER Types 57 LOWPASS ALL POLE MINIMUM CAPACITOR FILTER C pf R ohm C pf R ohm C pf Q ohm R2 C pf Q2 R ohm R4? ohm This type is a direct transform of the LC minimum capacitor filter using the 1/s transform. For odd order filters, there are fewer D elements in this type than in a comparable minimum inductor filter. However, there are more resistors in series with the signal path in this type. See Appendix E for a complete discussion of GIC transforms. The minimum capacitor filter is tuned exactly as the minimum inductor type. Resistor R4 in the schematic tunes the cutoff frequency of the response. Thisfiltertypeallowstheusertochooseavalueforall specifiable capacitors and resistors. For equal termination filters (e.g. Butterworth and odd-order Chebyshev), all capacitors have the same value. Gain is not available in this type, and there is an inherent loss of 6dB.

70 58 A/FILTER Types LOWPASS ALL POLE SINGLE FEEDBACK FILTER R1? ohm pf C1 R ohm C2 100 pf Q1 R ohm R ohm The single feedback type has a minimum number of parts, and allows gain. The user may specify one resistor and one capacitor value per section (C2 and R2 in the schematic above). This type also allows added feedback resistors for gain (R3 and R4 above), but does not use them if unity gain is requested. This allows even fewer parts if gain is not needed. R1 tunes the response Q and cutoff frequency. This type is sensitive to component tolerances, but has a highly flexible gain allowance.

71 A/FILTER Types 59 LOWPASS ALL POLE MULTIPLE FEEDBACK R ohm C2 100 pf FILTER R ohm R2? ohm Q1 C pf The multiple feedback filter uses few parts, and provides gain without additional components. This type requires one less component than the single feedback type with gain, but one more than the single feedback type without gain. One capacitor value per section is selected arbitrarily (C2 in the schematic above). Resistor R2 in the schematic tunes the Q and cutoff frequency of the filter. This type has a high sensitivity to component tolerances.

72 60 A/FILTER Types LOWPASS ALL POLE LOW SENSITIVITY C2 FILTER R1? ohm 100 pf Q1 R ohm Q2 C1 100 pf The low sensitivity realization uses two op-amps per pole pair, but has a low sensitivity to the op-amp open loop gain. This topology allows two capacitors per section (C1 and C2 in the schematic) to be chosen. Resistor R1 on the schematic is used to tune the response. This type has a low sensitivity to differences in op-amp open loop gain between sections, but requires the two amplifiers within each section to have similar characteristics. Usually, opamps on a dual or quad package will have closely matched, if not identical operating parameters. This topology does not allow gain.

73 A/FILTER Types 61 LOWPASS ALL POLE VCVS (Voltage Controlled Voltage Source) C2 100 pf 100 ohm R4 100 ohm FILTER R1? ohm R3 R ohm Q1 C1 100 pf The VCVS has uniform capacitors throughout the structure, whose values are specifiable. There are also two user selectable resistors per section (R3 and R4 on the schematic above). This filter allows tuning of response Q and frequency using resistor R1. There is a high sensitivity to component tolerances in this structure. Gain is selectable for odd order filters with this type, but even orders provide a gain of 2 (6.02 db) per section.

74 62 A/FILTER Types LOWPASS ALL POLE STATE VARIABLE (Biquad)? ohm R6 R5? ohm FILTER R1? ohm C2 100 pf Q1 R ohm C1 100 pf Q2 R3 100 ohm R4 100 ohm Q3 The state variable filter is best known for its tunability. This type contains many parts per section, but every aspect of the filter response is tuned directly. This gives a large degree of freedom for component tolerances. This type also exhibits low sensitivity to operational amplifier characteristics, such as narrow bandwidth and open-loop gain. The state variable structure allows user specifiable uniform capacitors throughout the entire circuit as well as two resistors per section (R3 and R4 in the above schematic). For tuning, refer to the above schematic: 1) Adjust R5 for correct cutoff frequency 2) Adjust R6 for desired Q 3) Adjust R1 for overall gain desired

75 A/FILTER Types 63 LOWPASS ELLIPTIC MINIMUM CAPACITOR FILTER C1 470 pf R ohm R2?158.9 ohm R ohm C4 470 pf R ohm C2 470 pf Q ohm R3 C3 470 pf Q2 R ohm R5?279.3 ohm The minimum capacitor elliptic type uses a 1/s transformation. See Appendix E for a complete discussion of the transform types. This filter is tuned by adjusting the grounded resistor (R5) in each D element (see Appendix E). The zero frequency is tuned by using R2 in the schematic above. This topology has a very low sensitivity to component tolerances, and a loss of 6dB within the filter passband. Gain is not available with this topology.

76 64 A/FILTER Types LOWPASS ELLIPTIC VCVS C5 FILTER 500 pf C4 R1? ohm C1 R ohm C ohm R6 R ohm Q1 R7? ohm 500 pf R ohm Q2 250 pf 250 pf R ohm C pf R4? ohm The VCVS uses user selected capacitors throughout the structure. There is also one user selectable resistor per section (R5 on the above schematic). This type has a low sensitivity to component tolerances, and does not usually require tuning, however the filter is tuned using the resistors R1 and R4 shown on the schematic above. This filter type produces gain, but does not allow its specification by the user.

77 A/FILTER Types 65 LOWPASS ELLIPTIC STATE VARIABLE C2? ohm R5 R4? ohm R ohm 500 pf Q ohm R8 R ohm Q3 C3 500 pf C1 R12 FILTER R ohm 500 pf Q1 R2?10000 ohm? ohm R9 R10? ohm R11 Q4? ohm ohm Q5 R ohm This type contains many parts per order, but every aspect of the filter response is tuned directly. This gives a high degree of freedom for component tolerances. This type also exhibits low sensitivity to operational amplifier characteristics, such as narrow bandwidth and gain. This structure allows user specifiable uniform capacitors throughout the entire circuit as well as two resistors per section. For tuning, refer to the above schematic: 1) R6 tunes the cutoff frequency, and the zero frequency. 2) R2 tunes the quality of the zero. 3) R4 tunes the response Q. 4) R5 tunes the passband gain. 5) R10 tunes the overall gain.

78 66 A/FILTER Types HIGHPASS ALL POLE MINIMUM INDUCTOR FILTER C pf C pf R ohm Q ohm R2 R ohm Q2 C2 470 pf R4? ohm The minimum inductor type is a direct element transformation of an LC minimum inductor filter using the GIC. See Appendix E for a discussion of GIC transforms. This filter is insensitive enough to component tolerances that tuning is not usually needed. However, the cutoff frequency is tuned by adjusting the grounded resistor in each GIC (R4 in the schematic above). This filter type allows the user to choose a value for capacitors and resistors. For equal termination filters (e.g. Butterworth and odd-order Chebyshev) all capacitors havethesamevalue. This filter provides power gain, rather than voltage gain. This means that S21 should be displayed, rather than E21. Gain is not available in this type, and there is an inherent loss of 6dB.

79 A/FILTER Types 67 HIGHPASS ALL POLE MINIMUM CAPACITOR C2 FILTER pf R ohm Q ohm R2 R ohm Q2 C1 470 pf R4? ohm This type is a direct LC GIC transform. For odd order filters, there are more GIC elements in this type than in a minimum inductor filter of the same order. However, there are fewer capacitors in series with the signal path in this type. See Appendix E for a complete discussion of the transform types. Resistor R4 in the schematic above tunes the cutoff frequency of the response. The user may choose a value for capacitors and resistors. For equal termination filters (e.g. Butterworth and oddorder Chebyshev) all capacitors have the same value. This filter provides power gain, rather than voltage gain. This means that S21 should be displayed, rather than E21. Gain is not available in this type, and there there is an inherent loss of 6dB.

80 68 A/FILTER Types HIGHPASS ALL POLE SINGLE FEEDBACK C ohm R1 C2 FILTER?47000 pf pf R ohm Q1 R ohm R ohm This type has a minimum number of parts, and allows gain. This section also allows added feedback resistors (R3 and R4) but does not use them if unity gain is requested. This allows even fewer parts if gain is not needed. This filter is tuned by adjusting R1 shown in the schematic above. The user may specify a single value for uniform capacitors in this filter; however, if the value specified for the capacitors is too small, A/FILTER will be unable to set both capacitors to the same value. If this occurs, you may simply specify a larger value for the capacitance.

81 A/FILTER Types 69 HIGHPASS ALL POLE MULTIPLE FEEDBACK C3 100 pf R2 FILTER C1 100 pf C2 200 pf R1?5627 ohm ohm Q1 The multiple feedback filter uses few parts, and provides gain without additional components. This type requires one less component than the single feedback type with gain. Two capacitors per section are selected arbitrarily (C1 and C3 in the schematic above). Resistor R1 is used to tune this filter. This type has a high sensitivity to component tolerances.

82 70 A/FILTER Types HIGHPASS ALL POLE LOW SENSITIVITY R2 C1? ohm Q1 C2 Q2 FILTER 560 pf 280 pf R ohm The low sensitivity realization uses two op-amps per pole pair, but has a low sensitivity to the op-amp open loop gain. This topology allows one capacitor per section (C1 in the schematic above) to be chosen. Resistor R2 on the schematic is used to tune the response. This type has a low sensitivity to differences in op-amp open loop gain between sections, but requires the two amplifiers per section to have similar characteristics. Usually, op-amps on a dual or quad package will have closely matched, if not identical, operating parameters. This topology does not allow gain.

83 A/FILTER Types 71 HIGHPASS ALL POLE VCVS R4? ohm ohm R ohm R2 Q1 C1 C2 FILTER 560 pf 280 pf R ohm The VCVS has three user specifiable components in each section: capacitor C1, and resistors R2 and R3 on the schematic above. This filter is tuned using resistor R4 shown on the schematic above. There is a high sensitivity to component tolerances in this structure. Gain is specifiable for odd order filters with this topology. Even order filters have a set gain of 6.02dB per section.

84 72 A/FILTER Types HIGHPASS ALL POLE STATE VARIABLE? ohm R7 R6? ohm C2 FILTER R ohm 220 pf Q1 R ohm C1 220 pf Q2 R ohm R ohm Q3 R ohm R ohm R10 R ohm?10000 ohm Q4 The state variable filter is best known for its tunability. This type contains many parts per section, but every aspect of the filter response is tuned directly. This gives a large degree of freedom for component tolerances. This type also exhibits low sensitivity to operational amplifier characteristics, such as narrow bandwidth and open-loop gain. The state variable structure allows user specifiable uniform capacitors throughout the entire circuit as well as two resistors per section (R4 and R5 in the above schematic). For tuning, refer to the above schematic: 1) Adjust R5 for correct cutoff frequency 2) Adjust R6 for desired Q 3) Adjust R1 for overall gain desired

85 A/FILTER Types 73 HIGHPASS ELLIPTIC MINIMUM INDUCTOR FILTER C pf C2? pf C pf R ohm Q ohm R2 R ohm Q2 C pf R4? ohm This type is a direct LC transform. This topology is particularly useful when low sensitivity is needed. See Appendix E for a complete discussion of GIC transforms. This filter is insensitive enough to component tolerances that tuning is not usually needed. However, the cutoff frequency is tuned by adjusting the grounded resistor in each GIC (R4). Capacitor C2 is tuned to adjust the zero frequency. The user may choose a value for capacitors and resistors. For equal termination filters (e.g. Butterworth and oddorder Chebyshev) all capacitors have the same value. This filter provides power gain, rather than voltage gain. This means that S21 should be displayed, rather than E21. Gain is not available in this type, and there is an inherent loss of 6dB.

86 74 A/FILTER Types HIGHPASS ELLIPTIC VCVS R pf C3 R1? ohm R ohm 1000 ohm R6 R ohm Q1 C4? ohm C pf Q2 FILTER C1 C pf 500 pf 500 pf R ohm R4? ohm The VCVS uses uniform capacitors throughout the structure. There is also one user selectable resistor per section (R5 on the above schematic). This type has a low sensitivity to component tolerances, and does not usually require tuning. However, the filter is tuned using the resistors R1 and R4 shown on the schematic above. This filter type produces gain, but does not allow its specification by the user.

87 A/FILTER Types 75 HIGHPASS ELLIPTIC STATE VARIABLE C2? ohm R5 R4? ohm R ohm 1000 pf Q ohm R8 R ohm Q3 R11? ohm C1 C4 FILTER R ohm 1000 pf Q1 R2?1000 ohm? ohm R9 R10?1000 ohm Q4 C pf 1000 pf Q5 R ohm This type contains many parts per order, but every aspect of the filter response is tuned directly. This gives a large degree of freedom for component tolerances. This type also exhibits low sensitivity to operational amplifier characteristics, such as narrow bandwidth and gain. This structure allows user specifiable uniform capacitors throughout the entire circuit as well as five resistors per section (R2, R4, R5, R6 and R10 in the schematic above). For tuning, refer to the above schematic: 1) R6 tunes the cutoff frequency, and the zero frequency. 2) R2 tunes the quality of the zero. 3) R4 tunes the response Q. 4) R5 tunes the passband gain. 5) R10 tunes the overall gain.

88 76 A/FILTER Types BANDPASS ALL POLE TOP C FILTER C pf R ohm C pf C pf Q ohm R2 R ohm Q2 C pf R4?350 ohm The top C transform type is a direct GIC transformation from the top C coupled LC filter. See Appendix E for a complete discussion of the GIC transform. There are three resistors and one capacitor per section that are user specifiable: R1, R2, R3 and C2 in the schematic above. This type has fewer resistors per section than the Top L bandpass filter. This filter provides power gain, rather than voltage gain. This means that S21 should be displayed, rather than E21. This structure does not allow gain.

89 A/FILTER Types 77 BANDPASS ALL POLE TOP L FILTER C pf R ohm R ohm R ohm C pf C pf Q ohm R3 C pf Q2 R ohm R5? ohm The top L transform type is a direct GIC transformation from the top L coupled LC filter. See Appendix E for a complete discussion of the transform types. There are three specifiable capacitors and two resistors per section: C1, C2, C3, R3 and R4 in the above schematic. This type has fewer capacitors per section than the Top C bandpass filter. For equal termination filters (e.g. butterworth and odd-order chebyshev) all capacitors have the same value. This structure does not allow gain, and there is an inherent loss of 6dB.

90 78 A/FILTER Types BANDPASS ALL POLE MULTIPLE FEEDBACK C2 C4 FILTER R ohm C1 100 pf R ohm 100 pf R ohm Q1 R ohm C3 100 pf R ohm 100 pf R ohm Q2 The multiple feedback filter uses few parts, and provides gain without additional components. This type requires fewer components than the single feedback type with gain, but more than the single feedback type without gain. One value is user specified for uniform capacitors within this filter. This type has a high sensitivity to component tolerances. For tuning, refer to the above schematic: 1) Adjust R2 and R3 for the correct cutoff frequencies 2) Adjust R1 for the desired gain

91 A/FILTER Types 79 BANDPASS ALL POLE MULTIPLE FEEDBACK MAX GAIN C2 C4 FILTER R ohm C1 100 pf 100 pf R2? ohm Q1 R ohm C3 100 pf 100 pf R4? ohm Q2 The multiple feedback filter uses few parts, and provides gain without additional components. This type requires one less component per section than the multiple feedback type with controllable gain. One user specified capacitor value is used. This type has a high sensitivity to component tolerances. For tuning, refer to the above schematic: 1) Adjust R2 for the correct lower cutoff 2) Adjust R4 for the desired Q and overall gain

92 80 A/FILTER Types BANDPASS ALL POLE DUAL AMPLIFIER R5 R11 Q1 C ohm R ohm Q3 C ohm R ohm FILTER ohm R2 R ohm 100 pf ohm R6 Q ohm R8 R ohm 100 pf ohm R12 Q4 R ohm C2 100 pf R ohm C4 100 pf The dual amplifier topology allows gain, but has a high sensitivity to component tolerances. This filter is tuned by adjusting R1 and R7 shown in the schematic above. These resistors act together to tune the high and low sides of the response. If R2 is tuned up to a standard value, R6 should be tuned down by the same percentage. Conversely, if R2 is tuned down to a standard value, R6 should be tuned up by the same percentage. Resistors R4 and R5 must be nearly equal and therefore may require small tolerance parts. If they differ too much, the response may not be recoverable by the suggested tuning method. In this case, R6 in the first section is tuned to correct the filter response.

93 A/FILTER Types 81 BANDPASS ALL POLE DUAL AMPLIFIER MAX GAIN R4 R9 Q1 C ohm R ohm Q3 C ohm R ohm FILTER ohm R2 R ohm 100 pf ohm R5 Q ohm R7 R ohm 100 pf ohm R10 Q4 C2 100 pf C4 100 pf The dual amplifier maximum gain type requires one less resistor per section than the standard dual amplifier filter. This topology allows gain, but has a high sensitivity to component tolerances. This filter is tuned by adjusting R1 and R6 shown in the schematic above. In general, the bandpass types exhibit symmetry. Within each stage, if resistors R2 and R5 in the schematic above are to be set to standard values, one should be tuned up while the other is tuned down. This will correctly adjust the response. If R3 and R4 differ in the constructed filter, the response may not be recoverable by the suggested tuning method. In this case, R6 in the first section is tuned to correct the filter response.

94 82 A/FILTER Types BANDPASS ALL POLE LOW SENSITIVITY FILTER R ohm R ohm C2 100 pf Q4 R ohm R ohm R ohm Q1 R ohm R ohm Q2 C1 100 pf R5? ohm This type has a low sensitivity to op-amp characteristics. It uses generalized impedance converters, and exhibits better behavior at high frequencies than the dual amplifier type. However, it requires one more op-amp per section. This type has a low sensitivity to differences in op-amp open loop gain between GIC sections, but requires the two amplifiers per section to have similar characteristics. Usually, op-amps on a dual or quad package will have closely matched operating parameters. This filter is tuned by adjusting the grounded resistor in each section (R5 in the above schematic). Gain is allowed in this filter.

95 A/FILTER Types 83 BANDPASS ALL POLE STATE VARIABLE? ohm R6 R5?2999 ohm FILTER R1? ohm C2 100 pf Q1 R ohm C1 100 pf Q2 R ohm R ohm Q3 The state variable filter is best known for its tunability. This type contains many parts per section, but every aspect of the filter response is tuned directly. This gives a high degree of freedom for component tolerances. This type also exhibits low sensitivity to operational amplifier characteristics, such as narrow bandwidth and open-loop gain. The state variable structure allows user specifiable uniform capacitors throughout the circuit as well as two resistors per section (R3 and R4 in the above schematic). For tuning, refer to the above schematic: 1) Adjust R6 for correct cutoff frequency 2) Adjust R5 for desired Q 3) Adjust R1 for overall gain desired

96 84 A/FILTER Types BANDPASS ELLIPTIC VCVS ohm R pf C3 R1 R3 R ohm Q1 FILTER? ohm C ohm C pf 2350 pf R ohm R4? ohm This type has one user selectable resistor per section (R5 on the above schematic). R1 is used to adjust the cutoff frequency, whereas R4 is used to tune the response Q. This filter type produces gain, but does not allow its specification by the user.

97 A/FILTER Types 85 BANDPASS ELLIPTIC STATE VARIABLE C2? ohm R5 R4? ohm R ohm 100 pf Q ohm R8 R ohm Q3 C1 FILTER R ohm 100 pf Q1 R2?10000 ohm? ohm R9 R10? ohm Q4 R ohm This type contains many parts per order, but every aspect of the filter response is tuned directly. This gives a high degree of freedom for component tolerances. This type also exhibits low sensitivity to operational amplifier characteristics, such as narrow bandwidth and gain. This structure allows user specifiable uniform capacitors throughout the entire circuit as well as four resistors per section (R2, R3, R7 and R8 in the schematic above). For tuning, refer to the above schematic: 1) Adjust R2 to tune the quality of the zero 2) Adjust R15 to tune the response Q. 3) Adjust R10 to tune the overall gain.

98 86 A/FILTER Types BANDSTOP ALL POLE VCVS C4 100 pf R ohm ohm R2 R3 R5 Q2 FILTER? ohm ohm C pf C pf R1? ohm C pf R4? ohm This type has one user selectable resistor per section and one capacitor per section (R5 and C4 on the schematic). This filter is tuned by adjusting resistor R1 shown on the schematic above. There is a high sensitivity to component tolerances in this structure. Gain is available for odd order filters with this topology.

99 A/FILTER Types 87 BANDSTOP ALL POLE STATE VARIABLE C2? ohm R5 R4? ohm R ohm 100 pf Q ohm R8 R ohm Q3 C1 FILTER R ohm 100 pf Q1 R2?10000 ohm? ohm R9 R10? ohm Q4 R ohm The state variable filter is best known for its tunability. This type contains many parts per section, but every aspect of the filter response is tuned directly. This gives a high degree of freedom for component tolerances. This type also exhibits low sensitivity to operational amplifier characteristics, such as narrow bandwidth and open-loop gain. The state variable structure allows user specifiable uniform capacitors throughout the entire circuit as well as four resistors per section (R2, R3, R7 and R8 in the above schematic). For tuning, refer to the above schematic: 1) Adjust R5 and R9 for the correct zero frequency 2) Adjust R4 for desired Q 3) Adjust R10 for desired overall gain

100 88 A/FILTER Types Filter Type Tunability Simplicity Insensitivity L O W P A S S H I G H P A S S B A N D P A S S A L L P O L E E L A L L P O L E E L A L L P O L E E L Minimum Inductor Minimum Capacitor Single Feedback Multiple Feedback Low Sensitivity VCVS State Variable Minimum Capacitor VCVS State Variable Minimum Inductor* Minimum Capacitor* Single Feedback Multiple Feedback Low Sensitivity VCVS State Variable Minimum Inductor* VCVS State Variable Top C* Top L Multiple Feedback Multiple Fb, Max Gain Dual Amplifier Dual Amplified, Max Gain Low Sensitivity State Variable VCVS State Variable B S A P VCVS State Variable *Starred filters provide power gain (S21) and use finite termination impedances. All other filters provide voltage gain (E21) unless Zo matching buffers are added. The circuit file defaults should be changed accordingly.

101 Chapter 6 A/FILTER Examples In this chapter, some helpful tips are presented with practical examples using filters designed by A/FILTER. All were built and the results of the actual measurements are presented along with the SuperStar simulation. EXAMPLE 1 - LOWPASS MINIMUM INDUCTOR The following files are used in this example: AFEX1.AF$ Initial design AFEX1.SCH/CKT Circuit file written out by A/FILTER A third order lowpass minimum inductor Chebyshev filter with 0.1 db ripple and a 10 khz cutoff is designed and simulated with µa741 op-amps. Measured results are included. The A/FILTER design screen is shown in Figure 6-1. This filter is designed using LC/GIC transforms. For more information on LC/GIC transforms, see Appendix E. In this particular filter, the transform yields a circuit that does not have a DC path to ground. This results in possible railing of bias voltages. To compensate, A/FILTER automatically includes a 100kΩ resistor to ground at the output. This will work fine, as long as 100kΩ is large compared to the impedance of the output capacitor within the filter passband. If it is not, the parallel combination of the shunt resistor and capacitor may cause a mismatch

102 90 A/FILTER Examples Figure 6-1 A/FILTER Screen For Example 1 ( AFEX1.AF$) at the load. Therefore, if small valued capacitors must be used, the output resistor may need to be increased to restore the filter response. There is an inherent loss of 6dB in this filter type. If your application requires no loss or requires gain, this can be achieved by the use of an output buffer. Output buffering is setup from the Setup menu, Preferences Window. Once enabled, the main A/FILTER window will have an input cell for gain to control the gain of the output buffer. Tuning the grounded resistor in each D element (R3 and R7 in the schematic above) directly affects the cutoff frequency. The D elements are independent enough that usually only one resistor needs to be adjusted unless a wide tuning range is needed. This type is very sensitive to op-amp bandwidth. With a 1 MHz bandwidth amplifier, a 10 khz filter may start to

103 A/FILTER Examples 91 experience rolloff prematurely. This can usually be fixed by optimization within SuperStar. A/FILTER automatically writes an optimization block into the circuit or schematic file. Several components within each filter type are marked for tuning and/or optimization. These parts can be used to tune the filter response back if other components are set to standard values, or vary slightly due to tolerances. (This will be illustrated in Example 4.) Figure 6-2 shows the predicted and measured responses. The circles show the response when using 347 op-amps (3 MHz bandwidth), while the triangles show the response when using µa741 op-amps (1 MHz bandwidth). Figure 6-2 Predicted and measured responses for Example 1. The solid, predicted response is contained in AFEX1.CKT/SCH. The circles show the constructed filter using LF347 op-amps. The triangles show the constructed filter using µa741 op-amps.

104 92 A/FILTER Examples A final note on this filter type is that, even though it is a lowpass type, it will not actually pass DC due to the series capacitor at the input. If your application needs to pass DC, then a large resistor can be added in parallel to the input capacitor. The proper resistor value must be determined experimentally in SuperStar, but is generally in the neighborhood of a 100kΩ. If the value is too large, it will have no effect; if it is too small, the filter will have gain at DC. EXAMPLE 2 - LOWPASS MINIMUM CAPACITOR The following files are used in this example: AFEX2.AF$ Initial design AFEX2.SCH/CKT Circuit file written out by A/FILTER A fifth order lowpass minimum capacitor Chebyshev filter Figure 6-3 A/FILTER Screen For Example 2 (AFEX2.AF$)

105 A/FILTER Examples 93 with 0.1dB ripple, 0.1dB Aa, and a 5 khz cutoff frequency is designed and tested with µa741 op-amps. The A/FIL- TER design screen is shown in Figure 6-3. Resistors R4 and R8 can be used to completely tune the response to a different cutoff frequency. This filter is very insensitive to component tolerances, but fairly sensitive to op-amp bandwidth. This type of filter has an inherent loss of 6dB within the passband. The circuit in Figure 6-3 was initially constructed with 5% parts, and the response was 6.5dB down in the passband. All resistors and capacitors were replaced with 1% parts, and the new attenuation was 5.9dB. Figure 6-4 shows the predicted and measured responses for example 2. Figure 6-4 Predicted and Measured Responses For Example 2. The solid, predicted response is contained in AFEX1.CKT/SCH.The circle trace shows the measured response.

106 94 A/FILTER Examples EXAMPLE 3 - LOWPASS SINGLE FEEDBACK The following files are used in this example: AFEX3.AF$ Initial design (see Figure 6-5) AFEX3A.SCH/CKT Circuit file as written out by A/FILTER AFEX3B.SCH/CKT Circuit file after putting parts on standard values and optimizing the filter response using SuperStar AFEX3T1.SCH/CKT Output of probe from first section demonstrate the tuning process) AFEX3T2,AFEX3T3.SCH/CKT Output of probe from second and third sections. An eighth order single feedback lowpass Chebyshev filter with 0.1dB ripple, 0.1dB Aa and 10 khz cutoff with 0dB gain is designed, simulated, and measured. The A/FIL- TER screen is shown in Figure 6-5. Figure 6-5 A/FILTER Screen For Example 3 (AFEX3.AF$)

107 A/FILTER Examples 95 This filter was designed with non-ideal op-amp parameters. In SCHEMAX, all non-tuned parts were placed on available values, and SuperStar then optimized the response to compensate. Figure 6-6 shows a plot of the predicted response of this filter. The solid trace shows the optimized response using LF347 op-amp parameters. The dotted trace shows the same circuit response, except that near-ideal op-amp parameters were added. The ideal response starts to roll-off prematurely, while the nonideal response behaves as expected. This illustrates the necessity to correct for non-ideal elements. AFEX3A.SCH was written from A/FILTER. All non-tuned components were set to standard values and the file was optimized in SuperStar to correct for the non-ideal components and for the standard values. The final response as shown in Figure 6-6 is contained in AFEX3B.SCH. This filter was tuned in stages. After optimizing the LF347 Op-Amps Ideal Op-Amps Figure 6-6 Example 3 Response Using Real And Ideal Op-Amps

108 96 A/FILTER Examples overall response, the output node was moved from the output of the filter to points between each stage to allow SuperStar to show the calculated response for that stage. When the filter was constructed, each stage was tuned by referring to these cumulative responses. Figure 6-7 shows the filter schematic modified to give the first stage response. The output of each successive stage was probed in the same way to obtain the individual responses. Note that when the second and third stages were probed that the responses are actually the cumulative response from all previous stages. The output of the fourth stage is, of course, the complete output of the filter. The responses from probing the output of each of the four sections are shown in figures 6-8, 6-9, 6-10 and 6-11, respectively. FILTER R1? ohm pf C1 R ohm C pf Q pf C3 R3 R4? ohm 1000 ohm C pf Q pf C5 R5 R6? ohm 1000 ohm C pf Q pf C7 R7 R8? ohm 1000 ohm C pf Q4 FIRST SECTION OUTPUT CONTRACT NO. DWN ENGR CHK PROD Eagleware Corporation (404) =A/FILTER= Example 3 AP Lowpass Single Feedback 10kHz,AMin=50 APVD APVD SIZE DWG NO. REV A 3 T1 SHEET 1 OF 1 Figure 6-7 First Section Output For Example 3 (AFEX3T1.SCH/CKT)

109 A/FILTER Examples 97 Figure 6-8 Section 1 Response (AFEX3T1.SCH/CKT) Figure 6-9 Section 2 Response (AFEX3T2.SCH/CKT) Figure 6-10 Section 3 Response (AFEX3T3.SCH/CKT) Figure 6-11 Overall Response for Example 3

110 98 A/FILTER Examples The input level should be kept low, since the first section provides almost 20dB of gain near the cutoff (see Figure 6-8). If the input level gets too large, the second and third sections can saturate, destroying the response. If the filter must handle larger signal levels, then the Reverse order of poles" option in the Setup Menu, Preferences window should be toggled. In this example, the Reverse order option was set. EXAMPLE 4 - LOWPASS MULTIPLE FEEDBACK AFEX4.AF$ Initial design AFEX4A.SCH/CKT Circuit file as written out by A/FILTER AFEX4B.SCH/CKT Circuit file after putting parts on standard values and optimizing the filter response using SuperStar A fifth order lowpass multiple feedback Chebyshev filter with a 10kHz cutoff, 0.1dB ripple and 0.1 Aa is designed Figure 6-12 A/FILTER Screen For Example 4 (AFEX4.AF$)

111 CONTRACT NO. DWN ENGR CHK PROD APVD APVD A/FILTER Examples 99 and simulated with µa741 op-amp parameters. Figure 6-12 shows the A/FILTER design screen. This filter should be tuned as in Example 3 by placing the output between sections and tuning them separately. In this example, all the capacitors were set to standard values, and the response was tuned using the resistors. Element Tuning Effects: R1 - adjusts gain with minimal perturbation of the response R4 & R5 - flattens gain, but cannot fix cutoff frequency R3 - adjusts gain of filter but distorts response R6 - redundant adjustment of R4 & R5. Only adjust if cap values are changed drastically. R2, R4, R5 and R6 were optimized since the capacitors were changed drastically. Once optimized, only R2, R4 and R5 were adjusted on the bench. R ohm C2 FILTER R ohm R2? ohm C pf 470 pf Q1 R4 820 ohm pf C5 R5 R6? ohm? ohm C pf Q2 C pf Eagleware Corporation (404) =A/FILTER= Example 4 AP Lowpass Multiple Feedback Chybyshev, 10kHz SIZE DWG NO. REV A 4 B SHEET 1 OF 1 Figure 6-13 Schematic for Example 4 After Optimization (AFEX4.SCH)

112 100 A/FILTER Examples Figure 6-13 shows the final schematic with standard value caps and optimized resistor values. EXAMPLE 5 - BANDPASS MAXIMUM GAIN DUAL AMPLIFIER The following files are used in this example: AFEX5.AF$ Initial design AFEX5A.SCH/CKT Circuit file as written out by A/FILTER AFEX5B.SCH/CKT Circuit file after putting parts on standard values and optimizing the filter response using SuperStar A fourth order bandpass dual amplifier Chebyshev filter with 0.1dB ripple and 0.1 Aa is designed, simulated, and measured with µα741op-amps. Figure 6-14 shows the A/FILTER design screen. This filter should be tuned by probing between sections and tuning the sections individually. The filter response can be completely tuned by adjusting the series resistors between sections. Figure 6-14 A/FILTER Screen for Example 5 (AFEX5.AF$)

113 A/FILTER Examples 101 Figure 6-15 Predicted and Measured Responses For Example 5 (AFEX5B.SCH/CKT) The predicted and actual (measured) responses for this example are shown in Figure 6-15.

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115 Chapter 7 M/FILTER Menus M /FILTER is launched by starting GENESYS and then selecting M/FILTER from the Synthesis menu (top of the screen). Other GENESYS supported simulators such as Touchstone and Spice simulators are less well suited for distributed filters than they are for other circuits. These simulators do not have certain models required for many distributed filters and reduced functionality may result if SuperStar is not used. OVERVIEW OF THE M/FILTER SCREEN A sample M/FILTER screen is shown in Figure 7-1. This is a typical M/FILTER display with the Menu bar, current filter layout, procedure flowchart with selectable options, and user-specified filter parameters. USING THE PROCEDURE FLOWCHART In Figure 7-1, nine buttons are shown on the left side of the screen. These buttons are arranged in a flowchart pattern, with arrows to suggest the next step. M/FILTER and SuperStar manage the entire design procedure from Start-to-Art. Procedures are launched and the current status is indicated by this flowchart which contains selectable buttons. The basic design flow is as follows: Start by selecting a filter type

116 104 M/FILTER Menus Choose filter parameters in an interactive session while observing the on-screen layout Write a circuit file and run SuperStar Analyze, tune and optimize the responses in SuperStar Return to M/FILTER from the Shell menu in SuperStar Load modified values from SuperStar into M/FILTER Finalize layout information in a limited interactive mode Plot the layout to printer or disk file. Two procedure buttons automatically illuminate during M/FILTER execution. If Auto Recalc is set, when a filter parameter is modified the Calc button illuminates red while the new design and layout are recalculated, and then grays at completion. If Auto Recalc is not set, when a filter parameter is entered the Calc button stays illuminated and synthesis algorithms are not invoked until you Figure 7-1 Sample main M/FILTER screen

117 M/FILTER Menus 105 press F6 or press the Calc button. The Absorb button illuminates when parasitics are being absorbed by the synthesis algorithms. These procedures are highly automated by the M/FILTER program environment and the procedure flowchart. Simply follow the arrows until the design is complete. MENU BAR To activate the menu bar, hold the Alt key while pressing the underlined letter of the menu item that you desire. Once the menu is selected, the arrow keys highlight the available menu items. Press Enter to select the desired item once it has been highlighted. With a mouse, simply click on the target menu item. The menu bar has six main menus: File, Type, Schematic, Layout, Utilities, and Setup. FILE MENU Press Alt-F to select the File menu. The options listed are New Open File Save Save As Write CKT/SCH File Load Values From CKT/SCH File Print Screen Print Window Exit About The New option begins a new filter. M/FILTER prompts for the type of filter to use, as well as the shape of the filter, and the process to use for the final layout. If the current filter has not been saved since the last modification, M/FILTER prompts before continuing. All the data displayed on the screen and other information which defines a particular filter are stored in files with a

118 106 M/FILTER Menus default extention.mf$. The Open File option loads a previously saved filter. Do not confuse these files with circuit description files written for SuperStar which have the default extension.ckt or schematic description files with the default extension.sch. The Save option saves the current filter data using the current filename. If the filter has not been previously saved, or a filename has not been assigned, M/FILTER will prompt for one. The F2 beside Save in the menu simply means that the filter can be saved by pressing F2, rather than selecting the menu each time. The Save As option saves under a new filename, or assigns a filename to a new filter file. The Write CKT/SCH File option writes SuperStar circuit or schematic files, which can be loaded into SuperStar for optimization. The Load Values From CKT/SCH File option loads values from a previously saved circuit or schematic file. This also replaces any current values that may have been optimized using SuperStar. The Print Screen option dumps the entire screen to a printer. Pressing Alt-F7 also selects this option. The Print Window option dumps only the current window to the printer. Pressing Alt-F8 also selects this option. Choosing Exit (Return to SuperStar) will exit M/FILTER and return to the SuperStar environment. Selecting Exit to DOS or Exit to Windows will return to the operating system. The About option displays the Eagleware copyright notice and the amount of available conventional memory.

119 M/FILTER Menus 107 TYPE MENU Press Alt-T to select the Type menu. The options listed are: Topology Shape Process The Type menu options change particular filter characteristics without restarting the whole design. The Topology option selects the general type of filter to design (combline, hairpin, elliptic lowpass, etc.). The Shape option selects the transfer function approximation shape of the filter (Butterworth, Chebyshev, etc.) The Process option selects the construction process used for the filter layout (Coaxial, Stripline, etc.) SCHEMATIC MENU Press Alt-C to select the Schematic menu. The options listed are: Display Electrical Display Phsical The Schematic menu displays the current schematic (either the electrical or the physical version) in the schematic box. The Display Electrical and Display Physical options select (Check mark is shown), or deselect the display options. LAYOUT MENU Press Alt-L to select the Layout menu. The options listed are: Display Layout Plot Layout

120 108 M/FILTER Menus Write DXF File Write Viahole List The Layout menu plots the current filter layout, display the layout, write a DXF format display file, and write a viahole data file. The Display Layout option selects (Checkmark is shown), or deselects the layout display option. The Plot Layout option plots the filter layout using a printer or plotter. Most options in the print/plot dialog box are self-explanatory. Outlines only causes the output to not be filled in (useful for RubyLithe). Film Negative causes the file to be plotted as white on black. A non-zero etch factor causes all traces to be wider by the amount given. A negative etch factor is legal and may be useful to compensate for spreading when using a laser printer to print transparencies. The etch factor uses the units set up in the Setup/Units window. The Write DXF File option writes a DXF format graphics file that is readable by many drawing packages. The Layers and Colors subwindow customizes the DXF layers and line colors used in the DXF file. The etch factor is identical to the etch factor described above for the Plot option. The Write Viahole List writes a file containing viahole coordinates relative to a point that you choose. UTILITIES MENU Press Alt-U to select the Utilities menu. listed are: N-Help Show G-Values Edit G-Values The options

121 M/FILTER Menus 109 Show Errors Recalculate View Electrical Variables View Physical Variables The N-Help option assists in determination of the required order to meet specific passband and stopband requirements. This feature can be used prior to beginning the design process, and the filter should be one order higher than suggested by N-Help. The Show G-Values option shows the current filter s G- Values. The Edit G-Values option allows editing of G-Value disk files for user customized transfer approximations. The Show Errors option shows all the errors accumulated during the last calculation. The Recalculate option recalculates the filter layout and schematic based on the current parameters. The View Electrical Variables option shows the values of all the variables used in the electrical calculations. The View Physical Variables option shows the values of all the variables used in the physical filter model calculations. SETUP MENU Press Alt-S to select the Setup menu. The options listed are: Auto Recalc Capacitors Cross Hair Setup Output Block Units Viaholes

122 110 M/FILTER Menus The Setup menu allows setup of automatic recalculation, capacitor dimensions, layout window cross hairs customzation, SuperStar output format, length units, and viaholes configuration. The Auto Recalc option selects manual or automatic recalculation. In the manual mode, press F6 or the illuminated Calc button each time filter parameters are changed. In the automatic mode the synthesis algorithms are automatically invoked each time a change is made. Auto Recalc is suggested for fast computer systems while manual recalculation saves waiting time each time a parameter is changed on slower machines. The Capacitors option specifies the length of lumped capacitors used in the layout as defined by the edge-to-edge separation of lines leading up to the capacitor. The Cross Hair Setup option customizes the appearance of the viahole cross hairs on the layout. To completely remove the cross hairs from the layout, deselect each cross hair box. The auto size option forces the right and bottom margins to be equal to the left and top margins, respectively. Negative margins are legal and are often useful on the left and right to allow extra lead line which will later be cut off. The Output Block option selects the default format for CKT/SCH files. For example, to see a polar response plot, select POL, a display parameter and the desired polar chart radius. When SuperStar circuit files are written by M/FILTER, the parameters selected are used to set-up the display window. Options are described in more detail in the SuperStar manual. The Units option specifies what units to use in the board layout. All lengths and displacements use the units chosen in this window.

123 M/FILTER Menus 111 The Viaholes option customizes the dimensions of the viaholes. Viaholes are only taken into account for microstrip circuits. LAYOUT WINDOW The layout/schematic window shows the filter during the design process. The layout shown is exactly what the final board will look like. To view a schematic or layout, select Schematic/Display Electrical, Schematic/Display Physical, or Layout/Display Layout in the menu. The cursor in the window displays current coordinates as a relative distance from an origin that has been selected. To select a new origin, click the mouse button at the desired location. TUNING PARAMETERS A tune percentage is shown on the bottom of the screen. The tuning percentage is increased by pressing F7 and decreased by pressing F9. Wheninaparametercell, increase/decrease a number by pressing Page Up/Page Down. The number is changed by the percentage shown.

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125 Chapter 8 M/FILTER Operation The following design example demonstrates the M/FIL- TERdesignprocess. Inthisexample,wewilldesigna stepped lowpass filter with a cutoff frequency of 2 GHz. Run M/FILTER by shelling from SuperStar. When the M/FILTER screen appears, click on the New Start button to choose a new filter type. Select Stepped Lowpass from the Topology screen and press Enter twice, or click on the OK button. Next, select Chebyshev from the Shape screen and click the OK button. Choose Microstrip as the filter process, and click OK. This completes the first step in the flowchart. Notice that the flowchart shows your progress, with interactive now highlighted. ENTERING PARAMETERS Tab to the Shape box, or click on one of the boxes in the group and enter the following numbers: Order:7 Fc, MHz:2000 Ripple: Rin:50 Where Order is the desired order of the filter, Fc is the cutoff frequency in MHz, Ripple is the maximum ripple allowed, and Rin is the desired input resistance.

126 114 M/FILTER Operation For this type of filter, the output resistance is uniquely defined by the input resistance and the specified parameters. Move to the Topology box and enter the following: Zmin:20 Zmax:120 Zmin is the minimum impedance you feel is practical and Zmax is the maximum impedance you feel is practical. More extreme values result in more ideal responses before optimization and better stopband performance. Now, move to the Microstrip box and enter these numbers: ε r : 2.55 Tanδ: Rho: 1 Tmet: 0.71 Rough: H: 31 Lead: 100 ε r is the dielectric constant, Tanδ is the dielectric loss tangent, Rho is the resistivity (ρ), Tmet is the thickness of the metallization used, Rough is the metallization roughness, H is the height or thickness of the dielectric substrate material, and Lead is the desired length of the filter leads. Note: All lengths or displacements default to the units specified in the Setup/Units menu option. YouhavenowtoldM/FILTERthatyouwishtodesigna seventh-order stepped low-pass filter, with a cutoff at 2 GHz. This completes step two of the flowchart. Now click the Calc button (or press F6). If you have selected Show Layout in the Layout menu, a filter layout

127 M/FILTER Operation 115 appears on your screen. If the previously indicated parameters were entered, the Show Errors box should be shown in gray. If the box is illuminated, check all parameter values. This completes step three of the flowchart. Your screen should now look similar to Figure 8-1. Select the Write CKT button to save your filter in a SuperStar format. Choose Electrical CKT File and press the OK button. Type FIRST in the File box and press Enter to name your circuit. Now, select Run SS to shell to SuperStar for analysis and optimization of the new filter. USING SuperStar WITH M/FILTER SuperStar computes and displays the plots that you selected in M/FILTER. Notice that S21 is plotted using the left grid (using two different scales for the two traces) and S11 is plotted using the right grid. The cutoff frequency is shown center-graph by default. Choose Automatic Figure 8-1 Stepped-Z lowpass M/FILTER example screen.

128 116 M/FILTER Operation from the Optimize menu to begin optimizing the electrical line lengths displayed near the bottom of the screen. The dotted lines indicate the frequency response using the newest optimized values. After several rounds, improvement halts. Press ESCAPE to stop the optimization. The screen should look similar to Figure 8-2. The plots now reflect the optimized line lengths. Important Note: This run was an electrical circuit and does not contain physical dimensions or losses. Since we will do a physical circuit next, select Run M/FILTER from the Synthesis menu to return to M/FILTER and select Interactive from the flowchart. ELECTRICAL OR PHYSICAL? M/FILTER now contains SuperStar optimized electrical line lengths. The next step is to create a SuperStar circuit file using physical microstrip elements which accurately model line loss, dispersion and discontinuities. At this point a physical CKT or SCH file should be written. Note that SuperStar can optimize both electrical and physical circuit parameters. Select Write Physical CKT file from the Write CKT/SCH item of the File menu, type FIRSTPHY for the filename and run SuperStar. When SuperStar computes and displays the response for the microstrip lowpass, press F3 to begin optimization of the physical line lengths. Notice the analysis and optimization of the physical model is slower than optimization of the electrical description of the circuit. This is because the physical elements which accurately model microstrip behavior are quite complex.

129 M/FILTER Operation 117 Figure 8-2 SuperStar computed responses for the stepped-z lowpass created by M/FILTER and optimized by SuperStar. NOTE: Physical circuits should be used in most cases. WRITING DXF/GERBER FILES Starting with Version 7, M/FILTER should no longer be used to create a layout. Instead, follow these steps:

130 118 M/FILTER Operation Table 8-1 7th-order stepped-z lowpass CKT file FILE: TEST.CKT TYPE: Stepped Lowpass Fc: 3000 MHz PROCESS: Microstrip CIRCUIT SUB ER=2.55 TAND= & RHO=1 TMet=0.71 ROUGH=0.06 & UNITS= MLI 1 2 W=WI H=H L=LI MST 2 3 O=SY NAR=WI W=Whi H=H MLI 3 4 W=Whi H=H L=L1 MST 4 5 O=SY NAR=Whi W=Wlo H=H MLI 5 6 W=Wlo H=H L=L2 MST 6 7 O=SY NAR=Wlo W=Whi H=H MLI 7 8 W=Whi H=H L=L3 MST 8 9 O=SY NAR=Whi W=Wlo H=H MLI 9 10 W=Wlo H=H L=L4 MST O=SY NAR=Wlo W=Whi H=H MLI W=Whi H=H L=L5 MST O=SY NAR=Whi W=Wlo H=H MLI W=Wlo H=H L=L6 MST O=SY NAR=Wlo W=Whi H=H MLI W=Whi H=H L=L7 MST O=SY NAR=Whi W=WOUT H=H MLI W=WOUT H=H L=LOUT DEF2P 1 18 FILTER EQUATE H=31 WI= LI=100 Whi= Wlo= L1=? L2=? L3=? L4=? L5=? L6=? L7=? WOUT= LOUT=100 WINDOW FILTER(50,50) GPH S GPH S GPH S GPH DLY 0 40 FREQ SWP OPT S11< S21<-30

131 M/FILTER Operation Write a physical Circuit file 2. From GENESYS, create a layout (Right-click on Designs in the workspace tree) 3. Choose Edit/Select All 4. Choose Layout/Connect Selected Parts 5. Choose File/Export/Gerber or DXF [This section intentionally left blank.]

132 120 M/FILTER Operation SELECTING OUTPUT OPTIONS The Output parameters shown in SuperStar can be selected in M/FILTER. For example, to view a graph on the left of S21 and a Smith chart on the right of S11, perform the following steps: Select Setup/Output Block from the menu bar. Click on the 1 button to choose the first plot type. Select GPH from the Type box to choose a rectangular plot (GPH=Graph). Now choose S21 from the Options box. Tab to the Range cells and select -5 to 5. This specifies a plot of S21 from -5 to 5 db. Next, click the 2 button and choose GPH, S21, and -100 to 0. Click the 3 button and choose SMH (Smith Plot), and S11. Click the 4 button and choose None under Type. This means that a fourth plot will not be shown. Now select Close to return to the main screen.

133 M/FILTER Operation 121 Table 8-2 Sample minimized equate block for Table 8-1 EQUATE H=31 WI= LI=100 Whi= Wlo= L1=? L2=? L3=? L4=? L5=L3 L6=L2 L7=L1 WOUT= LOUT=100

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135 Chapter 9 M/FILTER Types M/FILTER synthesizes thirteen filter topologies and supports variations on several of the structures. Access to a wide range of filter topologies is important because a given type is best suited for a given range of applications. A structure which is ideal for a narrow- band bandpass may yield impractical element values for a moderate bandwidth requirement. A filter which has desirable realization attributes may have poor stopband performance. There is no best choice. These issues are much more critical in the bandpass class than in the lowpass or highpass. This is why the greatest variety of types in all Eagleware filter programs are associated with the bandpass class. The integrated design environment of M/FILTER and SuperStar allows quick evaluation of alternative designs to find approaches best suited for each application. M/FILTER types are accessed from the Type/Topology menu, or by selecting New Start. Available types include: Stepped Bandpass End Coupled Bandpass Edge Coupled Bandpass Hairpin Bandpass Combline Bandpass Interdigital Bandpass

136 124 M/FILTER Types Elliptic Bandpass Stepped Lowpass Stub Lowpass Elliptic Lowpass Stub Highpass Direct Coupled Bandstop Edge Coupled Bandstop FILTER SHAPES AND PROCESSES M/FILTER supports numerous filter transfer approximation shapes and manufacturing processes. Transfer approximations are discussed in Appendix A. Available transfer functions are: Elliptic Cauer-Chebyshev, Normal Terminations Cauer-Chebyshev, Equal Terminations Elliptic Bessel Elliptic User File All-Pole Butterworth Chebyshev Bessel Transitional Gaussian to 6 and 12 db Equiripple Phase Error of 0.05 and 0.5 o Singly-Equalized Singly-Terminated Chebyshev & Butterworth All-Pole User File Available manufacturing processes include:

137 M/FILTER Types 125 Microstrip Slabline Stripline Coaxial General Electrical FILTER PHYSICAL SIZE At low frequencies the physical size of distributed filters can be quite large. The most compact type is the combline but it requires lumped capacitors. The table below compares physical dimensions for 3rd and 7th order implementations at 1 and 5 GHz for each of the topologies. All filters were designed with zero length 50 ohm leader lines. Dimensions are given in inches in the format L x W. All bandpass filters were designed using a 10% bandwidth. Where applicable a resonator impedance of 50 ohms was used. The substrate dielectric constant, ε r, was 2.55 and the board thickness was 31 mils. Filter 1 GHz Order=3 1 GHz Order=7 5 GHz Order=3 5 GHz Order=7 Edge-Coup BP 16 x x x x 1.0 Hairpin BP 4.0 x x x x 0.49 Stepped LP 1.5 x x x x 0.41 Stepped BP 18 x x x x 0.84 Combline BP 1.2 x x x x 1.0 Interdig BP 2.1 x x x x 1.2 Elliptic LP 2.0 x x x x 0.42 Elliptic BP 11 x x x x 2.6 End-Coup BP 10 x x x x 0.11 Stub LP 1.5 x x x x 0.28 Stub HP 0.24 x x x x 0.23 Edge-Coup BS 10 x x x x 0.20

138 126 M/FILTER Types FILTER EXAMPLES The remaining portion of this chapter includes brief descriptions of available M/FILTER topologies. More detailed information on the suitability of each of these topologies for a given application and specific data important for each type is provided in HF Filter Design and Computer Simulation.

139 M/FILTER Types 127 EDGE COUPLED BANDPASS The edge-coupled bandpass is a natural choice for narrowband specifications, especially when a long and narrow shape is desired. The example layout above is rotated a few degrees (cross hair setup box) to force the input and output lines to lie on a horizontal axis. The minimum bandwidth is limited by close spacing of the input and output sections. This problem is reduced by using Zres >50 ohms. This widens the spacings but increases dissipative insertion loss. The practical bandwidth range is further extended by using the tapped version which taps the leader directly into the first and last resonators. Radiation is a severe problem in this structure. To reduce radiation the filter should be mounted in a channel which is as narrow as possible and at least below cut-off through-

140 128 M/FILTER Types out the passband frequency range. Higher resonator impedance also reduces radiation. The Slide factor decreases the length of each resonator which couples to adjacent resonators. This is generally undesirable because it tightens the spacings and increases spacing tolerance requirements. However, sliding the coupled sections is necessary in preparation for bending the filter into a hairpin, so the factor was included as an option. The slide factor is the number of degrees each coupled section is moved relative to resonator center. This number is usually zero for an Edge Coupled Bandpass filter.

141 M/FILTER Types 129 HAIRPIN BANDPASS The hairpin bandpass is mathematically identical to the edge-coupled bandpass with a slide factor and bend discontinuities. Like the edge-coupled bandpass it is most suitable for narrowband applications. Spacing issues are similar to the edge-coupled. The practical bandwidth range is further extended by using the tapped version. As the frequency is increased a higher resonator impedance is desirable. Folding reduces radiation significantly. Folding also saves considerable space at lower frequencies. Resonator self-coupling is avoided by separating hairpin arms by the greater of 3X the spacings or 5X the substrate thickness.

142 130 M/FILTER Types STEPPED-Z LOWPASS The stepped-impedance lowpass implements the series inductors of the lowpass prototype as high-imedance lines and the shunt capacitors as low-impedance transmission lines. The responses are more ideal and the stopband rejection is greater for extreme impedance ratios. Zmin and Zmax are the minimum and maximum impedances to be used for synthesis of the filter. They should be set at the most extreme values that can be realized.

143 M/FILTER Types 131 STEPPED-Z BANDPASS The stepped-impedance bandpass utilizes high-impedance resonators slightly longer than 180 degrees decoupled from each other using low-impedance lines. This structure provides better attenuation in the upper stopband than in the lower stopband. Element values are unrealizable below about 20% bandwidth. The structure tends to be very long except on high dielectric constant substrates. Zmin and Zres are the impedance of the wide decoupling lines and the half-wave resonators, respectively. Zmin values of 15 to 30 ohms and resonator line impedances from 80 to 120 ohms are reasonable values.

144 132 M/FILTER Types COMBLINE BANDPASS The combline bandpass is one of the most compact of all distributed filters. It is used in both printed planar and machined slabline. The air slabline version yields exceptional Q u so this structure is well suited for narrowband filters. It has excellent stopband performance which improves with shorter Res θ,attheexpenseofq u. Loading capacitors are required for each resonator, but this provides a means of tuning. Zres is the impedance of the resonators and Res θ is the phase length of the resonators which must be <90 and is typically 15<θ<45. The above example is tapped. A coupled input/output version is also available.

145 M/FILTER Types 133 INTERDIGITAL BANDPASS Each resonator in the interdigital bandpass is 90 degrees long and they are grounded at alternating ends. The resonant line lengths eliminate the need for loading capacitors. The longer line lengths result in even higher unloaded Q than the combline at the expense of narrower stopbands. Zres is the line impedance of the resonator fingers. The interdigital and combline bandpass use viaholes in microstrip and stripline to ground one end of the resonators. The above example is tapped. A coupled input/output version is available.

146 134 M/FILTER Types ELLIPTIC LOWPASS The elliptic lowpass uses high-impedance lines to emulate the series inductors in the elliptic lowpass prototype and high and low-impedance stub lines to emulate series L-C resonators to ground. At higher frequencies the high-impedance lines become shorter and the stubs are likely to collide or couple to each other. This problem is mangaged by using alternating stubs (Alt Stubs), more moderate line impedances, or a thinner substrate. Zmin and Zmax are the minimum and maximum line impedances. More extreme values improve performance but increase collision probability.

147 M/FILTER Types 135 ELLIPTIC BANDPASS The direct coupled elliptic bandpass works best for bandwidths greater than 10%. It tends to be physically large which makes it more practical for higher frequencies and higher dielectric constant materials. Realizability is improved with small passband ripple and large Amin. Zmin (typ ) sets the impedance below which stubs switch to double stubs. Zmch (typ ) sets the impedance of the end matching sections. Rint (typ ) defines the internal filter impedance. Zinv (typ ) is the impedance of the impedance invertors.

148 136 M/FILTER Types END COUPLED BANDPASS The end-coupled bandpass is suited for narrowband applications in mounted very narrow channels. As the bandwidth is increased above a few percent, the gaps (particularly at the ends) quickly become vanishingly small. Lumped capacitors may be substituted for line gapsattheendsoratallgaps. Min G is the minimum gap spacing which is accepted between resonators. If the required gap drops below this value, the gap will default to the capacitor setup spacing so that a lumped capacitor may be used. WARNING: The capacitors don t appear on the layout. Check the schematic window or ckt/sch file to see whether capacitors or gaps were used.

149 M/FILTER Types 137 STUB LOWPASS The stub lowpass implements the series inductors of the lowpass prototype as high-impedance lines and the shunt capacitors as open-end stub lines. Higher stub impedances result in longer stubs which cause finite transmission zeros at the frequency where the line is 90 degrees long. These notches can be used to enhance the stopband performance at particular frequencies. Zstub is the stub-line impedance and Zmax is the impedance of the series lines. Zmax should be chosen as high as possible and Zstub is selected for best rejection in the stopband of interest. A low value of Zstub is best for wide stopbands.

150 138 M/FILTER Types STUB HIGHPASS Series capacitors are difficult to realize in distributed form. This popular highpass is a hybrid form which utilizes shorted shunt stubs to emulate shunt inductors and lumped capacitors for the series elements. Zstub is the impedance of the stubs. It should be as high as practical to improve the passband bandwidth. Lead θ is electrical length of the series lines which are required to mount the capacitors and separate the stubs. Lead θ is set as small as possible to avoid coupling between the stubs. Stubs spacings should be at least 5X the substrate thickness. Alternating stubs without crosses provide the best stub separation at the expense of filter size.

151 M/FILTER Types 139 EDGE COUPLED BANDSTOP The edge-coupled bandstop works best for narrowband applications. With wide stopbands the spacings become critically small.

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153 Chapter 10 M/FILTER Error Messages M/FILTER includes absorption algorithms which compensate the perturbations caused by transmission line discontinuities. These absorption algorithms significantly improve the responses of distributed filters and reduce required subsequent optimization time. These absorption algorithms compensate the discontinuities by adjusting the lengths of lines adjacent to the discontinuity. If insufficient line is present to accommodate absorption, then in the layout window the appropriate filter elements turn red and the Show Errors button illuminates red. Selecting the Show Errors button displays a description list of one or more error messages. If absorption fails at a given discontinuity, no compensation is attempted and the file is not corrupted, but simply uncompensated. Therefore it is feasible to continue and obtain desired results by tuning or optimization in Super- Star. However, it is best to input alternative filter parameters which avoid absorption failure. In general, thinner substrates help avoid absorption failure. End-effect discontinuities touch one line. Step discontinuities touch two lines. The step absorbs length from both lines. Any or all lines which touch a discontinuity may be too short to allow compensation.

154 142 M/FILTER Error Messages The descriptive error messages are: Line (W,L) connected to bend is too short to compensate Two lines contact each bend. The length of line used to compensate the adjacent bend is too short to absorb the bend. If this occurs in the hairpin try using a larger slide factor and/or a higher resonator impedance. Line (W,L) connected to cross is too short to compensate The length of line used to compensate the adjacent cross is too short to absorb the cross. Four lines contact each cross. Adjust line impedances or use a thinner substrate. Line (W,L) connected to end is too short to compensate The length of line used to compensate the adjacent end is too short to absorb the end. One line contacts each end. For elliptic filters try using a higher value of Zmin. For tapped combline and interdigital, continue with the design and tune or optimize the length of the end resonators. Line (W,L) connected to gap is too short to compensate The length of line used to compensate the adjacent gap is too short to absorb the gap. Two lines contact each gap. This problem is more likely to occur at higher frequencies. Try adjusting the impedance of lines which contact the gap. Line (W,L) connected to step is too short to compensate The length of line used to compensate the adjacent step is too short to absorb the step. Two lines contact each step. For stepped-z filters try increasing Zmin. Line (W,L) connected to tee is too short to compensate The length of line used to compensate the adjacent tee is too short to absorb the tee. Three lines contact each tee. Adjust line impedances or use a thinner substrate.

155 M/FILTER Error Messages 143 Capacitor (C=) connected to viahole is too small to compensate The value of a capacitor connected to a viahole is too small to absorb the viahole. One capacitor or line contacts each viahole. For combline try using a shorter resonator length. Line (W,L) connected to viahole is too short to compensate The length of line used to compensate the adjacent viahole is too short to absorb the viahole. One line contacts each viahole. Try adjusting the impedance of the line contacting the viahole. Error sliding resonators, try decreasing slide factor The slide factor is too large and the synthesis algorithms have failed. Try using a smaller slide factor. A higher resonator impedance may help improve the resonator aspect ratio and decrease the need for a large slide factor. Warning!!! Reduced Zmin to (value) To avoid synthesis failure, the low line impedance has automatically been adjusted lower to the specified value. This is only a warning. This message is unique to the stepped-z bandpass. With other structures, too high a value for Zmin does not cause synthesis failure but simply degrades performance. (W, L) in all the above error descriptions signifies the width and length variable names for the line being adjusted to compensate the listed discontinuity. LAYOUT COLLISIONS Certain filter parameter choices result in element collisions. This becomes immediately apparent in the M/FIL- TER Layout display window where the elements appear

156 144 M/FILTER Error Messages to overlap. This problem is managed by adjustment of input parameters, for example decreasing Zmax. These collisions are more likely at higher frequencies and thicker substrates. When they occur, it is likely that the substrate is too thick for the operating frequency. It is advisable to critically review if the substrate is too thick (radiation and undesired coupling paths in the finished circuit become problematic).

157 Appendix A Filter Shapes For each filter type such as lowpass, bandpass, etc. there are a number of response shapes. The design of all filters is based on a lowpass filter with that shape of response. This lowpass filter is called the lowpass prototype and the values of elements in that filter are called the prototype G values. The values are normalized to 1 ohm input impedance and a cutoff frequency of 1 radian/sec [1]. To design a filter, FILTER computes these prototype values, makes the transformation to the desired type and normalizes to the specified impedances and frequencies. FILTER computes the prototype G values for Butterworth, Bessel, Chebyshev, singly-equalized delay and elliptic Cauer-Chebyshev shapes. Also FILTER allows storing of frequently used prototype G values in disk files which are automatically read to design other filter responses. Included on the FILTER disk are lowpass prototype G values for several different filter responses. The included response types are discussed later in this chapter. Other lowpass prototype files may be entered by the user using the editor in SuperStar, or many other word processors or ASCII file editors. Prototype G values may also be manually entered into FILTER at runtime. Dozens of tables of prototype G values have been published through the years for specific

158 146 Filter Shapes applications, and more may be expected in the future. Many tables of values are given in the references cited in this manual. BUTTERWORTH The Butterworth lowpass response is useful when match and delay in the passband, particularly low frequencies, are important. The shape is characterized by monotonically increasing attenuation in the pass band to 3 db at the cutoff frequency. Attenuation monotonically increases with increasing frequency in the transition and stopbands. Filters with infinite attenuation only at DC or infinite frequency, and therefore which have no zeros of transmission at finite frequencies, are called all-pole filters. The Butterworth is a simple filter, with suitable characteristics for many applications. For straightforward filtering applications, the Butterworth is the filter response of choice. Its disadvantage is only fair selectivity. The frequency response of the Butterworth lowpass filter is given by: Atten = 10 LOG 10 [1 + (f/f c ) 2N ]db where f = frequency fc= 3 db cutoff N = order The equations used in FILTER to compute the lowpass prototype G values for the Butterworth filter are given in reference [2]. The output impedance of the Butterworth lowpass proto- Figure A-1 Butterworth responses

159 Filter Shapes 147 type filter is equal to the input impedance, therefore G(0), thefirstprototypegvalue,isequaltog(n+1),thelast prototype G value. The normal definition for the cutoff of Butterworth filters is the 3 db attenuation frequency. FILTER allows the user to specify the desired attenuation at the requested cutoff frequency. For example, the user may specify a cutoff frequency at 1 db attenuation. Any cutoff attenuation greater than zero may be specified for the Butterworth response. CHEBYSHEV The Chebyshev lowpass response is characterized by equal attenuation ripple in the passband, with attenuation equal to the ripple at the cutoff frequency. The Chebyshev is an all-pole filter. The Chebyshev filter gives better selectivity than the Butterworth filter. The Chebyshev filter is an excellent choice when passband attenuation and return loss ripple can be tolerated. The frequency response of the Chebyshev lowpass filter above cutoff is given by: Atten = 10 LOG10{1+εcosh 2 [N cosh -1 (f/fc)]} db where f = frequency f c = 3 db cutoff N = order ε = 10 RIPPLE/10-1 The equations used in FILTER to compute the lowpass prototype G values for the Chebyshev filter are given in reference [2]. The output impedance for Chebyshev prototype filters of odd order are equal to the input impedance,therefore G(0), the first prototype G value is equal to G(N+1), the last prototype G value.

160 148 Filter Shapes Figure A-2 Chebyshev responses For even order Chebyshev prototype filters, the output impedance is less than or greater than the input impedance, depending on whether the subtype is ML or MC. The difference is related to the passband ripple and is greater for larger passband ripple. FILTER automatically determines and displays the output impedance on the lower right of the main window. The help screen (accessed with F1) for the Shape subwindow indicates which even order filter types and subtypes have higher and which have lower output impedance. Two normal definitions for the cutoff of Chebyshev filters are often used. Some contributors have defined the cutoff attenuation as 3 db, and others define the cutoff attenuation as the passband ripple value, with the latter perhaps somewhat more generally accepted. We will define the cutoff attenuation as the ripple value. However, FILTER allows the user to specify any attenuation equal to or greater than the ripple attenuation as the cutoff. For example, the user may specify a cutoff frequency for a.25 db ripple Chebyshev at.25, 1.07, 3, 6 db, etc. attenuation. Any cutoff attenuation greater than the ripple may be specified for the Chebyshev response.

161 Filter Shapes 149 BESSEL The Bessel filter produces a maximally flat group delay in the frequency domain. It is sometimes referred to as a maximally flat group delay filter and sometimes as a Thompson filter. Maximally flat group delay is often an advantage in pulse communication system applications. This filter has excellent characteristics in the time domain. The disadvantage is extremely poor selectivity. However, for applications where good phase or time domain performance is critical, it is often the best choice. FILTER will design Bessel filters through 10th order. Bessel filters through order 21 may be designed by user entry or file entry of lowpass prototype G values. BLINCHIKOFF FLAT DELAY BANDPASS Transformation of lowpass filters to bandpass filters results in the modification of the group delay characteristics Figure A-3 Blinchikoff Flat Delay Bandpass

162 150 Filter Shapes of the lowpass prototype. Consequently, bandpass filters designed using Bessel, minimum phase equiripple error and other controlled delay prototypes do not exhibit the desired delay characteristics. This phenomenon worsens with increasing bandpass filter bandwidth. Some transform types, such as the top-c coupled bandpass, are worse than others, such as the shunt-c coupled bandpass. The reasons for this phenomena is discussed in the EQUALI- ZATION chapter. Blinchikoff and Savetman [3][4] offered a solution to this dilemma for 2nd and 4th order all-pole filters. The poles of the transfer function were optimized by computer for constant delay over the passband directly as a bandpass filter. The lowpass to bandpass transform is therefore avoided. The process is not numerically efficient, but the effort provides a useful set of constant delay bandpass filters for 30 to 70% bandwidth. The extremely desirable delay characteristics of a 4th order Blinchikoff bandpass filter with 40% bandwidth centered at 70 MHz are demonstrated in the accompanying response. As might be expected, the amplitude selectivity characteristics of the filter are poor. SINGLY-EQUALIZED DELAY All ladder, passive, filter structures are minimum-phase; the amplitude and phase responses are inseparably related via the Hilbert transform. Selectivity and flat delay cannot be simultaneously achieved. To resolve this difficulty, selective filters are sometimes cascaded with non-ladder all-pass delay equalization networks. Unfortunately several all-pass sections may be required and each requires several components. Developed by Eagleware, the singly-equalized prototype offers selectivity far better than Bessel and other control-

163 Filter Shapes 151 led phase prototypes but it is perfectly delay equalized with a single all-pass network. This prototype may be selected from the Shape dialog box. The theory behind the development of these prototypes is described as an example in HF Filter Design and Computer Simulation, provided with FILTER. SINGLY-TERMINATED Sometimes a filter which is singly-terminated is required. FILTER will design Butterworth and Chebyshev filters terminated on the input with a specified impedance and terminated on the output with either zero or an infinite impedance. The input and output of these filters may be swapped. Other filter shapes may be designed for single termination by user or file entry of the lowpass prototype G values. The Help screen in the Shape subwindow may be used to determine which subtype for a given filter type will have an infinite or a zero output impedance. Since singly-terminated filters are not really matching networks, the insertion loss of these filters is not 0 db in the passband. Consider a lowpass filter consisting of series inductors and shunt capacitors inserted between a source of 50 ohms and a zero impedance load. As the frequency approaches zero, the capacitors effectively become open circuits and the inductors effectively disappear. How can these components match the source to the load if they are effectively absent? The answer is they can not. Singly-terminated filters preserve the shape of the amplitude response and the shape of the voltage response, but when the power transferred between the source and load is calculated or measured, the insertion loss is proportional to the difference in input and output impedances. When writing SuperStar files for singly-terminated filters in order to avoid infinite attenuation in the calculated loss of the passband, FILTER sets the output impedance at 398

164 152 Filter Shapes or 1/398 times the input impedance, instead of infinity or zero. The response of a filter changes little when the ratio is greater than about 20. The ratio of 398 results in an attenuation offset of approximately 20 db, so singly-terminated filters analyzed using SuperStar require adding a 20 db offset to the scale of S21 and S12. CAUER-CHEBYSHEV Elliptic function filters have zeros of transmission at finite as well as infinite frequencies. Zeros of transmission at finite frequencies can reduce the width of the transition region, therefore increasing the selectivity or sharpness of the response. An important class of elliptic function filters is the Cauer-Chebyshev, which exhibits equiripple passbands and equal minimum attenuation, A min,inthe stopband. FILTER designs Cauer-Chebyshev filters with user specified passband ripple and stopband ripple. These routines are based on work by Pierre Amstutz [5]. In the Amstutz paper, distinctly different routines were given for even and odd order Cauer-Chebyshev prototype filters. The routines used different input data for determining values in the odd or even case. The FILTER routines remove this disadvantage. FILTER computes prototype G values for both type B and type C Cauer-Chebyshev filters. Type B Cauer-Chebyshev filters are similar to Chebyshev filters in that the input and output impedances for even order are dissimilar. Figure A-4 Cauer-Chebyshev

165 Filter Shapes 153 A type C filter approximates the filter response for equal input and output impedances for even order. The selectivity suffers slightly for type C, but this is a minor inconvenience when equal input and output impedance is required. USER FILTERS Specifying user file in the Shape subwindow allows entering lowpass prototype G values at run time. This is convenient for designing filters from G values found in the literature or that you have developed. The powerful optimizing routines in SuperStar can be used to develop prototype G values with a limitless variety of amplitude or delay characteristics. An example of using SuperStar to develop a new lowpass prototype class is given in the FILTER Examples chapter. When G-file is selected, FILTER will first prompt for a file under which to store the new G values. To create a new file, simply specify a non-existant filename. FILTER will then display an editor in which you can enter the G file. The first line must contain a comment or note and must not contain data. Each remaining line (lines are separated by the <return> key) contains G values for a specific order. The first number is the order (N). The G values from G(0) to G(N) follow. The exact number of required prototype G values must be specified. G(0) is the normalized input impedance. It is normally 1. For all-pole filters, G(1) through G(N) are the prototype values, and G(N+1) is the normalized output impedance. For elliptic filters designed by FILTER, the number of finite frequency zeros of the lowpass prototype, M is given by: For N odd, M =.5(N-1)

166 154 Filter Shapes and for N even, M =.5(N-2) There are N+M prototype G values for elliptic filters. The normalized output impedance is G(N+M+1). The Figure A-5 Elliptic Cauerform of the elliptic Chebyshev prototype format lowpass prototype filter is given on the previous page. For even order filters, the final series branch is non-elliptic. The Cauer-Chebyshev and many other elliptic function filters utilize this topology. The general case for filters with zeros of transmission at finite frequencies may not utilize this topology. For example, the older class of m-derived filters have designer selected topologies. OBSERVING G VALUES Occasionally, the user may want to know the the internally generated G values. A typical application might be the synthesis of a filter topology not included in FILTER, but for which the user has synthesis procedures when the G values are know. To read the internally generated G values, first use FIL- TER to design any topology of filter with the desired transfer function shape. Next, select the display G values item in the Utilities menu. FILTER displays the G values in a subwindow. Press Enter to select the Close button and return to the main window. PROTOTYPE FILES Some frequently used prototype G values have been supplied with FILTER. These files have the same format as

167 Filter Shapes 155 files which you manually create. The form of these files is: Remark line describes type and must be included This particular file is for Butterworth prototype filters of 3rd through 5th and 7th order. The remark line is used to describe the type of lowpass prototype for reference. The remark line must be present. One line of data is used for each order. One or more orders may be in a file. The first number in a line is the order. The second number is G(0), the third G(1), etc. up to G(N+1), or up to G(N+M+1) for elliptic function filters. When reading a file, if a data line for the specified filter order is not found, the message Data for order N not found in file. is displayed. Either edit the file or specify a new one. An incorrect number of data points in a line of data adversely effects program operation so please carefully check prototype files you create. We recommend using the extension.pro for all-pole lowpass prototype files and the extension.pre for elliptic lowpass prototype files you create. INCLUDED PROTOTYPE FILES To begin your collection of special purpose lowpass prototype filters kept as files, the FILTER disk contains a number of lowpass prototype files. Included are: Linear phase 0.05 degree equiripple error: orders Linear phase 0.5 degree equiripple error: orders Transitional Gaussian to 6 db: orders 3-8. Transitional Gaussian to 12 db: orders 3-8.

168 156 Filter Shapes Singly-terminated Cauer-Chebyshev: orders 3-7. (Ripple = 72 db which is 24 files.) Bessel passband elliptic: orders 3-4 for A min = 18, 24: orders 3-8 for Amin = 34, 42, 50, 58, 66, 70 db. The prototype files except Bessel passband elliptic are provided with permission from reference [1], Handbook of Filter Synthesis, by Anatol I Zverev, published by John Wiley and Sons. This reference includes many other singly-terminated Cauer-Chebyshev prototypes and other useful lowpass prototypes. The Bessel passband elliptic stopband lowpass prototypes are provided with permission from reference [6], Electronic Filter Design Handbook, by Arthur B. Williams and Fred J. Taylor, published by McGraw-Hill. LINEAR PHASE EQUIRIPPLE ERROR Just as the Chebyshev prototypes are an optimum amplitude response solution, the linear phase prototypes are an optimum linear phase solution (constant group delay) given an allowable phase ripple. By allowing some phase ripple, improved selectivity is obtained. The two prototype files are named LP0R05.PRO and LP0R5.PRO. LP is an acronym for linear phase. 0R05 and 0R5 represent respectively 0.05 and 0.5 degrees phase ripple. TRANSITIONAL GAUSSIAN Also included on the disk are Gaussian to 6 db (G06.PRO) and Gaussian to 12 db (G12.PRO) transitional lowpass prototype filters for 3rd through 8th order. This class of filter approximates a Gaussian response to 6 or 12 db and is a compromise of delay and selectivity characteristics. Both the linear phase equiripple error and transitional Gaussian prototypes are doubly-terminated unsymmetri-

169 Filter Shapes 157 cal filters. The component values on the input and output are not mirror images of each other. SINGLY-TERMINATED CAUER-CHEBYSHEV FILTER synthesizes doubly-terminated Cauer-Chebyshev elliptic functions directly. However, it does not synthesize singly-terminated Cauer-Chebyshev functions. This class is useful for designing contiguous elliptic diplex filters, so a number of prototype files for this class are included on disk. The convention for naming these files is CCnNPPAA, where CC represents Cauer-Chebyshev, nn are the lowest and highest order included, PP is the reflection coefficient in percent, and AA is the approximate A min in decibels. For the most part, the orders included are 3rd through 7th. The reflection coefficients are 1, 2, 4, 8, 10, 15, 20, and 25%, which represents a passband ripple of.00043,.0017,.007,.028,.044,.098,.18 and.28 db respectively. Reference [1], which was so popular it has gone back into print, contains many other prototype files. BESSEL PASSBAND ELLIPTIC STOPBAND As was discussed previously, Bessel filters have excellent delay characteristics, but poor selectivity. The selectivity of flat delay filters can be improved by adding zeros of transmission at finite frequencies. Elliptic lowpass prototypes for such a class of filters is given in reference [6]. The amplitude and delay responses for 5th order Bessel (solid curves) and elliptic Bessel A min =50 db (dotted curves) filters with 1 MHz cutoffs are compared in the accompanying figure. PROTOTYPE FILE SELECTION ASSISTANCE To assist in the management and use of lowpass prototype files, a list of available prototype files is available on the

170 158 Filter Shapes Figure A-6 Bessel Passband Elliptic Stopband help screen (accessed with F1) when FILTER prompts for the prototype filename after you have selected the user file shape option. N-HELP FILTER, A/FILTER, and M/FILTER can help you determine the order required for Butterworth, Chebyshev and elliptic Cauer-Chebyshev filters. Suppose you need a bandpass filter which passes 10.5 to 10.9 MHz with a maximum ripple of.1 db. The rejection at 10.2 MHz and 11.2 MHz must be at least 50 db. We will determine the minimum order required for a Chebyshev and a Cauer-Chebyshev filter. Press F4, or select N-Help from the Utilities menu. Determine the Chebyshev order first. Select the Bandpass and Chebyshev radio buttons. Enter.1" for the ripple prompt. Enter 10.5" and 10.9" for the F l and F u prompts respectively.

171 Filter Shapes 159 You may then enter up to 10 separate stopband requirements. FILTER will automatically determine which requirement is the most stringent and compute the necessary order based on that requirement. In this case, at the F 0 and A 0 prompts, enter 10.2" and 50". At the next F 1 and A 1 prompts enter 11.2" and 50". When you are finished entering stopband requirements, enter 0". The necessary order is computed and displayed as The filter is therefore designed with the next higher integer order of 6. Next, determine the necessary order for a Cauer-Chebyshev elliptic bandpass filter. Select the Cauer-Chebyshev radio button. Enter 50" at the prompt A min, 10.5" at the F l prompt and 10.9" at the F u prompt. For Cauer-Chebyshev bandpass filters, only two stopband requirements are entered, because the required stopband attenuation is assumed equal to A min. Enter the lower and upper stopband requirements closest in frequency to the passband. For elliptic lowpass filters, only one stopband requirement is used. Therefore, enter 10.2" at the F sl prompt and 11.2" at the F su prompt. The required order is Because this is very close to 4, a 4th order filter might be chosen. Re-running N-Help with A min of 49 db gives a required order of 3.98, so you know that a 4th order filter will have between 49 and 50 db of attenuation. Select the close button to return to the main window.

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173 Appendix B Noise Bandwidth Filters are used in many electronic systems to band limit the noise, hopefully without distorting the signal. The noise power referred to the input of a system is given by: P Ni =ktb n F where k = Boltzman's constant F = the system noise figure T = the defining temperature of F, normally 290K Bn = the effective noise bandwidth of the system. The noise voltage refered to the input is: e = ktb FR Ni n eq where R eq = the equivalent noise resistance. Calculation of system performance parameters often requires knowledge of the effective noise bandwidth. The effective noise bandwidth is approximately equal to the 3 db bandwidth, but the actual value may vary significantly from this value. The noise bandwidth is defined 1 2 Bn = 2z Ha jωf dω H jω m b m g

174 162 Noise Bandwidth where H(jw)=the transfer function Hm(jwm)=maximum value at the frequency, wm, of the maximum value BUTTERWORTH NOISE BANDWIDTH The noise bandwidth of a bandpass filter is equal to the noise bandwidth of the lowpass prototype. Interestingly, the noise bandwidth of all-pole lowpass filters is equal to π 2Gn,whereGn is the shunt capacitance at the open circuit end of a singly-terminated lowpass filter of that type. Because close form equations are known for singlyterminated Butterworth G values [2], calculating the noise bandwidth of Butterworth filters is straightforward. The noise bandwidth for Butterworth filters is: B n p = BW 2 3dB F p I N sin H 2N K A similar process may be used for calculating the noise bandwidth of Chebyshev filters. The problem with this approach is that it is very restrictive. Equations for singly-terminated G values are known for only certain response shapes. Furthermore, practical filter responses are seldom ideal. What are the effects of finite-q components, approximate bandpass transforms and standard component values? GENERAL CASE The noise bandwidth for the general case can be found by integrating the actual filter response. FILTER and Super- Star automate this process. The filter response is com-

175 Noise Bandwidth 163 puted using SuperStar, and the output S-parameter data file is written using the Write S-data option in the SuperStar File menu. FILTER is then run and the Noise-BW routine is selected from the Utilities menu or by pressing F5. The *.OUT filename is requested. The file wriiten above is specified and FILTER computes and displays the noise bandwidth. The maximum value of S21 in the output file and the frequency at which this maximum value occurs are also displayed. A typical output screen is given in Figure B-1. NOISE BANDWIDTH EXAMPLE Consider a to MHz 5th order shunt-c coupled Butterworth bandpass filter constructed from inductors with an unloaded Q of 120 and capacitors with an unloaded Q of Figure B-1 Typical output screen