16 MICROSTRIP LINE FILTERS

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1 16 Microstrip Line Filters 16 MICRSTRIP LINE FILTERS Receiver De- Mod 99 Washington Street Melrose, MA 176 Phone Toll Free Visit us at.testequipmentdepot.com Antenna Lo-Pass Filter Lo-Noise Amplifier Mixer Band-Pass Filter De- Modulator Audio utput PLL Phase Locked Loop Antenna Poer Amplifier Attenuator Pre- Amplifier PLL Mixer Modulator Audio Input Mod Transmitter bjectives 1. Understand the basic concepts of microstrip line filters.. Learn ho to design microstrip line filters. 3. Learn ho to measure filter response. * For generic filter and its applications, refer to Chapter 7. 39

2 GRF-33 Manual Theory When the signal frequency is high, for example 3GHz, the avelength no longer becomes negligible as described in the generic circuit theory: in the example case, it reaches 1mm in free space. In other ords, higher frequency has shorter avelength. As the ave (signal) travels (flos) along the conductor, the phase of the voltage and current changes significantly over the physical length of the conductor. Therefore the conductor, hich orks as a short-circuit node in lo frequency, no orks as a distributed component in high frequency. It is a completely different conception from the standard circuit theory. In this chapter e ill introduce different methods to implement LPF, HPF and BPF by using the transmission line technique. The general filter related theory has been introduced in Chapter 7; here e ill just focus on microstrip line filters Transmission Line Basics Transmission line theory forms the basis of distributed circuits. For detailed study, e should start from Maxell s equations, then move on to electromagnetic ave analysis, and so on. In this section, e ill give the very basic concept of transmission line since introducing everything in this textbook is impossible. The key difference beteen circuit theory and transmission line theory lies in electrical size. The theory of circuit analysis assumes that the physical dimensions of a netork are much smaller than its electrical avelength; the size of transmission lines may be a fraction of single or several avelengths. Thus e can say that a transmission line is a distributed-parameter netork here voltages and currents can vary in magnitude and phase over the length of the netork. n the other hand, lumped elements in generic electronic circuit such as inductors and capacitors are generally available only for a limited range of values and are difficult to implement at microave frequencies, here distance beteen filter components is not negligible. 31

3 16 Microstrip Line Filters The transmission line is often represented as shon in Figure i( z, t) v (, t) z z z Figure 16-1, voltage and current definitions of a transmission line In Figure 16-1, the voltage and current are not only functions of t (time) but also functions of z (position), hich means the voltage and current ill change at different positions (different spots of - axis). The equivalent circuit is shon in Figure 16-. i( z, t) i( z z, t) Rz Lz v( z, t) Gz C z v( z z, t) z Figure 16-, equivalent circuit of a transmission line R=series resistance per unit length, for both conductors, in /m. L=series inductance per unit length, for both conductors, in H/m. G=shunt conductance per unit length, in S/m. C=shunt capacitance per unit length, in F/m. The series inductance L represents the total self-inductance of the to conductors, hile the shunt capacitance C occurs due to the close proximity of the to conductors. The series resistance R represents the resistance due to the finite conductivity of the conductors, hile the shunt conductance G occurs due to dielectric loss in the material beteen the conductors R and G. A finite length of transmission line can be vieed as a cascade of sections formed as in Figure Wave Propagation on a Transmission Line From Figure 16-, e define the traveling ave as: V ( z) V e V e (16-1) z z 311

4 GRF-33 Manual I( z) I e I e (16-) z z the complex propagation constant as: j ( R jl)( G jc) (16-3) The characteristic impedance o can be defined as: Vo o Io Vo Io R jl R jl (16-4) G jc From the electromagnetic theory, e kno: dz 1 dt (16-5) here is the permeability and is permittivity of the medium. In free space, e have 1/ c m / sec, hich is the speed of light.. For the transmission line, the phase velocity is 1/, (16-6) r r is the relative permittivity, also knon as dielectric constant of the medium (substrate of the PCB). We can find the avelength as: (16-7) f and the ave number: f =/ (16-8) here is the attenuation constant, and is the ave number. 31

5 16 Microstrip Line Filters Lossless Line The above solution is intended for general transmission line including loss effects, here the propagation constant and characteristic impedance are complex. Hoever in many practical cases, the loss of the line is very small and can be neglected, alloing simplification of the above results. Setting R=G= in (16-3) gives the propagation constant as: j j LC (16-9) LC (16-1) (16-11) Terminated Lossless Transmission Line Figure 16-3 shos a lossless transmission line terminated by an arbitrary load impedance L. This diagram illustrates the ave refection problem in transmission lines, a fundamental property of distributed systems. in V ( z), I( z), V L L I L z Figure 16-3 Assuming that a ave in the form V + e - z is generated from a source at <, e can see that the ratio of voltage to current for such traveling ave is, the characteristic impedance. But hen the line is terminated in an arbitrary load L, the ratio of voltage to current at the load must be L. Thus, to satisfy this condition, a reflected ave must be excited ith the appropriate amplitude. The amplitude of the reflected voltage ave normalized to the amplitude of the incident voltage ave is knon as the voltage reflection coefficient, expressed as: 313

6 GRF-33 Manual V V o o L L (16-1) When load mismatch occurs, not all generated poer is delivered to the load. This loss is called Return Loss (RL), and is defined (in db) as RL log db (16-13) V 1 max SWR (16-14) V 1 min The general form of the input impedance in Figure 16-3 is described as follos. in ( ( L L ) e ) e jl jl ( ( L L ) e ) e jl jl L cos l cos l j j L sin l sin l L j tan l (16-15) j tan l L Special Cases of Terminated Lossless Lines When a line is terminated in a short circuit, L becomes L =. From in is: in j tan l (16-16) When a line is terminated in an open circuit, from in is: in j cot l (16-17) When the line length is /: in L (16-18) When the line length is /4: 314

7 16 Microstrip Line Filters in (16-19) L Referring to and redraing Figure 16-3 as Figure 16-4, e get: / 4 1 R L in Figure 16-4 L is composed of a transmission line of characteristic impedance l and R L. In order for to become, e also need in=o. The shos the characteristic impedance as: R (16-) l L Which is called Quarter-ave matching transformer Simulation Tools The current simulation softare tools are very useful for the designers, since they can save lot of time for complicated calculations. Many tools are available meeting a variety of demands. AppCAD developed by Agient (HP) is one of the tools for calculating transmission line parameters, and it can be donloaded from the public domain. The other softare, like ADS and Momentum (by Agilent), MW ffice (by AWR), HFSS and Symphony (by Ansoft) etc., can simulate the design of a circuit so that the designer can calculate the ideal results rapidly. Using the ptimization function in the softare, the circuit design can be automatically tuned to meet the target specifications Suggestions and Reference of Microstrip Line Filters The suggested steps of implementing microstrip line filters are as follos. 315

8 GRF-33 Manual 4. Find the L, C values according to the standard filter theory. 5. Convert the L, C to microstrip lines. 6. Construct and simulate the filters. 7. Fine tune and modify the design until the goal is met. 8. Fabricate the filters. When fabricating the RF circuit on the PCB, the substrate material is a key factor for the success. Usually the FR4 material is not suited for frequencies above 1GHz because of the folloing reasons: the dielectric constant is not uniform over the hole material, the dielectric constant also varies according to frequency change, most circuit board suppliers can guarantee dielectric constant ithin a range but not at a precise value, etc. In practice, microave substrate PCB such as ceramic and duroid substrates is the better choice for microave applications. In our experiment, FR4 is chosen because it is easier to obtain. The results may contain a margin of error, but the basic concept can definitely be established. The main theory reference of this chapter is the folloing textbook: Microave Engineering, by David, M. Pozar, Addison-Wesley Publish Company, Inc Stepped Impedance Lo Pass Filter A common ay to implement a lo pass filter is to use alternating sections of very high and very lo characteristic impedance lines, hich is referred to as stepped impedance, or hi- / lo- filter Design Example Design a stepped-impedance type Butterorth lo pass filter ith cutoff frequency at GHz and > db attenuation at 3GHz. The input and output impedance are both 5. The PCB material is FR4 ith dielectric constant 4. and thickness 1.mm. 316

9 16 Microstrip Line Filters Solution Referring to Table 7-5, since /c=1.5 db attenuation is db at 3GHz, the order becomes 7. From Table 7-1, e find the normalized values of g1 to g8 as follos: g1=g7=.445 g=g6=1.47 g3=g5=1.819 g4=. g8=1. The equivalent circuit is illustrated in Figure L L 4 L 6 C 1 C 3 C5 C7 Figure 16-5 We then convert the L, C value to electronic length by the folloing equations: =LRo/ h, for inductor (16-1) =C l /Ro, for capacitor (16-) Ro is the filter impedance, is the ave number, is the line length, L and C are the normalized values, h and l are the highest and loest line impedance, respectively. According to Figure 16-3, g1, g3, g5 and g7 are capacitor sections in l, and g, g4 and g6 are inductor sections in h. The PCB substrate is 1. mm thick, FR4 material, r = 4.4. In order to make the PCB fabrication realistic, the line idths are adjusted to.5mm for h and 5mm for l before e start designing. The item left to be designed is the length of each section. 317

10 GRF-33 Manual Let s start from the l sections hich are capacitor sections including g1, g3, g5 and g7. By using the microstrip line calculation tool, hen the line idth is 5mm, l = 9.67, avelength =78.847mm. According to 16-, the first capacitor value is: g1=c1=.445 We get 1 =C 1 l /Ro =.445*9.67/5 =.64 rads (16-3) Combining 16.8 and 16.3, the line length of 1 and 7 are: 1 =.64/ =.64/(/) =.64/(/78.847) =3.31 mm. By the same method, section 3 is: 3 =1.69 rads 3 = 5 =13.4 mm. The h (inductor) sections are also designed by the same method. By using the calculation tool, h =11.73 and avelength = 86.87mm hen the line idth is.5mm. According to 16-1: g=l=1.47 We get 318

11 16 Microstrip Line Filters =L Ro/ h =1.47*5/11.73 =.613 rads (16-4) Combining 16-8 and 16-4, the line length of and 6 is: =.613/ =86.87*.613/(*) =8.4 mm. The section 4 is: 4 =.983 rads 4 =13.5 mm We have to consider another issue in addition to the filter itself. The transmission line contains 5 impedance and is frequently put in front of the filter at both ends. Its idth is.3mm defined by the PCB structure. In addition, SMA terminals are attached to the test module for external connection. The.3mm transmission line is too ide to be directly connected to the SMA terminals, therefore an extra 1.6mm line section is necessary for bridging them together. Summarizing the above results, the entire filter is designed as in Figure L1, L7: 53.3 mm L, L6:.58.4 mm L3, L5: mm L4: mm Lo:.35 mm, for 5 transmission line 319

12 GRF-33 Manual Lp: 1.68 mm, for SMA connector pin. L p L p L 1 L L 3 L 4 L 5 L 6 L 7 Figure Fine tune and Modification Just as mentioned in the previous section, the simulation tool is very useful and important for microave circuit design. We can simulate our design to check if the result meets our design target. If not, e can do fine tuning and simulate again. By repeating this fine tune and simulate step, e can make the design as close as possible to the design target. In the above case, e find that the roll-off at fc=ghz is 5dB more than e expected from the simulation result. It could be caused by the extra sections of the transmission line. Here e try to fine tune again by changing the 4 from 13.5mm to 1mm here the roll-off becomes.5db but the attenuation at 3GHz becomes less than db, hich is a trade-off. Both simulation results are dran in Figure Insertion Loss (db) Stepped LPF line4 = 13.5mm line4 = 1mm Frequency (GHz) Figure 16-7 In the experiment, e ill take the 1mm case for measurement. 3

13 16 Microstrip Line Filters Coupled line Band Pass Filter Coupled line filter is a good choice if e ant to design a band pass filter in microstrip form hich requires bandidth about less than %. Wider bandidth filter generally require tightly coupled lines, hich are hard to fabricate Design Example We ill design a coupled line filter ith.5db ripple,.4ghz center frequency, 15dB attenuation at GHz, and 1% bandidth. The input and output impedance are both 5. The PCB material is FR4 ith dielectric constant of 4. and thickness of 1.mm Solution First, e need to decide the order of the filter. c is the bandidth ration and is equal to.1. Referring to Figure 16-6, since c and attenuation is 15dB at GHz, the order (N) becomes. From Table 16-1, e find the normalized values of g1 to g3 as follos: g1=1.49 g=.771 g3=

14 GRF-33 Manual Figure dB Ripple N g1 g g3 g4 g5 g6 g7 g8 g9 g1 g Table

15 16 Microstrip Line Filters After that, e can use the follo equation to evaluate the even and odd mode of the characteristic impedance. J J J e o 1 N N 1 g 1 g N 1 g g 1 J 1 J N 1 g N N J J e can get: J J J e1 o1 1 e o e3 o Due to the complexity of calculating the coupling coefficiency, e can use CAD tools to find out the gap beteen coupling lines. The list belo shos the results after the calculation: l1 l3 =17.45mm mm s1 s3=.6mm l =17mm =.mm s =1mm 33

16 GRF-33 Manual We still need to consider to issues: one is that the minimum practical distance is.5mm, and the other one that the impedance of pin connection lines is not 5 hich affects the filter frequency response. Therefore, after fine tuning, the final result becomes as follos. l s l 1 s 1 l 1 s 16.9mm 17mm mm.mm.9mm 1.1mm Summarizing the above result, e get: L1, L3=1.1x16.9mm, gap=.5mm L=.x17mm, gap=.9mm Lo=.3x5mm, for 5 Lp=1.6x8mm, for pin connection The entire filter is designed as Figure The simulation results are shon in Figure L p L 1 L L 3 L p Figure

17 16 Microstrip Line Filters -5 Insertion Loss (db) Coupled Line BPF before fine tune after fine tune Frequency (GHz) Figure 16-8 Fine-tuned values ere used for actual measurements ptimized High Pass Filter There are several ays to design a high pass filter in microstrip form. In this section, e ill introduce an easy ay to fabricate a high pass filter, hich can also be considered as a ideband band pass filter Design Example We ill design a high pass filter ith.1db ripple and 1.5GHz cut off frequency. The input and output impedance are both 5. The PCB material is FR4 ith dielectric constant of 4. and thickness of 1. mm Solution First, e assume that the pass band is from 1.5GHz to 4.7GHz..7GHz 1 f c 35 c 4 c Referring to Table 16-, e choose c = become as follos: y1=.4467 y1= and N = 4, then y1, y1, y and y3 35

18 GRF-33 Manual y=.657 y3= Figure 16-9 shos the structure of the filter. y1 y1, y y,3 y3 n yn yn-1,n yn-1 yn-, n-1 yn- y3, Table 16- c c y 1 y 1, y n1, n y 1 y1 y n1 y yn c Short-circuited stub of electrical length c Figure

19 16 Microstrip Line Filters No e can use the folloing equations to evaluate the line impedance. i i, i1 y i, y i, i1 c, c We get: And then e can use CAD tools to find out the real length and idth of each section. l l l l mm mm 1.189mm.43mm 11.mm 3.867mm 1.mm.35mm We still need to consider to issues: one is that the minimum practical distance is.5mm, and the other one is the cross section of each line. Therefore, after fine tuning, the final result becomes as follos. l l l l mm 1.8mm 1.mm.3mm 1.7mm 3 1mm 1.mm.3mm 37

20 GRF-33 Manual Summarizing the above results, e get L1 =.8x1.7mm, L1=.3x1.mm, gap=.9mm L=1x1.7mm L3=.3x1.mm Lo=.3x5mm, for 5 Lp=1.6x8mm, for pin connection The end of L1 and L are grounded. Figure 16-1 shos the design of the entire filter. The simulation results are shon in Figure L p L p L1 L3 L1 Lo L1 L L L 1 Figure Insertion Loss (db) ptimize HPF after fine tune before fine tune Frequency (GHz) Figure Fine-tuned values ere used for actual measurements. 38

21 16 Microstrip Line Filters Questions Question 1: What is the possible factor, other than the design of the filter itself, that affects implement the transmission line filter? Question : Describe ho to limit the tolerance caused by connectors. Question 3: Describe ho to choose the right PCB for implementing microstrip line filters. 39

22 GRF-33 Manual Experiments Insertion Loss Measurement 1 bjective: Implement a microstrip lo pass filter. Refer to Figure 16-1 or R-11 module in the GRF-33. L p L p L 1 L L 3 L 4 L 5 L 6 L 7 Figure 16-1 Microstrip line lo pass filter 9. Prepare the folloing items. GRF-33, R-11 (Microstrip Lo-Pass Filter) module N-SMA Adaptor x RF cable, 75cm x Spectrum Analyzer (SA) 1. Configure the SA as follos. Frequency span: Full Span Resolution bandidth (RBW): Auto Step 1: Span Full Span Step : BW RBW Auto/ Manu RBW Auto Figure Spectrum analyzer configurations (GSP-83) 11. Activate and adjust the Tracking Generator (TG) as follos. TG Reference level: 1dBm TG level: dbm TG reference value: dbm 33

16 Microstrip Line Filters TG output: on TG normalization: on Step 1: Amplitude Ref Level dbm Step : ption TG TG Level dbm Step 3: Ref ption TG dbm Value Step 4: TG ption TG N N FF Step 5: Normal

23 16 Microstrip Line Filters TG output: on TG normalization: on Step 1: Amplitude Ref Level dbm Step : ption TG TG Level dbm Step 3: Ref ption TG dbm Value Step 4: TG ption TG N N FF Step 5: Normal ption TG N N FF Figure TG configurations 1. Connect the SA and R-11 as follos. TG output R-11 input R-11 output SA RF input TG utput RF Input N-SMA Adaptor x 75cm RF cable x RF I/P RF /P Figure SA to R-11 connections 13. Turn on a marker in the SA, set the marker frequency to 3dB bandidth of the filter, and record the amplifier gain into Chart

24 GRF-33 Manual Insertion Loss Measurement bjective: Implement a microstrip line band pass filter. Refer to Figure or T-1 module in the GRF-33. L p L 1 L L 3 L p Figure Microstrip line band pass filter Follo the same steps as in the Insertion Loss Measurement 1 section but change some items as follos. R-11 module T-1 module Chart 16-1 Chart 16- Insertion Loss Measurement 3 bjective: Implement a microstrip line high pass filter. Refer to Figure or T-6 module in the GRF-33. L p L p L1 L3 L1 Lo L1 L L L 1 Figure Microstrip line high pass filter Follo the same steps as in the Insertion Loss Measurement 1 section but change some items as follos. R-11 module T-6 module Chart 16-1 Chart

25 16 Microstrip Line Filters Experiment Results Insertion Loss Measurement Chart 16-1 Measurement result of R-11 microstrip line lo pass filter insertion loss Chart 16- Measurement result of T-1 microstrip line band pass filter insertion loss 333

26 GRF-33 Manual Chart 16-3 Measurement result of T-6 microstrip line high pass filter insertion loss 334

X.-T. Fang, X.-C. Zhang, and C.-M. Tong Missile Institute of Air Force Engineering University Sanyuan, Shanxi , China

Progress In Electromagnetics Research Letters, Vol. 23, 129 135, 211 A NOVEL MINIATURIZED MICRO-STRIP SIX-PORT JUNCTION X.-T. Fang, X.-C. Zhang, and C.-M. Tong Missile Institute of Air Force Engineering