Case Study: Parallel Coupled-Line Combline Filter. Microwave filter design. Specifications. Case Study: Parallel Coupled- Line Combline Filter

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1 MIROWAVE AND RF DESIGN MIROWAVE AND RF DESIGN ase Study: Parallel oupled- ine ombline Filter ase Study: Parallel oupled-ine ombline Filter Presented by Michael Steer Reading: b t b 5 S (db) 6 S (db) Index: S_P_Filter Based on material in Microwave and RF Design: A Systems Approach, nd Edition, by Michael Steer. SciTech Publishing,. Presentation copyright Michael Steer ADA opyright M. Steer and IET 5 S S Bandpass filter Specifications enter frequency: GHz % Bandwidth Steep filter skirts requires hebyshev response, choose a ripple factor of. ow loss in passband Microstrip technology (Also low fabrication cost and very good performance.) Microwave filter design ombination of Art and Science Art: knowing the structures that intrinsically have the desired response. Science: knowing how to use mathematics in a synthesis process to obtain the required tailoring of the response.

2 Art: choice of topology Parallel microstrip lines in combline configuration. Science: synthesis procedure How to go from db - S to using mathematical synthesis, while maintaining desired electrical characteristics. (perhaps more complicated) 5 Optimization: an alternative to synthesis Optimization given a final structure that almost has the right response, use optimization to get the exact final response. E.G. Adjust line widths and lengths; number of microstrip lines, capacitor values. Works if the starting solution is very close. Does not provide insight or lead to new solutions. Even then, optimization with more than 6 variables is a problem. 5 5 Summary Filter design, as with most RF design, is a combination of art and science. The art is identifying the structures that intrinsically have the desired response. The science is developing the mathematical procedure to go from the mathematical specification of the desired response to the final microstrip realization. hoose topology (art), use synthesis procedure (science), use optimization to almost perfect design, use fabrication and test to perfect design. 6 7

3 Outline ase Study: Parallel oupled-ine ombline Filter. Part B Begin with a lumped element filter. Filter design is based on circuit transformations. Vg or onsider circuit model of coupled lines Work out the steps to go from the lumped element circuit to a transmission line-based circuit. 9 Third-order filter Network model of a pair of coupled lines The lumped element filter has three resonators: So (perhaps) the transmission line equivalent has three resonators: V g The equivalent circuit of a pair of coupled lines Is obtained by equating symbolic ABD equations onsider as two pairs of coupled lines: : n n :

4 ombline section and network models ombline section and network models : n n: : n n: ombline section ombline section : n n: ( f r = f ) : n : n Translation of a circuit with stubs to coupled lines omparison of lumped element filter and Pi arrangement of stubs So if the following structure is seen in a circuit (a Pi arrangement of shorted stubs) Pi arrangement of shorted stubs. Three connected resonators. Then it can be replaced by a combline section Each stub is a resonator. A shorted stub corresponding to a parallel resonator. An open circuit stub corresponds to a series resonator. So the conversion from a lumped element filter to Pi network of shorted stubs is not direct. But The Idea is Starting to ome Through 5

5 Summary The key idea is to begin with a lumped element filter prototype and put the circuit in the form of a collection of shorted stubs in a PI configuration. Want basic circuit structure to be But cannot start from here (rd order BPF) ase Study: Parallel oupled-ine ombline Filter. Part, Step : Develop owpass Prototype Filter (Model of two P in combline configuration.) 6 7 Outline Begin with a lumped element filter. alculate element values. This is the 6 th order hebyshev response ε is called the ripple factor. Passband ripple, PBR = (+ ε ) Ripple in db, R db = log(pbr) TRANSMISSION REFETION Steeper filter skirt for Higher order arger ripple 9

6 Third-order hebyshev filter A third-order hebyshev lowpass filter prototype oefficients of a hebyshev lowpass prototype filter normalized to a radian corner frequency of ω = rads and a Ω system impedance (i.e., g = = g n+ ). The ripple factor is ε. ε =. is a ripple of. db. ω is the radian frequency at which the transmission response of a hebyshev filter is down by the ripple. Here ω = radians. g = g =.55 g =.6 g =.55 g = ω = rads =.55 F =.6 H =.55 F hebyshev filter coefficients from recursive formula Summary Step : developed rd order hebychev lowpass prototype filter. ω = rads =.55 F =.6 H =.55 F

7 ase Study: Parallel oupled-ine ombline Filter. Part D, Step : Remove Series Inductor Outline Use an inverter(s) to replace series inductor. An inverter can be implemented using transmission lines. Where there are transmission lines it may be possible to equate them to an inverter (if they are long). Vg 5 Impedance inverter A long line is an inverter = in Inverters in in = ossless telegrapher s equation: jtan( ) in ; tan( ) j tan( ) in j j tan( ) tan( ) An inverter can be realized using a transmission line. in onsider combline section and network model ombline section A combline section of coupled lines long inherently presents two impedance inverters. :n n: Wherever there are long transmission lines an impedance inverter can be realized (probably). 6 7

8 Replacement of a series inductor by a shunt capacitor plus inverters Equivalence of a series inductor and a shunt capacitor plus inverters -: -: T T Equivalence is demonstrated using ABD parameters. s T For the cascade ASADE j j -: T s T s j j s T T T T j s j Drop negative unity transformer as it only affects phase and not filter response. 9 Inverter form of lowpass prototype filter adder prototype filters using impedance inverters g g n ( n odd) Vg g g g g g gn ( neven) n+ ω = rads =.55 F =.6 H =.55 F ω = rads =.55 F =.6 F =.55 F Vg -: -: -: g g g g Vg g g g g g 5

9 Summary: Inverter form of lowpass prototype filter ω = rads =.55 F =.6 F =.55 F ase Study: Parallel oupled-ine ombline Filter. Part E, Step : Bandpass Transformation ' ' ' ' ' ' First lumped element transformation to BPF, GHz BPF and center frequency transformation Vg Vg T(s) PF T ( s) HPF 95MHz, 5MHz MHz fractional bandwidth,, RdB (rads) + (rads) This assumes that the PF corner frequency is radians. 5

10 Transformation to BPF, GHz =.55 nf = =.69 ph = =.7 pf =.7557 nh BPF and center frequency transformation ' ' ' ' ' ' S (db) 5 S S 6 S (db) 6 95MHz, 5MHz MHz fractional bandwidth,, RdB This assumes that the PF corner frequency is radians. 7 Prototype BPF and center frequency transformation ' ' ' ' ' ' = 55. pf = =.69 nh = = pf =.7 nh Recall: desired basic circuit structure Summary prototype BPF ' ' ' ' ' ' = 55. pf = =.69 nh = = pf =.7 nh (Model of two P in combline configuration.) 9

11 ase Study: Parallel oupled-ine ombline Filter. Part F, Step : Impedance Scaling ' ' ' ' ' ' Principle of impedance scaling Every impedance in the circuit is scaled by the same amount So to go from to 5 The value of a resistor is increased by a factor of 5. The value of an inductor is increased by a factor of 5. The value of a capacitor is reduced by a factor of 5. The value of an impedance inverter is increased by a factor of 5. The value of an admittance inverter is reduced by a factor of 5. Summary, Step : BPF scaled to 5. ' ' ' ' ' ' = 55. pf = =.69 nh = = pf =.7 nh ase Study: Parallel oupled-ine ombline Filter. Part G, Step 5: onversion of umped-element Resonators, = 7.66 pf = =.96 nh = = 5.7 pf =.759 nh

12 Outline entral idea: Obtain a broadband realization of the resonators in the BPF without using inductors. Realize the resonant circuit by a circuit with and a stub. Equate admittances and the derivatives of admittances Narrowband resonator equivalence at ω degrees of freedom. degrees of freedom. an only match admittance at one frequency. is the characteristic impedance of the transmission line and is the input impedance of the shorted transmission line. 5 Broadband resonator equivalence at ω Broadband resonator equivalence at ω Y in Y in degrees of freedom. degrees of freedom., is the characteristic impedance of the line and is the input impedance of the shorted line. Y in Y in degrees of freedom. degrees of freedom., is the characteristic impedance of the line and is the input impedance of the shorted line. Broadband match at is obtained Yin by matching Yin and at. Broadband match at is obtained Yin by matching Yin and at. Specific design choice r (most common). The admittance of the networks are equivalent (at ) when: The derivatives of the admittance of the networks are equivalent (at ) when: Also (at ) = j, r is, the radian resonant frequency of the stub (i.e. the frequency at which it is long). 6 7

13 Step 5. Bandpass combline filter with broadband realization of lumpedelement inverters onvert resonators to hybrid stub resonators. 5 5 The commensurate frequency, f r, of the design is the resonant frequency of the stubs. By default all the stubs have the same f r. The design choice here is that f r = f. f is the center frequency of the design. 7. pf. pf The transmission line stubs present impedances = j, = j, and = j since the resonant frequencies of the stubs are twice that of the design center frequency. Summary, Step Broadband, but stubs have different characteristic impedances. 7. pf Really want them to be the same as they will be realized by microstrip lines and we want them to have the same width. (ind of, this is a little imprecise as the inverters are yet to be realized.) 9. pf ase Study: Parallel oupled-ine ombline Filter. Part H Step 6: Equalize Stub Impedances Outline Result of Step 5 (previous): 5 5. pf 7. pf Broadband, but want stubs to have the same characteristic impedances. Result of this step (Step 6): pf

14 Target combline filter physical layout ompare prototype with combline network model Very approximately The impedances of the shunt stubs are mostly determined by the impedances of the individual microstrip lines. For manfacturability reasons we would like the microstrip lines to have the same width Therefore we want the shunt stubs to have the same characteristic impedance. The impedances of the series stubs are mostly determined by the coupling of the individual microstrip lines. 5 5 Want scaled so that new =. Procedure pf. pf A Inverter impedance scaling J J y J Original network J J B -jj jj jj -jd y jj J jj -jj -jd Admittances are the same if d = J x J J y J Better to use admittance now as the analysis is based on building a nodal admittance matrix. J J J x J x Element values are impedances except for y and y, which are admittances. y y = yx Scaled original network J J jd jd y jd jd y = yx Procedure is: (A) Develop nodal admittance matrix of original network. (B) Develop nodal admittance matrix of scaled network. Then equate to find required parameters. J 5 55

15 Realization of a series inductor as a shunt capacitor with inverters. nh IMPEDANE OR ADMITTANE INVERTERS Example y nf ADMITTANE INVERTERS J x =. S y = yx J x =. S Summary, step 6 After scaling so that = : pf 7.57 Note the impact on the size of the capacitor! IMPEDANE INVERTERS pf The stubs now have the same impedance, and the capacitances are the same ase Study: Parallel oupled-ine ombline Filter. Part I Step 7: Inverter Realization Outline The prototype filter from Step 6 is Realize inverters using stubs. ombine adjacent stubs. Result of this step (Step 7): 5 59

16 Inverter realization using stubs Inverter translation j j56.9 -j 56.9 j j j pf 7.57 Impedance inverter Realization as a lumped element circuit Realization using shortcircuited stubs resonant at twice the passband center frequency. j j j Equivalence was established using ABD parameters. j7.57 -j 56.9 x = 7.57 = 56.9 Stubs can be combined. 6 6 j7.57 -j 56.9 x = 7.57 = 56.9 ombining stubs j j56.9 Represent parallel stubs as parallel impedances. Bandpass filter prototype without inverters j j =.76 onvert to a single impedance. Represent impedance as one stub.. pf f r = f f is the center frequency of the design. Note that in many designs f r = f. This is simply assumed sometimes. But f r could have another relationship. 6 6

17 ompare prototype with combline network model An issue with resonant frequency ombline section Model: ombline section Model: ( f r = f ) Here f is the center frequency of the bandpass filter. With capacitors: ( f r = f ) So the f s are different! What do we do? We need to re-examine the development the lead to 6 Here f is the center frequency of the match. the assignment of f r. 65 onsider exact network model of combline section Reconsider network models of combline section ombline section Exact model: I I V V : : : : IW V W I X V X e e V Y V IY I : : : : V V I I ombline section Here f is the operating frequency There is nothing here that depends on the relationship of f r and f. Exact model: I I V V : : : : IW V W I X V X e e o o V Y V IY I : : : : V V I I o o There is nothing here that depends on the relationship of f r and f. This is believed to be most accurate when f r = f. That is, when the lines are long at the operating frequency. But it is a reasonably good model all frequencies, even when it is long. Approximate model: : n n: 66 67

18 Reconsider simplified network model of combline section : n n: ompare prototype with combline network model ombline section ombline section ( f r = f ) : n : n Model: With capacitors: 5 5 ( f r = f ) These lines are long at f. Pretty good model even when f r = f (e.g when it is long) Summary, Step 7 ase Study: Parallel oupled-ine ombline Filter. Part J Step :Scaling haracteristic Impedances of Stubs. pf t t t t t t t t 7 7

19 Outline Desired stub impedances From Step 7. pf The impedances of the shunt stubs are mostly determined by the impedances of the individual microstrip lines. For manfacturability reasons we would like the microstrip lines to have reasonable width. Want the characteristic impedances of the shunt stubs to be between and. On Alumina ( r around ) that means that we want the characteristic impedances of the stubs to be between and. 7 The impedances of the series stubs are mostly determined by the coupling of the individual microstrip lines. 7 Scale Impedances Scale Impedances. pf Scale to. Want characteristic impedances of the stubs to be between and. Multiply impedances by a factor of.75. t Multiply impedances by a factor of.75. t t t t t t t. pf pf t t t t t t t

20 Summary, Step t t ase Study: Parallel oupled-ine ombline Filter. Part Step 9: 5 Match t t t t t t.7759 pf t t t t t t t t t t t t t t t Use Impedance Inverters Summary, Step 9 Result of Step : t t 9. t t 9. t t t t t t t t t t t t 9. t t pf t t t t t t t t t t t t t 7 79

21 ase Study: Parallel oupled-ine ombline Filter. Part Step : Implementing the Inverters From Step 9 9. Outline t t 9. t t t t t t b t t b Implement input and output inverters. t t t t An inverter as a capacitor network An inverter as a capacitor network b These are equivalent but only for resistive loads. Equate admittances, note that Y in of inverter is real. R a a b R These are equivalent but only for resistive loads. This is can be shown by using a complex load and calculating the input impedance of the capacitive network with a complex load. a b Y in Y in This is not the same as general matching which works with complex conjugate impedances. It is the same as matching If input and output are resistances.

22 Derivation capacitor network (at GHz) a R Y in b External inverters as capacitive networks 9. t t 9. Y R 5 s s R in a b a b.6 pf.7 pf b a t t t t t t a b Note that a and are in parallel. 5 b Summary, Step t t b ase Study: Parallel oupled-ine ombline Filter. Part M Physical Design of ombline Filter t t t t.676 pf t.7759 pf b.7 pf t t t. t a t t 5 t b b 5 6 7

23 Outline ey oncept From Step b t t b t t t t apacitors stay as lumped-element capacitors Implement the following in microstrip: t t an treat three coupled lines as two pairs of coupled lines with the center line shared. Error is small. t t t One transmission path that is missing is direct coupling of the first line to the third line. This coupling is very small. 9 Physical design of the three coupled lines t b b Implement one pair at a time. t t t t t t s s t t s w w w w w Equivalent circuits for a combline section. t t : n t t s t t s w w w w 9 9

24 Derivation of parameters Equivalent circuits for a combline section: : n Derivation of parameters Equivalent circuits for a combline section. : n From model theory: n n n and n 69.7 Two estimates of coupled line system impedance: S, 6.56 and S, 55. This happened because the shunt stubs in the Pi arrangement of stubs is not symmetrical. So take mean: S S, S, Derivation of parameters Equivalent circuits for a combline section. Physical design of the three coupled lines t b b : n onductor pattern h t w Strip r w s s w w S 6. n 55. n o S 7.9 e S o Dimensions of microstrip lines determined using tables or iteratively solving coupled line equations. hoose alumina substrate with r =, h = 65 m. S o e Use lookup table for a 5 system impedance. w w w 59 m (6 m rounded) s s 65 m (65 m rounded) 7., 5.95 ee eo Take 6.56 e ee eo 9 95

25 Physical design Revisit Assumptions t b w s s w w apacitor values are unchanged (e.g. implement using surface mount capacitors). b GHz g r =, h = 65 m w = w = w = 6 m s = s = 65 m = g =.65 mm (recall f r = f ) ayout (to scale) e via w s w s w t b w s s w w b r =, h = 65 m w = w = w = 6 m s = s = 65 m =.65 mm These values were derived looking up a table for a 5 system impedance. However S = Revisit Assumptions, w t b w s s w Have three system impedances: S S, S, w b S, 6.56 S, r =, h = 65 m w = w = w = 6 m s = s = 65 m =.65 mm These values were derived looking up a table for a 5 system impedance. This choice mostly affects w, w, and w. ould optimize in EM simulation, but better to get closer now. hoose S = 55.. t b w s s w w Update w b Use S = 55.. r =, h = 65 m w = w = w = 5 m s = s = 65 m =.65 mm 9 99

26 Revisit Assumption, Summary, physical design t b w s s w w b r =, h = 65 m w = w = w = 5 m s = s = 5 m =.65 mm For e, used geometric mean of even and odd mode effective permittivity (affects ). t b w s s w w b t b.676 pf.7759 pf.7 pf Alumina ( r = ), h = 65 m w = w = w = 5 m s = s = 65 m =.65 mm optimization (to get right) we can tune capacitor ( ). Instead of adjusting in EM based ase Study: Parallel oupled-ine ombline Filter. Part N Microwave ircuit Simulation 5 b t b 5 Physical Design Outline First developed lumped-element BPF reference Microwave circuit simulation Use microstrip coupled line element (MIN) ompare and interpret response Optimize via w s w s w t b w s s w w b

27 umped-element BPF for Reference = 5 Ω = = 7.7 pf = = 9.7 ph =.5 ff = 7.77 nh S (db) 5 S S 6 S (db) Wideband Response S (db) 5 S S S (db) 5 S of the lumpedelement BPF S (db) 5 S. GHz. GHz S 6 S (db).9 GHz.9 GHz. GHz. GHz.9 GHz.9 GHz.6 GHz. GHz The zeros of the S response, and hence the poles of the S response, are at.96,., and. GHz. S of the lumped-element BPF. GHz. GHz.9 GHz.9 GHz. GHz. GHz.96 GHz. GHz. GHz.9 GHz. GHz.9 GHz.6 GHz zeros 6 7

28 S of the lumped-element BPF. GHz.9 GHz.9 GHz.96 GHz. GHz. GHz.9 GHz.9 GHz ircuit model using MIN element 5 b t b 5 b t b 5 5. GHz.6 GHz S S zeros S (db). GHz. GHz. GHz zeros t b.676 pf.7759 pf.7 pf Alumina ( r = ), h = 65 m w = w = w = 5 m s = s = 65 m =.65 mm Details: 6 μm gold metallization MIN 9 Response with MIN element (a) s = s = 65 m (b) s = s = 5 m S (db) 5 (b) S (b) S (a) S S (db) S response with MIN element ocus gets close to origin twice.. GHz. GHz. GHz.6 GHz.9 GHz. GHz. GHz. GHz. GHz.96 GHz Response of lumpedelement BPF S (db) 5 S S S (db) S S (db).9 GHz.9 GHz.9 GHz. GHz. GHz

29 Optimized S response with MIN element Alumina ( r = ), h = 65 m w = w = w = 5 m s = s = 5 m =.65 mm b S (db) 5 S, MIN S, umped S, MIN pf.676 pf.7759 pf t 5 t b b 5 t.976 pf.7 pf Values for optimized response. Account for error in. 6 S (db) S response with optimized MIN element Path not considered in synthesis. At. GHz Path and Path cancel. At. GHz Path and Path reinforce. S (db) There is partial reinforcement below.9 GHz. There is partial cancellation above. GHz. S, umped 5 S, MIN S, MIN t b b 5 Path Path 6 S (db) S response with optimized MIN element. GHz. GHz omparison of S response umped BPF BPF with optimized MIN.9 GHz.9 GHz. GHz. GHz.9 GHz.6 GHz.96 GHz. GHz. GHz. GHz.9 GHz. GHz. GHz.9 GHz. GHz.9 GHz.6 GHz.9 GHz.6 GHz.96 GHz. GHz. GHz. GHz.9 GHz. GHz. GHz.9 GHz.9 GHz. GHz. GHz. GHz.9 GHz.9 GHz. GHz 5

30 S response with with optimized MIN.9 GHz. GHz.6 GHz.96 GHz. GHz. GHz. GHz. GHz.9 GHz. GHz Wideband response of lumped-element BPF S (db) 5 S, MIN S, MIN S (db).9 GHz.9 GHz. GHz During manual tuning look at both rectangular S plot and Smith chart plot. 6 S (db) 5 S S S (db) 7 Optimized S response with MIN element S (db) 5 f r = f S S 6 S (db) Effect of higher f r? S (db) 5 f r = f S S 6 S (db) Spurious basebands at f,f, 7.5f, 5 t b b Recall that f r = f. So transmission lines look the same at f r,f r, 5f r, i.e. f,6f, f BUT impedance of capacitance is not the same, hence the spurious passbands are shifted. 5 t b b What if f r = f? Spurious passbands would be shifted higher in frequency. BUT diminishing returns, design becomes more sensitive. 9

31 Summary, optimized physical design Alumina ( r = ), h = 65 m w = w = w = 5 m s = s = 5 m =.65 mm S (db) 5 t b b 5 5 S, MIN S, umped S, MIN b t.7 pf.976 pf.7 pf Only adjusted, t, and. 6 S (db) ase Study: Parallel oupled-ine ombline Filter. Part O EM Simulation 5 b t b 5 5 b t b 5 5 t b b 5 omparison of responses EM Subcircuit Use optimized MINbased BPF values b.7 pf.976 pf,.7 pf t Enclosure Alumina ( r = ), h = 65 m w = w = w = 5 m s = s = 5 m X DIM =.65 mm μm μm tantalum vias 6 μm gold metallization. EM enclosure has perfect conducting walls with X DIM = mm, Y DIM = mm and height = 5.65 mm. via Y DIM w s w s w S (db) 5 S, EM ould further optimize... S, MIN S, EM 6 S (db)

32 omparison of responses Bandwidth is smaller Indicates lower overall coupling Notch above passband has shifted lower. Overall response is almost the same as with MIN based analysis Perhaps slight mismatch at center of passband. Use MIN based analysis to optimize design. S (db) 5 S, EM S, MIN S, EM Gridding in EM analysis (5 m used here could have resulted in EM analysis differences). Some subtle effects are captured in EM Simulation not in MIN analysis E.G. via coupling. 6 S (db) S response on a Smith chart EM Analysis.6 GHz. GHz. GHz. GHz. GHz. GHz.9 GHz.9 GHz.9 GHz. GHz.96 GHz.9 GHz. GHz S response (optimized). GHz. GHz S response (optimized) MIN Analysis.6 GHz.96 GHz. GHz. GHz. GHz.9 GHz. GHz.9 GHz MIN Analysis EM Analysis.9 GHz.9 GHz. GHz 6 7

33 S response on a Smith chart Wideband response S (db) S 6 S (db) S (db) 5 S, EM S, MIN S, EM 6 S (db) 5 S Same as with MIN based analysis Manufactured filter considerations It will be necessary to tune every filter manufactured. Fabrication tolerances are about %. Greater accuracy than that is required. Tuning done by adjusting capacitor values. 5 t b b 5 Enclosure Y DIM w s w s w via X DIM Summary, Parallel oupled-ine ombline Filter Filter synthesized using a methodical process. Microwave simulation required to optimize design. 5 b t b 5 EM simulation as a check as there are coupling mechanisms that cannot be captured otherwise. Every filter manufactured will require tuning.