ECE 145a / 218 a, notes set 4: Impedance Matching

Transcription

1 ECE 145a / 218 a, notes set 4: Impedance Matching Mark Rodwell University of California, Santa Barbara rodwell@ece.ucsb.edu , fax

2 Impedance-Matching: Goals

3 Recall: ine Reflections At end of line : V At beginning of line : V ( z 0) V ( z l) V s (z 0) where ( z l) T V s gen where o o s 1 1 s o 1 1 s o

4 ine Reflections and Standing Waves Reflections : V ( z Waves traveling along line : V ( z 0) V l) V (z 0) and ( z 0) e j2l / V ( z and V l) V ( z s l) V ( z ( z l) T V 0) e s gen j2l / Varying frequency, V and V will vary from in - phase to out and will vary from constructive to destructive interference. load voltage will vary withfrequency. - of - phase...

5 Matching to Eliminate Gain Ripple Gain ripplesresulting from standing waves on line Matching will eliminate this One reason for impedance - matching is to eliminate gain ripplefrom standing waves on lines

6 Maximum Power Transfer Theorem (M aximum) P avg V gen 2 Power Available / 4 Re{ gen } from the Generator (RM Squantities) : oad Power : P P P P AVG AVG iff otherwise * gen ;

7 Matching For Maximum Power Transfer By adding a *lossless* matching network (no resistances) between the generator and we obtain P P AVG the load, Another reason for impedance - matching is to increase signal power transferred.

8 Matching for no reflection vs. matching for max Power Transfer 1 st case : out, line gen nd case : out, line gen 0 0 If, 0 out, line then matching for zero reflection and matching for maximum power transfer are not thesame.

9 Direct Interstage Matching vs. Matching Each to o Matching each to 0 Direct Stage -Stage Matching Note: in 2 jl 2 jl, line o(1 e ) /(1 e ), l can be any length, including zero.

10 Impedance-Matching: Using Agilent / ADS in "tune" mode as a study tool.

11 Use CAD Tool (Agilent) ADS to Explore Matching Classic Texts : present Matching with On - Paper Smith - Chart Exer cises. Today : Matchingeasily presented graphicall y in CAD program. First : Show how to tune networksin ADS. Second : Illustrate matching examples.

12 Tuning Elements in ADS (1) " Match"here is a circuit, having a MOSFETand an input matching network

13 Tuning Elements in ADS (2) Use series, shunt C network tomatch in to 0. Very simple MOSFET small - signal model

14 Setting Up Element Tuning in ADS: Double - click on 1, then presstune/opt/stat...: Enable tuning, then set min, max, step values...

15 Setting Up Element Tuning in ADS: 1 is now a tunable element : Do thesame for C1 :

16 Setting Up Element Tuning in ADS: Go to the main testbench and select tuning : Then manipulate windows until youcan see both the"tune Parameters" window and the Plot window

17 Setting Up Element Tuning in ADS: Usually easiest to make plot updateafter every tuning change : the Need to updateschematic after tuning : otherwise, you will lose the changes made.

18 Impedance-Matching: Methods/Examples

19 Trajectories for adding series / shunt and C Adding Series or C Adding Shunt (Parallel) or C

20 1st umped -C Matching Network: Network Topology S 11 before matching at 100 GHz

21 1st umped -C Matching Network: Increase until Yin / Y 1.0 jb : Reached when ph We have moved on a constant - r circle towards values of higher reactance jx. Increase C until in / 1.0 j0: Reached when C ff We have moved on a constant - g circle towards values of higher susceptance jb.

22 1st umped -C Matching Network: Final Values Performance vs Frequency (DC- 200 GHz frequency sweep,marker at 100 GHz)

23 2nd umped -C Matching Network: Network Topology S 11 before matching at 100 GHz

24 2nd umped -C Matching Network: Increase until Yin / Y0 1.0 jb : Reached when ph We have moved on a constant - r circle towards values of higher reactance jx. Increase from until in / j0: Reached when ph We have moved on a constant - g circle towards values of higher susceptance jb.

25 2nd umped -C Matching Network: Final Values Performance vs Frequency (DC- 200 GHz frequency sweep,marker at 100 GHz) Moredirect matching trajectory broader bandwidth

26 3rd umped -C Matching Network: Matching network with values S 11 matching trajectory at 100 GHz A: original in C : after adding D : after adding C 2 1 in parallel in series

27 3rd umped -C Matching Network: Final Values Performance vs Frequency (DC- 200 GHz frequency sweep,marker at 100 GHz) ong matching trajectory narrower bandwidth

28 4th umped -C Matching Network: Matching network with values S 11 matching trajectory at 100 GHz A: original in B : after adding D : after adding 2 1 in parallel in series

29 4th umped -C Matching Network: Final Values Performance vs Frequency (DC- 200 GHz frequency sweep,marker at 100 GHz) short matching trajectory wider bandwidth

30 Multi-Section -C Matching Network: Tuning with multiple series/shunt elements infinite # of possible matching networks.

31 ines of Constant Q: Q (maximum energy stored)/(energy dissipated per radian) X B series series / R / G series series for simple 2 - element impedances curves of constant Q look roughly like this. M atching networks passing through high - Q pointswill have narrow bandwidth.

32 Narrowband vs. Wideband Matching Networks 4-element : wideband 2-element : narrowband

33 imits to Matching Network Bandwidth ow -Q load High -Q load Starting point ( ) is low -Q match can be made wide or narrow Starting point ( ) is high -Q match cannot be made wide

34 Shunt-Stub Matching Networks

35 Trajectories for Adding a Series ine of Impedance o Adding Series TRXline : increasing the line length rotates the load reflection coefficien t : in 2 jl / e Series line : line system_sta ndard 0 (if the standard impedance is 50, theline is 50)

36 Recall: Trajectory for adding Shunt Susceptance Adding Shunt (Parallel) Susceptance Susceptance can be an ideal { or C}. Susceptance can be a shunt transmission - line stub. Susceptance can radial stub. be a shunt

37 Susceptance of Shunt Stub (Open-Terminated) Open - Terminated Short -Terminated

38 Shunt-Stub Matching Network: Series toy / Y line 0 1 brings jb load Shunt stubadds Y stub / Y 0 jb Combination brings toy / Y 0 1 j0 load

39 1st Shunt-Stub Matching Network Network Topology S 11 before matching at 100 GHz

40 1st Shunt-Stub Matching Network Increase T length until Yin / Y0 1.0 jb : Reached when 2l 1 / 1 68 degrees We have moved on a constant circle. Increase T2 length until Yin / Y0 1.0 j0: Reached when 2l 2 / 65 degrees We have moved on a constant - g circle towards values of higher susceptance jb.

41 1st Shunt-Stub Matching Network Final Values Performance vs Frequency (DC- 200 GHz frequency sweep,marker at 100 GHz)

42 2nd Shunt-Stub Matching Network A shorter series line section T1 brings from A to B matched Theshunt stubmust now be inductive

43 3rd Shunt-Stub Matching Network Series toy / Y line 0 1 brings jb load M icrostrip Radial Shunt stubadds Y stub / Y 0 jb Combination brings toy / Y 0 1 j0 load Radial stub: a wedge - shaped capacitor with distributed effects accurately modelled.

44 3rd Shunt-Stub Matching Network Final Values Performance vs Frequency (DC- 200 GHz frequency sweep,marker at 100 GHz)

45 Shunt-Stub Matching Networks......with general line impedance

46 Trajectories for Adding a High-o Series ine Adding Series inductance Adding series line line 0 Adding series line line 0 Behavior is intermediatebetween series inductance &series line of impedance 0

47 Matching Network with High-o Series & ow-o Shunt ines Series toy / Y line 0 1 brings jb Shunt stubadds Y stub / Y 0 jb load Series line is mostly inductive, shunt line is mostly capacitive.

48 umped vs. Distributed Matching Networks shunt shunt shunt C shunt shunt shunt series series series C series series series If while holding then C and we force series shunt C series series shunt and series / 2 shunt & C 2 series shunt 0 shunt constant, 0 -C matching network is limiting case of 0, high - /low- network. Distributed matching networkscan be approximated by Cnetworks

49 Trajectories for Adding a ow-o Series ine Adding shunt capacitance Adding series line line 0 Adding series line line 0 Behavior is intermediatebetween shunt capacitance & series line of impedance 0

50 Matching Network with High-o Series & ow-o Series ines Series line is mostly inductive. Shunt line is mostly capacitive Dottedlines show lumped (,C) trajectory

51 umped vs. Distributed Matching Networks high high high C high high high low low low C low low low If while holding then C and we force high low C low high high and high / 2 low & C 2 high 0 low 0 low 0, constant, -C matching network is limiting case of high - /low- network. Distributed matching networkscan be approximated by Cnetworks

52 umped vs. Distributed Matching Networks Given this mask layout......your eyes should see this.

53 umped vs. Distributed Matching Networks Given this mask layout......your eyes should see this.

54 Quarter-wave and related Matching Networks...

55 Quarter-wave Impedance Tranformer At load : At input : line in line ~ 1 ~ 1 ~ 1 1 in in But : ~ ~ e in -j 4l / ~ if l / 4 So : in line line 1 if l / 4 in 2 line if l / 4 ~ ~ and in are relfection coeffiecie nts using line as the impedance standard, not 0

56 Insight: Series ines Regardless of and ending point ( thestarting point ( ), the impedance trajectory contains the points(a,b), with resistive input impedance such that in ), R in, A R in, B 2 line

57 Quarter-wave Impedance Tranformer: Resistive oads R in R R 2 line Pick line impedance to match line 0 in to 0 :

58 Quarter-wave Impedance Tranformer: General oads For a general load impedance where Y susceptance to' R' G jb 1/ G jb, 1/ Y one can add a shunt, bringing theload impedance R jx Then one adds a quarter - wavelength line of impedance line R 0 tomatch theinput impedance to 0.