R. Ludwig and G. Bogdanov RF Circuit Design: Theory and Applications 2 nd edition. Figures for Chapter 5

Transcription

1 R. Ludwig and G. Bogdanov RF Circuit Design: Theory and Applications 2 nd edition Figures for Chapter 5 IL, db IL IL, db IL 1 Low-pass filter Ω 1 High-pass filter Ω IL, db IL, db IL IL IL Ω Ω 1 Ω 2 Ω 1 Ω 2 Bandpass filter Bandstop filter Ω Figure 1-1 Four basic filter types.

2 IL, db IL, db 1 Binominal filter Ω 1 Chebyshev filter Ω IL, db 1 Elliptic filter Ω Figure 1-2 Actual attenuation profile for three types of low-pass filters.

3 IL, db BW 6 db 6 db Rejection Passband insertion loss 3 db f L 6 db /f C f L 3 db /f C BW 3 db 1 f U 3 db /f C f U 6 db /f C Passband ripple Ω Figure 1-3 Generic attenuation profile for a bandpass filter.

4 Z G V G Filter Z L Figure 1-4 Filter as a two-port network connected to an RF source and load.

5 Z G = Z R + + V G V 1 C V 2 Z L = Z Figure 1-5 Low-pass filter connected between a source and load.

6 + V G Z G R C Z L + V 2 Figure 1-6 Cascading four ABCD networks.

7 IL, db R = 1 Ω R = 1 Ω R = 5 Ω R = 2 Ω Frequency, Hz (a) Attenuation profile R = 5 Ω R = Ω Phase, deg R = Ω R = 5 Ω R = 2 Ω R = 5 Ω R = 1 Ω R = 1 Ω Frequency, Hz (b) Phase response Figure 1-7 First-order low-pass filter response as a function of various parasitic resistance values.

8 Z G R Z G R V G L Z L V G L Z L V 2 (a) High-pass filter with load resistance (b) Network and input/output voltages Figure 1-8 First-order high-pass filter.

9 35 3 IL, db R = 1 Ω 1 R = 1 Ω 5 R = 5 Ω R = 5 Ω R = Ω R = 2 Ω Frequency, Hz (a) Attenuation profile Phase, deg R = 2 Ω R = 1 Ω R = 1 Ω R = 5 Ω 3 R = 5 Ω 2 1 R = Ω Figure 1-9 values Frequency, Hz (b) Phase response High-pass filter response as a function of various parasitic resistance

10 Z G R L C V G Z L Figure 1-1 Bandpass filter implemented in series configuration.

11 IL, db Phase, deg Frequency, Hz Figure 1-11 Bandpass filter response.

12 1 9 C 8 Z G R 7 V G L Z L IL, db Z G = Z L = Z = 5 Ω R = 2 Ω C = 2 pf L = 5 nh Frequency, Hz (a) Magnitude of transfer function Phase, deg Frequency, Hz (b) Phase of transfer function Figure 1-12 Bandstop filter response.

13 Table 1-1 Series and parallel resonators C Parameter R L C G L Impedance or Admittance Resonance Frequency 1 1 Z = R + jωl Y = G + jωc jωc jωl 1 1 ω = ω = LC LC Dissipation Factor d R = = Rω ω L C d G = = Gω ω C L Quality Factor Q ω L = = Q R Rω C ω C = = G Gω L Bandwidth BW f 1 = --- = R Q 2π -- BW f = --- = L Q G 2π --- C

14 V G + R L C R E Figure 1-13 Circuit used for the definitions of loaded and unloaded quality factors.

15 Z G V G Z Z L (a) Matched transmission line system. Z G R L C V G Z Z Z L (b) Insert bandpass filter. Figure 1-14 Insertion loss considerations.

16 Insertion loss, db f L 3 db BW = 35 MHz Frequency, GHz f f U Figure 1-15 Insertion loss versus frequency.

17 35 3 Insertion loss, db db N = 5 N = 4 N = 3 N = 2 N = Normalized frequency, Ω Figure 1-16 Butterworth low-pass filter design.

18 R G = g = 1 g 2 g 1 g 3 g N + 1 (a) G G = g = 1 g 1 g 3 g 2 g N + 1 (b) Figure 1-17 Two equivalent realizations of the generic multisection low-pass filter with normalized elements.

19 Table 1-2 Coefficients for maximally flat low-pass filter (N = 1 to 1) N g 1 g 2 g 3 g 4 g 5 g 6 g 7 g 8 g 9 g 1 g

20 Attenuation, db N = 8 N = 9 N = 1 N = 7 N = 6 N = 5 N = 4 N = 3 N = 2 N = Normalized frequency, Ω Figure 1-18 frequency. Attenuation behavior of maximally flat low-pass filter versus normalized

21 Table 1-3 Coefficients for linear phase low-pass filter (N = 1 to 1) N g 1 g 2 g 3 g 4 g 5 g 6 g 7 g 8 g 9 g 1 g

22 1.8 T T 3 T T Normalized frequency, Ω.8 1 Figure 1-19 Chebyshev polynomials T 1 ( Ω) through T 4 ( Ω) in the normalized frequency range 1 Ω 1.

23 Loss factor Normalized frequency, Ω 3 N = 4 N = 2 N = 3 N = 1 Insertion loss, db N = 4 N = 2 N = db ripples N = Normalized frequency, Ω Figure 1-2 Frequency dependence of the loss factor and insertion loss of the Chebyshev low-pass filter.

24 8 7 6 N = Attenuation, db N = Normalized frequency, Ω Figure 1-21 Attenuation response for 3 db Chebyshev design.

25 8 7 Attenuation, db N = N = Normalized frequency, Ω Figure 1-22 Attenuation response for.5 db Chebyshev design.

26 Table 1-4 (a) Chebyshev filter coefficients; 3 db filter design (N = 1 to 1) N g 1 g 2 g 3 g 4 g 5 g 6 g 7 g 8 g 9 g 1 g

27 Table 1-4 (b) Chebyshev filter coefficients;.5 db filter design (N = 1 to 1) N g 1 g 2 g 3 g 4 g 5 g 6 g 7 g 8 g 9 g 1 g

28 12 Attenuation, db dB Chebyshev Butterworth Linear phase Normalized frequency, Ω Figure 1-23 Comparison of the frequency response of the Butterworth, linear phase, and 3-dB Chebyshev third-order filters.

29 3 25 Attenuation, db Normalized frequency, Ω Figure 1-24 Fourth-order low-pass Chebyshev filter with 3 db ripples in the passband.

30 3 25 Attenuation, db Frequency, GHz Figure 1-25 Conversion of standard low-pass filter prototype into low-pass realization. Cutoff frequency is f c = 1 GHz.

31 3 25 Attenuation, db Frequency, GHz Figure 1-26 Conversion of standard low-pass filter prototype into high-pass realization. Cutoff frequency is f c = 1 GHz.

32 2 1.5 L Normalized frequency, Ω U U 1.5 L Frequency, Figure 1-27 Mapping from standard frequency Ω into actual frequency ω. Lower cutoff frequency is ω L = 1 and upper cutoff frequency is ω U = 3.

33 3 25 Attenuation, db Frequency, GHz Figure 1-28 Conversion of standard low-pass filter prototype into bandpass realization with lower cutoff frequency f L =.7 GHz, upper cutoff frequency f U = 1.3 GHz, and center frequency of f =.95 GHz.

34 3 25 Attenuation, db Frequency, GHz Figure 1-29 Conversion of standard low-pass filter prototype into bandstop realization with center frequency of f =.95 GHz. Lower cut-off frequency is f L =.7 GHz and upper cutoff frequency is f U = 1.3 GHz.

35 Table 1-5 Transformation between normalized low-pass filter and actual bandpass and bandstop filter BW = ω U ω L, ω = ω U ω Low-pass prototype Low-pass High-pass Bandpass Bandstop L = g k L c 1 cl L BW BW 2 L 1 (BW)L (BW)L 2 C = g k C c 1 cc C BW BW 2 C 1 (BW)C (BW)C 2

36 R G = 5 Ω L 1 C 1 L 3 C 3 C 2 L 2 R L = 5 Ω 7 6 Attenuation, db Frequency, GHz Figure 1-3 Attenuation response of a three-element 3 db ripple bandpass Chebyshev filter centered at 2.4 GHz. The lower cutoff frequency is f L = 2.16 GHz and the upper cutoff frequency is = 2.64 GHz. f U

37 Table 1-6 Kuroda s identities Initial Circuit Kuroda s Identity Y C = S/Z 2 Z L = SZ 1 /N Unit element Z 1 Unit element Z 2 /N Z L = Z 1 S Y C = S/(NZ 2 ) Unit element Z 2 Unit element NZ 1 Y C = S/Z 2 Unit element Z 1 Y C = S/(NZ 2 ) Unit element NZ 1 N : 1 Z L = Z 1 S Unit element Z 2 Unit element Z 2 /N Z L = SZ 1 /N 1 : N N = 1 + Z 2 Z 1

38 r G = 1 L 2 L 4 C 1 C 3 C 5 r L = 1 C 1 = C 5 = C 3 = L 2 = L 4 = Figure 1-31 Normalized low-pass filter of order N = 5.

39 s.c. s.c. r G = 1 Z 2 Z 4 r L = 1 Z 1 o.c. Z 3 Z 5 o.c. o.c. Figure 1-32 Replacing inductors and capacitors by series and shunt stubs (o.c. = open-circuited line, s.c. = short-circuited line).

40 s.c. s.c. r G = 1 Z 2 Z 4 Z UE1 = 1 Z UE2 = 1 UE UE r L = 1 Z 1 Z 3 Z 5 o.c. o.c. o.c. Figure 1-33 Deployment of the first set of unit elements (UE = unit element).

41 Z 1 =.634 s.c. Z 2 = Z 4 = Z 2 Z 5 = Z 1 s.c. s.c. s.c. r G = 1 Z UE1 =.3696 Z UE2 = Z UE 1 UE UE r L = 1 o.c. Z 3 =.3936 Figure 1-34 Converting shunt stubs to series stubs.

42 Z 1 =.634 Z 2 = Z 4 = Z 2 Z 5 = Z 1 s.c. s.c. s.c. s.c. r G = 1 Z UE3 = 1 Z UE1 =.3696 Z UE2 = Z UE1 Z UE4 = 1 UE UE UE UE r L = 1 o.c. Z 3 =.3936 Figure 1-35 Deployment of the second set of unit elements to the fifth-order filter.

43 r G = 1 Z UE3 = Z UE1 = Z UE2 = Z UE4 = UE UE UE UE r L = 1 o.c. o.c. o.c. o.c. o.c. Z 1 = Z 2 =.487 Z 3 =.3936 Z 4 =.487 Z 5 = Figure 1-36 Realizable filter circuit obtained by converting series and shunt stubs using Kuroda s identities.

44 5 Ω 81.5 Ω 8. Ω 8. Ω 81.5 Ω 5 Ω Ω Attenuation, db 24. Ω 19.7 Ω 24. Ω Ω (a) Microstrip line low-pass filter implementation Frequency, GHz (b) Attenuation versus frequency response Figure 1-37 Final microstrip line low-pass filter.

45 r G = 1 L 1 = 1 L 3 = 1 C 2 = 2 r L = 1 Figure 1-38 Normalized third-order low-pass filter.

46 s.c. s.c. Z 1 =.4142 Z 3 =.4142 r G = 1 r L = 1 Z 2 = o.c. Figure 1-39 Replacing inductors and capacitors by series and shunt stubs.

47 s.c. s.c. r G = 1 Z 1 Z 3 UE Z UE1 = 1 UE Z UE2 = 1 r L = 1 Z 2 o.c. (a) Unit elements at source and load sides r G = 1 Z UE1 = Z UE2 = UE Z UE1 UE Z UE2 r L = 1 Z 1 Z 2 Z 3 o.c. o.c. o.c. Z 1 = Z 2 = Z 3 = (b) Conversion from series to shunt stubs Figure 1-4 Introducing unit elements and converting series stubs to shunt stubs.

48 5 Ω 7.7 Ω 7.7 Ω 5 Ω 17.7 Ω 6.4 Ω 17.7 Ω Figure 1-41 Characteristic impedances of final microstrip line implementation of bandstop filter design.

49 Attenuation, db Frequency, GHz Figure 1-42 Attenuation versus frequency response for third-order bandstop filter.

50 S d W W r Figure 1-43 Coupled microstrip lines.

51 I 1 (z + z) I 1 (z) + V 1 (z) I 2 (z) z C 11 + V 2 (z) L 11 C 12 C 22 L 12 L 22 + V 1 (z + z) I 2 (z + z) + V 2 (z + z) Figure 1-44 Equivalent circuit diagram and appropriate voltage and current definitions for a system of two lossless coupled transmission lines.

52 Even mode impedance Z e, Ω d S/d W/d S W W Odd mode impedance Z o, Ω Figure 1-45 Even and odd characteristic impedance for microstrip lines.

53 Filter element l Z in, Z e, Z o Z in (a) Arrangement of two coupled microstrip lines (b) Transmission line representation Figure 1-46 Bandpass filter element.

54 5 Input impedance Re(Z in ), Ω Z e Z o / π π Electrical length, l 1.5π 2π Figure 1-47 Input impedance behavior of equation (5.76). Z e and Z o are arbitrarily set to 12 and 6 respectively. Ω Ω,

55 Z Z e, Z o Z e, Z o, 1 1, 2 Z e, Z o Z e, Z o Z e, Z o Z e, Z o N 1, N N, N + 1 Z Figure 1-48 Multielement configuration of a fifth-order coupled-line bandpass filter (N = 5).

56 3 25 Attenuation, db Frequency, GHz Figure 1-49 Simulations of the fifth-order coupled-line Chebyshev bandpass filter with 3 db ripple in the passband. The lower cutoff frequency is 4.8 GHz and the upper cutoff frequency is 5.2 GHz.

57 db(s(2,1)) db(s(1,1)) S11 S21 db(s(2,1)) db(s(1,1)) S11 S freq, GHz freq, GHz (a) (b) (c) Figure 1-5 S-parameters of the 1.5 GHz microstrip low-pass filter: (a) Matlab simulation, (b) ADS simulation, (c) network analyzer mesurement.

58 (a) (b) Figure 1-51 Microstrip pattern for the 1.5 GHz low-pass filter: (a) ADS simulation, (b) PCB implementation.