Figure 8. 1 (p. 371) Examples of periodic structures Figure 8.1 (p. 371) Examples of periodic structures. (a) Periodic stubs on a microstrip line. (b) Periodic diaphragms in a waveguide. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.2 (p. 372) Equivalent circuit of a periodically loaded transmission line. The unloaded line has characteristic impedance Z0 and propagation constant k. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.3 (p. 374) A periodic structure terminated in a normalized load impedance ZL. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.4 (p. 376) k-β diagram for a waveguide mode. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.5 (p. 376) A capacitively loaded line. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.6 (p. 377) k-β diagram for Example 8-1. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.7 (p. 378) A two-port network terminated in its image impedances. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.8 (p. 379) A two-port network terminated in its image impedances and driven with a voltage generator. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.9 (p. 380) Low-pass constant-k filter sections in T and  form. (a) T-section. (b) -section. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.10 (p. 382) Typical passband and stopband characteristics of the low-pass constant-k sections of Figure 8.9 Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.11 (p. 383) High-pass constant-k filter sections in T and  form. (a) T-section. (b) -section. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.12 (p. 383) Development of an m-derived filter section from a constant-k section. (a) Constant-k section. (b) General m-derived section. (c) Final m-derived section. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.13 (p. 384) f-derived filter sections. (a) Low-pass T-section. (b) High-pass T-section. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.14 (p. 384) Typical attenuation responses for constant-k, m-derived, and composite filters. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8. 15 (p. 385) Development of an m-derived -section Figure 8.15 (p. 385) Development of an m-derived -section. (a) Infinite cascade of m-derived T-sections. (b) A de-embedded -equivalent. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.16 (p. 386) Variation of Zi in the passband of a low-pass m-derived section for various values of m. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.17 (p. 386) A bisected -section used to match Zi to ZiT Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.18 (p. 387) The final four-stage composite filter. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.19 (p. 388) Low-pass composite filter for Example 8.2 Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.20 (p. 389) Frequency response for the low-pass filter of Example 8.2. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.21 (p. 390) Maximally flat and equal-ripple low-pass filter responses (N = 3). Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.22 (p. 391) Elliptic function low-pass filter response. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.23 (p. 392) The process of filter design by the insertion loss method. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.24 (p. 392) Low-pass filter prototype, N = 2. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.25 (p. 393) Ladder circuits for low-pass filter prototypes and their element definitions. (a) Prototype beginning with a shunt element. (b) Prototype beginning with a series element. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.26 (p. 395) Attenuation versus normalized frequency for maximally flat filter prototypes. Adapted from G.L. Mattaei et al., Microwave Filters, Impedance-Matching Networks, and Coupling Sructures (Artech House, 1980) Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.27a (p. 397) Attenuation versus normalized frequency for equal-ripple filter prototypes. (a) 0.5 dB ripple level. Adapted from G.L. Mattaei et al., Microwave Filters, Impedance-Matching Networks, and Coupling Sructures (Artech House, 1980) Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.27b (p. 397) Attenuation versus normalized frequency for equal-ripple filter prototypes. (b) 3.0 dB ripple level. Adapted from G.L. Mattaei et al., Microwave Filters, Impedance-Matching Networks, and Coupling Sructures (Artech House, 1980) Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.28 (p. 399) Frequency scaling for low-pass filters and transformation to a high-pass response. (a) Low-pass filter prototype response for ωc = 1. (b) Frequency scaling for low-pass response. (c) Transformation to high-pass response. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.29 (p. 401) Low-pass maximally flat filter circuit for Example 8.3. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.30 (p. 404) Frequency response of the filter design of Example 8.3. (a) Amplitude response. (b) Group delay response. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8. 31 (p. 402) Bandpass and bandstop frequency transformation Figure 8.31 (p. 402) Bandpass and bandstop frequency transformation. (a) Low-pass filter prototype response for ωc = 1. (b) Transformation to bandpass response. (c) Transformation to bandstop response. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.32 (p. 404) Bandpass filter circuit for Example 8.4 Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.33 (p. 405) Amplitude response for the bandpass filter of Example 8.4. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8. 34 (p. 407) Richard’s transformation Figure 8.34 (p. 407) Richard’s transformation. (a) For an inductor to a short-circuited stub. (b) For a capacitor to an open-circuited stub. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.35 (p. 408) Equivalent circuits illustrating Kuroda identity (a) in Table 8.7. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8. 36a (p. 409) Filter design procedure for Example 8. 5 Figure 8.36a (p. 409) Filter design procedure for Example 8.5. (a) Lumped-element low-pass filter prototype. (b) Using Richard’s transformations to convert inductors and capacitors to series and shunt stubs. (c) Adding unit elements at ends of filter. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8. 36b (p. 410) (d) Applying the second Kuroda identity Figure 8.36b (p. 410) (d) Applying the second Kuroda identity. (e) After impedance and frequency scaling. (f) Microstrip fabrication of final filter. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.37 (p. 411) Amplitude responses of lumped-element and distributed-element low-pas filter of Example 8.5. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8. 38a/b (p. 412) Impedance and admittance inverters Figure 8.38a/b (p. 412) Impedance and admittance inverters. (a) Operation of impedance and admittance inverters. (b) Implementation as quarter-wave transformers. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8. 38c/d (p. 412) Impedance and admittance inverters Figure 8.38c/d (p. 412) Impedance and admittance inverters. (c) Implementation using transmission lines and reactive elements. (d) Implementation using capacitor networks. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.39 (p. 413) Approximate equivalent circuits for short sections of transmission lines. (a) T-equivalent circuit for a transmission line section having (b) Equivalent circuit for small and large Z0. (c) Equivalent circuit for small and small Z0. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8. 40 (p. 414) Filter design for Example 8. 6 Figure 8.40 (p. 414) Filter design for Example 8.6. (a) Low-pass filter prototype circuit. (c) Stepped-impedance implementation. (c) Microstrip layout of final filter. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.41 (p. 415) Amplitude response of the stepped-impedance low-pass filter of Example 8.6, with (dotted line) and without (solid line) losses. The response of the corresponding lumped-element filter is also shown. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.42 (p. 417) Definitions pertaining to coupled line filter section. (a) A parallel coupled line section with port voltage and current definitions. (b) A parallel coupled line section with even- and odd-mode current sources. (c) A two-port coupled line section having a bandpass response. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.43 (p. 420) The real part of the image impedance of the bandpass network of Figure 8.42c. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.44 (p. 421) Equivalent circuit of the coupled line section of Figure 8.42c. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.45(a-c) (p. 422) Development of an equivalent circuit for derivation of design equations for a coupled line bandass filter. (a) Layout of an N + 1 section coupled line bandpass filter. (b) Using equivalent circuit of Figure 8.44 for each coupled line section. (c) Equivalent circuit for transmission lines of length 2. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.45 (d-f) (p. 422) Development of an equivalent circuit for derivation of design equations for a coupled line bandass filter. (d) Equivalent circuit for the admittance inverters. (e) Using results of (c) and (d) for the N = 2 case. (f) Lumped-element circuit for a bandpass filter for N = 2. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.46 (p. 426) Amplitude response of the coupled line bandpass filter of Example 8.7. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.47 (p. 427) Bandstop and bandpass filters using shunt transmission line resonators ( = /2 at the center frequency). (a) Bandstop filter. (b) Bandpass filter. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.48 (p. 428) Equivalent circuit for the bandstop filter of Figure 8.47a. (a) Equivalent circuit of open-circuited stub for  near /2. (b) Equivalent filter circuit using resonators and admittance inverters. (c) Equivalent lumped-element bandstop filter. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.49 (p. 430) Amplitude response of the bandstop filter of Example 8.8. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.50a/b (p. 431) Development of the equivalence of a capacitive-gap coupled resonator bandpass filter to the coupled line bandpass filter of Figure 8.45. (a) The capacitive-gap coupled resonator bandpass filter. (b) Transmission line model. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.50cd (p. 431) Development of the equivalence of a capacitive-gap coupled resonator bandpass filter to the coupled line bandpass filter of Figure 8.45. (c) Transmission line model with negative-length sections forming admittance inverters (i/2 <0). (d) Equivalent circuit using inverters and /2 resonators ( =  at 0). This circuit is now identical in form with the coupled line bandpass filter equivalent circuit in Figure 8.45b. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.51 (p. 433) Amplitude response for the capacitive-gap coupled series resonator bandpass filter of Example 8.10. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.52 (p. 433) A bandpass filter using capacitively coupled shunt stub resonators. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.53a/b (p. 435) Equivalent circuit for the bandpass filter of Figure 8.52. (a) A general bandpass filter circuit using shunt resonators with admittance inverters. (b) Replacement of admittance inverters with the circuit implementation of Figure 8.38d. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.53c/d (p. 435) Equivalent circuit for the bandpass filter of Figure 8.52. (c) After combining shunt capacitor elements. (d) Change in resonant stub length caused by a shunt capacitor. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons

Figure 8.54 (p. 437) Amplitude response of the capacitively coupled shunt resonator bandpass filter of Example 8.10. Microwave Engineering, 3rd Edition by David M. Pozar Copyright © 2004 John Wiley & Sons