Passive, active, and digital filters (3ed., CRC, 2009) - tiera.ru

Design of Broadband Matching Networks 10-210.5 μH100 ΩV g1.31 μH1.32 μH522 pF1.82 μHpF1.31 μH+80–N0.902 μH195 pF50 pF100 ΩZ 22 (s)FIGURE 10.10Fifth-order Butterworth matching network.SinceRCv c ¼ 0:5 < 2 sin 22:5 ¼ 0:76537 (10:116)and from Equation 10.93L a2 ¼ 1:462 mH < L ¼ 3 mH (10:117)Case 4 applies, and from Equation 10.98s 1 ¼ 1:63129 10 8 (10:118)where Equation 10.99p ¼ 0:0188898, w ¼ 0:2304, w ¼ 5:17894 (10:119)From Equation 10.90, the maximum attainable DC gain is obtained as2(1 100 50 10 12 1:63129 10 8 ) sin 22:5 8K 4 ¼ 1 1100 50 10 12 10 8¼ 0:929525 (10:120)giving from Equation 10.85ba ¼ (1 K 4 ) 1=8 ¼ 0:717802 (10:121)Finally, the normalized reflection coefficient r(s) is obtained asr(s) ¼ (y 1:63129)(y4 þ 1:87571 y 3 þ 1:75913 y 2 þ 0:966439 y þ 0:265471)(y þ 1:63129)(y 4 þ 2:61313 y 3 þ 3:41421 y 2 þ 2:61313 y þ 1)(10:122)