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

7-6 Passive, Active, and Digital Filters0.015 H 8.28 mH 0.048 H1F 6.48 F 12.88 FFIGURE 7.8First Cauer canonical form.10.87 F 1.52 F 4.03 F0.071 H 0.02 H 5.2 mHFIGURE 7.9Second Cauer canonical form.For the second Cauer canonical form, we rearrange the polynomials in ascending order of s, thenexpand the resulting function in a continued fraction, and obtainZ(s) ¼14:06sþ0:092sþ49:84s1þ10:66s111þ192:26þ 1s 0:248s(7:19)The desired LC ladder is shown in Figure 7.9.7.3 RC One-Port NetworksIn this part, we exploit the properties of impedance functions of the RC one-ports from the knownproperties of the LCM one-ports of Section 7.2.From a given RC one-port N RC , we construct an LC one-port N LC by replacing each resistor of resistanceR i by an inductor of inductance L i ¼ R i . Suppose that we use loop analysis for both N RC and N LC , andchoose the same set of loop currents. In addition, assume that the voltage source at the input port istraversed only by loop current A. Then the input impedance Z LC (s)ofN LC is determined by the equationZ LC (s) ¼ ~ D(s)~D 11 (s)(7:20)where~D is the loop determinant~D 11 is the cofactor corresponding to loop current 1 in N LC