Figure P17.52 shows a generalized form of the Antoniou circuit of Fig. 17.20(a). Here

Chapter 17, Problem 17.52

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Figure P17.52 shows a generalized form of the Antoniou circuit of Fig. 17.20(a). Here, R5 is eliminated and the other four components are replaced by general impedances Z1, Z2, Z3, and Z4. (a) With an impedance Z5 connected between node 2 and ground, show that the input impedance looking into port 1 (i.e., between node 1 and ground) is Z11 = Z1Z3 Z2Z4 Z5 A1 A2 Z1 Z2 Z3 Z4 1 2 Figure P17.52 (b) From the symmetry of the circuit, show that if an impedance Z6 is connected between terminal 1 and ground, the input impedance looking into port 2, which is between terminal 2 and ground, is given by Z22 = Z2Z4 Z1Z3 Z6 (c) From the expressions above, observe that the two-port network in Fig. P17.52 acts as an impedance transformer. Since by the appropriate choice of Z1, Z2, Z3, and Z4, the transformation ratio can be a general function of the complex frequency variable s, the circuit is known as a generalized impedance converter, or GIC.