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Extra info for Analog and Digital Filters: Design and Realization (Prentice-Hall series in electrical and computer engineering)
A case in point is a 2-port containing tW( nullators, as shown in Fig. 2-2(b). This 2 port is characterized by four equations: VI = 0 V z = 0, I I = 0, and /z = o. Chap. 2 Building Blocks / 19 (b) Admittance Representation [ I1 12 J=[Yll Yl2J[VIJ Y21 Y22 or I=YV (2-2) V2 (c) and (d) Hybrid Representations (2-3) and [VI2J = [~11 h21 1 ~12J[VIJ = ii[V J 12 12 (2-4) 1 h22 (e) and (f) Transmission or Chain Representations (2-5) and (2-6) e- e 1, and = C-l. Clearly, Z = Y-l, Y = Z-I, H = ii-I, ii = H-l, C = A 2-port is said to be reciprocal if Z12 = Z21 or Yl2 = Y21' All I-ports are reciprocal elements by definition.
2 Building Blocks I 33 4. 8 A generalized impedance converter, shown in Fig. 2-13(a) is a 2-port device capable of making the input impedance of one of its two ports the product of the impedance terminating its remaining port and some internal impedances. It is characterized by a chain matrix (2-44) where f(s) is called the impedance transformation function and k is usually normalized to unity. A circuit realization of a GIC with (2-45) k=1 is shown in Fig. 2-13(b). In particular, if we letZ 2 = R 2 , Z3 and Zs = IlsC s , then the 2-port is characterized by = R 3, Z4 = R 4, (2-46) Observe that if we now terminate port 2 with a resistor R 6 , as shown in Fig.
R, I, + 12 c,t V, - R2 I, + + V2 V, - - 12 + c'-f V2 - (b) (a) R, I, + + c, V, (c) Fig. P2-9 2-10. Find the transfer functions of the three circuits shown in Fig. P2-1O. C2 C, I, R, 1 f- , i ~ I, 12 V2 - ~A 1 + + Y R2 V , I ~ Y - Fig. P2-10(a), (b) + V2 - (b) (a) 12 I 44 Chap. 2 Building Blocks C1 11 + v1 Rl C2 ~ R2 IV ~ i LY 12 + V2 - - (e) Fig. P2-10(c) 2-11. Find a hybrid representation of the 2-port network shown in Fig. P2-11. 11 VI + - ~ lY 12 + V2 :%~ Fig. P2-11 2-12. (a) Verify that Fig.