T-II Equivalent networks Zhen Wan University of California, davis 9.1 Introduction Richard C. dorf 9.2 Three-Phase Connections 9.3 Wye s Delta Transformations 9.1 Introduction Two very important two-ports are the T and Il networks shown in Fig. 9. 1. Because we encounter these two geometrical forms often in two-port analyses, it is useful to determine the conditions under which these two networks are equivalent. In order to determine the equivalence relationship, we will examine Z-parameter equations for the T network and the Y-parameter equations for the Il network For the T network the equations are V1=(Z1+Z3)I1+Z3L2 V2=Z3I1+(Z and for the Il network the equations are ,=(Y+Y),-Yv ,=-Y,V,+(Y,+y Solving the equations for the T network in terms of I, and I,, we obtain +zyl_Z,v2 where D,=Z,,+ Z2Z,+ ZZ, Comparing these equations with those for the II network, we find that c 2000 by CRC Press LLC© 2000 by CRC Press LLC 9 T–P Equivalent Networks 9.1 Introduction 9.2 Three-Phase Connections 9.3 Wye ¤ Delta Transformations 9.1 Introduction Two very important two-ports are the T and P networks shown in Fig. 9.1. Because we encounter these two geometrical forms often in two-port analyses, it is useful to determine the conditions under which these two networks are equivalent. In order to determine the equivalence relationship, we will examine Z-parameter equations for the T network and the Y-parameter equations for the P network. For the T network the equations are V1 = (Z1 + Z 3)I1 + Z 3 I2 V2 = Z3 I1 + (Z 2 + Z 3)I2 and for the P network the equations are I1 = (Ya + Yb)V1 – YbV2 I2 = –YbV1 + (Yb + Yc)V2 Solving the equations for the T network in terms of I1 and I2, we obtain where D1 = Z1Z2 + Z2Z3 + Z1Z3. Comparing these equations with those for the P network, we find that I Z Z D V Z V D I Z V D Z Z D V 1 2 3 1 1 3 2 1 2 3 1 1 1 3 1 2 = Ê + Ë Á ˆ ¯ ˜ = + Ê + Ë Á ˆ ¯ ˜ – – Zhen Wan University of California, Davis Richard C. Dorf University of California, Davis