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Circuit Analysis: AC, Linear Circuits and Transients

Treating the T network in the figure as a two-port with R1 = 2 Ω, R2 = 3 Ω and R3 = 6 Ω, which of the following is the correct set of Z parameters (V1 = z11 I1 + z12 I2, V2 = z21 I1 + z22 I2)?

T network as a two-port R1 R2 R3 I1 I2 V1 V2 + − + − V1 = z11 I1 + z12 I2
T network as a two-port · View in diagrams
  1. Az11 = 2 Ω, z12 = 6 Ω, z22 = 3 Ω
  2. Bz11 = 11 Ω, z12 = 6 Ω, z22 = 11 Ω
  3. Cz11 = 8 Ω, z12 = 6 Ω, z22 = 9 Ω
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Answer: C. z11 = 8 Ω, z12 = 6 Ω, z22 = 9 Ω

z11 is the impedance V1/I1 seen from the input with the output open (I2 = 0): R1 and R3 in series, 2 + 6 = 8 Ω. z12 is V1/I2 with the input open (I1 = 0); I2 flows through R2 and R3, and the voltage across R3 appears directly as V1, so z12 = R3 = 6 Ω. Likewise z22 = R2 + R3 = 9 Ω and z21 = z12 = 6 Ω; in a circuit made only of passive elements, z12 = z21 (reciprocity) holds.

  • A. This leaves out R3, which is common to z11 and z22. Even with the other port open, there is a current path through R3.
  • B. This adds all three resistances. No current flows in the resistor on the open side (R2 for z11).
  • C. Correct. z11 = 8 Ω, z12 = 6 Ω and z22 = 9 Ω.
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