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Z-Parameters Calculation

 

Z-Parameters Calculation








Z-Parameters of Ladder Network

Definition:

V1 = Z11·I1 + Z12·I2
V2 = Z21·I1 + Z22·I2

Step 1: Find Z11 and Z21 (I2 = 0, Output Open)

  • 8Ω branch carries no current → ignore it
  • From node B: Z = 20Ω
  • Series: 8 + 20 = 28Ω
  • Parallel at node A: Z = (10 × 28)/(10 + 28) = 7.37Ω
  • Total input: Z11 = 2 + 7.37 = 9.37Ω

Z21 = 7.37 × (20 / 28) ≈ 5.26Ω

Step 2: Find Z22 and Z12 (I1 = 0, Input Open)

  • 2Ω branch open → no current
  • From node A: 10Ω
  • Series: 8 + 10 = 18Ω
  • Parallel at node B: Z = (20 × 18)/(38) = 9.47Ω
  • Total: Z22 = 8 + 9.47 = 17.47Ω

Z12 = 9.47 × (10 / 18) ≈ 5.26Ω

Final Z Matrix

[ 9.37    5.26
  5.26    17.47 ] Ω

ABCD Shortcut Method

If ABCD parameters are known:

T = [ A   B
C   D ]

Z11 = A / C
Z21 = 1 / C
Z22 = D / C
Z12 = (AD − BC) / C

Using:

A = 1.78, B = 25.84, C = 0.195, D = 3.3

Z11 = 9.13Ω
Z12 = 4.28Ω
Z21 = 5.13Ω
Z22 = 16.92Ω

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