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GATE 2014 EC (EC1) – Question 16

Networks, Signals and Systems · Sinusoidal Steady State Analysis · 1 mark · Multiple choice

For maximum power transfer between cascaded network sections, how should the first section’s output impedance Z₁ relate to the second section’s input impedance Z₂?

  1. $Z_2=Z_1$
  2. $Z_2=-Z_1$
  3. $Z_2=Z_1^*$
  4. $Z_2=-Z_1^*$

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Show answer and explanation

Correct answer: (C) $Z_2=Z_1^*$

Explanation

Write source impedance Z1=R1+jX1 and load Z2=R2+jX2. First cancel reactance by choosing X2=−X1. The remaining load power is proportional to R2/(R1+R2)², maximised at R2=R1 for a passive source. Thus **Z2=Z1*,C**, the complex conjugate match.