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If a two port network is passive, then we have, with the usual notation, the following relationship :

  • A.\(h_{12} = -h_{21}\)
  • B.\(h_{11} = h_{22}\)
  • C.\(h_{11}h_{22} - h_{12}h_{21} = 1\)
  • D.\(h_{12} = h_{21}\)

Answer: A

For a passive network, \(h_{12} = -h_{21}\).

A passive, linear, bilateral network is reciprocal. In terms of the other parameter sets reciprocity means \(z_{12} = z_{21}\), \(y_{12} = y_{21}\) and \(AD - BC = 1\). Converting the z-condition into hybrid parameters gives \(h_{12} = -h_{21}\), with a minus sign because \(h_{12}\) is a voltage ratio and \(h_{21}\) a current ratio defined in opposite senses.

\(h_{12} = h_{21}\) misses the sign. \(h_{11}h_{22} - h_{12}h_{21} = 1\) is the condition for a symmetrical network, not a reciprocal one, and \(h_{11} = h_{22}\) equates an impedance with an admittance.

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