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If 1 is transmit antenna and 2 is receive antenna, the Z21 (mutual impedance between antenna 1 and 2) is given by :

  • A.\(\left. \frac{V_{1oc} . V_{2oc}}{I_{2}} \right|_{I_{1}=0}\)
  • B.\(\left. \frac{V_{2oc}}{I_{1}} \right|_{I_{2}=0}\)
  • C.\(\left. \frac{V_{1oc}}{V_{2oc} . I_{1}} \right|_{I_{2}=0}\)
  • D.\(\left. \frac{V_{2oc}}{V_{1oc}} \times \frac{1}{I_{2}} \right|_{I_{1}=0}\)

Answer: B

The mutual impedance is \(Z_{21} = V_{2oc}/I_{1}\) with I2 = 0.

Treating the two antennas as a two-port network, Z21 is the open-circuit transfer impedance: drive antenna 1 with current I1, leave antenna 2 open-circuited so that I2 = 0, and measure the voltage V2oc induced at antenna 2. The ratio is the mutual impedance.

The other expressions multiply or divide two voltages, which gives the wrong units for an impedance, or take the condition I1 = 0, which would mean antenna 1 is not transmitting at all.

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