Antenna (radio) - Mutual Impedance and Interaction Between Antennas

Mutual Impedance and Interaction Between Antennas

Current circulating in any antenna induces currents in all others. One can postulate a mutual impedance between two antennas that has the same significance as the in ordinary coupled inductors. The mutual impedance between two antennas is defined as:

where is the current flowing in antenna 1 and is the voltage that would have to be applied to antenna 2–with antenna 1 removed–to produce the current in the antenna 2 that was produced by antenna 1.

From this definition, the currents and voltages applied in a set of coupled antennas are:

\begin{matrix} v_1&=&i_1Z_{11}&+&i_2Z_{12}&+& \cdots &+& i_nZ_{1n}\\ v_2&=&i_1Z_{21}&+& i_2Z_{22}&+&\cdots&+&i_nZ_{2n} \\ \vdots & & \vdots & & \vdots & & & & \vdots \\ v_n&=&i_1Z_{n1}&+&i_2Z_{n2}&+&\cdots&+&i_nZ_{nn}\end{matrix}

where:

  • is the voltage applied to the antenna
  • is the impedance of antenna
  • is the mutual impedance between antennas and

Note that, as is the case for mutual inductances,

This is a consequence of Lorentz reciprocity. If some of the elements are not fed (there is a short circuit instead a feeder cable), as is the case in television antennas (Yagi-Uda antennas), the corresponding are zero. Those elements are called parasitic elements. Parasitic elements are unpowered elements that either reflect or absorb and reradiate RF energy.

In some geometrical settings, the mutual impedance between antennas can be zero. This is the case for crossed dipoles used in circular polarization antennas.

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