Measuring Array Mutual Impedances Using Embedded Element Patterns

The radiation pattern of an antenna element embedded in a multiport antenna such as a phased array depends on the loads connected to the array element ports. If the embedded element patterns (EEPs) are measured using at least two known loading conditions, the patterns can be used to determine the array mutual impedance matrix. In previous work, this result has been derived with the simplifying assumption that the impedance of the source connected to the driven element changes along with the load impedances connected to the nondriven elements. In a practical test configuration, the source impedance cannot be readily changed. We analyze the case of EEPs measured with a fixed source impedance and changing impedances on the nondriven elements. The transformation from one set of EEPs to another with fixed source impedance is more complex than in the case of a source impedance that changes with the load impedances. The transformation depends on the coupling between elements and is only weakly sensitive to the element self-impedances. With measured EEPs for an array of identical elements, the impedance matrix can be found up to a scale factor. We demonstrate the method experimentally by measuring the patterns of an antenna array terminated with one loading condition and repeating the pattern measurements with a different loading condition. The mutual impedance matrix extracted from the pattern measurements compared to network analyzer mutual impedance measurements is accurate to within 1–
$2~\Omega $
for most of the mutual impedances.