Considerations for Mutual Coupling and Mutual Radiation Resistance of Array Antenna

In this paper, the mutual impedance and mutual radiation resistance of an array antenna are expressed and compared using the field expansion in terms of vector spherical harmonics. It is demonstrated that if the element fields are rotationally symmetric and the field expansion coefficients are real, the mutual radiation resistance is the real component of the mutual impedance.Furthermore, under the assumption that the current shapes are not affected by mutual coupling, the first-order approximation of the array gain, which explicitly incorporates the mutual impedance matrix, is derived. Also, the first-order approximation of the array directivity, which explicitly includes the mutual radiation resistance matrix, is derived. Both the expressions have similarities. However, the major difference is that the array directivity includes the Kronecker product of the conjugate of the input current, I
^*T
, and the input current, I, (I
^*T
⊗ I), whereas the array gain does not.