Impact of antenna load on embedded element patterns in aperture arrays. The single fault case

We present a simplified equation of the transformation between Embedded Element Patterns (EEPs) of an array of identically loaded elements, with the exception of one faulty termination of arbitrary offset. This new expression is proven to need only one column of the loaded admittance matrix to work out the new EEPs from the identically loaded ones. It can also be depicted as a circuit equivalent by superimposing two contributions of the EEPs referred to the original, scaled unitary matrix load for all elements, one of which multiplied by a proper voltage transfer function. Applications of this representation are also discussed. Finally, simple dipole simulations, as well as more complex EEPs of a real as-deployed radio astronomical antenna array corroborate the formula both by forward (EEPs) as well as inverse (impedance fault) calculations.