Measurements of microphone array phase and amplitude behavior towards controllable beamforming

Beamforming of miniature and MEMS microphone arrays often relies on only the array factor, with the microphone elements assumed to be ideal, i.e., identical, with linear phase and constant omnidirectional magnitude response over all frequencies. However, real-world element responses are not ideal and there is a shortfall of measurements of array-embedded microphone directional responses. This is a significant gap for estimating a real-world acoustic microphone array response. This paper presents a procedure for physically evaluating the phase and amplitude of miniature microphones using a two-port audio analyzer. While the phase is often the essence of array beamforming (hence the term phased array) the amplitudes are also weighted in general beamforming. Directional responses, or patterns, are perhaps the most difficult sensor parameter to measure, requiring specialized equipment; currently there are no accurate commercial systems readily available for 3D patterns. Our method estimates embedded microphone directional response samples, and shows that while the relative phase can behave similarly to that of isolated, electrically small sensors, the amplitudes differ significantly, which compromises accurate beamforming. The phase differences between a pair of embedded microphones can be modelled using basic geometric spacing. Comparisons between the measured and modelled signals of the microphone elements indicate that the individual embedded element responses should be included for accurate estimation of the array response, rather than just using the array factor.