Modeling and optimization of a shotgun condenser microphone

Abstract

This paper is focused on modeling and optimization of a shotgun microphone that is known to be a highly directional acoustic pick-up. A lumped-parameter model is established, with the aid of Zuckerwar's approach, to predict the frequency response of the condenser microphone. On the basis of the model, we use the simulated annealing ([SA]) method to optimize the microphone parameters, including the diaphragm radius, the diaphragm thickness, the air gap distance and the volume of back chamber, such that the sensitivity is maximized subject to a desired bandwidth. In our modified approach, the air gap resistance (Ra ) and the back chamber compliance (Cbc ) are used to calculate the D factor in Zuckerwar's model. To model the shotgun tube, T circuit and two-port network are utilized in formulating transfer matrices that is then converted to an impedance matrix representation. In addition, an array model is established to simulate the directional response. The results revealed that the shotgun microphone is highly directional at high frequencies, while the on-axis frequency response is influenced by the acoustic resonances of the tube. The simulation results suggest that the tube length should be greater than half of the wavelength, whereas and the spacing between holes should be less than half of the wavelength.