## What is the impact the distribution of microphones has on the beam width and dynamic range?

In order to correctly describe the mapping characteristics of microphone arrays, the terms beam width and dynamic range were introduced: An ideal microphone array would map acoustic sources with both, a small beam width and a high dynamic range. Besides the array dimension and the number of microphones, the mapping characteristics notably depend on the distribution of microphones, as the example in figures 1 and 2 indicates.

The figures show two different array types, the Ring and Fibonacci array. Both are constructed with a diameter of D=70 cm and a microphone number of N=120, differing only in the distribution of microphones. When simulating array measurements under identical conditions, the values for beam width and dynamic range given in the table can be determined.

Clearly, the Ring array consistently contains a smaller beam width while the Fibonacci array is provides a higher dynamic. However, the perfect conditions mentioned above are not met: Depending on the distribution of microphones, either the beam width or the dynamic range is optimized. The incompatibility of a small beam width and a high dynamic is one of the main characteristics of the microphone aperture: While a higher microphone density on edge regions, i. e. the Ring array, leads to a small beam width, the concentration of microphones near the array center will lead to a higher dynamic. The Fibonacci Array shows a nearly constant microphone density over its area, hence it represents a compromise for the described phenomenon.

Consequently, arrays can be adjusted for different fields of application by optimizing the microphone distribution. Additionally, other parameters like focal distance, frequency and the chosen beamforming approach have an impact on the point spread function of microphone arrays.

Frequency (Hz)Beam Width (m)Dynamic (dB)
RingFibonacciRingFibonacci
20000.520.778.219.3
31500.320.478.119.2
40000.250.378.119.1
80000.130.188.219.0