Thermal noise in condenser microphone back volumes

Open Access
Russo, Benjamin Marc
Graduate Program:
Master of Science
Document Type:
Master Thesis
Date of Defense:
April 29, 2013
Committee Members:
  • Stephen Thompson, Thesis Advisor
  • microphone
  • transducer
  • noise
  • thermal
  • condenser
The self-noise of a microphone is the sum of the cartridge noise and the electrical noise of the preamplifier. For many cases the electronic preamplifier noise is dominant, and as such, the mechanical and acoustical sources of noise in the capsule can be neglected. However, the relative levels of various noise components are strongly dependent on frequency and the design of the transducer, as each source of noise is filtered through the successive signal path. The thermal-acoustic noise in the capsule can then be the dominant source of noise in certain frequency ranges for some microphone designs. Previously, Zuckerwar has employed an acoustic isolation vessel to separate the noise present in the motion of the microphone diaphragm from the total output noise and found a significant component of 1/f noise on the diaphragm. To date, no physical explanation has been given for this spectral shape. This study uses the finite element method to examine the thermal-acoustic noise that is present in the back volume of microphones, a noise source that has historically been neglected. A simple finite element method for determining the thermal distributions in acoustic enclosures is described, and from this solution the impedance of any arbitrarily shaped enclosure may be obtained. This impedance is complex, in contrast to the usual adiabatic compliance approximation, which is purely imaginary. It is demonstrated using simple shapes that the resistive part of this impedance is flat at low frequencies and falls off as f^(-3/2) at higher frequencies. According to the Fluctuation-Dissipation theorem, this resistance causes a noise fluctuation, which is proportional to the resistance. The frequency dependence of the resistance thus controls the spectral shape of the resultant noise. This method is applied to the internal geometries of two commonly used and commonly studied measurement condenser microphones. The simulation results reveal that the enclosure resistances of these microphones have the same frequency dependence as for the simple enclosure shapes. Equivalent circuit models for these microphones with their preamplifiers are presented. Using a circuit simulator, the relative noise contributions of each acoustical noise source are compared. The simulated back volume noise dominates the other sources of acoustical noise for about two decades in the mid-band of the audible frequency range. When the electrical noise from the bias resistor is also included it dominates all other sources of noise in the microphone for much of the audio band. These results compare well with several other authors’ published measurements and calculations. The noise does not show a significant 1/f dependence, and it is possible that no such dependence exists, as several errors in Zuckerwar’s methodology and data presentation were discovered.