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Frequency Responses of Figure 8 Mics

Anyone have any frequency response curves of a Figure 8 mic? I believe that they should exhibit a 6 dB/octave slope, but I haven't seen any data.

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Boswell Fri, 06/05/2009 - 02:22
dpd wrote: Anyone have any frequency response curves of a Figure 8 mic? I believe that they should exhibit a 6 dB/octave slope, but I haven't seen any data.
Are you trying to find the on-axis frequency responses or how the polar responses vary with frequency? Of single-element mics, only the pressure-gradient types are inherently fig-8, and as with any mechanical system, the ultimate high-frequency slope is -6dB/octave. Similarly, the sub-low-frequency end is +6dB/octave due to the gradient.

dpd Sat, 06/06/2009 - 07:05
Boswell wrote: [quote=dpd]Anyone have any frequency response curves of a Figure 8 mic? I believe that they should exhibit a 6 dB/octave slope, but I haven't seen any data.
Are you trying to find the on-axis frequency responses or how the polar responses vary with frequency? Of single-element mics, only the pressure-gradient types are inherently fig-8, and as with any mechanical system, the ultimate high-frequency slope is -6dB/octave. Similarly, the sub-low-frequency end is +6dB/octave due to the gradient.
Frequency response...Yup, just what I expected. I do similar work with figure 8 pressure gradient underwater hydrophones and they all exhibit a 2nd order bandpass response. However, I've not seen any published data. I may have to go do some measurements myself.

Boswell Mon, 06/08/2009 - 04:58
BobRogers wrote: [quote=Boswell]....as with any mechanical system, the ultimate high-frequency slope is -6dB/octave. Similarly, the sub-low-frequency end is +6dB/octave due to the gradient.
I wasn't aware of that. Why is it true? A perfect mechanical damped second-order system that responds to a pressure gradient will inherently have a +6dB/octave response from d.c. up to frequencies approaching its resonant frequency just because of the displacement-velocity relationship. Above its resonant frequency, the mechanical output will be falling at 12dB/octave, and taken with the still-rising displacement-velocity characteristic, results in a 6dB/octave fall at high frequencies.

Now a microphone is not a perfect system, as it is not infinite in extent, resulting in leakage round the diaphragm and finite path lengths for the sound to reach the rear as well as the front. It's the job of the microphone designer to position the resonant frequency so that the microphone has the required low-frequency response. Additionally, control of the damping factor, the acoustic path lengths and attenuation in the leakage path from front to rear of the diaphragm can all be manipulated to keep the response acceptably flat up to high audio frequencies. Above that, the natural mechanical responses dominate, which in the non-perfect model of a microphone, will probably be a -6dB/octave characteristic rapidly becoming a -12dB/octave.

[[url=http://[/URL]="http://www.tonmeist…"]This[/]="http://www.tonmeist…"]This[/] is an interesting on-line book, with links to other sections. There's also more about the mechanical response of pressure-gradient microphones here.
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