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Re: How one can demonstrate that microphone is a nonlinear device?

You don't mention what type of microphone you are using.  
However, if you use a condenser type there is a really 
impressive way to demonstrate the 2nd order term.  

Note that condensers are inherently 2nd order and are only 
linearized by using a hefty bias voltage.  So you *could* 
just remove the bias and you'd get a pure 2nd order 
microphone response, although it may be hard to measure.  
(Haven't actually tried that.)

Much more dramatic is to use the fact that (most) 
microphones are reversible, and can be used as sound 
sources.  (Condenser types have especially flat responses 
at high frequencies, so make good sources for working with 

The demonstration is to apply a pure sine wave voltage.  
Without bias, rhe microphone is a pure square-law device 
and the sound output is a pure sine wave at *twice* the 

To get reasonable sound output you should use a 1/2 inch or 
1 inch diameter unit.  You'll probably want something like 
+/-100V max, which you can get from a step-up transformer 
on the output of a conventional "home stereo" power amp.  
(A typical 50-watt/channel amp can put out about +/-20V 
max.  You might want to listen to that first, without the 
transformer. If it meets your needs, just go with that.)

Don't go crazy with the step-up... more is not better.  If 
you go too high (say, more than +/-200 on a half-inch mic) 
the diaphragm excursion can bring it into contact with the 
backing plate: It spot-welds instantly... very expensive!   
Monitor the voltage before you apply it to the microphone.  
The mic is essentially an open circuit, so there is no load 
on the amp or transformer.  (Unless you go too high!)

I've used B&K and ACO Pacific 1/2 inch units for this with 
good results.  Normally, these would be run with +200 V 
bias, with the audio applied on top of that and limited to 
less than +/-100 V. (That's the absolute max.)  

Without the bias a sine wave output has much lower 
distortion (except being at 2x frequency).  But it turns 
out to be not especially useful as a stimulus for hearing 
research, because there is also a large DC component.  
Remember the old "sum and difference" terms from the 
product of 2 sines?  The difference is 0 Hz.  That means 
that if you want to apply tone bursts, you get a thump at 
no extra charge.  No problem for continuous tones, since 
you can't hear DC, but onset and offset of bursts can be 
quite audible.

Best regards,

Bob Masta

On 11 Jun 2012 at 14:13, Hafiz Malik wrote:

> Hi Every 1,
> Microphone is generally modeled using a second-order nonlinear function,
> that is, y(n) = ax(n) + b x(n)^{2} where x(n) is the microphone input.
> How can one demonstrate this non-linearity?
> Any suggestions/comments/literature in this regard.
> Thanks,
> -- 
> Hafiz Malik
> Assistant Professor
> Electrical and Computer Engineering Department,
> University of Michigan - Dearborn
> Dearborn, MI 48128
> RN: 220 ELB
> Tel: (313)5935677
> Fax: (313)5836336
> http://www-personal.engin.umd.umich.edu/~hafiz

Bob Masta
            D A Q A R T A
Data AcQuisition And Real-Time Analysis
Scope, Spectrum, Spectrogram, Signal Generator
    Science with your sound card!