# Re: Sensitivity of Directional Microphones

```Hello all,

I have a question regarding hearing aid micropohones.  I am looking at the
Knowles website, more specifically at one of their directional hearing aids.
I am trying to predict the response (polar plot) of a 2 mic based
directional hearing aid.  I came across a paper which showed that I would
need the sensitivities of each microphone, like so:

The polar pattern for two mics separated by a distance "d" is equal to:
S1    = Sensitivity of Mic#1
S2    = Sensitivity of Mic#2
k     = 2*pi*f/c
theta = angle between line joining the microphone and the propogation
direction of the incoming front

R(theta) = (S1 + S2) + (j*k*d/2)*(S2-S1)*cos(theta)

Now, I can easily calculate (or have fixed in my testing) all the parameters
except the sensitivites of the mics.  I know data sheets provide the
sensitivites at different frequencies, but since S1 and S2 are complex
numbers, can I recover the phase information from those graphs provided by
the hearing aid manufacture (as given on the following link
http://www.knowleselectronics.com/images/products/pdf/Thin%20Mic%20data%20sh
eet%20-%20Issue%2003.pdf --> Using a plot like the one on the first page of
this pdf file).  It appears to be only the "magnitude" response associated
with typical Bode plots.  Does any one have any suggestions how I can model
the sensitivities with the given limitations?  Also, can someone confirm
that the term (S2-S1) will not be equal to 0, are the values (being complex
in nature) accounting for the internal time delay between the two mics?

Thanks guys,
Chirag Patel

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Chirag Patel
National Centre for Audiology
cpatel@nca.uwo.ca
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