## Basic Equations For Microphone And Earphone

The quantitative study of the microphone shows the microphone functions as an amplitude modulator. Similarly the study on earphone indicates that it can recover the speech signals from the varying current received.

Microphone as amplitude modulator: When the sound waves impinge on the draphragm, the instantaneous resistance is given by, ri = rq - rm sin at ...(A.1)

when ri = instantaneous resistance rq = quiescent resistance of the microphone when there is no speech signal. rm = maximum variation in resistance offered by the carbon granules rm < rq w = 2nf f = frequency measured in Hz.

The negative sign indicates the decrease in resistance when the carbon granules are compressed and vice versa. At ideal condition, the instantaneous current in the microphone is given by v i =-:---...(A.2)

where Iq = quiescent current in the microphone rm m = — ; m < 1 ...(A.5)

By binomial theorem, Eq. (A.5) may be expressed as i = Iq (1 + m sin at + m2 sin2 at + ...) ...(A.6)

As the amplitude of the higher order terms are smaller those terms are neglected. Thus i = Iq (1 + m sin at) ...(A.7)

The equation (A.7) resembles the amplitude modulation equation and hence the microphone acts as modulator.

Earphone as sound detector. The variations in current through the coils wound on the electromagnet results in change in flux. This instantaneous flux linking the poles of the electromagnet and the diaphragm is given by

where ^ = instantaneous flux

= flux due to quiescent current = maximum amplitude of flux variation, <

The instantaneous force exerted on the diaphragm is proportional to the square of the instantaneous flux linking the path. Thus

where k = proportionality constant

neglecting the second order term, we have

where K1 = constant

I0 sin mi = the current through the coil. Thus the force experienced by the diaphragm is in accordance with the signals produced by the microphone.

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