Question

Explain simple telephone communication system with circuit and equation of current flow in microphone?

Answer 1

Simple Telephone Communication: In the simplest form of a telephone circuit, there is one way communication involving two entities, one receiving (listening) and the other transmitting (talking).

 

Simplex communication: The microphone and the earphone are the transducer elements of the telephone communication system. Microphone converts speech signal to electrical signals and the earphone converts the electrical signals into audio signals. Most commonly used microphone is carbon microphone. Carbon microphones do not produce high fidelity signals, but give out strong electrical signals at acceptable quality levels for telephone conversation. In carbon microphones, a certain quantity of small carbon granules is placed in a box. Carbon granules conduct electrically and the resistance offered by them is dependent upon the density with which they are packed. One side the box is covered is flexible and is mechanically attached to a diaphragm. When sound waves impinge on the diaphragm, it vibrates, causing the carbon granules to compress or expand, thus changing the resistivity offered by the granules. If a voltage is applied to the microphone, the current in the circuit varies according to the vibration of the diaphragm. 

When the sound waves impinge on the diaphragm, the instantaneous resistance of

the microphone is given by

 r_i = r₀ – r sin ωt

 Where

 r₀ = Quiescent resistance of the microphone when there is no speech signal.

 r = Maximum variation in resistance offered by the carbon granules, r < r₀ .

 The negative sign indicates that when the carbon granules are compressed the

resistance decreases and vice versa. Ignoring impedances external to the

microphone in the circuit given in Fig. without loss of generality, the instantaneous

current in the microphone is given by

 i = V/(r₀ – r sin ωt) = I₀(1 – m sin ωt)^-1

 Where

 I0 = V/r₀ = Quiescent current in the microphone .

 m = r/r₀ , m < 1

By binomial theorem, the Eq. may be expanded as

i = I₀ (1+ m sin ωt + m²  sin² ωt + ….)

If the value of m is sufficient small, which is usually the case in practice, higher order terms can be ignored in the above Eq. Giving thereby

 i = I₀ (1+ m sin ωt)  

Thus, the carbon granule microphone acts as a modulator of the direct current I which is analogous to the carrier wave in AM system. The quantity m is equivalent to the modulation index in AM.