Telephone Transmitter Operation in Resistive Circuits

The total resistance at any instant of the circuit of Fig. 4 is

In this expression, R_t is the steady-state transmitter resistance, R_c is the resistance of the remaining portion of the circuit, and r is the maximum variation in transmitter resistance from R_t. When the

Figure 4. Telephone transmitter in resistive circuit.

Figure 5. Line A represents direct-current component or current flow when diaphragm is at rest. Line B represents current flowing when diaphragm is excited by a pure tone.

sound-wave pressure is maximum, the diaphragm will be pressed in and the circuit resistance will be (R_c + R_t) - r. When the soundwave pressure is least, the transmitter diaphragm will be bent out and the circuit resistance will be increased to the value (R_c + R_t) + r. The current through the transmitter at any instant will be similar to that shown by Fig. 5. It consists of direct and alternating components and is given by the relation

This equation is in the form of the series

Equation 2 may be expanded according to this series, becoming

This equation indicates that, in addition to current variations having

the same frequency as the impinging sound waves

harmonics, such as obtained when

is expanded.

are produced. These harmonics were not present in the original variations assumed, and thus distortion has been produced, although it is usually not serious. In fact, all terms higher than the first may usually be neglected, and the total instantaneous transmitter current can be written

or

where I₀ is the normal or steady-state current flowing when the diaphragm is at rest. This equation becomes

From a telephone standpoint, interest is in the largest value that the alternating component may have, that is, in the portion

Since

> the maximum value of the alternating component becomes, from equation 7,

To illustrate the application of this equation, suppose that a number of transmitters of different normal resistance Rt are available for connection to a circuit of resistance R_c, and also assume that for each one the ratio r/R_t = p is a constant value. That is, the percentage change of resistance r when excited by the same source is the same. Then, equation 8 becomes

Now let it be assumed that all the factors in this equation are constant except R_t and that the expression is differentiated with respect to R_t. Then,

The greatest value of the alternating component I_max will be obtained if equation 10 is equated to zero. Thus,

and

For the maximum useful alternating (speech) component of current in a circuit the steady-state resistance of the transmitter R_t should equal the resistance of the external circuit. If these relations are obtained, the useful output can be increased by substituting a transmitter having a greater change in resistance r.