FLUCTUA TIONS IN MICROPHONES AND OTHER RESISTANCES 213 



than for the telephone transmitter under its normal condition of use, 

 and hence, the contact noise becomes a limiting factor when the carbon 

 microphone is used in weak sound fields. 



Equation (2) is not suited for representing contact noise as a function 

 of resistance in grid leaks since a change in resistance is brought about 

 by variations in the dimensions and materials of the conducting film 

 rather than by a change in contact displacement as is done in the case 

 of loose contacts. For this reason the constant given above applies 

 only to 100,000-ohm resistances of a given type. 



It is of interest to note that the constant for the carbon grid leak 

 resistor is smaller than that for the single contact by a factor of 10^. 

 This is due, in part, to the fact that the total voltage V across the grid 

 leak resistor is divided among a network of contacts each of which 

 produces noise independently of the others. The total noise from such 

 an assemblage, as will be shown in the following section, is less than 

 that arising from a single contact. This suggests that the contact noise 

 in a solid carbon filament, if it exists at all, should be still smaller than 

 that in the grid leak. We have made measurements on such a filament 

 having a diameter of 0.0025 cm. and a resistance of 75,000 ohms. 

 After taking great precautions to eliminate all the noise at the terminal 

 connections we were unable to detect any noise in addition to that of 

 thermal agitation for d.-c. loads as great as the filament would carry 

 without being destroyed (a current density of 3 X 10^ amperes per 

 square cm.). 



Noise From a Contact Assemblage 



A transmitter cell contains an assemblage of contacts and we have 

 shown that the noise from such an assemblage follows the empirical law 

 set forth in Eq. (5), which also holds for single contacts. Several 

 important deductions are possible when we study the noise from an 

 assemblage as a function of the number and arrangement of the 

 contacts within it. 



Assemblage With Contacts in Parallel 



Consider n contacts, Ri, R2 • • • Rn, placed in parallel across a direct 

 current supply and inductance as shown in Fig. 12 A. The inductance 

 is large enough so that it offers an effectively infinite impedance to the 

 fluctuation voltage we expect to study. Due to the fluctuation of 

 resistance in the contacts and the passage of direct current they will act 

 as a.-c. generators. Figure 12B is the equivalent a.-c. circuit, where 

 «i, 62 • • • e„ are the instantaneous a.-c. voltages generated because of 

 the fluctuating resistance in the respective contacts. The instantane- 



