PRESSURE MICROPHONES 



173 



the carbon granules between the diaphragm and carbon cup without 

 impeding the motion of the diaphragm. A displacement of the diaphragm 

 produces a change in the pressure between the carbon granules which 

 changes the resistance from granule to granule. The net result is a change 



MICROPHONE 



I-H|.|.h-i' 



ELECTRICAL CIRCUIT 



CASE 

 CROSS -SECTIONAL VIEW 



-'I 



Fig. 9.1. Cross-sectional view and the electrical circuit diagram of a single button carbon 

 microphone. The graph shows the free space open circuit voltage response frequency 

 characteristic. 



in the resistance between the diaphragm and the carbon cup. For small 

 displacements the change in resistance is proportional to the displacement. 

 Consider the circuit of Fig. 9.1, for sinusoidal motion of the diaphragm, 

 the current, in amperes, in the circuit is given by 



reo + hx sin co/ 



9.1 



where e = voltage of the battery, in volts, 



Veo = total resistance of the circuit when ^ = 0, in ohms, 

 X = amplitude of the diaphragm, in centimeters, 

 h = constant of the carbon element, in ohms per centimeter, 

 CO = 2Tf, and 

 ■ / = frequency, in cycles per second. 

 Equation 9.1 may be expanded as follows, 



rEo\ 



hx . h'^x^ . 

 — sm CO/ + sm^ co/ 



,„) 



e 



hx . AV. h^x^ 



— sm CO/ -f - — ^ — - — - cos 2co/ 



i'eq 2r£o" 2r£:o 



.„) 



9.2 



Equation 9.2 shows that there is a steady current, an alternating current 

 of the frequency of the diaphragm vibration and harmonics of this vibra- 



