TELEPHONE DIAPHRAGMS. 423 



these coils increases when the frequency is increased, although not in 

 direct proportion. Thus, Figure 1 represents the locus of the imped- 

 ance of a particular receiver when measured by Rayleigh bridge, with 

 constant sinusoidal alternating-current strength, but with varying 

 frequency. Apparent resistances are measured parallel to the axis 

 QR, and apparent reactances parallel to the axis QX. As the fre- 

 quency of the exciting alternating current is increased from 400 ^ 

 to 2500 c^J , the locus of the impedance is the curve A B C D. Thus 

 at 804 f^^ , the impedance is found to be OB, and at 1190 c^^ , it is in- 

 creased to OC, where O is the origin (not shown). The increase 

 in apparent resistance is due to increasing power loss at rising fre- 

 quencies. The increase in reactance j X = ; Leo ohms, is to be attrib- 

 uted to increase in the angular velocity co = 2 tt/ radians per second; 

 where / is the frequency. The apparent inductance L henrys actually 

 diminishes as the frequency rises; so that the increase in the re- 

 actance OX is less rapid than the increase in frequency. The imped- 

 ance measured in this manner is called the "damped impedance." 



If now the measurement of the impedance is repeated over the same 

 range of frequency' but with the diaphragm released, so as to be able 

 to react electromagnetically on the winding, the locus is found to be a 

 looped curve, such as is represented in Fig. 2; so that one and the 

 same vector impedance OP is found at two distinctly different fre- 

 quencies. Thus at 702 ~, the "free impedance" has a magnitude 

 of 153 +i 161.5 ohms, and at 1050 ~ , 148 + j 144 ohms. This 

 peculiar dual valued behavior of the free impedance is due to the 

 motion of the diaphragm. 



If at each of a series of successive rising frequencies, we subtract 

 the vector damped impedance from the vector free impedance, as 

 indicated in Figure 3, it is found that the successive vector differences, 

 due to the motion of the diaphragm, and, therefore, called " motional 

 impedances," lie approximately on a certain circular locus as shown in 

 Figure 4. This circular locus is called the motional-impedance circle 

 for the particular instrument. 



The same facts may also be presented in a scalar or non-vector 

 diagram. Figure 5. Here the abscissas represent impressed frequency. 

 The ordinates represent, to the left-hand scale, the magnitude or 

 "vector modulus" of the telephone-receiver impedance. To the 

 right-hand scale, they represent the phase angle or "argument." 

 Heavy curves represent measurements of free impedance, and broken 

 curves corresponding measurements of damped impedance. The 

 measurements made on the particular receiver C, referred to in Figures, 

 1 to 5, are recorded in Table I. 



