OSCILLATIONS IN ELECTROMECHANICAL SYSTEM 443 



a close approximation to the assumed one. On the electrical side the 

 parallel system had the advantage that the current of the impressed 

 frequency (o}g) flowed around the outside while the sum (oig + com) 

 and difference (cjd = oog — w^) frequency components flowed through 

 the mid-branch. The sum frequency component was the most dif- 

 ficult one to suppress. This could be done in the parallel system by 

 means of a piezo-crystal impedance element/ tuned to cuj without at 

 the same time putting in a high impedance to Ug. This piezo-crystal 

 element had so sharp a resonance that, while its impedance at resonance 

 (30 kilocycles per second) was only 125 ohms, it was about 60,000 

 ohms only 1000 cycles per second away from resonance. Thus the 

 very high impedance to the sum frequency was obtained. There were, 

 however, some modulation products which flowed around the outside 

 with the impressed current. Only the impedance of a simple tuned 

 circuit was available around this circuit so any product near in fre- 

 quency to the impressed frequency would not face a very high im- 

 pedance. The nearest one was a)(, — 2 Wm. This was not as completely 

 suppressed as the other unwanted products but changing the impedance 

 so that this component was considerably different in magnitude had 

 no appreciable effect on the other electrical components. While this 

 circuit gives a good approximation to the hypothetical one, the result 

 is a highly critical system demanding very fine adjustment and a 

 highly stable generator, since a very slight frequency change has an 

 appreciable effect on the impedances presented by the very sharply 

 tuned circuits. 



The measurement of impressed current was made by the thermo- 

 couple across small resistors in the input transformer and checked by 

 a current analyzer.* Corrections were made in the results when 

 necessitated by the presence of the current component of frequency 

 a>5 — 2com. The corresponding voltage was obtained by measuring 

 the current of that frequency through the large resistors Ri by means 

 of a current analyzer. The current of the difference frequency was 

 measured by a thermocouple in the mid-branch. Measurement was 

 also made of the voltage of frequency cog — lo^m across the fork, by 

 measuring the corresponding current through the resistances R2. 

 There was no simple means available for measuring the mechanical 

 amplitude but it could be obtained from this measurement of oj^, — Icom 

 voltage as will be explained later. 



On Figs. 2 and 3 are shown curves computed from equations 28, 29 

 and 30 of the preceding paper for two cases, and the results of the 



* Designed by Mr. W. P. Mason. 



* See A. G. Landeen: "Analyzer for Complex Electric Waves," Bell Sys. Tech. 

 Jour., April, 1927. 



