MODULATION IN VACUUM TUBES 451 



which yields, after some reduction, 



R, \ ' X2 + R,R + i?2 



As to the order of magnitude of the various quantities involved, 

 R~ is usually negligible before X'^, while Rq and R may be of the same 

 order of magnitude, so that we have 



In the specific case of a 101-D tube we had X = 2.1 X 10% i? = 7 

 X 103 and 



M = |-"(1 +0.002). 



The correction term, amounting to two parts in a thousand, drops 

 out without the retard coil and we arrive at Miller's formula jx — RjRg. 

 In measuring the output impedance of the tube after the settings for 

 fx have been determined, Rg is doubled and Rp is connected in the 

 plate circuit and varied until balance is again attained. It has been 

 shown ^ by extension of the method used above that 



Rn — R, 



r^l^- 



m 



and the correction term is of the same order of magnitude as that 

 previously found for the amplification factor. 



Balances may be obtained precise to one part in a thousand or 

 better, but in much of our own work the observations are not ordinarily 

 corrected for finite reactance. In order for the balancing action to 

 take place the two reactances must be of opposite sign since amplifica- 

 tion produces a 180° phase shift. If we balanced by a reactance 

 shunted around R^ instead of around Rg, the inserted reactance would, 

 of course, be of the same sign as that of the plate retard coil, which 

 was inductive at the frequency of 1,000 cycles at which the balances 

 were made. The alternative scheme of shunting a variable condenser 

 around Rg was adopted purely as a matter of convenience. 



Applications of the Analysis 



Second Order Modulation in Voltage Amplifiers 



A striking illustration of the difference in the results of the two 

 analyses, one based on the assumption of constant amplification 



•5 By Mr. V. A. Schlenker. 



