694 BELL SYSTEM TECHNICAL JOURNAL 



It has three stages, the first two tubes being space charge grid pentodes, 

 and the last one a triode. The interstage coupHng circuits were made 

 up of simple inductances and resistances as shown. The amplifier was 

 designed by E. L. Norton and E. E. Aldrich to provide a transfer factor 

 characteristic having the desired shape, i.e., a loop crossing the zero 

 phase axis in the neighborhood of 10 kilocycles. It will be observed 

 that the feed-back circuit is connected between bridge networks in 

 both input and output circuits, which were provided to eliminate reac- 

 tion of the input and output circuits upon the feed-back network.^^ 



Experimental Results 



The transfer factor was measured for a zero setting of the feed-back 

 attenuator over a frequency range of 0.5 to 1200 kilocycles. The re- 

 sults are shown in Fig. 10. The method of plotting this figure requires 

 some discussion. In order to keep the curve within a reasonable size 

 and still show the necessary details the scale has been made logarithmic 

 by plotting the gain around the loop in decibels instead of the corre- 

 sponding numerical ratios. It is of course impossible to carry this out 

 completely on a polar diagram since the transfer factor goes to zero at 

 high frequencies. To take care of this the scale is made logarithmic 

 only above zero gain, corresponding to unit transfer ratio, and is linear 

 below. It should be noted that if the logarithmic portion of the scale 

 is translated outward so that the zero decibel point lies successively in 

 the regions marked A, B, C, and D, the indicated amplifier conditions 

 correspond to those designated above as (1), (2), (1) and (3) respec- 

 tively. Experimentally an increase of the feed-back attenuator 

 corresponds to such a translation of the logarithmic scale by an amount 

 equal to the increase in attenuation. Therefore, the transition from 

 one condition to another should occur when the attenuator setting is 

 equal to the gain at a zero phase point in the curve as measured with a 

 zero attenuator setting. 



The test of the stability criterion consists of a determination of the 

 attenuator settings at which oscillations begin, and a comparison of 

 these settings with those at which a transition from a stable to an un- 

 stable condition is predicted by the theory. Experimentally oscilla- 

 tions were found to occur in regions A and C and not in regions B and D 

 which is in qualitative agreement with Nyquist's predictions. Quanti- 

 tatively the measured and predicted transition points agreed within 

 one decibel which is estimated to be within the experimental error. 



It should be noted that the plotted curve has been drawn up for 

 A(jo}), no points of ^(— jco) being shown, although both are required 



1' H. S. Black, Bell Sys. Tech. Jour., January, 1934. 



