896 



THE BELL SYSTEM TECHNICAL JOURNAL, JULY 1953 



Amplifier Formulas 



Using the equivalent circuit of the coupling network shown in Fig. 

 8(c), the circuit of the input amplifier can be represented as on Fig. 10a, 

 and the formulas shown can be derived from straight forward nodal 

 analysis of the circuit. Similar formulas can be derived for the more 

 complicated output amplifier. From these, using Thevenin's theorem, 

 the gain of the tandem combination can be computed, as well as the 

 feedbacks on the various tubes. 



Similarly the input ampHfier can be replaced, for convenience in re- 

 flection coefficient calculations, by the pi of admittances and the driving 

 current of Fig. 10(b). The formulas of Fig. 10(b) expressed in terms 

 of the co-factors of the circuit determinant are of general application 

 for the reduction of a multi-node circuit to simpler form. 



Regulating Network 



Like the coupling networks, the regulating network between the 

 amplifiers is outside the feedback loops, and the gain of the amplifier 

 is very nearly a direct function of the impedance seen looking into the 

 network. This impedance is controlled by a single variable resistance — 

 the thermistor — which is directly heated by the dc output current of 

 the regulator. The output of the regulator, in turn, is a function of the 



20- 



rg>9 



^>3l 



X 



I = X.E, 



= Y,. 



^^i-^Aiii^r 



^y = 



A12-A21 

 A12-12 



Yz + ^a + OS+PaSaRv 



'■^' Y33 ^^J 



WHERE THE CO-FACTOR A, 2-, 2 <S FOUND BY STRIKING OUT THE 

 FIRST AND SECOND ROW AND FIRST AND SECOND COLUMN OF THE 

 CIRCUIT DETERMINANT, THE SIGN FOLLOWING THE USUAL RULES 

 FOR THE SIGN OF A CO-FACTOR 



Fig. 10 (b) 

 work. 



Equivulcnt circuit of input amplifier as seen by coupling net- 



