TRANSISTOR CIRCUITS FOR ANALOG AND DIGITAL SYSTEMS 299 



tion, is related to a by the equation 



aZe -{■ n /^x 



Ze + n 



For most junction transistors the base resistance, n , is much smaller 

 than the collector impedance | Zc |, at frequencies less than Wa/27r. There- 

 fore, a ^ a and Ua/^ir is very nearly equal to the alpha-cutoff frequency, 

 the frequency at which | a | is down by 3 db. 



The transistor parameters r^ and n are actually frequency sensitive 

 and should be represented as impedances. However, good agreement 

 between theory and experiment is obtained at frequencies less than 

 Wa/27r with re and n assumed constant. 



The choice of an appropriate transistor connection for a direct coupled, 

 negative feedback amplifier, is based on the following reasoning. The 

 common base connection may be ruled out immediately because this 

 connection does not provide current gain unless a transformer interstage 

 is used. The common emitter connection provides short circuit current 

 gain and a phase reversal for each stage. Thus if the amplifier is com- 

 posed of an odd number of common emitter stages, all three requirements 

 previously listed, are satisfied. A common emitter cascade has the addi- 

 tional practical advantage, that by alternating n-p-n and p-n-p types of 

 transistors, the stages can be direct coupled with practically zero inter- 

 stage loss. 



The common collector connection provides short circuit current gain 

 but no phase reversal. Consequently, the dc amplifier cannot consist 

 entirely of common collector stages and operate as a negative feedback 

 amplifier. This paper will consider only the common emitter connection 

 since, in general, for the same number of transistor stages, the common 

 emitter cascade provides more current gain than a cascade composed of 

 both common collector and common emitter stages. 



2.1 Evaluation of External Voltage Gain 



Since the equivalent circuit of the junction transistor is current acti- 

 vated, it is convenient to treat feedback in a single loop transistor ampli- 

 fier as a loop current transmission (refer to Appendix I) instead of as a 

 loop voltage transmission which is commonly used for single loop vacuum 

 tube amplifiers.^ Fig. 3 shows a single loop feedback amplifier in which 

 a fraction of the output current is fed back to the input. A is defined as 

 the short circuit current gain of the amplifier without feedback, and jS is 

 defined as the fraction of the short circuit output current (or Norton 



