390 BELL SYSTEM TECHNICAL JOURNAL 



changes near an assumed operating point. For their general study a most 

 convenient tool is provided by the set of static characteristics of the unit. 



Since most analyses begin with the static characteristics, perhaps some 

 excuse is needed for the unorthodox approach which has delayed them to 

 tliis point. Two reasons may be cited: First, the small-signal behavior is in 

 a sense simpler, being capable of discussion by the familiar linear methods 

 of circuit theory. Second, the small-signal behavior has brought out some 

 features, notably short-circuit instability, which have a bearing on certain 

 features of the static characteristics, on the methods of measuring them, 

 and on the particular manner of expressing them. 



A set of characteristics representative of Type A transistor performance 

 is shown in Fig. 23, consisting of four plots, one of each of the electrode 

 voltages against each of the currents with the other current as parameter. 

 Contrary to electron tube practise, rather than the voltages we take the 

 currents as the independent variables. This choice avoids the experimental 

 difficulty that the short-circuit unstable transistors might oscillate if we 

 were to attempt to hold the electrode voltages constant, as well as the con- 

 comitant analytical trouble that in that case the voltage-dependent char- 

 acteristics become double-valued. 



The relationship of these characteristics to the open-circuit impedances 

 is direct and quickly shown. Suppose the voltages are expressed formally 

 as functions of the currents: 



V6 = fl (l6, Ic) (2) 



Vc = f2 (le, Ic) 



Differentiating, and identifying the differentials as small-signal variables, 

 we get immediately the equations for the open-circuit resistances: 



. dh , . dii 



(3) 



. afo , . dh 



Accordingly, the open-circuit resistances are the slopes of these static 

 characteristics. The reactive components do not appear because our as- 

 sumptions (2) were not sufficiently general to take them into account or, 

 in other words, the reactive information is not contained in the static char- 

 acteristics. 



Just as there are five other pairs of small signal parameters which could 

 have been chosen, so there are five other ways in which the static character- 

 istics could have been expressed. Often these other ways are convenient 

 for special purposes or are closely connected with particular large signal 

 circuits. 



