DUALITY AS GUIDE IN TRANSISTOR CIRCUIT DESIGN 405 



it has been carried out. We are indebted to Mr. B. McMillan and also to 

 Messrs. Harold Barney, R. J. Kircher, L. A. Meacham, J. A. Morton, L. C. 

 Peterson and R. M. Ryder for encouragement and helpful comments. 



APPENDIX 



The appendix is a brief account of some of the circuits which have been 

 investigated with the aid of the methods described in the main text. The 

 circuits shown do not exhaust all possibilities, and the specific configurations 

 shown are not to be regarded as optimal choices. 



Figure 14 shows a one-stage resistance-capacitance coupled amplifier and 

 its dual. In the input circuit of 14(a), C is a series element which passes alter- 

 nating currents and blocks direct currents. The dual element, Z,, in the input 

 circuit of 14(b) is a shunt element which is a short circuit to direct voltages, 

 but not to alternating voltages. The resistance Ri is a shunt element which 

 provides a path through the battery without creating a short circuit to 

 ground for the alternating signal. Correspondingly, the resistance Ri pro- 

 vides a path around the current supply, which otherwise would be an open 

 circuit for the alternating signal. 



The passive elements in the input circuit are also capable of acting as a 

 source of self-bias. Suppose, for example, that Ri be connected directly to 

 ground with no battery interposed and that the emitter current supply be 

 removed. The resulting vacuum tube circuit is famiUar. The usual explana- 

 tion of its behavior is that when the grid is driven positive and draws grid 

 current, the condenser C becomes charged, and that subsequently the con- 

 denser discharges through the resistance Ri , supposed large enough to as- 

 sure a long discharge time constant. In this way the condenser is kept charged 

 so that grid current flows only a small portion of the time. 



The behavior of the dual circuit is exactly analogous, but is much harder 

 to explain simply because words and expressions dual to those used above 

 do not exist or are not in current use. For example, we speak of a condenser 

 as ''charged" when there is a potential between the terminals. There is no 

 corresponding term for an inductor with a current passing through it. The 

 explanation, nevertheless, might be as follows: The emitter normally pre- 

 sents a low impedance to positive input currents, and a high impedance to 

 negative input currents. When the input current is negative, the high im- 

 pedance of the emitter blocks the current and a current is therefore drawn 

 through the inductor L, in an upward direction as the figure is drawn. Sub- 

 sequently, when the input current becomes positive, the emitter presents a 

 low impedance, and the current in the inductor is free to pass through Ri 

 and the emitter. It is supposed that the inductance is large enough so that 

 the decay time constant of the inductor through Ri and the emitter is large. 

 Then the current through the inductor will be approximately constant over 

 a short period and will be a bias current. This current will regulate itself 



