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This mathematical relationship exists because the completely reciprocal or bilateral character of passive networks. That is, power loss is identical in both directions. On the other hand by definition in active - non-reciprocal networks the power gain or loss is different in forward and reverse directions. I t will be shown now how to recognize from the parameter matrix whether one deals with a reciprocal or non-reciprocal network. 47 ALGEBRA OF FOUR-TERMINAL NETWORKS (a) PASSIVE or RECIPROCAL NETWORKS Consider as an example the four-terminal structure of Fig.

Current gain and output voltage responses will be derived for a variety of output network configurations. Results are obtained by algebraic manipulation involving the individual matrices of the transistor and cascaded coupling networks. 1. The Common-base Connection DERIVATION OF TRANSMISSION M A T R I X The grounded or common-base connection of a junction transistor is shown in Fig. 1a; corresponding linear models in form of active T networks are shown in Fig. 1c. I n the former the internal active element is represented as a current source and in the latter as a voltage source.

28 BASIC MATRIX ALGEBRA AND TRANSISTOR CIRCUITS Reverting to Fig. 3). When adding a second Y element across terminals 1-2 a n network will be formed as shown in Fig. 4. The transmission matrix of this ■OZl· ϊ T M I -o + V2 F I G . 4. The four-terminal π network network is found by successive multiplication of the component elementary matrices: Hence from Fig. 3). 26) ALGEBRA OF FOUR-TERMINAL NETWORKS 29 The input and output quantities of the π network in Fig. 27) is expanded by matrix multiplication: Λ.

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