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Equivalent Passive 'T' Network

Author: Leonard Krugman

In the analysis of the transistor on a four-terminal basis, the entire device is treated as a sealed box with three external terminals e, b, c, designating the emitter, base, and collector, respectively. This basic four-terminal network is illustrated in Fig. 3-7 (A), in which the input signal is applied between emitter and base. The input signal Eg is taken from a signal generator that has an internal resistance Rg. The output circuit is between the collector and the common base and consists of a load resistance RL. In the small-signal analysis which follows, it is assumed that the transistor is biased in the linear region of its operating characteristics. It is also assumed that the operating frequency is low enough so that the transistor parameters may be considered pure resistances, and the capacitive junction effects may be considered negligible.

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Fig. 3-7. (A) The basic circuit for transistor four-terminal network analysis.
(B) Transistor equivalent "T" on a passive basis.
(C) Transistor equivalent "T" on an active basis.

The simplest method of approaching the analysis of the equivalent transistor circuit is by an equivalent "T" network with no internal generating sources (passive basis). This circuit is illustrated in Fig. 3-7 (B). Under these conditions, the transistor parameters can be completely specified by the following terminal measurements:

A Input resistance with output terminals open,
r11 = ei/ie when ic = 0, r11 = re + rb.
B The forward transfer resistance with the output terminals open
r21 = eo/ie when ic = 0, r21 - rb.
C The output resistance with the input terminals open,
r22 = eo/ic when ie = 0, r22 = rc + rb.
D The backward transfer resistance with the input terminals open
r12 = ei/ic when ie = 0, r12 = rb.

Notice that the forward transfer resistance is equal to the backward transfer resistance. This is typical of a four-terminal passive network. In the practical case, then, it is only necessary to measure r12 or r21.

Last Update: 2011-01-30