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Equivalent Operating Circuit

Author: Leonard Krugman


Fig. 3-9. Equivalent circuit for grounded base connection.

At this point, the transistor equivalent circuit must be considered using a practical circuit, such as illustrated in Fig. 3-9. The signal generator Eg, having an internal resistance Rg, is connected between the emitter and the base.
A load resistance RL is connected between the collector and the common base. The input current is designated i1, and for the common base connection is equal to the emitter current ie. The collector output current is designated i2. A cursory look at Fig. 3-9 makes it fairly evident that the input resistance r11 as seen by the signal generator depends to some extent on the value of the load resistance RL, and the output resistance r22 as seen by the load resistance is determined to some extent by the value of the generator's internal resistance Rg. On a basis of Kirchoff's Law, the loop equations for the circuit of Fig. 3-9 are:

Input loop 1:

Eg = i1 (Rg + re + rb) + i2rb [3-1]

Output loop 2: -rmie = i1rb + i2 (rc + rb + RL). Since ie = i1, then

0 = i1 (rb + rm) + h (rc + rb + RL) [3-2]

Since these two loop equations are independent, they may be solved simultaneously for the two unknown currents i1 and i2. Then


Under ideal conditions, namely, when Rg equals zero, and RL is infinite, it was previously found that r11 = re + rb, r12 = rb, r21 = rb + rm, and r22 = rc + rb.

If these values are substituted in equations 3-3 and 3-4, i1 and i2 can be evaluated in terms of the ideal or open-circuit parameters.


Last Update: 2010-11-17