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 E_g, having an internal resistance R_g, is connected between the emitter and the base. A load resistance R_L 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 i_e. 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 R_L, 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 R_g. 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: -r_mi_e = i₁r_b + i₂ (r_c + r_b + R_L). Since i_e = 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

	[3-3]
	[3-4]

Under ideal conditions, namely, when R_g equals zero, and R_L is infinite, it was previously found that r₁₁ = r_e + r_b, r₁₂ = r_b, r₂₁ = r_b + r_m, and r₂₂ = r_c + r_b.

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.

	[3-5]
	[3-6]