Output Resistance for the Grounded Collector Connection

Author: Leonard Krugman

The output resistance is defined by equation 3-21:

In terms of the internaltransistor parameters, the output resistance becomes:

Eq. (4-16)

The variation of r_o with respect to the generator resistance R_g is illustrated for both transistors in Figs. 4-12 and 4-13. In the point-contact characteristic, the output resistance is positive over the range of R_g from 0 to approximately 50 ohms. When the generator resistance is increased beyond 50 ohms, r_o becomes negative, and gradually approaches a limiting value equal to r₂₂(-11,850 ohms) for large values of R_g. The output resistance of the junction transistor starts at a value of approximately 75 ohms at Rg = 0 and gradually approaches a value equal to r22 (100,050 ohms) for large values of generator resistance.

Fig. 4-12. Output resistance vs generator resistance for typical point-contact transistor (grounded collector).

Fig. 4-13. Output resistance vs generator resistance for typical junction transistor.

As in the case of the grounded emitter, the grounded collector circuit using the point-contact transistor cannot be matched on an image basis without external modification, since the stability factor of this circuit is greater than one. However, the grounded collector does exhibit a unique characteristic when external resistance is added in the collector arm. For example, assume that a resistor R_c is added to the collector arm so that R_c + r_c = r_m. For this modification,

r₁₁ = r_b + r_c + R_c

r₁₂ = r_c + R_c- r_m = 0

r₂₁ = r_c + R_c and

r₂₂ = r_e + r_c + R_c - r_m = r_e

Since r₁₂ = 0, the stability factor .Thus, the modified circuit is stable. The input image matched resistance (equation 3-37) is then

and the output image matched resistance (equation 3-41) becomes

Notice also that r_i = r₁ = r₁₁ and r_o = r₂ = r₂₂. Thus, adding a suitable external resistor in the collector arm causes the circuit to act as a perfect buffer stage in which both the input and output resistances are independent of R_L and R_g.

Numerical values for the typical point-contact transistor modified to act as a buffer stage are:

r_i = r₁ = r₁₁ = r_b + r_c + R_c = 100 + 11,900 + 12,000 = 24,000 ohms; r_o = r₂ = r₂₂ = r_e = 150 ohms.

The image matched input and output equations can be applied to the junction transistor since its stability factor is always slightly less than one. A practical method to use in selecting values to be substituted in these equations indicates that r₁ should be chosen to equal 2 percent of r₁₁, and r₂ equal to 2 percent of r₂₂. The exact determination of the linage matched resistances in the grounded collector circuit is not important, because the power gain is constant over a wide range of load resistances when the signal generator is matched to the input resistance.

In the junction transistor, numerical values for image matched resistances are

If the approximate values are used

r₁ = .02r₁₁ = .02 (2,000,000) = 40,000 ohms

r₂ = .02r₂₂ = .02(100,050) = 2,001 ohms