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Power Gain in the Grounded Collector Connection

Author: Leonard Krugman

The operating power gain as defined by equation 3-46 is:

transistor_basics_04-89.gif

transistor_basics_04-90.gif Eq. (4-17)*

In terms of the internal transistor parameters for the grounded collector connection, the voltage gain becomes:

As in the case of the grounded emitter connection, this gain equation is conditional for the point-contact transistor when the stability factor is greater than one. The conditional equation is:

(Rg + r11) (RL + r22) - r12r21 > 0

Substituting the numerical values of the typical point-contact transistor into this equation:

(Rg + 12,000) (RL - 11,850) + 12,000 (11,900) > 0

The conditional stability characteristic is plotted in Fig. 4-14.

transistor_basics_04-91.gif

Fig. 4-14. Conditional stability characteristic (grounded collector).

The grounded collector circuit can be stabilized by adding an external resistance Rc. in the collector arm. For example, assume that a resistor Rc = 3,100 ohms is placed in series with rc. The open-circuit parameters now become:

r11 = rb + rc + Rc = 100 + 11,900 + 3,100 = 15,100 ohms

r12 = rc + Rc- rm = 11,900 + 3,100 - 23,900 = -8,900 ohms

r21 = rc + Rc = 11,900 + 3,100 = 15,000 ohms

r22 = re + rc + Rc- rm = 150 + 11,900 + 3,100 - 23,900 = -8,750 ohms

The conditional equation now becomes:

(Rg + 15,100) (RL - 8,750) + 8,900 (15,000) > 0.

This stabilized conditional stability line is also plotted on Fig. 4-14.

The maximum available gain, defined by equation 3-55

transistor_basics_04-92.gif

can be applied to junction transistors, since the stability factor is not greater than one. In the grounded collector connection, since δ is always very near unity, this equation can be simplified as:

transistor_basics_04-96.gif Eq. (4-18)*

Notice that this result is nothing more than the product of the maximum voltage gain - and the maximum current gain - transistor_basics_04-93.gif .The

maximum available gain transistor_basics_04-94.gif in terms of the transistor internal parameters is:

transistor_basics_04-97.gif Eq. (4-19)
and since ro and re are negligible compared to the large values of rc and (rc - rm), the maximum available gain is:
transistor_basics_04-98.gif Eq, (4-20)

For the typicaljunction transistor

transistor_basics_04-95.gif


Last Update: 2010-11-17