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# Power Gain

Author: Leonard Krugman

Before determining the power gain included in transistor circuits, some definitions must be considered. Figure 3-16 illustrates a signal generator Eg with an internal resistance Rg feeding into a load RL. The total power delivered by the generator ; the power dissipated in the load . Since then .

Fig. 3-16. Simplified transistor equivalent circuit for analysis of power gain.

By using conventional calculus methods for determining conditions for maximum power, it is found that the load power is maximum when Rg = RL. Under this condition the power available from the generator

The operating gain, G, of a network is defined as the ratio of the power dissipated in the load to the power available from the generator.

For the general transistor circuit of Fig. 3-9

 Eq. (3-44)

The power dissipated in the load

 Eq. (3-45)

The operating gain

 Eq. (3-46)*

The available gain, AG, of a network is defined as tne ratio of the power dissipated in the load to the power available from the generator when the load is matched to the output resistance. When RL = ro = , then .

Substituting in equation 3-46, the available gain

 Eq. (3-47) Eq. (3-48) Eq. (3-49) *

The maximum available gain, MAG, of a network is defined as the ratio of the power dissipated in the load to the power available from the generator when the generator internal resistance is matched to the input transistor resistance, and when the load resistance is matched to the transistor output resistance. In order to solve for the maximum power gain in terms of the open-circuit parameters, the image-matched input and output resistances, previously determined, are substituted in the operating gain equation 3-46. Then, the maximum available gain,

 Eq. (3-50)

where

 Eq. (3-37)

and

 Eq. (3-41)

Substituting: equations 3-37 and 3-41 in equation 3-50, for r1 and r2,

 Eq. (3-51)
which is equal to
 . Eq. (3-52)
 . Eq. (3-53)

from which derives

 Eq. (3-54)
 Eq. (3-55)*

For the typical point-contact transistor, when r11 = 250 ohms, r12 =100 ohms, r21 = 24,000 ohms, r22 = 12,000 ohms, and when assuming Rg = 50 ohms and RL = 8,000 ohms, the operating gain G, becomes

Notice that the stability factor, , is = 0.8. If the stability factor is greater than one, the numerical value of the quantity must be negative, which indicates an unstable condition. For the typical junction transistor in which r11 = 550 ohms, r12 = 500 ohms, r21 = 1,900,000 ohms, and r22 = 2,000,000 ohms; when assuming Rg = 100 ohms and RL = 1,000,000 ohms, the operating gain

From equation (3-55)

Last Update: 2007-07-12