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 E_g with an internal resistance R_g feeding into a load R_L. 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 R_g = R_L. 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

The power dissipated in the load

The operating gain

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 R_L = r_o = , then .

Substituting in equation 3-46, the available gain

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,

where

and

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

from which derives

For the typical point-contact transistor, when r₁₁ = 250 ohms, r₁₂ =100 ohms, r₂₁ = 24,000 ohms, r₂₂ = 12,000 ohms, and when assuming R_g = 50 ohms and R_L = 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 R_g = 100 ohms and R_L = 1,000,000 ohms, the operating gain

From equation (3-55)