Design Considerations - Overall Power Gain

Author: Leonard Krugman

In any given problem requiring more than one stage of amplification, several cascade arrangements are possible. This flexibility is a desirable design feature; however, it complicates the problem of selecting the best combination of the three general forms of transistor connections with respect to the input and output resistances, and to the required gain of the system Every design is fixed to some extent by the function of the circuit, but the requirement for maximum gain is invariably included.

Fig. 5-16. Block schematic of cascade operation

Figure 5-16 is the block schematic of a three stage circuit. It is evident from inspection that the overall current gain of the system is the product of the individual stage gains, thus α = α₁α²α₃. The operating gain as defined in equation 3-45 is

which can be modified to

Since the current gain as defined in equation 3-8 is:, and the input resistance as defined by equation 3-13 is r_i = r₁₁ -, these values may be substituted in the operating gain equation, which then becomes

This is a useful form of the equation. For the cascade stages, illustrated in Fig. 5-16, the overall power gain based on equation 5-1 can now be written as

On this basis, a cascade system has maximum gain when each of the stages is separately designed for a maximum value of its associated gain factors.

Selection of Stage Connection. The first stage requires that its gain factor be as large as possible. The following general rules for this stage are based on an analysis of the gain factor vs R_g characteristic:

1.  When R_g has a low value (0 to 500 ohms), use either the grounded base or the grounded emitter connection.
2.  When R_g has an intermediate value (500 to 1,500 ohms), use the grounded emitter connection.
3.  When R_g has a high value (over 1,500 ohms), use the grounded emitter or the grounded collector connection.

In the intermediate stage α₂² is made as large as possible. This requirement generally can be met by either the transistor grounded emitter or grounded collector connection. The intermediate stage equivalent load should be less than (r_c - r_m). If r_c is nearly equal to r_m, the grounded collector should not be used. This equality would cause the input and output resistances of the stage to become independent of the values of the connecting circuits. (An analysis of this buffer effect was covered in the discussion of input and output resistance of the grounded collector stage in Chapter 4.)

It must be noted that the intermediate stage represented by the current gain α₂ in this discussion may actually consist of several intermediate stages having a total current gain equal to α₂. This analysis of the three-stage circuit of Fig. 5-14, therefore, is applicable to any number of cascaded stages.

In the final stage, the gain factor R_Lα₃² is made as large as possible. The following general rules for this stage are based on the analysis of the gain factor vs R_L characteristic for the three basic transistor connections.

1.  When R_L has a small value (0 to 10,000 ohms), use a grounded collector or a grounded emitter connection.
2.  When R_L has an intermediate value (10,000 to 500,000 ohms), use a grounded emitter connection.
3.  When R_L has a high value (over 500,000 ohms), use a grounded emitter or grounded base connection.

(The numerical values listed above apply to those junction transistors with characteristics similar to the Western Electric Type 1752 transistor; however, the general values can be extended on a relative basis to cover all types.)

Based on the foregoing rules, it might appear that the choice of the grounded emitter connection is the best under all conditions. However, specific design problems often dictate the use of grounded base and grounded collector circuits when the coupling network, biases, feedback, and other factors are taken into consideration.