Cascade Design

Author: Leonard Krugman

As an illustration of these principles, consider the design of a three-stage cascade system using the typical junction transistor with r_e = 50 ohms, r_b = 500 ohms, r_c = 1,999,500 ohms, and r_m = 1,899,500 ohms. Assume that R_g is adjustable but limited to low values, R_L = 150 ohms requires the use of the grounded emitter or grounded collector connections. Assume that other design factors limit the choice to the latter case. Then for the last stage:

r₁₁ = r_c + r_b = 1,999,500 + 500 = 2,000,000 ohms;

r₁₂ = r_c - r_m = 1,999,500 - 1,899,500 = 100,000 ohms;

r₂₁ = r_c = 1,999,500 ohms;

r₂₂ = r_c + r_e- r_m = 1,999,500 + 50 - 1,899,500 = 100,050 ohms.

The input resistance of the last stage (equation 3-13) is expressed as:

and the current gain (equation 3-8) is:

Since r_m is close to the value of r_c, the intermediate stage is restricted to the grounded emitter connection. For this stage:

r₁₁ = r_e + r_b = 50 + 500 = 550 ohms;

r₁₂ = r_e = 50 ohms;

r₂₁ = r_e-r_m = 50 - 1,899,500 = -1,899,450 ohms; and

r₂₂ = r_e + r_c - r_m = 50 + 1,999,500 - 1,899,500 = 100,050 ohms.

Since the input resistance of the last stage is the output resistance of the intermediate stage, R_L = 5,000 ohms. The input resistance of the intermediate stage is

and the current gain is:

Since a low value of R_g is specified, the first stage must use either the grounded emitter or the grounded base connection. The load of the first stage equals the input resistance of the intermediate stage and is a low value. Therefore, the best choice for the first stage is the grounded emitter connection. Since R_g was specified as being adjustable, its value will be made equal to the input resistance,

The current gain is:

The overall currentgain of the cascaded system

α = α₁α₂α₃ = (-18.75) (-18.1) (19.99) = 6,780 The operating gain (equation 5-1) is

The resulting cascade circuit is shown in Fig. 5-17. This circuit does not include biasing arrangements, coupling networks and feedback loops. The values of the elements necessary for introducing these requirements may be computed by the methods in preceding paragraphs.

The cascade system may be changed considerably by the addition of external resistance arms to the circuits. These have the effect of increasing the effective values of the transistor parameters. For example, consider the effect of adding a stabilizing resistor R_E = 50 ohms in series with the emitter arm of the input stage. The effective resistance of the emitter is now r_e -f- R_E = 50 -f 50 = 100 ohms, and the general four-terminal parameters are now:

r₁₁ = r_e + R_E + r_b = 50 + 50 -f 500 = 600 ohms;

r₁₂ = r_e + R_E = 50 + 50 = 100 ohms;

r₂₁ = r_e + R_E - r_m = 50 + 50 - 1,899,500 = -1,899,400;

r₂₂ = r_e + R_E + r_c - r_m = 50 + 50 + 1,999,500 - 1,899,500 =100,100 ohms.

The input resistance

and the current gain

The overall current gain

and the operating gain

Thus, a simple change reduces the overall system gain by a factor of one-half. It is evident that even after the basic stage connections are fixed, a considerable variation in the cascade performance and resistance terminal characteristics can be attained by changes in the effective value of the transistor parameters.