Coupling and Decoupling Circuits

Author: Leonard Krugman

Fig. 5-18. R-C interstage coupling; X_c less than r_i at lowest frequency to be amplified; R at least 10 times r_i

To obtain the absolute maximum gain from a cascaded system, image resistance matching between stages is required. The analysis and conditions for matching the three basic transistor connections are covered in Chapters 3 and 4.

The stage can be matched by interstage transformers. In i-f strips, transformer coupling is convenient and invariably used, because the transformers are also required for selectivity. In audio circuits, however, the increased gain due to the transformer is seldom worth its expense. In audio cascades, therefore, resistance-capacitance coupling is the most practical and economical choice. Figure 5-18 represents a typical R-C coupled stage. The capacitance must be large enough to pass the lowest frequency to be amplified. Its value can be computed as indicated in the preceding paragraphs dealing with single stage amplifiers. Resistor R must be large compared to the input resistance r₁. The interstage loss in gain is less than one db if R is chosen to be ten times as great as r_i.

Fig. 5-19. Typical decoupling network.

When cascaded stages are connected to produce an overall gain of 60 db or more, consideration must be given to the addition of a decoupling circuit, as indicated by the combination R₁C₁, as shown in Fig. 5-19, Decoupling is required to prevent positive feedback through the battery resistance which is common to all the stages. High-gain transistor cascades almost always require a decoupling network, since even low values of battery resistance are significant when compared to the low input resistance of transistor stages. The product of R₁ and C₁ (time constant) should be equal to or greater than the inverse of the lowest frequency to be amplified by the stage. While this specified frequency sets the time constant, there are any number of combinations of C₁ and R₁ which can be used. In general, R₁ is made small enough so that it does not affect the supply voltage greatly, and at the same time is not made so low that a very high value of C₁ is required. The following example illustrates the calculation of the decoupling network: Suppose that for the circuit illustrated in Fig. 5-19, the d-c base bias I_b = 500 μa, and a drop of one-quarter of a volt in the battery supply through R_x can be tolerated. The maximum value of R₁ equals the allowable voltage drop divided by the base current, =500 ohms. If 100 cps is the lowest frequency to be passed, then

and . (In this equation, f is expressed in cycles per second, R₁ in ohms, and C₁ in farads.) The value of C₁ depends on the allowable voltage drop through R₁. If a larger drop is allowable the value of C₁ will decrease proportionately. In this example, assume that only a 10 μf capacitor is available, and that the maximum drop through R₁ can be increased. Then R₁, for the same cut-off frequency, equals , and the voltage drop through R₁ equals R₁I_b = 1000 (500 x 10^-6) = 0.5 volt. The base bias resistor now must be adjusted to compensate for the reduced value of the effective supply voltage. Thus

as compared to the value (without decoupling),

In general then, when the value of the decoupling resistor is significant in comparison to the value of the bias resistor, R_B must be decreased by an amount equal to that of R₁ to maintain the specified d-c base current. In the form of an equation, this condition can be specified as:

Figure 5-20 illustrates an experimental two-stage amplifier using grounded emitter circuits designed specifically to amplify the output of a 50 ohm dynamic microphone. The output terminates in a 600 ohm line. The overall gain of the system is 46 db.

Fig. 5-20. Experimental two-stage amplifier.