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Coupling and Decoupling CircuitsAuthor: Leonard Krugman Fig. 518. RC 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.
Fig. 519. 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 R_{1}C_{1}, as shown in Fig. 519, Decoupling is required to prevent positive feedback through the battery resistance which is common to all the stages. Highgain 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 R_{1} and C_{1} (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 C_{1} and R_{1} which can be used. In general, R_{1} 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 C_{1} is required. The following example illustrates the calculation of the decoupling network: Suppose that for the circuit illustrated in Fig. 519, the dc base bias I_{b} = 500 μa, and a drop of onequarter of a volt in the battery supply through R_{x} can be tolerated. The maximum value of R_{1} 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, R_{1} in ohms, and C_{1} in farads.) The value of C_{1} depends on the allowable voltage drop through R_{1}. If a larger drop is allowable the value of C_{1} will decrease proportionately. In this example, assume that only a 10 μf capacitor is available, and that the maximum drop through R_{1} can be increased. Then R_{1}, for the same cutoff frequency, equals , and the voltage drop through R_{1} equals R_{1}I_{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 R_{1} to maintain the specified dc base current. In the form of an equation, this condition can be specified as: Figure 520 illustrates an experimental twostage 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. 520. Experimental twostage amplifier.


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