Look at Figure 1. To get started we’ve drawn the familiar common-emitter amplifier with emitter degeneration. Thinking of the transistor in the Ebers–Moll sense, the small-signal voltage from base to emitter (ΔVBE) programs the collector current. But ΔVBE is less than the input voltage Vin, because of the drop across RE. If the output is unloaded, it’s easy to get the equation in the figure. In other words, the common-emitter amplifier with emitter degeneration is a grounded-emitter amplifier with negative feedback, as we hinted earlier.
This circuit has some subtleties, which we’d like to sidestep for now by looking instead at the more straightforward configuration shown in Figure 1B. Here we’ve
drawn a differential amplifier (with differential gain A), with a fraction of its output signal subtracted from the circuit input vin. That fraction, of course, is given simply by the voltage divider equation, as shown. This is a very common configuration, widely used with op-amps, and known simply as a “non-inverting amplifier.” When talking about negative feedback, it’s conventional to draw a diagram like Figure 1C, in which the feedback fraction is simply labeled B. This is useful because it allows more generality than a voltage divider (feedback can include frequency-dependent components like capacitors, and nonlinear components like diodes), and it keeps the equations simple. For a voltage divider, of course, B would simply be equal to R2/(R1+R2).
Let’s figure out the gain. The amplifier has open-loop voltage gain A, and the feedback network subtracts a fraction B of the output voltage from the input. (Later we will generalize things so that inputs and outputs can be currents or voltages.) The input to the gain block is then Vin−BVout. But the output is just the input times A:
In other words,
and so the closed-loop voltage gain, Vout/Vin, is just
Some terminology: the standard designations for these quantities are as follows: G = closed-loop gain, A = open loop gain, AB = loop gain, 1+AB = return difference, or
desensitivity. The feedback network is sometimes called the beta network (no relation to transistor beta, hfe).
Effects of Feedback on Amplifier Circuits
Let’s look at the important effects of feedback. The most significant are predictability of gain (and reduction of distortion), changed input impedance, and changed output impedance.
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