
typically lower in voltage than the desired output voltage, so the circuit of figure 4.2 is used to give arbitrary output voltages, as long as Vout is greater than Vref. R1 and R2 form a voltage divider that reduces Vout to the Vref voltage. If a potentiometer is placed between the junction of R1 and R2, the output voltage can be made variable. The voltagedivider effect of R1 and R2 reduces the feedback loop gain. If Vref is much smaller than Vout, then errors in Vref (drift, noise, etc.) and offset voltages in the comparison device are greatly magnified, and the regulation effectiveness is reduced. Because of these factors, a relatively high Vref is desirable, not less than about 1/4 of Vout, unless very high quality devices are used.
Optimization #1 By adding a capacitor across R1, the loss of loop gain for AC is eliminated. Since DC accuracy is less important in audio applications than AC performance, this is a very useful optimization. In order to be effective, the reactance of the capacitor should be less than the Thevenin equivalent of R1 and R2. In other words, Xc >> R1  R2. Since Xc = 1/(2* pi * f * C) and R1  R2 = (R1 * R2)/(R1 plus R2), C >> (R1 plus R2)/(2 * pi * f * (R1 * R2)), where f is the lowest expected audio frequency. Another variation of the series regulator topology is

