Series Regulator where output is greater than  reference voltage

  In the second part of this series we looked at the very simple single-device series regulator. We will now look at the more complex series regulator topologies. As before, the emphasis will be on tube regulators, but solid-state devices can be used in these circuits as well.

Basic Topologies
   The basic and most common form of series regulator is shown in figure 4.1. The control element (pass device) is in the positive leg, the voltage reference (Vref) is in the negative leg. The feedback is negative, so the circuit will tend to bring the minus input of the comparison device to the same voltage as the plus input, just like an inverting Op Amp circuit.

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 voltage-divider 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

   In the circuit of figure 4.1, this feedback will strive to make Vout the same as Vref. How close these voltages are depends on the loop gain (the gain of the comparison device times the gain of the control element) and the offset voltage of the comparison device. If the comparison device is a modern Op Amp, the error in the output voltage will be very small: in the millivolts. However, when tubes or discrete transistors are used, the gain is limited and offset voltages can be as large as a few volts. In these cases, more care in the circuit design is needed to maintain a constant output voltage. Keep in mind, though, that if a single audio stage is being supplied by the regulator, only modest performance is needed in the regulator.
   Voltage references only come in a few fixed values,

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