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R3 serves as the plate load resistor for V2. To get high gain, R3 should be a big as possible. However, if it is too big, the frequency response of the regulator suffers and the current through V2 gets so small that the tube is running in a non-linear "starvation" mode. For high-mu triodes, typical values are from 100K to over 1M, although the latter value is higher than I would recommend.
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The dilemma of choosing R3 is made much easier by using a pentode instead of a triode. The gain of a pentode in this case is essentially Gm * R3, so high-transconductance pentodes give very good voltage gain without running in the starvation mode. Figure 4.7 shows this configuration. The only added complication is the screen supply. Many regulators use the voltage divider pair of either R5 and R7 or R6 and R7. These are chosen so that the screen voltage is roughly about 100 volts or so above the cathode.
Optimization #2
Since the screen grid injects signal into the feedback loop, by choosing the right combination of R5 and R6, input voltage variations can be completely canceled (a form of "feed-forward"). The simplest way to achieve this cancellation is to temporarily replace R5 and R6 temporarily with a potentiometer with the wiper connected to R7 and the screen. While injecting a signal at Vin (maybe just the power supply ripple) with the regulator supplying its normal load, adjust the pot for minimum output. Measure each side of the pot and use these resistances for R5 and R6. This technique is dependent of input voltage, load current, tube characteristics, etc., so don't rely on it for perfect cancellation all the time.
The tube implementation of figure 4.5 is shown in figure 4.8. This is just the same as the circuit in figure 4.6 without the regulator tube. A pentode could also be used for V2. The main caution with this circuit is that nearly the entire output voltage appears across V2. If run well below its maximum power dissipation, you can often get
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