by Fred Nachbaur, Dogstar Music ©1998, 2000


So far we have a pre-amplifier with an open-loop passband gain of about 60 dB, with 3-dB corners at about 40 Hz and 2 kHz. (See Fig. 7.) While the low-frequency end isn't bad, the high-frequency end is pretty awful. This is partly because of the compensation intentionally introduced by R115 and C108 and partly because of tube electrode and circuit wiring capacitances. Not to worry, our bandwidth automatically increases again when we apply negative feedback, just as it does with solid-state compensated op-amps.

Fig. 7: Preamplifier Open-Loop and Phono gain
Fig. 7: Preamplifier Open-Loop and Phono Gain Curves

As hinted already, this circuit behaves very much like an operational amplifier (op-amp). But before we get on with designing feedback networks, we'll point out the ways in which it is not like an op-amp:

The not-quite-ideal Tube Opamp

Keeping these restrictions in mind, we can use the formula for the classic non-inverting op-amp to approximate our gain with feedback. Note that the inverting input (-IN) has a 47K resistor (R113) to "AC Ground". This is our "default" value for input resistance to the feedback input. Let's call that resistance Ri, though (as in the case of the tone control amp discussed later) it can be considerably higher, as needed. The bare-minimum feedback network would consist of just a single resistance (we'll call it Rf ) in series with a DC blocking capacitor between output and -IN. The theoretical gain with feedback would then be:

      Av = ( Rf / Ri ) + 1

For instance, let's compute our gain if we connect a "bare bones" feedback network consisting of a 430K resistor in series with a DC blocking capacitor between "OUT" and "-IN". That is, Rf / Ri = 9.15, so our gain would be 10.15, or about 20 dB.

The feedback elements do not have to be pure resistances; the above formula could be generalized to include complex impedances.

      Av = ( Zf / Zi ) + 1

The circuit's actual performance follows this predicted formula very closely, verifying that our gain-matching shortcut described earlier works just fine. See Figure 6 for an actual plot of the prototype. The slight curve at the low end is caused by that "+1" factor in the equation; as Rf / Ri increases, that factor becomes less significant, and the graph approaches a straight-line relationship. However, at gain settings above about 200 (46 dB), the relationship begins to fall apart as we approach the amplifier's open-loop gain. Incidentally, this gain setting is also the practical maximum as regards frequency response; the 3 dB corner at this gain will be on the order of 16 kHz.

Fig. 6: Preamplifier Gain vs. Feedback Ratio
Fig. 6: Preamplifier Gain vs. Feedback Ratio

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