Name: Randall Aiken
E-Mail: reaiken@aikenamps.com
Date: 1/12/100 6:40 PM
Subject: Re: Adding resistor across pot to change taper (revisited)


That circuit was not new even 20 years ago! It has been around since the
dinosaurs played tube amps. I suspect Mr. Dumble stole it from one of
Fender's schematics, who probably stole it from a tube manual or textbook. It
is nothing more than the standard single-stage, inverting feedback amplifier.

If you read the paper on my website entitled "Designing single-stage
inverting feedback amplifiers", you will find the equations needed to
calculate the gain and response, the effect of the coupling capacitor, and the
reasons for the filtering effect.

The open-loop gain is controlled by the tube, the 100k plate load resistor,
and the partially-bypassed cathode. The partially-bypassed cathode reduces
the normal gain of -63 or so down to -36, not a good thing for a feedback
amp, which depends on excess loop gain to work properly. The series
resistor shapes the response to get it more or less flat at the lower open-loop
gain, although it still has some droop on the low end. This partial bypassing
also raises the effective open-loop output impedance from 38.5K to around
60K. It does help the transient response to not have a long time constant on
the cathode, though, at the expense of loop gain and output impedance. 

The feedback resistor, Rf, is either 22M or 32M, depending on the switch
setting. 

The input resistor, Ri, varies all over the place, depending on the setting of
the volume pot (even more so with the 1M taper-modifying resistor).
Ignoring the 38.5K output impedance of the first stage (because it is low in
relation to the resistances in the gain control), and assuming the input signal
is the signal at the top of the pot, if the pot is at zero, Ri is 100K. If the pot is
at max, Ri is 1M in parallel with 500K, plus 100K, or 433K. At midpoint, Ri
is (1M + 500K) in parallel with (500K in parallel with 1M) plus 100K, or
373K. As you can see, the effective input resistor value varies from 100k to
433K, depending on the pot setting.

Using the equations shown in the paper, the gain of the stage (from top of
volume pot to output before coupling cap) varies from -30/-32 (for
22M/32M) at zero pot setting to -22/-25 at midpoint, to -21/-24 at max. Note
that the effective attenuation of the input signal also changes as the pot is
varied, as does the effective input impedance. As the gain is increased with
the pot, the gain of the amp is decreased, effectively creating yet another
modified taper. This is why the taper doesn't feel like a "normal" audio-taper
volume pot.

The lower-3dB frequency response is controlled primarily by the 0.022uF
input coupling cap. The lower-3dB point varies from 0.6Hz to 3.6Hz,
depending on the setting of the pot. Either way, it is plenty low enough,
possibly too low, considering the potential transient response problems these
feedback amps have. You could probably go as low as 0.01uF without
affecting the low end too much. Remember, the -1dB point is a full octave
away from the -3dB point, and you will still see some attenation a full
decade away, so for flat response at 80Hz, this can be designed for a 8Hz
cutoff.

The .047uF feedback coupling cap is way too large for the resistor values,
giving a -3dB response of 0.15Hz, which is not good for low-frequency
transient response. This cap should be around 1500pF for the feedback
resistor values used. The feedback loop will take out any changes in
frequency response, so changing this cap value from .047uF to 1500pF is not
as drastic as it sounds. It will only improve the transient response. The
transient response problems show up as a "bounce", or slowly decaying shift
of the waveform average DC level at the plate when a large transient input
signal is present. It can cause an audible distortion, even if it doesn't result in
clipping at the plate, due to the change in operating point.

The upper -3dB frequency response point is set by the stray capacitance
across the 22M/32M resistor, in addition to the rolloff due to the finite
gain/bandwidth product of the amplifier. As shown, assuming no stray
capacitance, the response out of the first stage is around 40kHz at the -3dB
point. The response out of the second stage is around 8.5kHz at the -3dB
point with a 22M resistor and 7.2kHz at the -3dB point with a 32M resistor
(with the pot at max). The 560pF/470k network following the amp peaks it
back up so the -3dB point is around 28kHz with the 32M resistor, but in
doing so, creates a +7dB peak at around 3.4kHz. A large input capacitance of
a following stage would reduce this a bit. However, even a small stray
capacitance across the large value feedback resistors will effectively cut the
frequency response way down.

Randall Aiken