Here is a quick and dodgy cut-and-paste out of MS Word of a brief paper that I composed this evening. It is probably full of grammatical typos and punctuation errors, but that's it for this evening.
Can anyone cite precedence for what looks like a really obvious idea here?
Can anyone cite precedence for what looks like a really obvious idea here?
Better Feedback for the “Blameless” amplifier.
Once in a blue moon in electronics design, one comes up with an incremental improvement upon convention that appears to be so basic and obvious that he or she is then left wondering why it is not standard fare already.
To start with, let's consider the standard arrangement of negative feedback and input termination for a typical amplifier with a bipolar junction transistor long-tail-pair input (LTP) stage, as shown here:
An amplifier rated at 100W into a 4-ohm load will require a closed loop gain of approximately 20 for an input sensitivity of 1V rms.
The values shown for feedback network resistors R2 and R3 get close enough to this target.
Capacitor C2 establishes a DC gain of unity and a high-pass pole so that that input stage offset errors do not become unmanageable by being amplified at the speaker terminals by the passband value of closed loop gain.
The capacitance value of C2 is typically chosen to corner with R3 at a frequency significantly lower than what would otherwise be required for acceptable passband gain flatness down to 20Hz. This is because C2, for practical reasons, generally needs to be an electrolytic dielectric type due to the large value of capacitance required.
Electrolytic capacitors are imperfectly linear and if C2 has significant reactance at low audio frequencies then the non-linearity that it introduces to the feedback network can easily limit and define the amplifiers low-frequency distortion performance.
Resistor R1 DC-terminates the base of the opposing input transistor. At 33k, the high value of R1 presents a desirably light load to whatever circuity is driving the amplifier and permits coupling capacitor C1 to be a more desirable film dielectric type.
An important thing to note here is that R1 is the same value as R2. This is necessary so that input offset error caused by the base currents of the input transistors cancel out.
Suppose that the tail current of the LTP is set to 5mA. If the input transistors have a hfe of 200, then the base currents will produce a voltage drop greater than 400mV across resistors R1 and R2. It is therefore clear that a large difference in value between resistors R1 and R2 would be unacceptable in terms of input offset error.
Noise
Now here is where the dilemma begins. Feedback resistors R2 and R3 present an impedance much higher than what would be desirable for the lowest noise performance.
We would be in much better shape if the values of R2, R3 and C2 were revised to 4k7, 240R and 680uF respectively. But the input offset error due to the base currents of Q1 and Q2 would become intolerable unless input resistor R1 is reduced to 4k7 also.
4700 ohms is lower than what one would generally like for the input resistance of a power amplifier. In addition to this, the capacitance value of input capacitor C1 will have to be raised proportionally, making the selection of a film dielectric type much more impractical.
A typical compromise here is to settle on an acceptable minimum value of 10k for the input resistance, scale feedback resistances accordingly and then just live with the resultant performance.
But what if we should wish to increase the creativity and complexity just a little bit, with the goal of getting away with less of a compromise in this regard?
Here is one possible solution suggested by Self [1]:
The input is now DC-terminated by the series combination of R1 and Rboot, the sum of their resistances being equal to the value of feedback resistor R8. However, the input resistance is bootstrapped for audio frequency signals which effectively multiplies the value of input resistance as seen by the signal source.
Things, though, are not entirely ideal. Riso is necessary for HF stability when the signal source is disconnected from the amplifier and it puts a handbrake on the degree of input impedance multiplication that can be practically achieved.
Self theorises that the observed problem of HF instability is due to additional capacitive loading at the base of Q3. Whether or not this is an adequate explanation is not something that I am concerned with for the purposes of this brief paper, but the important points are as follows:
A value of 100R for Riso “seemed to effect a complete cure” for the sporadic HF instabilities.
The measured value of input impedance was 13.3k (Riso=100R), reducing to 7.5k (Riso=220R)
13.3k is comfortably greater than the 10k minimum that we are generally content with and the feedback impedance has been reduced dramatically – the bonus for improved noise performance that we are after.
This is arguably a worthwhile improvement in performance for little extra complexity, but the potential for having to empirically test and tweak any variation of the scheme to ensure HF stability sours things considerably.
Another potential issue not mentioned by Self is that input impedance bootstrapping typical causes infrasonic peaking in the amplifier’s frequency response. The Bode plot below shows the simulated low frequency gain of Self’s example circuit. The degree of peaking can generally be kept to reasonable limits, but if one is unaware and consequently designs the bootstrapping network poorly, it can become quite pronounced.
An alternative approach
Here is an alternative approach which I have come up with that avoids these problems:
I have simply modified the feedback network so that it is split into separate DC and AC paths.
The complexity overhead is the addition of a single extra resistor and the new circuit arrangement makes use of no special tricks like positive-feedback for bootstrapping which might result in problems with stability or infrasonic gain peaking.
DC feedback is provided via R2, establishing a DC gain of unity. R2, being equal to the value of R1, meets the requirements for balancing the input stage offset error incurred by the transistor base currents.
Feedback via R2 at audio frequencies is largely shunted, via C2, by the alternative feedback derived from the junction of R3 and R4. This feedback network has a much lower impedance and thus defines the noise contribution of the feedback network at audio frequencies.
There is in fact complete freedom here to select the resistance values of feedback resistors R3 and R4 to be as arbitrarily low as anyone might desire, though beyond a certain point the returns are diminishing in terms of their contribution to total amplifier noise and one must be cognizant of power dissipation and non-linearity in these resistors.
The 100uF capacitance value of C2 results in a high-pass pole frequency just under 1Hz. One might superficially conclude that the value of capacitance ought to be much lower, but they would be mistaken.
The design equations are as follow:
Note the multiplication of the corner frequency by the value of closed loop gain.
Keeping the high-pass corner frequency quite low, in the order of one or two Hertz as you would conventionally, to minimise the distortion contribution of the electrolytic capacitor, is probably still a good idea. However, keep in mind that the actual AC signal current flowing through capacitor C2 in this scheme is much lower than it is in a conventional arrangement where the closed loop gain is set by feedback resistors similarly low in value. This is likely of benefit as far as capacitor distortion is concerned.
Glen Kleinschmidt March 2025
www.glensstuff.com
[1] Self on Audio Second Edition, “Trimodal Audio Power Part I, Improving noise performance”, page 342
