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In some audio circuits (e.g. instrument amplifiers and guitar effects), I've seen something similar to the following op-amp circuit with back-to-back VBE multipliers in the feedback loop to provide gain while limiting the output signal.

The idea is that the user will start to hear relatively gentle clipping, and ease off on the upstream gain before driving the output to the rails.

schematic

simulate this circuit – Schematic created using CircuitLab

The transfer function looks like this: enter image description here

I'm wondering about the noise performance of this circuit, and whether the choice of transistors makes much difference in that regard.

The resistor values in the simulation are not based on any particular "real life" instance of this circuit, but just to illustrate the likely orders of magnitude. I selected the multiplier ratio so that the output swing might stay within the limits of an op-amp powered by a 9V battery.

I have used the custom "Ideal-ish" op-amp because CircuitLab doesn't have a properly ideal component. I wanted to focus on the noise component of the discrete components rather than get into a discussion about op-amp types. However (see my concluding parenthetical remark) if most real-life op-amps are going to produce considerably more noise, then please point that out.

In the "important" part of the signal swing (close to ground, far from rails), we have very little current flowing in the transistors (current noise from the transistors is lowest when Ic is low) and most of the current through the feedback loop flowing in the resistors.

It seems like the noise introduced by the transistors should be negligible compared to the noise from the resistors, but I'm not sure how to approach it quantitatively. (Or whether the orders of magnitude involved will tell us not to bother looking at it quantitatively.)

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  • \$\begingroup\$ My bet is that a real op amp will be the biggest culprit so, saying it is ideal (ish) might be missing the point. Try simulating it. \$\endgroup\$
    – Andy aka
    Commented Jan 12, 2022 at 23:17
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    \$\begingroup\$ It might make a big difference trying to find a low rbb BJT in certain cases. But in this case your source impedances to the BJTs are around 200 Ohms and 400 Ohms, thereabouts. So the rbb won't factor much in the noise question on this point. Common BJTs have rbb around 20-40 Ohms, more or less. \$\endgroup\$
    – jonk
    Commented Jan 13, 2022 at 0:10
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    \$\begingroup\$ What dynamic range are you expecting? Since clipping won't start until about 5V p-p and noise will be in the sub-microvolt level is it relevant? \$\endgroup\$ Commented Jan 13, 2022 at 0:45
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    \$\begingroup\$ I think you can ignore any noise the transistors may contribute because the transistors are completely off in the “important” part (Input<0.5Vpk), and after that the intentional distortion introduced by the transistors will dominate any THD+N measurement. The output noise will be the opamp’s voltage noise times the noise gain of 6.3 and swamp any noise contributed by your small resistors unless you buy a really nice opamp, but why would you bother in what is essentially a distortion circuit? \$\endgroup\$
    – td127
    Commented Jan 13, 2022 at 1:20
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    \$\begingroup\$ @Theodore Yes, that's the transfer I was imagining in my head. Adding it will help others. Your noise question included a question about the BJTs, themselves. I don't think their noise will dominate though I do admit that the BJT collector currents have quite a dynamic range in that circuit. The noise sources are many (every PN junction generates shot noise, everything else (almost) generates kT/C or Johnson noise (same thing, either way.) An analysis for S/N over the linear range would take me time. Perhaps not others. Shot noise leads to very bad S/N at low currents, though. It was my bane. \$\endgroup\$
    – jonk
    Commented Jan 13, 2022 at 18:00

2 Answers 2

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Ltspice can simulate the noise contributions.

But from looking at the schematic a few things become apparent:

  • the BJT are off at low signal level, so the noise of the feedback block is dominated by the three feedback resistors.
  • at high signal level, the feedback impedance drops (hence rolling back gain), so that means that noise drops too. and anyway the signal will be loud.
  • different transistors will slightly change the clipping threshold and even more slightly the THD content when clipping, but not the noise.
  • in all of these cases the largest noise contribution will be from the input resistor, as it will be multiplied by the circuit gain..The same applies to the opamp input voltage and current noise, so if these sources are more than the thermal noise of the input resistor, the opamp itself will indeed be the dominant noise source.
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  • \$\begingroup\$ I think you're correct that the feedback resistor noise will dominate the BJT noise, but the input resistor noise is amplified by the gain -(R2+R3+R4)/R1, so @td127's comment above is correct that R1 is the most important noise source. \$\endgroup\$
    – Theodore
    Commented Jan 13, 2022 at 21:43
  • \$\begingroup\$ @Theodore yes correct.. My reasoning applies only to the noise sources in the feedback block. Added a bullet \$\endgroup\$
    – tobalt
    Commented Jan 14, 2022 at 4:31
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Note: The circuit can be simplified by merging the function of a Vbe-multiplier with that of a diode when the transistor is operating with emitter and collector swapped:

schematic

simulate this circuit – Schematic created using CircuitLab

BC337 were chosen because they have decent reverse beta. That allows them to act like a diode when driven from emitter to collector (backwards).

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  • \$\begingroup\$ Seeing some analog stuff from you always makes days a little bit brighter ;) And such multifunctional simplifications are always welcome \$\endgroup\$
    – tobalt
    Commented Apr 24 at 11:29
  • \$\begingroup\$ @tobalt Thank you, that's very kind! \$\endgroup\$ Commented Apr 24 at 19:43

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