Feedback caps in op amp design

[armdnrdy]

I've looked around a bit and haven't found anything that really explains the purpose of and how to size feedback capacitors in op amp designs.

Can somebody lead me to a tutorial that will unlock the mystery? I realize that this is probably covered in op amps 101 but.....I haven't found that page!

[Derringer]

this pdf has proven itself invaluable to be

http://www.eng.yale.edu/ee-labs/morse/compo/sloa058.pdf

see page 13 for filter circuits 

[R O Tiree]

You'll sometimes also see little tiny caps (100pF or so) in parallel with the "feedback" resistor, which will kill very high frequency oscillations that can occur.

[armdnrdy]

Thank you both!

I've got some reading to do.

[brett]

Hi

You'll sometimes also see little tiny caps (100pF or so) in parallel with the "feedback" resistor, which will kill very high frequency oscillations that can occur.

That's true, at very high frequencies (e.g. 1 Mhz), a 100 pF cap has a tiny resistance compared with the feedback resistor and reduce the gain at those frequencies to low levels.

However, these caps can also affect the upper audible range. For a feedback resistor of 220k, a 100pF cap gives a roll-off frequency of 7.2 kHz (fc=1/(2.pi.R.C). That'll take a fair bit of nasty 'fizz' out of the signal. I dislike the 'broken glass in the ears' sound that many high-gain distortion designs seem to give, so I'm often inclined to increase the feedback cap.

The feedback caps in the BMP work the same way, but around BJT gain stages. Those caps give a very low cuttoff frequency and play a big roll in the creamy sound of the BMP.
cheers

[Mark Hammer]

Op-amps want to go full tilt.  We regulate their gain at something less than full tilt by applying negative feedback from the output.  Te more negative feedback is applied, the less gain is produced.

The feedback path from output to input on an op-amp is one half of a virtual pot (voltage divider) that attenuates the negative feedback.  If that virtual pot conserves a lot of feedback, then very little gain is produced.  If much of that negative feedback is dumped (attenuated), then the brakes are lifted and the op-amp gets to run at closer to full tilt.

The textbook case of conserving all possible negative feedback is one where there is a straight wire connection between output and inverting input.  All that negative feedback goodness finds its way to the inverting input, and not a single electron is wasted.  And, of course, when we do that we get unity gain.

If the feedback resistance is much larger than whatever the resistance is connected to the inverting input (and this is true whether used in inverting or non-inverting mode), we start to move in the direction of full tilt.  Think of it.  If we have a 1M feedback resistor, in a non-inverting op-amp, an 1k from the inverting input to ground (or Vref, depending), then their combination behaves like a 1001k pot, turned down to practically nothing.  And with the negative feedback soooooo reduced/attenuated, you can bet that op-amp will behave much more in the direction of "full tilt".

So, what about the caps?

As already noted by others, feedback caps present an alternate path for the negative feedback, where the resistance/impedance they present decreases as the signal gets higher in frequency..  Of course, as it decreases in impedance, it starts to behave more and more like a straight-wire connection between output and inverting input. and when we conserve as much of that negative feedback as we can, what do we get?  LESS gain.  So, the general gain is set by the feedback and ground resistance, but gain gets lower than that as frequency increases, based on the traditional formula: F = 1 / [2 * pi * R * C].

To identify what sort of feedback cap would work for you, you simply plug the feedback resistance into R in that formula, and identify what standard value of C nails what it is you're trying to accomplish.  I find in a great many instances, the cap value chosen in commercial product is often much smaller than you'd think.  I imagine it is simply to avoid instability at high gains, rather than providing any sort of deiberate tone-shaping.

[armdnrdy]

Thanks Mark and Brett,

I'll have to read through this a few times.

So am I wrong in thinking that a feedback cap can act as sort of a gain limiter for certain frequencies?

[Mark Hammer]

Not completely wrong.  Probably better to think of it simply as a lowpass filter.

[MrSimple]

If you look at an op amp data sheet, or even if you don't, it'll show a graph called "Gain-Bandwidth".  This shows what gain and bandwidth the amp has with no feedback, which is very high gain and very low frequency response.  Any time you put a resistor or a capacitor in the feedback loop you are manipulating this graph.  You have to be aware of what bandwidth you want.  If you want too much, you end up with nasty sound quality.

You can read all about it here -- scroll down to the sidebar about taming op amp distortion.  This isn't referring to knucklehead guitar player distortion, it is distortion relative to the amplifier's accuracy.

http://oriongateway.org/hubble-super-regulator/allen-burdick-rf-gain/