# Understanding op-amp circuits with extra capacitors in the feedback path

When looking at circuits like this one

circuit http://dt.prohosting.com/hacks/what1.gif

I often find (see U6-A in linked schematic) extra capacitors in the pF range slapped in parallel with the feedback resistors, although the op-amp has a buffering or gain function:

simulate this circuit – Schematic created using CircuitLab

Doesn't that make it a low-pass filter instead? Is it supposed to filter out high frequencies or what other role does it play?

• Reduce ringing / overshoot. – jippie Oct 20 '15 at 16:58
• It does make it a low-pass filter, but given that it had finite bandwidth anyway, you could already say that it was a low-pass filter even without the cap. These sort of things tend to be added to avoid amplifying signals which are wildly out of band - a typical example is stopping RF signals passing down audio signal paths. – user1844 Oct 20 '15 at 16:58
• Thanks a lot everybody. Should I start adding those extra caps on a regular basis in my designs to filter out HF noise/signals? – jilski Oct 20 '15 at 17:14
• It depends - I use them to reduce overall wideband noise a lot of the time. – Andy aka Oct 20 '15 at 17:30

I'll do the circuit analysis.

This is an inverting amplifier with a gain of $$|A_V| = \left| \frac{R_1 || -\frac{j}{\omega C}}{R_2}\right| = \left| \frac{R_1 / R_2 }{1 + j \omega R_1 C} \right| = \frac{R_1 / R_2 }{\sqrt{1 + (\omega R_1 C)^2}}$$ which gives you all of the information you need:

• At low frequencies ($\omega \approx 0$), the gain is $$|A_V| = \frac{R_1}{R_2}$$ so the DC gain of this amplifier is the same as it was without the capacitor.
• At high frequencies, the $1/\omega$ term makes the gain shrink, so high frequencies noises and sharp edges are filtered out.
• The cutoff frequency of the amplifier is at $$\omega R_1 C = 1 \implies \omega = \frac{1}{R_1 C}$$ which is fairly high, since $C$ is small.

Finally (thanks to LvW), if your circuit is ringing, this capacitor adds an extra pole in the amplifier's frequency response, which can increase the phase margin and make the circuit more stable. This is a bit more complex and depends on the properties of the op-amp, so I won't go into detail.

• No problem. Feel free to upvote and accept my answer if you're happy with it! – Greg d'Eon Oct 20 '15 at 17:42
• May I add a short correction? Ringing is not "filtered out". Such a filtering would apply to unwanted signals contained in the input signal only. Here, the feedback cap takes care that - from the beginning - ringing is inhibited or (at least) reduced. This is because this capacitor improves stability properties of the whole feedback circuit - provided the value of this cap is selected properly. It is a kind of lag compensation. – LvW Oct 20 '15 at 17:43
• A more intuitive way to understand it is that at high frequencies the cap acts as a short, so the gain for those frequencies is reduced/cut to unity. When this is done to prevent oscillation it's sometimes called lead compensation; see p. 13 in ti.com/lit/ml/sloa079/sloa079.pdf – Fizz Oct 20 '15 at 18:22
• @tcrosley: The ideal integrator has no resistor in the feedback path. The resistor is added for practical purposes. – Fizz Oct 20 '15 at 19:08
• @RespawnedFluff The last paragraph in your linked article says "The practical integrator circuit is equivalent to an active first-order low-pass filter" which ties in with the answer above. Nice. – tcrosley Oct 20 '15 at 19:13