# Feedback capacitor vs Miller capacitor in discrete op amp circuits

This is an overly simplified operational amplifier circuit with a feedback applied. The common way to make it stable is to add a dominant pole to the transfer function usually in a form of a Miller capacitor which (correct me please) creates a pole together with input pair's output resistance. It works as expected by rolling down the open loop gain bandwidth until a desired phase margin is met. Another method is to add a capacitor across the feedback resistor. It's effect looks differently on a Bode plot. For my circuit (not shown here as it's not very representative) it doesn't affect the point of the first kink of the gain curve but flattens it as well as phase at high frequencies. So I assume it creates a zero with R2 and R3. So which way is preferable (and why) when designing the circuit as a whole and not just an op amp? simulate this circuit – Schematic created using CircuitLab

It would be a very unconventional approach to try to stabalise an amplifier by leaving out Cdom and including Cfb instead - I have never seen it attempted. The usual approach is to stabalise the amp with Cdom and then in some instances you would see Cfb included to improve the already adequate stability margins but also to reduce high frequency noise.

Cfb introduces a zero into the loop response, simultaneously adding a pole to the closed loop gain (the closed loop gain rolls off at a lower frequency). But what we are interested in is how Cfb affects the loop response because it is the gain and phase of the loop response that determines stability margins.

So Cfb introduces a zero to the loop response (going backwards from output to input). This feedback zero acts to increase the loop gain, which you may think would be detrimental to stability margins but there is a greater benefit caused by the zero's phase advance.

However Cfb also introduces a pole at a higher frequency than the zero (think of the gain increase in the feedback loop reaching a limit, Cfb starting to short out R2 as frequency is increased to some value). If Cfb is sized too large then this pole can occur at too low a frequency and stability can be compromised.

• Cool, thank you. It's actually Cfb that was confusing me most. "There is a greater benefit caused by the zero's phase advance." — Yep, that's exactly what I observed. Jul 31 at 20:59

Another method is to add a capacitor across the feedback resistor.

Not true.

The dominant pole created by adding the miller capacitor (Cdom in your diagram) does not close the loop around the op-amp and, it does not destabilize the transistor it is connected across.

So, without Cdom, you might have a problem when you close the loop and, adding a feedback capacitor from output to inverting input could well cause a big instability.

Adding a capacitor across the feedback resistor is asking for trouble if Cdom isn't present. But, you can usually get-away with a small capacitor (pF) across the feedback resistor (before it becomes unstable) and, you can usually add micro-farads across the feedback resistor but, anywhere in between is likely to destabilize the circuit.

Of course I'm talking generalisms based on experience.

Cfb is not really considered a feedback capacitor.

At low frequencies, Cfb has little effect and loop gain has a term R3/(R2+R3) in it. At higher frequencies, Cfb 'shorts' R2, eliminating that term (it becomes 1.0). Thus the effect of Cfb is to increase gain slightly from the lower value including R3/(R2+R3). This improvement in gain occurs over a relatively narrow frequency range (from approx w=1/(R2.Cfb) to R2/R3 times that (all depending on the relative values of R2, R3). The net result is that the corresponding zero and pole broaden the bandwidth of the whole amplifier; thus allowing Cdom to be chosen slightly smaller (thus a higher crossover frequency).