# Opamp Compensation For Input Capacitance

I am going through the datasheet of LM7171 for one of my applications. Please see the below circuit. May I know how they arrived at the equation for CF?

Is this equation is valid for non-inverting configuration also?

How the input parasitic capacitance causes instability.If the pole created by the gain setting resistors and parasitic capacitance falling inside the closed-loop bandwidth will create instability?

Stability problems are caused when the loop gain (gain of the complete open loop) has at least two poles. In this case, the slope of the loop gain function at the unity.gain crossing can be rather close to -40dB/dec.

That means: The phase of the loop gain function is pretty close to the -180deg line. (Remember that for -180deg - together with the sign inversion at the inv. input - we would have positive feedback causing oscillation).

The first pole (-20dB/dec) is caused by the open-loop gain of the opamp and the second one is caused by the feedback lowpass (RG||Xin)/[(RG||Xin)+RF] with Xin=1/jwCin.

This unwanted effect can be cancelled using the principle of "matched voltage division". It can be shown that a voltage divider consisting of two R-C parallel combination has no frequency dependence when R1C1=R2C2 (equal time constants) or R1/R2=C2/C1 . (In your case: RGCin=RFCF).

When CF is made larger than necessary, we ave a kind of "over compensation" with an improved stability margin at the cost of reduced closed-loop signal bandwidth.

As another example: Oscilloscope probes uses this principle for compensating the unwanted influence of the (parasitic) input capacitance of the HF input.

• Thank you very much. The same set of equations(R1/R2=C1/C2) is applicable for non-inverting configuration also? – HARI T O Apr 7 at 9:48
• Please note that the correct ratio is R1/R2=C2/C1. To answer your question: The loop gain is identical for inverting and nin-inverting operation. Hence, also the stabilization effect is identical. – LvW Apr 7 at 9:56

"May I know how they arrived at the equation for CF?"

That equation comes out when studying the stability of that circuit.

Study the Bode plot.

"Is this equation is valid for non-inverting configuration also?"

Yes.

As pointed out by LvW (See his/her comment below), stability depends solely on tha loop gain which is equal in both cases: non-inverting and inverting configurations.

• could you please tell me the formula for non inverting configuration – HARI T O Apr 7 at 12:56
• I do not agree to the above answer. What means " ...changes a little" ? Where is the explanation (evidence)? Stability is determined by the loop gain only - and the loop gain is identical for both circuit alternatives. – LvW Apr 8 at 8:42
• Yes, you are right. I modified my answer. Stability is an intrinsic property of the loop gain of the circuit with all the sources off. It does not depend on where I put the voltage or current sources. – Enrico Migliore Apr 8 at 8:49