# Input Capacitance—common-mode?...differential?… huh?

The input capacitance specifications of op amps are often confused or ignored. Let’s clarify how these specs can best be used.

Stability of an op amp circuit can be affected by input capacitance at the inverting input by causing phase shift—a delay of the feedback reaching the inverting input. The feedback network reacts with input capacitance to create an unwanted pole. Scaling the impedance of the feedback network in relation to the input capacitance is an important step to assure a stable amplifier circuit. But which capacitance matters—differential?… common-mode?… both?

The input capacitance of an op amp is generally found in an input impedance specification showing both a differential and common-mode and capacitance.

Input capacitance is modeled as a common-mode capacitance from each input to ground and a differential capacitance between the inputs, figure 1. Though there is no ground connection on an op amp with dual supply voltages, consider the common-mode capacitances as connected to the V- supply terminal, the AC equivalent of ground.

At high frequency where stability is a concern, the op amp has little open-loop gain and there is substantial AC voltage between the two inputs. This causes the differential capacitance to combine with the inverting common-mode capacitance to alter the phase of the feedback signal. So add the two capacitances that connect to the inverting input. Include an estimate of stray wiring capacitance (perhaps around 2pF). This total capacitance reacts with the parallel impedance of the feedback network (R1//R2) to create a pole.

A guideline:  The frequency of this pole should be should be greater than two-times the closed-loop bandwidth of the amplifier. A pole at two-times the closed-loop bandwidth will reduce the phase margin of the circuit by approximately 27°. This is generally okay for most circuits in a closed-loop gain of two or greater. Applications with critical settling requirements or capacitive load may require even greater margin. Reduce the feedback network impedance or consider adding a capacitor across the feedback capacitor, R2.

Today’s “general purpose” op amps often have wider bandwidths, from 5MHz to 20MHz and more. Feedback network resistances that may have been okay with 1MHz op amps can now create problems, a reason to be diligent in checking stability of your designs.

SPICE simulation is very helpful in checking sensitivities to input capacitance and feedback impedance and good op amp macro-models accurately model input capacitances. A transient response check with a 1mV input step should not cause excessive overshoot and ringing. But remember, reality always trumps guidelines and simulations. This is the type of circuitry may require fine tuning in a final circuit layout.

This discussion relates to several previous blogs. Some are linked in the text above. Here’s a summary of ones that you may find helpful…

Bruce       email:  thesignal@list.ti.com (Email for direct communications. Comments for all, below.)

# Other interesting “The Signal” Topics.

• This is a good topic as it is a typical 'gotcha' when first designing with op-amps. I am a bit surprised that you are using a 1mV signal to test for ringing and overshoot. It makes sense for a noiseless simulator, but what about a real world lab test? I have always presumed (assumed??) a 25mVp to 100mVp step is ok to avoid slewing and is pretty darn close to 'small signal' analysis used in text books. I would love to see a real world lab test to determine stability by referring %overshoot to phase margin.

-Ken

• You are correct, Ken, 1mV input is unnecessarily small to stay in the small-signal range of an op amp. It's convenient number for simulations but may be too small to conveniently view output on a scope. For lab measurements, anything up to 50mV input step should be okay. I suggest going no higher than 50mV, or so, as some input stages start to lose gain significantly beyond this point. -- Bruce

• I'm affraid I need some clarification regarding Figure 1. As far as I remember the common-mode capacitance is measured between the op-amp inputs connected together and the graound. If this definition is correct, the op-amp in Fig. 1 has 2*C_CM of common-mode capacitance. The question is what is listed in the datasheet, C_CM or 2*C_CM?

• Pawel--The common-mode capacitance value in the data sheet appears two places--one on each input to ground.-- Bruce

• Some how I feel the definition of common mode and differential input capacitance and resistance of an op amp to be confusing.

In TI's  white paper Understanding Operational Amplifier Specifications (sloa011),  Cp and Cn are in the position  of Ccm of this article on the positive and negative input. The common mode input capacitance is defined as Cic = Cp // Cn; so I can also derive that the differential input capacitance is

Cid = Cd // (Cp in series with Cn).

Similarly for the input resistance, ric = Rp // Rn, rid = Rd // (Rp + Rn) where Rp and Rn are the resistance from each positive and negative input to ground.

It seems these definition are not consistent with the definition in this article. So I am not sure what definition the datasheets are using for common mode and differential input capacitance and resistance.