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# When designing an operational amplifier, capacitance will have the following effects

elecfans | 24/12/2021

When designing an operational amplifier, it is impossible to exclude input capacitance, and the printed circuit board of the operational amplifier contains more (Figure 1). Except for the feedback capacitor CF, all other capacitors are stray capacitances, which will affect the stability of the circuit. For example, if these capacitors are artificially set to zero, Equation 1 can be used to find the loop gain. The open loop gain a of the operational amplifier contains amplitude and phase components, so a phase shift occurs in the Baud (logarithmic stability) graph. The critical point on the Bode plot is the point where the gain amplitude is equal to zero (gain=1); the difference between 180° and the actual phase shift is the phase margin.

The external components are resistive; let RG=RF to reduce the loop gain by 6dB. This can further enhance stability and reduce the vertical intercept on the Bode plot by 6dB, while the pole position remains the same. Equation 2 gives the loop gain of an inverting amplifier with actual input capacitance (CF = 0), as shown in Figure 1.

This input capacitance adds a pole to the loop gain, and when the parallel value of RG and RF is small, such as 500Ω, the pole position is at f = 16.76 MHz. The phase shift caused by this pole at one-tenth of the frequency of its location is basically zero, so the input capacitance will not affect operational amplifiers with a gain bandwidth of less than 1.676 MHz. When the gain bandwidth of the op amp exceeds 1.676 MHz, the phase shift caused by this pole will increase to the loop gain phase shift, and the op amp will produce overshoot, ringing, and subsequent oscillation, depending on its phase response.

Increasing the parallel value of RG and RF will cause the pole frequency to decrease (RF || RG = 5kΩ, f = 0.1676 MHz). Therefore, the faster the phase shift occurs, the more serious the instability problem. The traditional solution is to make the resistance in the high-frequency operational amplifier circuit smaller to minimize the influence of stray input capacitance. Another solution to the problem of input capacitance is to add a feedback capacitor CF. When there are input and feedback capacitors in the circuit, the loop gain can be calculated by Equation 3.

The zero in Equation 3 always precedes the pole; therefore, its phase shift cancels out part of the negative phase shift until the pole takes effect. By making RFCF = RGCG, the circuit can be independent of two capacitors. This method is usually not the best choice for closed-loop bandwidth performance, so engineers choose to use a smaller CF value. The best high-frequency performance can be obtained by optimizing the resistance value, capacitance value, and operational amplifier bandwidth, but in the laboratory, 2CF = CG is an excellent starting point.

The stability of an inverting op amp is the same as that of a non-inverting op amp because the stability has nothing to do with the input. The work of the inverting operational amplifier is very similar to the theoretical prediction, but the anti-common mode ability of the non-inverting operational amplifier is low, because part of the input signal is fed into the inverting node through the differential capacitor (CD). The degradation of anti-common mode performance is only noticeable at high frequencies.

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# Operational Amplifiers

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