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Op-Amp Frequency Compensation

op-amp Frequency Compensation
Written by Andrew Levido

We all know that an op-amp has a very high open-loop gain, typically 100 to 120dB (100,000 to 1,000,000), but how does this vary with frequency? The answer may surprise you. Figure 1 shows a typical curve I have taken from a data sheet for a general-purpose op-amp. The open-loop gain (blue curve) is above 110 dB only at very low frequencies and rolls off rapidly from about 2 Hz at 20dB per decade to a gain of 0dB (1) at about 1MHz. The phase shift is -90° over most of the frequency range, dropping to -180° at about 10MHz.

op-amp frequency
Figure 1
This is the open-loop frequency & phase response for a typical general-purpose op-amp extracted from the data sheet. The gain (blue curve) is above 110dB for very low frequencies but rolls off at 2Hz by -20dB per decade until it reaches 0dB at around 1MHz. This behavior is due to the op-amp compensation which ensures it is stable under all normal conditions.

The op-amp frequency response looks like a single-pole RC filter with a corner frequency at about 2Hz. Surely the designers could do better? In fact, this is a deliberate (and indeed necessary) design decision to ensure the op-amp will be stable under all operating conditions. It is called frequency compensation.

Before getting into details of compensation, it’s worth looking at why this gain-frequency characteristic is not such an issue in practice. The key is that this is an open-loop characteristic, and we almost always use op-amps with the loop closed by negative feedback. Figure 2 shows how this works. The open-loop gain shown in blue looks like that of f\Figure 1, but with a closed-loop gain of 10 (20dB) the frequency response is shown by the red line. The gain is flat up to 100kHz, where it rolls off according to the open-loop response.

Figure 2
The closed-loop frequency response for a gain of 20dB (10) is shown in red. The gain is flat from DC to 100kHz, where it intersects the open-loop curve. Thus, the product of gain and bandwidth for a given op-amp is a constant. This op-amp has a gain-bandwidth product of 1MHz.

The same will be true of any other closed-loop gain. For a voltage follower with a gain of one, the gain will be flat to 1MHz where it intersects the open-loop gain curve. The closed-loop bandwidth for an op-amp is always proportional to its gain. Put another way, the product of gain and bandwidth is a constant. This gain-bandwidth product (GBW) is how op-amp bandwidth is specified in the data sheets. The original op-amp in Figure 1 for example is specified to have a gain-bandwidth product of 1MHz.

Now back to compensation. An uncompensated op-amp might have a frequency response like that shown in Figure 3. Each stage of the op-amp will have a low-pass RC characteristic due to the finite output impedance of the previous stage and unavoidable parasitic capacitances. These cascaded low pass filters will each introduce a pole at their respective corner frequency, f1, f2, and f3 in the figure. These would typically be in the high kHz to MHz range,

Figure 3
This hypothetical uncompensated op-amp has a frequency response as shown in red. For dominant pole compensation, extra capacitance is added to the lowest frequency pole to shift it left to the point that the roll-off hits 0dB before the phase shift falls below -180° ensuring stability at all gain levels.

Each of these poles will also introduce a 90° lagging phase shift. Since there are several stages, at frequency the overall phase shift will reach 180° degrees and, since the gain is greater than one, the amplifier will inevitably oscillate. This is why we need frequency compensation!

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The simplest way to eliminate the possibility of oscillation is called dominant pole compensation. In this case, we deliberately introduce additional capacitance to the first pole to shift the initial -20dB/decade slope left, such that the gain of the amplifier reaches 0dB at some phase shift lower than 180° – eliminating the conditions for oscillation.

The upshot of this is that the phase shift of the amplifier can never reach -180° while the gain is above 0dB. This is perfectly illustrated by the phase curve (green) in Figure 1. In this case, the gain hits 0dB at around 1MHz while the phase is still around -90°.

The difference between the 0dB phase and -180° is known as the phase margin and is typically between 45 and 90°. We need some phase margin to ensure stability with additional phase shifts than might be created by outside the op-amp, for example when driving capacitive loads.

While it’s handy that most op-amps are fully compensated and therefore generally stable in any application, it does mean we have limited the bandwidth to meet the worst-case scenario (unity gain). If we will always use an op-amp in applications with a gain greater than one, we could get away with less compensation.

Enter the “decompensated” op-amp (which should be more accurately called the “under-compensated” op-amp. These are compensated to be stable for gains above some minimum threshold (typically 5 to 10) and so have better high-frequency characteristics than their fully compensated equivalents. You need to be careful to use them only in their stable range.

A very small selection of completely uncompensated op amps is available for specialist applications. It is up to the user to provide the compensation according to the application, although the data usually suggests compensation capacitor values for different gains.

References

Horowitz, Paul, and Winfield Hill. The Art of Electronics. Third edition, 11th printing, with Corrections. Cambridge New York, NY: Cambridge University Press, 2017.

“Phase Margin.” In Wikipedia, December 31, 2021. https://en.wikipedia.org/w/index.php?title=Phase_margin&oldid=1062964931.

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Texas Instruments. “AN-1604 Decompensated Operational Amplifiers.” https://www.ti.com/lit/an/snoa486b/snoa486b.pdf?ts=1653606315340&ref_url=https%253A%252F%252Fwww.google.com%252F.

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Andrew Levido (andrew.levido@gmail.com) earned a bachelor’s degree in Electrical Engineering in Sydney, Australia, in 1986. He worked for several years in R&D for power electronics and telecommunication companies before moving into management roles. Andrew has maintained a hands-on interest in electronics, particularly embedded systems, power electronics, and control theory in his free time. Over the years he has written a number of articles for various electronics publications and occasionally provides consulting services as time allows.

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Op-Amp Frequency Compensation

by Andrew Levido time to read: 4 min