Frequency compensation
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In electrical engineering, frequency compensation is a design technique for amplifiers which use negative feedback or those, such as operational amplifiers, that are intended for use with negative feedback. The primary goal of frequency compensation is to avoid unintentionally creating positive feedback, which will cause the amplifier to oscillate.
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[edit] Explanation
Most amplifiers use negative feedback to trade gain for other desirable properties, such as decreased distortion or improved noise reduction. Ideally, the phase characteristic of an amplifier's frequency response would be constant; however, device limitations make this goal physically unattainable. More particularly, capacitances within the amplifier's gain stages cause the output signal to lag behind the input signal by 90° for each pole they create.[1] If the sum of these phase lags reaches 360°, the output signal will be in phase with the input signal. Feeding back any portion of this output signal to the input when the gain of the amplifier is sufficient will cause the amplifier to oscillate. This is because the fed-back signal will reinforce the input signal. That is, the feedback is then positive rather than negative.
Frequency compensation is implemented to avoid this result.
[edit] Use in operational amplifiers
Because operational amplifiers are so ubiquitous and are designed to be used with feedback, the following discussion will be limited to frequency compensation of these devices.
It should be expected that the outputs of even the simplest operational amplifiers will have at least two poles. An unfortunate consequence of this is that at some critical frequency, the phase of the amplifier's output = -180° compared to the phase of its input signal. The amplifier will oscillate if it has a gain of one or more at this critical frequency. This is because (a) the feedback is implemented through the use of an inverting input that adds an additional -180° to the output phase making the total phase shift -360° and (b) the gain is sufficient to induce oscillation.
A more precise statement of this is the following: An amplifier will oscillate at the frequency at which its open loop gain equals its closed loop gain if, at that frequency,
- 1. The open loop gain of the amplifier is >= 1 and
- 2. The difference between the phase of the open loop signal and phase response of the network creating the closed loop output is more negative than -180°. Mathematically,
-
- ΦOL – ΦCLnet = -180°
[edit] Practice
Frequency compensation is implemented by modifying the gain and phase characteristics of the amplifier's open loop output or of its feedback network, or both, in such a way as to avoid the conditions leading to oscillation. This is usually done by the internal or external use of resistance-capacitance networks.
[edit] Dominant pole compensation
The method most commonly used is called dominant pole compensation, which is a form of lag compensation. It can be shown that adding a pole to the open loop response at a very low frequency will reduce the gain of the amplifier, at the frequency of existing higher frequency poles, to one or less. This newly added pole is called the dominant pole because it dominates the effect of all of the higher frequency poles. The result is that the difference between the open loop output phase and the phase response of a feedback network having no reactive elements never reaches −180° while the amplifier has a gain of one or more.
Dominant pole compensation is implemented in most general purpose operational amplifiers by adding an integrating capacitance to the second stage. The size of the capacitance is sufficient to create a pole at a frequency of approx. 4 Hz, which reduces to one the gain at which the next higher frequency pole occurs. The result is a phase margin of 45° (dominant pole yields -90° from approx. 40 Hz to next highest frequency pole, which adds another -45° for a total of -135°). This is sufficient to prevent oscillation in the most commonly used feedback configurations.
Though simple and effective, this kind of conservative dominant pole compensation has two drawbacks:
- 1. It reduces the available open loop gain of the amplifier at higher frequencies, reducing its bandwidth. This, in turn, reduces the amount of feedback available for distortion correction, etc. at higher frequencies.
- 2. It reduces the amplifier's slew rate. This reduction results from the time it takes the finite current driving the second stage to charge the compensating capacitor. The result is the inability of the amplifier to reproduce high amplitude, high frequency signals accurately.
[edit] Other methods
Other compensation methods are lead compensation, lead-lag compensation and feed-forward compensation.
- Lead compensation. Whereas lag compensation places a pole in the open loop response, lead compensation places a zero[2] in the open loop response to cancel one of the existing poles.
- Lead-lag compensation places both a zero and a pole in the open loop response, with the pole usually being at an open loop gain of less than one.
- Feed-forward compensation uses a capacitor to bypass a stage in the amplifier at high frequencies, thereby eliminating the pole that stage creates.
The purpose of all three of these is to allow greater open loop bandwidth while still maintaining amplifier closed loop stability. They are often used to compensate high gain, wide bandwidth amplifiers.
[edit] Footnotes
- ^ In this context, a pole is the point in a frequency response curve where the amplitude decreases by 3db due to an integrating resistance and capacitive reactance. Ultimately, each pole will result in a phase lag of 90°, i.e., the output signal will lag behind the input signal by 90° at this point. For the mathematical concept of a pole, see, Pole (complex analysis).
- ^ In this context, a zero is the point in a frequency response curve where the amplitude increases by 3db due to a differentiating resistance and capacitive reactance. Ultimately, each zero will result in a phase lead of 90°, i.e., the phase of the output signal will be 90° ahead of the phase of the input signal at this point. For the mathematical concept of a zero, see, Zero (complex analysis).
