Frequency compensation
Encyclopedia
In electrical engineering
, frequency compensation is a technique used in amplifiers, and especially in amplifiers employing negative feedback. It usually has two primary goals: To avoid the unintentional creation of positive feedback
, which will cause the amplifier to oscillate
, and to control overshoot
and ringing
in the amplifier's step response
.
for other desirable properties, such as decreased distortion or improved noise
reduction. Ideally, the phase
characteristic of an amplifier's frequency response
would be linear; 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. 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 feedback signal will reinforce the input signal. That is, the feedback is then positive rather than negative.
Frequency compensation is implemented to avoid this result.
Another goal of frequency compensation is to control the step response
of an amplifier circuit as shown in Figure 1. For example, if a step in voltage is input to a voltage amplifier, ideally a step in output voltage would occur. However, the output is not ideal because of the frequency response of the amplifier, and ringing
occurs. Several figures of merit to describe the adequacy of step response are in common use. One is the rise time
of the output, which ideally would be short. A second is the time for the output to lock into its final value, which again should be short. The success in reaching this lock-in at final value is described by overshoot
(how far the response exceeds final value) and settling time
(how long the output swings back and forth about its final value). These various measures of the step response usually conflict with one another, requiring optimization methods.
Frequency compensation is implemented to optimize step response, one method being pole splitting
.
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 operational amplifier will oscillate at the frequency at which its open loop gain equals its closed loop gain if, at that frequency,
) for a frequency at or just below the location of the next highest frequency pole. The lowest frequency 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 falls below −180° while the amplifier has a gain of one or more, ensuring stability.
Dominant-pole compensation can be implemented for general purpose operational amplifiers by adding an integrating capacitance to the stage that provides the bulk of the amplifier's gain. This capacitor creates a pole that is set at a frequency low enough to reduce the gain to one (0 dB) at or just below the frequency where the pole next highest in frequency is located. The result is a phase margin of ≈ 45°, depending on the proximity of still higher poles. This margin is sufficient to prevent oscillation in the most commonly used feedback configurations. In addition, dominant-pole compensation allows control of overshoot
and ringing
in the amplifier step response
, which can be a more demanding requirement than the simple need for stability.
Though simple and effective, this kind of conservative dominant pole compensation has two drawbacks:
A strong example of this can be found at http://www.ece.utah.edu/~harrison/ece3110/Compensation.pdf
Often, the implementation of dominant-pole compensation results in the phenomenon of Pole splitting
. This results in the lowest frequency pole of the uncompensated amplifier "moving" to an even lower frequency to become the dominant pole, and the higher-frequency pole of the uncompensated amplifier "moving" to a higher frequency.
The purpose of these three methods 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.
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...
, frequency compensation is a technique used in amplifiers, and especially in amplifiers employing negative feedback. It usually has two primary goals: To avoid the unintentional creation of positive feedback
Positive feedback
Positive feedback is a process in which the effects of a small disturbance on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system that responds to a perturbation in a way that reduces its effect is...
, which will cause the amplifier to oscillate
Electronic oscillation
Electronic oscillation is the continuous recurrence of the same electrical periodic waveform.The recurrence may be in the form of a varying voltage or a varying current. The waveform may be sinusoidal or some other shape when its magnitude is plotted against the duration of its cycle...
, and to control overshoot
Overshoot (signal)
In signal processing, control theory, electronics, and mathematics, overshoot is when a signal or function exceeds its target. It arises especially in the step response of bandlimited systems such as low-pass filters...
and ringing
Ringing (signal)
In electronics, signal processing, and video, ringing is unwanted oscillation of a signal, particularly in the step response...
in the amplifier's step response
Step response
The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from...
.
Explanation
Most amplifiers use negative feedback to trade gainGain
In electronics, gain is a measure of the ability of a circuit to increase the power or amplitude of a signal from the input to the output. It is usually defined as the mean ratio of the signal output of a system to the signal input of the same system. It may also be defined on a logarithmic scale,...
for other desirable properties, such as decreased distortion or improved noise
Noise
In common use, the word noise means any unwanted sound. In both analog and digital electronics, noise is random unwanted perturbation to a wanted signal; it is called noise as a generalisation of the acoustic noise heard when listening to a weak radio transmission with significant electrical noise...
reduction. Ideally, the phase
Phase (waves)
Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...
characteristic of an amplifier's frequency response
Frequency response
Frequency response is the quantitative measure of the output spectrum of a system or device in response to a stimulus, and is used to characterize the dynamics of the system. It is a measure of magnitude and phase of the output as a function of frequency, in comparison to the input...
would be linear; 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. 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 feedback signal will reinforce the input signal. That is, the feedback is then positive rather than negative.
Frequency compensation is implemented to avoid this result.
Another goal of frequency compensation is to control the step response
Step response
The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from...
of an amplifier circuit as shown in Figure 1. For example, if a step in voltage is input to a voltage amplifier, ideally a step in output voltage would occur. However, the output is not ideal because of the frequency response of the amplifier, and ringing
Ringing (signal)
In electronics, signal processing, and video, ringing is unwanted oscillation of a signal, particularly in the step response...
occurs. Several figures of merit to describe the adequacy of step response are in common use. One is the rise time
Rise time
In electronics, when describing a voltage or current step function, rise time refers to the time required for a signal to change from a specified low value to a specified high value...
of the output, which ideally would be short. A second is the time for the output to lock into its final value, which again should be short. The success in reaching this lock-in at final value is described by overshoot
Overshoot (signal)
In signal processing, control theory, electronics, and mathematics, overshoot is when a signal or function exceeds its target. It arises especially in the step response of bandlimited systems such as low-pass filters...
(how far the response exceeds final value) and settling time
Settling time
The settling time of an amplifier or other output device is the time elapsed from the application of an ideal instantaneous step input to the time at which the amplifier output has entered and remained within a specified error band, usually symmetrical about the final value.Settling time includes a...
(how long the output swings back and forth about its final value). These various measures of the step response usually conflict with one another, requiring optimization methods.
Frequency compensation is implemented to optimize step response, one method being pole splitting
Pole splitting
Pole splitting is a phenomenon exploited in some forms of frequency compensation used in an electronic amplifier. When a capacitor is introduced between the input and output sides of the amplifier with the intention of moving the pole lowest in frequency to lower frequencies, pole splitting causes...
.
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 operational 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 = -180°. Mathematically,
-
- ΦOL – ΦCLnet = -180°
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.Dominant-pole compensation
The method most commonly used is called dominant-pole compensation, which is a form of lag compensation. A pole placed at an appropriate low frequency in the open-loop response reduces the gain of the amplifier to one (0 dBDB
DB may refer to:In science and technology:*Decibel , a logarithmic unit of measurement in acoustics and electronics*Dubnium , a chemical element*DB connector, a size of D-subminiature electrical connector...
) for a frequency at or just below the location of the next highest frequency pole. The lowest frequency 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 falls below −180° while the amplifier has a gain of one or more, ensuring stability.
Dominant-pole compensation can be implemented for general purpose operational amplifiers by adding an integrating capacitance to the stage that provides the bulk of the amplifier's gain. This capacitor creates a pole that is set at a frequency low enough to reduce the gain to one (0 dB) at or just below the frequency where the pole next highest in frequency is located. The result is a phase margin of ≈ 45°, depending on the proximity of still higher poles. This margin is sufficient to prevent oscillation in the most commonly used feedback configurations. In addition, dominant-pole compensation allows control of overshoot
Overshoot (signal)
In signal processing, control theory, electronics, and mathematics, overshoot is when a signal or function exceeds its target. It arises especially in the step response of bandlimited systems such as low-pass filters...
and ringing
Ringing (signal)
In electronics, signal processing, and video, ringing is unwanted oscillation of a signal, particularly in the step response...
in the amplifier step response
Step response
The step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from...
, which can be a more demanding requirement than the simple need for stability.
Though simple and effective, this kind of conservative dominant pole compensation has two drawbacks:
- 1. It reduces the bandwidth of the amplifier, thereby reducing available open loop gain at higher frequencies. This, in turn, reduces the amount of feedback available for distortion correction, etc. at higher frequencies.
- 2. It reduces the amplifier's slew rateSlew rateIn electronics, the slew rate represents the maximum rate of change of a signal at any point in a circuit.Limitations in slew rate capability can give rise to non linear effects in electronic amplifiers...
. This reduction results from the time it takes the finite current driving the compensated stage to charge the compensating capacitor. The result is the inability of the amplifier to reproduce high amplitude, rapidly changing signals accurately.
A strong example of this can be found at http://www.ece.utah.edu/~harrison/ece3110/Compensation.pdf
Often, the implementation of dominant-pole compensation results in the phenomenon of Pole splitting
Pole splitting
Pole splitting is a phenomenon exploited in some forms of frequency compensation used in an electronic amplifier. When a capacitor is introduced between the input and output sides of the amplifier with the intention of moving the pole lowest in frequency to lower frequencies, pole splitting causes...
. This results in the lowest frequency pole of the uncompensated amplifier "moving" to an even lower frequency to become the dominant pole, and the higher-frequency pole of the uncompensated amplifier "moving" to a higher frequency.
Other methods
Some other compensation methods are: lead compensation, lead–lag compensation and feed-forward compensation.- Lead compensation. Whereas dominant pole compensation places or moves poles in the open loop response, lead compensation places a zero in the open loop response to cancel one of the existing poles.
- Lead–lagLead-lag compensatorA lead–lag compensator is a component in a control system that improves an undesirable frequency response in a feedback and control system. It is a fundamental building block in classical control theory.- Applications :...
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 these three methods 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.
See also
- Pole splittingPole splittingPole splitting is a phenomenon exploited in some forms of frequency compensation used in an electronic amplifier. When a capacitor is introduced between the input and output sides of the amplifier with the intention of moving the pole lowest in frequency to lower frequencies, pole splitting causes...
- Bode plotBode plotA Bode plot is a graph of the transfer function of a linear, time-invariant system versus frequency, plotted with a log-frequency axis, to show the system's frequency response...
- Negative feedback amplifier
- Step responseStep responseThe step response of a system in a given initial state consists of the time evolution of its outputs when its control inputs are Heaviside step functions. In electronic engineering and control theory, step response is the time behaviour of the outputs of a general system when its inputs change from...