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In
electronics engineering Electronics engineering is a sub-discipline of electrical engineering which emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current ...
, frequency compensation is a technique used in
amplifiers An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the magnitude of a signal (a time-varying voltage or current). It may increase the power significantly, or its main effect may be to boost the ...
, and especially in amplifiers employing negative feedback. It usually has two primary goals: To avoid the unintentional creation of
positive feedback Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in th ...
, which will cause the amplifier to
oscillate Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
, and to control overshoot and ringing in the amplifier's
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 out ...
. It is also used extensively to improve the
bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...
of single
pole Pole may refer to: Astronomy * Celestial pole, the projection of the planet Earth's axis of rotation onto the celestial sphere; also applies to the axis of rotation of other planets *Pole star, a visible star that is approximately aligned with th ...
systems.


Explanation

Most amplifiers use negative feedback to
trade Trade involves the transfer of goods and services from one person or entity to another, often in exchange for money. Economists refer to a system or network that allows trade as a market. An early form of trade, barter, saw the direct exch ...
gain for other desirable properties, such as decreased distortion, improved
noise Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference aris ...
reduction or increased invariance to variation of parameters such as temperature. Ideally, the
phase Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...
characteristic of an amplifier's
frequency response In signal processing and electronics, the frequency response of a system is the quantitative measure of the magnitude and phase of the output as a function of input frequency. The frequency response is widely used in the design and analysis of s ...
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 Pole may refer to: Astronomy * Celestial pole, the projection of the planet Earth's axis of rotation onto the celestial sphere; also applies to the axis of rotation of other planets *Pole star, a visible star that is approximately aligned with th ...
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 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 out ...
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 In electronics, when describing a voltage or current step function, rise time is the time taken by a signal to change from a specified low value to a specified high value. These values may be expressed as ratiosSee for example , and . or, equivalen ...
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 In control theory the settling time of a dynamical system such as 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 ...
(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 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 freq ...
.A


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. A 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 Open or OPEN may refer to: Music * Open (band), Australian pop/rock band * The Open (band), English indie rock band * ''Open'' (Blues Image album), 1969 * ''Open'' (Gotthard album), 1999 * ''Open'' (Cowboy Junkies album), 2001 * ''Open'' (YF ...
gain equals its closed loop gain if, at that frequency, :# The open loop gain of the amplifier is ≥ 1 and :# 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. It is an external compensation technique and is used for relatively low closed loop gain. A pole placed at an appropriate low frequency in the open-loop response reduces the gain of the amplifier to one (0 dB) 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 Phase or phases may refer to: Science *State of matter, or phase, one of the distinct forms in which matter can exist *Phase (matter), a region of space throughout which all physical properties are essentially uniform *Phase space, a mathematica ...
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 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 out ...
, which can be a more demanding requirement than the simple need for stability. This compensation method is described below: Let A be the uncompensated transfer function of op amp in open-loop configuration which is given by: where AOL=the Open loop gain of the Op-Amp w1, w2, w3= Frequencies at which gain rolls off by -20dB, -40dB and -60dB respectively. Thus, for compensation, introduce a dominant pole by adding an RC network in series with the Op-Amp as shown in the figure. The Transfer function of the compensated open loop Op-Amp circuit is given by: where fd < f1 < f2 < f3 The compensation capacitance C is chosen such that fd < f1. Hence, the frequency response of a dominant pole compensated open loop Op-Amp circuit shows uniform gain roll off from fd and becomes 0 at f1 as shown in the graph. The advantages of dominant pole compensation are: 1. It is simple and effective. 2. Noise immunity is improved since noise frequency components outside the bandwidth are eliminated. Though simple and effective, this kind of conservative dominant pole compensation has two drawbacks: # 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. # It reduces the amplifier's
slew rate In electronics, slew rate is defined as the change of voltage or current, or any other electrical quantity, per unit of time. Expressed in SI units, the unit of measurement is volts/second or amperes/second, but is usually expressed in terms of m ...
. 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. Often, the implementation of dominant-pole compensation results in the phenomenon of ''
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 freq ...
''. 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. To overcome these disadvantages, pole zero compensation is used.


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–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 or
Miller A miller is a person who operates a mill, a machine to grind a grain (for example corn or wheat) to make flour. Milling is among the oldest of human occupations. "Miller", "Milne" and other variants are common surnames, as are their equivalents ...
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.


Footnotes

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See also

*
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 freq ...
* Bode plot *
Negative feedback amplifier A negative-feedback amplifier (or feedback amplifier) is an electronic amplifier that subtracts a fraction of its output from its input, so that negative feedback opposes the original signal. The applied negative feedback can improve its perfor ...
*
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 out ...
Electronic design