page_title: Frequency compensation
section_title: Dominant-pole compensation
hierarchical_section_title: Frequency compensation / Use in operational amplifiers / Dominant-pole compensation
caption_attribution_description: English: This is the diagram of a dominant pole compensated open loop Op-Amp.
context_page_description: In electronics 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. It is also used extensively to improve the bandwidth of single pole systems.
context_section_description: 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 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.
  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.  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. 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.
caption: Diagram of a dominant pole compensated open loop Op-Amp
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