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The closed-loop transfer function is measured at the output. The output signal can be calculated from the closed-loop transfer function and the input signal. Signals may be waveforms, images, or other types of data streams. An example of a closed-loop block diagram, from which a transfer function may be computed, is shown below:
The loop gain is calculated by imagining the feedback loop is broken at some point, and calculating the net gain if a signal is applied. In the diagram shown, the loop gain is the product of the gains of the amplifier and the feedback network, −Aβ. The minus sign is because the feedback signal is subtracted from the input.
System in open-loop. If the closed-loop dynamics can be represented by the state space equation (see State space (controls)) _ ˙ = _ + _, with output equation _ = _ + _, then the poles of the system transfer function are the roots of the characteristic equation given by
that is, the sum of the angles from the open-loop zeros to the point (measured per zero w.r.t. a horizontal running through that zero) minus the angles from the open-loop poles to the point (measured per pole w.r.t. a horizontal running through that pole) has to be equal to , or 180 degrees.
The open-loop gain is a physical attribute of an operational amplifier that is often finite in comparison to the ideal gain. While open-loop gain is the gain when there is no feedback in a circuit, an operational amplifier will often be configured to use a feedback configuration such that its gain will be controlled by the feedback circuit components.
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, 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 ...
Without feedback the so-called open-loop gain in this example has a single-time-constant frequency response given by = + /, where f C is the cutoff or corner frequency of the amplifier: in this example f C = 10 4 Hz, and the gain at zero frequency A 0 = 10 5 V/V. The figure shows that the gain is flat out to the corner frequency and then drops.
Finite gain Open-loop gain is finite in real operational amplifiers. Typical devices exhibit open-loop DC gain exceeding 100,000. So long as the loop gain (i.e., the product of open-loop and feedback gains) is very large, the closed-loop gain will be determined entirely by the amount of negative feedback (i.e., it will be independent of open ...