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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:
In signal processing and control theory the bandwidth is the frequency at which the closed-loop system gain drops 3 dB below peak. In communication systems, in calculations of the Shannon–Hartley channel capacity , bandwidth refers to the 3 dB-bandwidth.
This closed-loop gain is of the same form as the open-loop gain: a one-pole filter. Its step response is of the same form: an exponential decay toward the new equilibrium value. But the time constant of the closed-loop step function is τ / (1 + β A 0), so it is faster than the forward amplifier's response by a factor of 1 + β A 0:
For transistors, the current-gain–bandwidth product is known as the f T or transition frequency. [4] [5] It is calculated from the low-frequency (a few kilohertz) current gain under specified test conditions, and the cutoff frequency at which the current gain drops by 3 decibels (70% amplitude); the product of these two values can be thought of as the frequency at which the current gain ...
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.
Paul Voigt patented a negative feedback amplifier in January 1924, though his theory lacked detail. [4] Harold Stephen Black independently invented the negative-feedback amplifier while he was a passenger on the Lackawanna Ferry (from Hoboken Terminal to Manhattan) on his way to work at Bell Laboratories (located in Manhattan instead of New Jersey in 1927) on August 2, 1927 [5] (US Patent ...
For an integrating process, a general transfer function is = (+), which, when combined with the closed-loop transfer function, becomes = (+) +.. Introducing a step change to the system gives the output response of () =.
The root locus plots the poles of the closed loop transfer function in the complex s-plane as a function of a gain parameter (see pole–zero plot). Evans also invented in 1948 an analog computer to compute root loci, called a "Spirule" (after "spiral" and " slide rule "); it found wide use before the advent of digital computers .