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A pole-zero plot shows the location in the complex plane of the poles and zeros of the transfer function of a dynamic system, such as a controller, compensator, sensor, equalizer, filter, or communications channel. By convention, the poles of the system are indicated in the plot by an X while the zeros are indicated by a circle or O.
In this case a point that is neither a pole nor a zero is viewed as a pole (or zero) of order 0. A meromorphic function may have infinitely many zeros and poles. This is the case for the gamma function (see the image in the infobox), which is meromorphic in the whole complex plane, and has a simple pole at every non-positive integer.
The transfer function of a two-port electronic circuit, such as an amplifier, might be a two-dimensional graph of the scalar voltage at the output as a function of the scalar voltage applied to the input; the transfer function of an electromechanical actuator might be the mechanical displacement of the movable arm as a function of electric ...
The s-plane poles and zeros of a 5th-order Chebyshev type II lowpass filter to be approximated as a discrete-time filter The z-plane poles and zeros of the discrete-time Chebyshev filter, as mapped into the z-plane using the matched Z-transform method with T = 1/10 second.
The zero-value time (ZVT) constant method itself is a special case of the general Time- and Transfer Constant (TTC) analysis that allows full evaluation of the zeros and poles of any lumped LTI systems of with both inductors and capacitors as reactive elements using time constants and transfer constants. The OCT method provides a quick ...
A strictly proper transfer function is a transfer function where the degree of the numerator is less than the degree of the denominator. The difference between the degree of the denominator (number of poles) and degree of the numerator (number of zeros) is the relative degree of the transfer function.
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 .
A few procedures can be followed for realizing passive two-ports with transmission zeroes. As long as transmission zeros are located at the origin or infinity, all that is needed is the application of Cauer 1 or 2 steps [clarification needed] to remove poles [clarification needed] from either the admittance or the impedance at the origin or infinity.