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where Z is an N × N matrix the elements of which can be indexed using conventional matrix notation. In general the elements of the Z-parameter matrix are complex numbers and functions of frequency. For a one-port network, the Z-matrix reduces to a single element, being the ordinary impedance measured between the two terminals. The Z-parameters ...
The input impedance of an infinite line is equal to the characteristic impedance since the transmitted wave is never reflected back from the end. Equivalently: The characteristic impedance of a line is that impedance which, when terminating an arbitrary length of line at its output, produces an input impedance of equal value. This is so because ...
where z = Z / Z 0 , i.e., the complex impedance, Z, normalized by the reference impedance, Z 0. The impedance Smith chart is then an Argand plot of impedances thus transformed. Impedances with non-negative resistive components will appear inside a circle with unit radius; the origin will correspond to the reference impedance, Z 0.
In electrical engineering, impedance is the opposition to alternating current presented by the combined effect of resistance and reactance in a circuit. [1]Quantitatively, the impedance of a two-terminal circuit element is the ratio of the complex representation of the sinusoidal voltage between its terminals, to the complex representation of the current flowing through it. [2]
The characteristic impedance or surge impedance (usually written Z 0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in the absence of reflections in the other direction. Alternatively and equivalently it can be defined ...
L networks for narrowband matching a source or load impedance Z to a transmission line with characteristic impedance Z 0. X and B may each be either positive (inductor) or negative (capacitor). If Z/Z 0 is inside the 1+jx circle on the Smith chart (i.e. if Re(Z/Z 0)>1), network (a) can be used; otherwise network (b) can be used. [2]
It is desired that the matrix [Z] represent an impedance, Z(s). For this purpose, the loop of one of the meshes is cut and Z ( s ) is the impedance measured between the points so cut. It is conventional to assume the external connection port is in mesh 1, and is therefore connected across matrix entry Z 11 , although it would be perfectly ...
Z Matrix or bus impedance matrix in computing is an important tool in power system analysis. Though, it is not frequently used in power flow study , unlike Ybus matrix , it is, however, an important tool in other power system studies like short circuit analysis or fault study .