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The equivalent circuit for Z-parameters of a two-port network. The equivalent circuit for Z-parameters of a reciprocal two-port network. The Z-parameter matrix for the two-port network is probably the most common. In this case the relationship between the port currents, port voltages and the Z-parameter matrix is given by:
Therefore, transformations P 1 to Q 1 and P 3 to Q 3 are from the Z Smith chart to the Y Smith chart and transformation Q 2 to P 2 is from the Y Smith chart to the Z Smith chart. The following table shows the steps taken to work through the remaining components and transformations, returning eventually back to the centre of the Smith chart and ...
A Y-parameter matrix describes the behaviour of any linear electrical network that can be regarded as a black box with a number of ports.A port in this context is a pair of electrical terminals carrying equal and opposite currents into and out of the network, and having a particular voltage between them.
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...
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 wave travelling in one direction along the line in the absence of reflections in the other direction.
Figure 1: Example two-port network with symbol definitions. Notice the port condition is satisfied: the same current flows into each port as leaves that port.. In electronics, a two-port network (a kind of four-terminal network or quadripole) is an electrical network (i.e. a circuit) or device with two pairs of terminals to connect to external circuits.
This is a table of orthonormalized spherical harmonics that employ the Condon-Shortley phase up to degree =. Some of these formulas are expressed in terms of the Cartesian expansion of the spherical harmonics into polynomials in x , y , z , and r .
Z i 2 is facing Z i 2 to provide matching impedances Showing how a 'Π' section is made from two cascaded 'L' half-sections. Z i 1 is facing Z i 1 to provide matching impedances. As an example, the derivation of the image impedances of a simple 'L' network is given below. The 'L' network consists of a series impedance, Z, and a shunt admittance, Y.