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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.
The characteristic impedance () of an infinite transmission line at a given angular frequency is the ratio of the voltage and current of a pure sinusoidal wave of the same frequency travelling along the line.
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.
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 ...
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 .
The parameter y o is termed the index function and z o is the normalised characteristic impedance of the network. The parameter y o is approximately 1 in the attenuation region; z o is approximately 1 in the transmission region. [4]: 383