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A Z-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.
Conversion from Z-parameters to Y-parameters is much simpler, as the Y-parameter matrix is just the inverse of the Z-parameter matrix. The following expressions show ...
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 reverse conversion is harder: given X-Y-Z can immediately get longitude, but no closed formula for latitude and height exists. See "Geodetic system." Using Bowring's formula in 1976 Survey Review the first iteration gives latitude correct within 10-11 degree as long as the point is within 10,000 meters above or 5,000 meters below the ellipsoid.
Although the cascaded T-parameters is a simple matrix multiplication of the individual T-parameters, the conversion for each network's S-parameters to the corresponding T-parameters and the conversion of the cascaded T-parameters back to the equivalent cascaded S-parameters, which are usually required, is not trivial.
Convert from geodetic coordinates to geocentric coordinates: Calculation of x, y and z relative to the reference ellipsoid of surveying 7-parameter transformation (where x , y and z almost always change by a few hundred metres at most, and distances by a few mm per km).
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.
Points with suffix P are in the Z plane and points with suffix Q are in the Y plane. 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 ...