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Model coplanar waveguide transmission line
The Coplanar Waveguide Transmission Line block models the coplanar waveguide transmission line described in the block dialog box in terms of its frequency-dependent S-parameters. A coplanar waveguide transmission line is shown in cross-section in the following figure. Its physical characteristics include the conductor width (w), the conductor thickness (t), the slot width (s), the substrate height (d), and the relative permittivity constant (ε).
The block lets you model the transmission line as a stub or as a stubless line.
If you model a coplanar waveguide transmission line as a stubless line, the Coplanar Waveguide Transmission Line block first calculates the ABCD-parameters at each frequency contained in the modeling frequencies vector. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters.
The block calculates the ABCD-parameters using the physical length of the transmission line, d, and the complex propagation constant, k, using the following equations:
$$\begin{array}{l}A=\frac{{e}^{kd}+{e}^{-kd}}{2}\\ B=\frac{{Z}_{0}*\left({e}^{kd}-{e}^{-kd}\right)}{2}\\ C=\frac{{e}^{kd}-{e}^{-kd}}{2*{Z}_{0}}\\ D=\frac{{e}^{kd}+{e}^{-kd}}{2}\end{array}$$
Z_{0} and k are vectors whose elements correspond to the elements of f, a vector of modeling frequencies. Both can be expressed in terms of the specified conductor strip width, slot width, substrate height, conductor strip thickness, relative permittivity constant, conductivity and dielectric loss tangent of the transmission line, as described in [1].
If you model the transmission line as a shunt or series stub, the Coplanar Waveguide Transmission Line block first calculates the ABCD-parameters at each frequency contained in the vector of modeling frequencies. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters.
When you set the Stub mode parameter in the mask dialog box to Shunt, the two-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown here.
Z_{in} is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as
$$\begin{array}{c}A=1\\ B=0\\ C=1/{Z}_{in}\\ D=1\end{array}$$
When you set the Stub mode parameter in the mask dialog box to Series, the two-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit as shown here.
Z_{in} is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as
$$\begin{array}{c}A=1\\ B={Z}_{in}\\ C=0\\ D=1\end{array}$$
Physical width of the conductor.
Physical width of the slot.
Thickness of the dielectric on which the conductor resides.
Physical thickness of the conductor.
Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space ε_{0}.
Conductivity of the conductor in siemens per meter.
Loss angle tangent of the dielectric.
Physical length of the transmission line.
Type of stub. Choices are Not a stub, Shunt, or Series.
Stub termination for stub modes Shunt and Series. Choices are Open or Short. This parameter becomes visible only when Stub mode is set to Shunt or Series.
For information about plotting, see Create Plots.