Model coplanar waveguide transmission line

Transmission Lines sublibrary of the Physical library

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

$$\begin{array}{c}A=1\\ B={Z}_{in}\\ C=0\\ D=1\end{array}$$

**Conductor width (m)**Physical width of the conductor.

**Slot width (m)**Physical width of the slot.

**Substrate height (m)**Thickness of the dielectric on which the conductor resides.

**Strip thickness (m)**Physical thickness of the conductor.

**Relative permittivity constant**Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space

*ε*_{0}.**Conductivity of conductor (S/m)**Conductivity of the conductor in siemens per meter.

**Loss tangent of dielectric**Loss angle tangent of the dielectric.

**Transmission line length (m)**Physical length of the transmission line.

**Stub mode**Type of stub. Choices are

`Not a stub`

,`Shunt`

, or`Series`

.**Termination of stub**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.

[1] Gupta, K. C., Ramesh Garg, Inder Bahl,
and Prakash Bhartia, *Microstrip Lines and Slotlines*,
2nd Edition, Artech House, Inc., Norwood, MA, 1996.

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