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Model microstrip transmission line

Transmission Lines sublibrary of the Physical library

The Microstrip Transmission Line block models the microstrip
transmission line described in the block dialog in terms of its frequency-dependent
S-parameters. A microstrip transmission line is shown in cross-section
in the following figure. Its physical characteristics include the
microstrip width (*w*), the microstrip thickness
(*t*), 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 microstrip transmission line as a stubless line,
the Microstrip 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, substrate height, conductor strip
thickness, relative permittivity constant, conductivity, and dielectric
loss tangent of the microstrip line, as described in [1].

If you model the transmission line as a shunt or series stub,
the Microstrip 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

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

**Strip width (m)**Width of the microstrip transmission line.

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

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

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

**Conductivity in conductor (S/m)**Conductivity of the conductor in siemens per meter.

**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., G. Ramesh, I. Bahl, and P.
Bhartia, *Microstrip Lines and Slotlines*, Second
Edition, Artech House, 1996. pp. 102-109.

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