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Model general transmission line

Transmission Lines sublibrary of the Physical library

The Transmission Line block models the transmission line described in the block dialog box in terms of its physical parameters. The transmission line, which can be lossy or lossless, is treated as a two-port linear network.

The block enables you to model the transmission line as a stub or as a stubless line.

If you model the transmission line as a stubless line, the 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} is the specified
characteristic impedance. *k* is a vector whose elements
correspond to the elements of the input vector `freq`

.
The block calculates *k* from the specified parameters
as *k* = *α _{a}* +

$${\alpha}_{a}=-\mathrm{ln}\left({10}^{\alpha /20}\right)$$

The wave number *β* is related to the
specified phase velocity, *V _{p}*,
by

$$\beta =\frac{2\pi f}{{V}_{p}}$$

The phase velocity *V _{P}* is
also known as the

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

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

**Characteristic impedance (ohms)**Characteristic impedance of the transmission line. The value can be complex.

**Phase velocity (m/s)**Propagation velocity of a uniform plane wave on the transmission line.

**Loss (dB/m)**Reduction in strength of the signal as it travels over the transmission line. Must be positive.

**Frequency (Hz)**Vector of modeling frequencies. The block performs the calculations listed in the Description section at each frequency you provide.

**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] Ludwig, Reinhold and Pavel Bretchko, *RF
Circuit Design: Theory and Applications*, Prentice-Hall,
2000.

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