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Model RLCG transmission line

Transmission Lines sublibrary of the Physical library

The RLCG Transmission Line block models the RLCG transmission line described in the block dialog box in terms of its frequency-dependent resistance, inductance, capacitance, and conductance. The transmission line, which can be lossy or lossless, is treated as a two-port linear network.

where *z*′ = *z* + Δ*z*.

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

If you model an RLCG transmission line as a stubless line, the
RLCG 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 resistance (*R*), inductance (*L*),
conductance (*G*), and capacitance (*C*)
per unit length (meters) as follows:

$$\begin{array}{c}{Z}_{0}=\sqrt{\frac{R+j\omega L}{G+j\omega C}}\\ k={k}_{r}+j{k}_{i}=\sqrt{(R+j\omega L)(G+j\omega C)}\end{array}$$

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

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

**Resistance per length (ohms/m)**Vector of resistance values in ohms per meter.

**Inductance per length (H/m)**Vector of inductance values in henries per meter.

**Capacitance per length (F/m)**Vector of capacitance values in farads per meter.

**Conductance per length (S/m)**Vector of conductance values in siemens per meter.

**Frequency (Hz)**Vector of frequency values at which the resistance, inductance, capacitance, and conductance values are known.

**Interpolation method**Specify the interpolation method the block uses to calculate the parameter values at the modeling frequencies. Your choices are

`Linear`

,`Spline`

, or`Cubic`

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

**Stub mode**Type of stub. Your 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] Pozar, David M. *Microwave Engineering*,
John Wiley & Sons, Inc., 2005.

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