# Documentation

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# Transmission Line

Model transmission line

Elements

## Description

Use the Transmission Line block to model delayed-based, lumped, and distributed transmission lines. Mask dialog options will change automatically to accommodate model type selection.

## Parameters

### Main Tab

Model type
Ground and hide negative terminals

Select this check box to internally ground and hide the negative terminals. Clear the check box to expose the negative terminals. By exposing these terminals, you can connect them to other parts of your model.

By default, this check box is selected.

#### Parameter Calculations for Distributed Transmission Line

When modeling distributed transmission lines, the block first calculates ABCD-parameters at a set of internal frequencies. The ABCD-parameters are converted S-parameters for simulation.

The block calculates the ABCD-parameters from the physical length of the transmission line, d, and the complex propagation constant, k, using the following set of equations:

`$\begin{array}{l}A=\frac{{e}^{kd}+{e}^{-kd}}{2}\\ B=\frac{{Z}_{0}*\left({e}^{kd}-{e}^{-kd}\right)}{2}\\ C=\frac{{e}^{kd}-{e}^{-kd}}{2*{Z}_{0}}\\ D=\frac{{e}^{kd}+{e}^{-kd}}{2}\end{array}$`

#### Transmission Line with Stub

When you set the Stub mode parameter in the mask dialog box to `Shunt`, the two-port network consists of a transmission line in series with a stub. You can terminate the stub with a short circuit or an open circuit as shown in the following figure.

Zin 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 comprises a series transmission line. You can terminate this line with either a short circuit or an open circuit as shown here.

Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are:

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

### Modeling Tab

Modeling options tab is activated for all transmission line options except `Delay-based and lossless`, ```Delay-based and lossy```, `Lumped parameter L-section`, and `Lumped parameter pi-section`.

Modeling options

SimRF provides two different ways to model S-parameters:

• Time-domain (rationalfit) technique creates an analytical rational model that approximates the whole range of the data.

• Frequency-domain computes the baseband impulse response for each carrier frequency independently. This technique is based on convolution. There is an option to specify the duration of the impulse response. For more information, see Compare Time and Frequency Domain Simulation Options for S-parameters.

• For the Amplifier and S-parameters blocks, the default value is `Time domain (rationalfit)`. For the Transmission Line block, the default value is `Frequency domain`.

`Time domain`

• Fitting options

The fitting options are `Share all poles`, ```Share poles by columns```, or `Fit individually`.

For the Amplifier block, the default value is ```Fit individually```. For the S-parameters block and Transmission Line block, the default value is ```Share all poles```.

• Relative error desired (dB)

Enter the desired relative error in decibels (dB). The default value is `-40`.

• Rational fitting results

Shows values of Number of independent fits, Number of required poles, and Relative error achieved (dB).

• When modeling using `Time domain`, the Plot in `Visualization` tab plots the data defined in `Data Source` and the values in the `rationalfit` function.

`Frequency domain`
• Automatically estimate impulse response duration

Select Automatically estimate impulse response duration to calculate impulse response duration automatically. Clear the selection to specify impulse response duration.

• When using `Frequency domain`, the Plot in `Visualization` tab plots the data defined in the `Data Source`.

### Visualization Tab

Source of frequency data

The only option for Source of frequency data is `User-specified`. To plot, specify a vector of frequencies in the Frequency data parameter and select units.

Plot type

Specify the type of plot that you want to produce with your data. When you model using `Frequency domain`, Visualization tab plots only the data defined in `Data Source`. When you model using `Time domain`, Visualization tab plots the data defined in `Data Source` and the `rationalfit` values. The Plot type parameter provides the following options:

• `X-Y plane` — Generate a Cartesian plot of your data versus frequency. To create linear, semilog, or log-log plots, set the Y-axis scale and X-axis scale accordingly.

• `Polar plane` — Generate a polar plot of your data. The block plots only the range of data corresponding to the specified frequencies.

• `Z smith chart`, ```Y smith chart```, and `ZY smith chart` — Generate a Smith® chart. The block plots only the range of data corresponding to the specified frequencies.

The default value is `X-Y plane`.

Parameter #

Specify the S-parameters to plot. From the Parameter1 and Parameter2 drop-down lists, select the S-parameters that you want to plot. If you specify two parameters, the block plots both parameters in a single window.

The default value for Parameter1 is `S11`. For the Transmission Line block, the default value for Parameter2 is `S22`.

Format #

For X-Y plots, format the units of the parameters to plot from the Format1 and Format2 drop-down lists. For polar plots and Smith charts, the formats are set automatically.

The default value is `Magnitude (decibels)`.

Y-axis scale

Scale for the Y-axis.

The default value is `Linear`.

X-axis scale

Scale for the X-axis.

The default value is `Linear`.

## Tip

In general, blocks that model delay effects rely on signal history. You can minimize numerical error that occur due to a lack of signal history at the start of a simulation. To do so, in the Configuration Parameters dialog box Solver pane you can specify an Initial step size. For models with delay-based Transmission Line blocks, use an initial step size that is less than the value of the Delay parameter.

## Examples

The example, Transmission Lines, Delay-based and Lumped Models, shows how to use `Delay-based` and `Lumped` Transmission Line blocks.

## References

[1] Sussman-Fort, S. E., and J. C. Hantgan. "SPICE Implementation of Lossy Transmission Line and Schottky Diode Models." IEEE Transactions on Microwave Theory and Techniques.Vol. 36, No.1, January 1988.

[2] Pozar, David M. Microwave Engineering. Hoboken, NJ: John Wiley & Sons, Inc., 2005.

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

[4] Ludwig, Reinhold and Pavel Bretchko. RF Circuit Design: Theory and Applications. Englewood Cliffs: NJ: Prentice-Hall, 2000.

[5] True, Kenneth M. "Data Transmission Lines and Their Characteristics." National Semiconductor Application Note 806, April 1992.