# Transmission Line (Equivalent Baseband)

Model general transmission line

**Libraries:**

RF Blockset /
Equivalent Baseband /
Transmission Lines

## Description

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.

## Parameters

### Main

**Characteristic impedance (ohms)** — Characteristic Impedance of transmission
line

`50`

(default) | scalar | complex scalar

Characteristic impedance of the transmission line, specified as a scalar or complex scalar in ohms.

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

`299792458`

(default) | scalar

Propagation velocity of a uniform plane wave on the transmission line, specified as a scalar in meters per seconds.

**Loss (dB/m)** — Reduction in strength of signal

`0`

(default) | positive scalar

Reduction in strength of the signal as it travels over the transmission line, specified as a positive scalar in dB/m..

**Frequency (Hz)** — modeling frequencies

`1e9`

(default) | positive vector

Modeling frequencies, specified as a positive vector in Hz.

**Interpolation method** — Method to interpolate network parameters

`Linear`

(default) | `Spline`

| `Cubic`

Method to interpolate the network parameters, specified as one of the following:

Method | Description |
---|---|

`Linear` | Linear interpolation |

`Spline` | Cubic spline interpolation |

`Cubic` | Piecewise cubic Hermite interpolation |

**Transmission line length (m)** — Physical length of transmission line

`0.01`

(default) | positive scalar

Physical length of the transmission line, specified as a positive scalar in meters.

**Stub mode** — Type of stub

```
Not a
stub
```

(default) | `Shunt`

| `Series`

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

#### Stubless Transmission Line

`Not a stub`

—**Not a stub**If you model a coaxial transmission line as stubless line, the Coaxial 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. For more information, see Stub Mode - Not a Stub.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}*iβ*, where*α*is the attenuation coefficient and_{a}*β*is the wave number. The attenuation coefficient*α*is related to the specified loss,_{a}*α*, by$${\alpha}_{a}=-\mathrm{ln}\left({10}^{\alpha /20}\right)$$

The wave number

*β*is related to the specified phase velocity,*V*, by_{p}$$\beta =\frac{2\pi f}{{V}_{p}}$$

The phase velocity

*V*is also known as the_{P}*wave propagation velocity*.

#### Shunt Transmission Line

`Shunt`

—This parameter provides a two-port network that consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown in these diagrams.*Z*is the input impedance of the shunt circuit and it is calculated as follows:_{in}for a short circuited transmission line

$${\text{Z}}_{\text{in}}=j{Z}_{0}\mathrm{tan}\gamma l$$

and for the open circuited transmission line

$${\text{Z}}_{\text{in}}=-j{Z}_{0}\mathrm{cot}\gamma l$$

where

*Z*is the characteristic impedance and_{0}$$\gamma $$ is the propagation constant

The ABCD-parameters for the shunt stub are calculated as

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

#### Series Transmission Line

`Series`

—This mode parameter provides a two-port network that consists of a series transmission line that you can terminate with either a short circuit or an open circuit as show in these diagrams.*Z*is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as_{in}$$\begin{array}{c}A=1\\ B={Z}_{in}\\ C=0\\ D=1\end{array}$$

**Termination of stub** — Stub termination

`Open`

(default) | `Short`

Stub termination for stub modes
`Shunt`

and
`Series`

. Choices are
`Open`

or
`Short`

#### Dependencies

To enable this parameter, select
`Shunt`

or
`Series`

in
**Stub mode**

### Visualization

**Source of frequency data** — Frequency data source

`User-specified`

(default)

Frequency data source, specified as
`User-specified`

.

**Frequency data (Hz)** — Frequency data range

`[1e9:1.0e6:3e9]`

(default) | vector

Frequency data range, specified as a vector in hertz.

**Reference impedance (ohms)** — Reference impedance

`50`

(default) | nonnegative scalar

Reference impedance, specified as a nonnegative scalar in ohms.

**Plot type** — Type of data plot

`X-Y plane`

(default) | `Composite data`

| `Polar plane`

| `Z Smith chart`

| `Y Smith chart`

| `ZY Smith chart`

Type of data plot to visualize using the given data, specified as one of the following:

`X-Y plane`

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

— Plot the composite data. For more information, see Create Plots Using Equivalent Baseband Library Blocks.`Polar plane`

— Generate a polar plot of the 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.

**Y parameter1** — Type of parameters to plot

`S11`

(default) | `S12`

| `S21`

| `S22`

| `GroupDelay`

| `OIP3`

| `IIP3`

| `NF`

| ...

Type of parameters to plot, specified as one of the following.

`S11` | `S12` | `S21` | `S22` |

`GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` |

`VSWROut` | `OIP3` | `IIP3` | `NF` |

`NFactor` | `NTemp` | `TF1` | `TF2` |

`TF3` | `Gt` | `Ga` | `Gp` |

`Gmag` | `Gmsg` | `GammaMS` | `GammaML` |

`K` | `Delta` | `Mu` | `MuPrime` |

**Note**

**Y parameter1** is disabled when you select **Plot type** to `Composite data`

.

**Y parameter2** — Type of parameters to plot

`S11`

(default) | `S12`

| `S21`

| `S22`

| `GroupDelay`

| `OIP3`

| `IIP3`

| `NF`

| ...

Type of parameters to plot, specified as one of the following.

`S11` | `S12` | `S21` | `S22` |

`GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` |

`VSWROut` | `OIP3` | `IIP3` | `NF` |

`NFactor` | `NTemp` | `TF1` | `TF2` |

`TF3` | `Gt` | `Ga` | `Gp` |

`Gmag` | `Gmsg` | `GammaMS` | `GammaML` |

`K` | `Delta` | `Mu` | `MuPrime` |

**Note**

**Y parameter2** is disabled when you select **Plot type** to `Composite data`

.

**Y format1** — Plot format

`Magnitude (decibels)`

(default) | `Mag`

| `Magnitude (linear)`

| `Angle`

| `Real`

| `Imaginary`

| ...

Plot format, specified as one of the following.

Y parameter1 | Y format1 |
---|---|

`S11` , `S12` , `S21` , `S22` , `GammaIn` , `GammaOut` , `TF1` , `TF2` , `TF3` , `GammaMS` , `GammaML` , and `Delta` . | `dB` , `Magnitude (decibels)` , `Abs` , `Mag` , `Magnitude (linear)` , `Angle` , `Angle(degrees)` , `Angle(radians)` , `Real` , `Imag` , and `Imaginary` . |

`GroupDelay` | `ns` , `us` , `ms` , `s` , and `ps` . |

`VSWRIn` and `VSWROut` . | `Magnitude (decibels)` and `None` . |

`OIP3` and `IIP3` . | `dBm` , `W` , and `mW` . |

`NF` | `dB` and `Magnitude (decibels)` . |

`NFactor` , `K` , `Mu` , and `MuPrime` . | `None` |

`NTemp` | `Kelvin` |

`Gt` , `Ga` , `Gp` , `Gmag` , and `Gmsg` . | `dB` , `Magnitude (decibels)` , and `None` . |

#### Dependencies

To enable **Y format1**, set **Plot type** to `X-Y plane`

.

**Y format2** — Plot format

`Magnitude (decibels)`

(default) | `Mag`

| `Magnitude (linear)`

| `Angle`

| `Real`

| `Imaginary`

| ...

Plot format, specified as one of the following.

Y parameter2 | Y format2 |
---|---|

`S11` , `S12` , `S21` , `S22` , `GammaIn` , `GammaOut` , `TF1` , `TF2` , `TF3` , `GammaMS` , `GammaML` , and `Delta` . | `dB` , `Magnitude (decibels)` , `Abs` , `Mag` , `Magnitude (linear)` , `Angle` , `Angle(degrees)` , `Angle(radians)` , `Real` , `Imag` , and `Imaginary` . |

`GroupDelay` | `ns` , `us` , `ms` , `s` , and `ps` . |

`VSWRIn` and `VSWROut` . | `Magnitude (decibels)` and `None` . |

`OIP3` and `IIP3` . | `dBm` , `W` , and `mW` . |

`NF` | `dB` and `Magnitude (decibels)` . |

`NFactor` , `K` , `Mu` , and `MuPrime` . | `None` |

`NTemp` | `Kelvin` |

`Gt` , `Ga` , `Gp` , `Gmag` , and `Gmsg` . | `dB` , `Magnitude (decibels)` , and `None` . |

#### Dependencies

To enable **Y format2**, set **Plot type** to `X-Y plane`

.

**X parameter** — Frequency plot

`Freq`

(default)

Frequency plot, specified as `Freq`

.

**X format** — Frequency plot format

`Hz`

(default) | `Auto`

| `kHz`

| `MHz`

| `GHz`

| `THz`

Frequency plot format, specified as one of the following.

`Auto` | `Hz` | `kHz` | `MHz` |

`GHz` | `THz` |

**Y scale** — Y-axis scale

`Linear`

(default) | `Log`

Y-axis scale, specified as `Linear`

or `Log`

.

#### Dependencies

To enable this parameter, set **Plot type** to ```
X-Y
plane
```

.

**X scale** — X-axis scale

`Linear`

(default) | `Log`

X-axis scale, specified as `Linear`

or `Log`

.

#### Dependencies

To enable this parameter, set **Plot type** to ```
X-Y
plane
```

.

**Plot** — Plot specified data

button

Plot the specified data using the plot button.

## References

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

## Version History

**Introduced before R2006a**

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