# Two-Wire Transmission Line

Model two-wire transmission line

**Libraries:**

RF Blockset /
Equivalent Baseband /
Transmission Lines

## Description

The Two-Wire Transmission Line block models the two-wire transmission line described
in the block dialog box in terms of its frequency-dependent S-parameters. A two-wire
transmission line is shown in cross-section in the following figure. Its physical
characteristics include the radius of the wires *a*, the separation
or physical distance between the wire centers *S*, and the relative
permittivity and permeability of the wires. RF Blockset™ Equivalent Baseband software assumes the relative permittivity and
permeability are uniform.

## Parameters

### Main

**Wire radius (m)** — Radius of conducting wires

`0.67e-3`

(default) | scalar

Radius of the conducting wires of the two-wire transmission line, specified as a scalar in meters.

**Wire separation (m)** — Separation in two-wire transmission line

`1.62e-3`

(default) | scalar

Physical distance between the wires, specified as a scalar in meters.

**Relative permeability constant** — Relative permeability of dielectric

`1`

(default) | scalar

Relative permeability of the dielectric, expressed as the ratio of the
permeability of the dielectric to permeability in free space
*μ*_{0}, specified as a scalar.

**Relative permittivity constant** — Relative permittivity of dielectric

`2.3`

(default) | scalar

Relative permittivity of the dielectric, expressed as the ratio of the
permittivity of the dielectric to permittivity in free space
*ε*_{0}, specified as a scalar.

**Loss tangent of dielectric** — Dielectric loss tangent

`0`

(default) | scalar

Loss tangent of the dielectric, specified as a scalar.

**Conductivity of the conductor (S/m)** — Conductivity of conductor

`inf`

(default) | scalar

Conductivity of the conductor, specified as a scalar in siemens per meter. Conductivity measures the ease with which current flows in the conductor.

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

`0.01`

(default) | scalar

Physical length of the transmission line, specified as a 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.

#### 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. The ABCD-parameters for the shunt stub are calculated as_{in}$$\begin{array}{c}A=1\\ B=0\\ C=1/{Z}_{in}\\ D=1\end{array}$$

#### 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

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

(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.

## More About

### Stub Mode- Not a stub

This block calculates the ABCD-parameters using the physical length of the
transmission line, *d*, and the complex propagation constant
*k* using the 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, determined by the Output Port block. Both can be
expressed in terms of the resistance (*R*), inductance
(*L*), conductance (*G*), and capacitance
(*C*) per unit length (meters)

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

where

$$\begin{array}{l}R=\frac{1}{2\pi {\sigma}_{cond}{\delta}_{cond}}\left(\frac{1}{a}+\frac{1}{b}\right)\\ L=\frac{\mu}{2\pi}\mathrm{ln}\left(\frac{b}{a}\right)\\ G=\frac{2\pi \omega {\epsilon}^{\u2033}}{\mathrm{ln}\left(\frac{b}{a}\right)}\\ C=\frac{2\pi {\epsilon}^{\prime}}{\mathrm{ln}\left(\frac{b}{a}\right)}\end{array}$$

In these equations:

*a*is the radius of the inner conductor.*b*is the radius of the outer conductor.*σ*is the conductivity of the conductor._{cond}*μ*is the permeability of the dielectric.*μ*=*μ*_{0}*μ*, where:_{r}*μ*_{0}is the permeability in free space.*μ*is the_{r}**Relative permeability constant**

The is a complex dielectric constant given by

*ε = ε′ − јε″= ε′ (1 − јtanδ)**ε′*is the real part of complex dielectric constant*ε*,*ε′*=*ε*_{0}*ε*._{r}*ε″*is the imaginary part of complex dielectric constant*ε*,*ε″*=*ε*_{0}*ε*tan_{r}*δ*where :*ε*_{0}is the permittivity of free space.*ε*is the_{r}**Relative permittivity constant**parameter value.tan

*δ*is the**Loss tangent of dielectric**parameter value.

*δ*is the skin depth of the conductor, which the block calculates as $$1/\sqrt{\pi f\mu {\sigma}_{cond}}$$._{cond}

## References

[1] Pozar, David M. *Microwave Engineering*. Hobken, NJ, John Wiley & Sons,
Inc., 2005.

## Version History

**Introduced in R2009a**

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