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Model two-wire transmission line

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. SimRF™ Equivalent
Baseband software assumes the relative permittivity and permeability
are uniform.

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

If you model a two-wire transmission line as a stubless line,
the Two-Wire 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:

*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:

where

and .

In these equations:

*σ*is the conductivity in the conductor._{cond}*μ*is the permeability of the dielectric.*ε*is the permittivity of the dielectric.*ε″*is the imaginary part of*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 ._{cond}*f*is a vector of modeling frequencies determined by the Output Port block.

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

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

**Wire radius (m)**Radius of the conducting wires of the two-wire transmission line.

**Wire separation (m)**Physical distance between the wires.

**Relative permeability constant**Relative permeability of the dielectric expressed as the ratio of the permeability of the dielectric to permeability in free space

*μ*_{0}.**Relative permittivity constant**Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space

*ε*_{0}.**Loss tangent of dielectric**Loss angle tangent of the dielectric.

**Conductivity of conductor (S/m)**Conductivity of the conductor in siemens per meter.

**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.

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