RF Blockset™

Two-Wire Transmission Line - Model two-wire transmission line

Library

Transmission Lines sublibrary of the Physical library

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 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.

Stubless Transmission 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:

Z₀ 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

In these equations, is the conductivity in the conductor and is the conductivity in the dielectric. is the permeability of the dielectric, is its permittivity, and skin depth is calculated as . f is the vector of modeling frequencies for the specified parameters. See the Output Port block reference page for information about determining the modeling frequencies.

The Two-Wire Transmission Line block normalizes the resulting S-parameters to a reference impedance of 50 ohms.

Shunt and Series Stubs

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.

Shunt ABCD-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

Series ABCD-Parameters

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

Dialog Box

Main Tab

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 .
Relative permittivity constant: Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space .
Conductivity in conductor (S/m): Conductivity of the conductor in siemens per meter.
Conductivity in dielectric (S/m): Conductivity of the dielectric 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.

Visualization Tab

For information about plotting the transmission line parameters, see Plotting Model Data.

References

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