rfckt.twowire

Two-wire transmission line

Description

Use the rfckt.twowire object to create two-wire transmission lines that are characterized by line dimensions, stub type, and termination.

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 Toolbox™ software assumes the relative permittivity and permeability are uniform.

two-wire transmission line

Note

txlineTwoWire is recommended over rfckt.twowire because it enables you to:

Create a two-wire transmission line.
Build a circuit object with a two-wire transmission line.
Model a two-wire transmission line element in an RF chain created using an rfbudget object or the RF Budget Analyzer app, and then export this element to RF Blockset™ or to rfsystem System object™ for circuit envelope analysis.

(since R2023b)

Creation

Syntax

h = rfckt.twowire

h = rfckt.twowire(Name,Value)

Description

h = rfckt.twowire returns a shunt RLC network object whose properties all have their default values. The default object is equivalent to a pass-through 2-port network; i.e., the resistor, inductor, and capacitor are each replaced by a short circuit.

example

h = rfckt.twowire(Name,Value) sets properties using one or more name-value pairs. For example, rfckt.twowire('Radius',7.5e-4) creates a two-wire transmission line with conducting wire radius of 7.5e^-4 meters. You can specify multiple name-value pairs. Enclose each property name in a quote. Properties not specified retain their default values.

Properties

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`AnalyzedResult` — Computed S-parameters, noise figure, OIP3, and group delay values
`rfdata.data` object

Computed S-parameters, noise figure, OIP3, and group delay values, specified as a rfdata.data object. This is a read-only property. For more information refer, Algorithms.

Data Types: function_handle

`Separation` — Distance between two wire centers
scalar

The separation or physical distance between the wire centers, specified as a scalar in meters. The default value is 0.0016.

Data Types: double

`EpsilonR` — Relative permittivity of dielectric
scalar

Relative permittivity of dielectric, specified as a scalar. The relative permittivity is the ratio of permittivity of the dielectric, $ε$ , to the permittivity in free space, $ε_{0}$ . The default value is 2.3.

Data Types: double

`LineLength` — Physical length of transmission line
scalar

Physical length of transmission line, specified as a scalar in meters. The default value is 0.01.

Data Types: double

`LossTangent` — Tangent of loss angle of dielectric
scalar

Tangent of loss angle of dielectric, specified as a scalar. The default value is 0.

Data Types: double

`MUR` — Relative permeability of dielectric
scalar

Relative permeability of dielectric, specified as a scalar. The ratio of permeability of dielectric, $μ$ , to the permeability in free space,

$μ_{0}$

. The default value is 1.

Data Types: double

`Name` — Object name
`'Two-Wire Transmission Line'` (default) | `1-by-N` character array

Object name, specified as a 1-by-N character array. This is a read-only property.

Data Types: char

`nport` — Number of ports
positive integer

Number of ports, specified as a positive integer. This is a read-only property. The default value is 2.

Data Types: double

`Radius` — Conducting wire radius
scalar

Conducting wire radius, specified as a scalar in meters. The default value is 6.7e-4.

Data Types: double

`SigmaCond` — Conductor conductivity
scalar in Siemens per meter

Conductor conductivity, specified as a scalar in Siemens per meter (S/m). The default value is Inf.

Data Types: double

`StubMode` — Type of stub
`'NotaStub'` (default) | `'Series'` | `'Shunt'`

Type of stub, specified as a one of the following values: 'NotaStub', 'Series', 'Shunt'.

Data Types: double

`Termination` — Stub transmission line termination
`'NotApplicable'` (default) | `'Open'` | `'Short'`

Stub transmission line termination, specified as one of the following values: 'NotApplicable', 'Open', 'Short'.

Data Types: double

Object Functions

`analyze`	Analyze RFCKT object in frequency domain
`calculate`	Calculate specified parameters for rfckt objects or rfdata objects
`circle`	Draw circles on Smith Chart
`extract`	Extract specified network parameters from rfckt object or data object
`listformat`	List valid formats for specified circuit object parameter
`listparam`	List valid parameters for specified circuit object
`loglog`	Plot specified circuit object parameters using log-log scale
`plot`	Plot circuit object parameters on X-Y plane
`plotyy`	Plot parameters of RF circuit or RF data on xy-plane with two Y-axes
`getop`	Display operating conditions
`polar`	Plot specified object parameters on polar coordinates
`semilogx`	Plot RF circuit object parameters using log scale for x-axis
`semilogy`	Plot RF circuit object parameters using log scale for y-axis
`smith`	Plot circuit object parameters on Smith Chart
`write`	Write RF data from circuit or data object to file
`getz0`	Calculate characteristic impedance of RFCKT transmission line object
`read`	Read RF data from file to new or existing circuit or data object
`restore`	Restore data to original frequencies
`getop`	Display operating conditions
`groupdelay`	Group delay of S-parameter object or RF filter object or RF Toolbox circuit object

Examples

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Two-Wire Transmission Line

Open Live Script

Create a two-wire transmission line object using rfckt.twowire.

tx1=rfckt.twowire('Radius',7.5e-4)

tx1 = 
   rfckt.twowire with properties:

            Radius: 7.5000e-04
        Separation: 0.0016
               MuR: 1
          EpsilonR: 2.3000
       LossTangent: 0
         SigmaCond: Inf
        LineLength: 0.0100
          StubMode: 'NotAStub'
       Termination: 'NotApplicable'
             nPort: 2
    AnalyzedResult: []
              Name: 'Two-Wire Transmission Line'

Algorithms

If you model the transmission line as a stubless line, the analyze method 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 analyze method calculates the ABCD-parameters using the physical length of the transmission line, d, and the complex propagation constant, k, using the following equations:

$\begin{array}{l} A = \frac{e^{k d} + e^{- k d}}{2} \\ B = \frac{Z_{0} * (e^{k d} - e^{- k d})}{2} \\ C = \frac{e^{k d} - e^{- k d}}{2 * Z_{0}} \\ D = \frac{e^{k d} + e^{- k d}}{2} \end{array}$
Z₀ and k are vectors whose elements correspond to the elements of f, the vector of frequencies specified in the analyze input argument freq. Both can be expressed in terms of the resistance (R), inductance (L), conductance (G), and capacitance (C) per unit length (meters) as follows:
$\begin{matrix} Z_{0} = \sqrt{\frac{R + j 2 π f L}{G + j 2 π f C}} \\ k = k_{r} + j k_{i} = \sqrt{(R + j 2 π f L) (G + j 2 π F C)} \end{matrix}$
where

$\begin{array}{l} R = \frac{1}{π a σ_{c o n d} δ_{c o n d}} \\ L = \frac{μ}{π} a \cosh (\frac{D}{2 a}) \\ G = \frac{π ω ε^{″}}{a \cosh (\frac{D}{2 a})} \\ C = \frac{π ε}{a \cosh (\frac{D}{2 a})} \end{array}$
In these equations:
- w is the plate width.
- d is the plate separation.
- σ_cond is the conductivity in the conductor.
- μ is the permeability of the dielectric.
- ε is the permittivity of the dielectric.
- ε″ is the imaginary part of ε, ε″ = ε₀ε_rtan δ, where:
  - ε₀ is the permittivity of free space.
  - ε_r is the EpsilonR property value.
  - tan δ is the LossTangent property value.
- δ_cond is the skin depth of the conductor, which the block calculates as $1 / \sqrt{π f μ σ_{c o n d}}$ .
- f is a vector of modeling frequencies determined by the Outport (RF Blockset) block.
If you model the transmission line as a shunt or series stub, the analyze method first calculates the ABCD-parameters at the specified frequencies. It then uses the abcd2s function to convert the ABCD-parameters to S-parameters.
When you set the StubMode property to 'Shunt', the 2-port network consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown in the following figure.

Z_in is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as:

$\begin{matrix} A = 1 \\ B = 0 \\ C = 1 / Z_{i n} \\ D = 1 \end{matrix}$
When you set the StubMode property to 'Series', the 2-port network consists of a series transmission line that you can terminate with either a short circuit or an open circuit as shown in the following figure.

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

$\begin{matrix} A = 1 \\ B = Z_{i n} \\ C = 0 \\ D = 1 \end{matrix}$

References

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

Version History

Introduced in R2009a

rfckt.twowire

Description

Creation

Syntax

Description

Properties

AnalyzedResult — Computed S-parameters, noise figure, OIP3, and group delay values rfdata.data object

Separation — Distance between two wire centers scalar

EpsilonR — Relative permittivity of dielectric scalar

LineLength — Physical length of transmission line scalar

LossTangent — Tangent of loss angle of dielectric scalar

MUR — Relative permeability of dielectric scalar

Name — Object name 'Two-Wire Transmission Line' (default) | 1-by-N character array

nport — Number of ports positive integer

Radius — Conducting wire radius scalar

SigmaCond — Conductor conductivity scalar in Siemens per meter

StubMode — Type of stub 'NotaStub' (default) | 'Series' | 'Shunt'

Termination — Stub transmission line termination 'NotApplicable' (default) | 'Open' | 'Short'

Object Functions

Examples

Two-Wire Transmission Line

Algorithms

References

Version History

See Also

`AnalyzedResult` — Computed S-parameters, noise figure, OIP3, and group delay values
`rfdata.data` object

`Separation` — Distance between two wire centers
scalar

`EpsilonR` — Relative permittivity of dielectric
scalar

`LineLength` — Physical length of transmission line
scalar

`LossTangent` — Tangent of loss angle of dielectric
scalar

`MUR` — Relative permeability of dielectric
scalar

`Name` — Object name
`'Two-Wire Transmission Line'` (default) | `1-by-N` character array

`nport` — Number of ports
positive integer

`Radius` — Conducting wire radius
scalar

`SigmaCond` — Conductor conductivity
scalar in Siemens per meter

`StubMode` — Type of stub
`'NotaStub'` (default) | `'Series'` | `'Shunt'`

`Termination` — Stub transmission line termination
`'NotApplicable'` (default) | `'Open'` | `'Short'`