rfckt.parallelplate

Parallel-plate transmission line

Description

Use the parallelplate class to represent parallel-plate transmission lines that are characterized by line dimensions and optional stub properties.

A parallel-plate transmission line is shown in cross-section in the following figure. Its physical characteristics include the plate width w and the plate separation d.

Creation

Syntax

h = rfckt.parallelplate

h = rfckt.parallelplate('Property1',value1,'Property2',value2,...)

Description

example

h = rfckt.parallelplate returns a parallel-plate transmission line object whose properties are set to their default values.

h = rfckt.parallelplate('Property1',value1,'Property2',value2,...) sets properties using one or more name-value pairs. You can specify multiple name-value pairs. Enclose each property name in a quote

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 rfdata.data object. Analyzed Result is a read-only property. For more information refer, Algorithms.

Data Types: function_handle

`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 parallel-plate transmission line
scalar

Physical length of parallel-plate 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

`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

`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
`1-by-N` character array

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

Data Types: char

`nport` — Number of ports
positive integer

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

Data Types: double

`Separation` — Thickness of dielectric
scalar

Thickness of the dielectric separating the plates, specified as a scalar in meters. The default value is 1.0e-3.

Data Types: double

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

Type of stub, specified as 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

`Width` — Physical width of parallel-plate transmission line
scalar

Physical width of parallel-plate transmission line, specified as a scalar in meters. The default value is 6.0e-4.

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 specified circuit object parameters on X-Y plane
`plotyy`	Plot specified parameters on X-Y plane with Y-axes on both left and right sides
`getop`	Display operating conditions
`polar`	Plot specified object parameters on polar coordinates
`semilogx`	Plot specified circuit object parameters using log scale for x-axis
`semilogy`	Plot specified circuit object parameters using log scale for y-axis
`smith`	Plot specified circuit object parameters on Smith chart
`write`	Write RF data from circuit or data object to file
`getz0`	Get characteristic impedance of 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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Parallel Plate Transmission Line

Open Live Script

Create a parallel plate transmission line using rfckt.parallelplate.

tx1=rfckt.parallelplate('LineLength',0.045)

tx1 = 
   rfckt.parallelplate with properties:

             Width: 0.0050
        Separation: 1.0000e-03
               MuR: 1
          EpsilonR: 2.3000
       LossTangent: 0
         SigmaCond: Inf
        LineLength: 0.0450
          StubMode: 'NotAStub'
       Termination: 'NotApplicable'
             nPort: 2
    AnalyzedResult: []
              Name: 'Parallel-Plate Transmission Line'

Algorithms

The analyze method treats the parallel-plate line as a 2-port linear network and models the line as a transmission line with optional stubs. The analyze method computes the AnalyzedResult property of the line using the data stored in the rfckt.parallelplate object properties as follows:

If you model the transmission line as a stub less 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

$\begin{array}{l} R = \frac{2}{w σ_{c o n d} δ_{c o n d}} \\ L = μ \frac{d}{w} \\ G = ω ε^{″} \frac{w}{d} \\ C = ε \frac{w}{d} \end{array}$
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.

Documentation

rfckt.parallelplate

Description

Creation

Syntax

Description

Properties

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

`EpsilonR` — Relative permittivity of dielectric
scalar

`LineLength` — Physical length of parallel-plate transmission line
scalar

`LossTangent` — Tangent of loss angle of dielectric
scalar

`SigmaCond` — Conductor conductivity
scalar in Siemens per meter

`MUR` — Relative permeability of dielectric
scalar

`Name` — Object name
`1-by-N` character array

`nport` — Number of ports
positive integer

`Separation` — Thickness of dielectric
scalar

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

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

`Width` — Physical width of parallel-plate transmission line
scalar

Object Functions

Examples

Parallel Plate Transmission Line

Algorithms

References

See Also

RF Toolbox Documentation

Support

Documentation

rfckt.parallelplate

Description

Creation

Syntax

Description

Properties

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

EpsilonR — Relative permittivity of dielectric scalar

LineLength — Physical length of parallel-plate transmission line scalar

LossTangent — Tangent of loss angle of dielectric scalar

SigmaCond — Conductor conductivity scalar in Siemens per meter

MUR — Relative permeability of dielectric scalar

Name — Object name 1-by-N character array

nport — Number of ports positive integer

Separation — Thickness of dielectric scalar

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

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

Width — Physical width of parallel-plate transmission line scalar

Object Functions

Examples

Parallel Plate Transmission Line

Algorithms

References

See Also

RF Toolbox Documentation

Support

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

`EpsilonR` — Relative permittivity of dielectric
scalar

`LineLength` — Physical length of parallel-plate transmission line
scalar

`LossTangent` — Tangent of loss angle of dielectric
scalar

`SigmaCond` — Conductor conductivity
scalar in Siemens per meter

`MUR` — Relative permeability of dielectric
scalar

`Name` — Object name
`1-by-N` character array

`nport` — Number of ports
positive integer

`Separation` — Thickness of dielectric
scalar

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

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

`Width` — Physical width of parallel-plate transmission line
scalar