rfckt.parallelplate

Parallel-plate transmission line

Description

Use the rfckt.parallelplate object to create a parallel-plate transmission line that is 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.

Note

txlineParallelPlate is recommended over rfckt.parallelplate because it enables you to:

• Create a parallel-plate transmission line.

• Build a circuit object with a parallel-plate transmission line.

• Model a parallel-plate 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.parallelplate

h = rfckt.parallelplate(Name,Value)

Description

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

h = rfckt.parallelplate(Name,Value) sets properties using one or more name-value pairs. For example, rfckt.parallelplate('LineLength',0.045) creates a parallel-plate transmission line object with a physical length of 0.045 meters. You can specify multiple name-value pairs. Enclose each property name in a quote. Properties not specified retain their default values.

Properties

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. AnalyzedResult 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,$$\epsilon$$, to the permittivity in free space, $${\epsilon }_0$$. 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, $$\mu$$, to the permeability in free space, $${\mu }_0$$. 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 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

Parallel Plate Transmission Line

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:

  $$\begin{array}{l}A=\frac{e^{kd}+e^{-kd}}{2}\\ B=\frac{Z_0*\left(e^{kd}-e^{-kd}\right)}{2}\\ C=\frac{e^{kd}-e^{-kd}}{2*Z_0}\\ D=\frac{e^{kd}+e^{-kd}}{2}\end{array}$$

  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:

  $$\begin{array}{c}{Z}_0=\sqrt{\frac{R+j2\pi fL}{G+j2\pi fC}}\\ k=k_r+j{k}_i=\sqrt{(R+j2\pi fL)(G+j2\pi FC)}\end{array}$$

  where

  $$\begin{array}{l}R=\frac{2}{w{\sigma }_{cond}{\delta }_{cond}}\\ L=\mu \frac{d}{w}\\ G=\omega {\epsilon }^{″}\frac{w}{d}\\ C=\epsilon \frac{w}{d}\end{array}$$

  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 $$1/\sqrt{\pi f\mu {\sigma }_{cond}}$$.

  • 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:

  $$\begin{array}{c}A=1\\ B=0\\ C=1/Z_{in}\\ D=1\end{array}$$

  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:

  $$\begin{array}{c}A=1\\ B=Z_{in}\\ C=0\\ D=1\end{array}$$

References

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

Version History

Introduced in R2009a