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

Description

example

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

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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

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

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

Data Types: double

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

Data Types: double

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

Data Types: double

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

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

Data Types: char

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

Data Types: double

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

Data Types: double

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

Data Types: double

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

Data Types: double

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 parameters of RF circuit or RF data 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 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 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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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:

$\begin{array}{c}{Z}_{0}=\sqrt{\frac{R+j2\pi fL}{G+j2\pi fC}}\\ k={k}_{r}+j{k}_{i}=\sqrt{\left(R+j2\pi fL\right)\left(G+j2\pi FC\right)}\end{array}$

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.

• σcond 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″  = ε0εrtan δ, where:

• ε0 is the permittivity of free space.

• εr is the EpsilonR property value.

• tan δ is the LossTangent property value.

• δcond 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.

Zin 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.

Zin 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.