Parallel-Plate Transmission Line

Model parallel-plate transmission line

Library:
RF Blockset / Equivalent Baseband / Transmission Lines

Description

The Parallel-Plate Transmission Line block models the parallel-plate transmission line described in the block dialog box in terms of its frequency-dependent S-parameters. 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.

Parameters

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Main

`Plate width (m)` — Width of parallel-plate transmission line
`5e-3` (default) | scalar

Physical width of the parallel-plate transmission line.

`Plate separation (m)` — Dielectric spacing in parallel-plate transmission line
`1e-3` (default) | scalar

Thickness of the dielectric separating the plates.

`Relative permeability constant` — Relative permeability of the dielectric material in the parallel-plate transmission line
`1` (default)

Relative permeability of the dielectric expressed as the ratio of the permeability of the dielectric to permeability in free space μ₀.

`Relative permittivity constant` — Relative permittivity of the dielectric material in the parallel-plate transmission line
`2.3` (default)

Relative permittivity of the dielectric expressed as the ratio of the permittivity of the dielectric to permittivity in free space ε₀.

`Loss tangent of dielectric` — Loss tangent of dielectric in the parallel-plate transmission line
`0` (default)

Loss angle tangent of dielectric, specified as a scalar.

`Conductivity of the conductor (S/m)` — Conductivity of the conductor in siemens per meter
`inf` (default)

Conductivity is a metric to measure the flow of current in a conductor.

`Transmission line length(m)` — Physical length of the transmission line
`0.01` (default)

Physical length of the transmission line in meters.

`Stub mode` — Type of stub
`Not a stub` (default) | `Shunt` | `Series`

The block enables you to model the transmission line as a stub or as a stubless line.

Stubless Transmission Line

Not a stub—Not a stub
If you model a parallel-plate transmission line as stubless line, the Parallel-Plate 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. For more information, see Stub Mode- Not a stub.

Shunt and Series Stubs

The stub mode of the parallel-plate transmission line is classified as following:
Shunt—Shunt parameter provides the users with 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
$\begin{matrix} A = 1 \\ B = 0 \\ C = 1 / Z_{i n} \\ D = 1 \end{matrix}$

Series—Series parameter provides the user with 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
$\begin{matrix} A = 1 \\ B = Z_{i n} \\ C = 0 \\ D = 1 \end{matrix}$

`Termination of stub` — Stub termination
`Open` (default)

Stub termination for stub modes Shunt and Series. Choices are Open or Short

Dependencies

To enable this parameter, select Shunt, or Series, or in Stub mode

Visualization

`Source of frequency data` — Frequency data source
`User-defined` (default)

When Source of frequency data is User-specified, specify a vector of frequencies in the Frequency data parameter. Also, specify units from the corresponding drop-down list.

`Frequency data` — Frequency data range
`[1e9:1e6:3e9]` (default) | vector | `Hz` | `kHz` | `MHz` | `GHz`

Frequency data range, specified as a vector

`Reference impedance(ohms)` — Reference impedance
`50` (default) | scalar

Reference impedance of the parallel-plate transmission line, specified as a scalar in ohms.

`Plot type` — Type of data plot
`X-Y plane` (default) | `Polar plane` | `Z Smith chart` | `Y Smith chart` | `ZY Smith chart`

Type of data plot that you want to produce with your data specified as one of the following:

X-Y plane — Generate a Cartesian plot of your data versus frequency. To create linear, semi-log, or log-log plots, set the Y scale and X scale accordingly.
Polar plane — Generate a polar plot of your data. The block plots only the range of data corresponding to the specified frequencies.
Z smith chart, Y smith chart, and ZY smith chart — Generate a Smith^® chart. The block plots only the range of data corresponding to the specified frequencies.

`Y Parameter 1` — Type of S-Parameters to plot
`S21` (default) | `S11` | `S12` | `S22` | `GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` | `VSWROut` | `OIP3` | `IIP3` | `NF` | `NFactor` | `NTemp` | `TF1`

Type of S-Parameters to plot, specified as one of the following S11, S12, S21, or S22. When noise is spectral NF, NFactor, NTemp plotting is possible.

`Y Parameter 2` — Type of S-Parameters to plot
`S11` (default) | `S12` | `S21` | `S22` | `GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` | `VSWROut` | `OIP3` | `IIP3` | `NF` | `NFactor` | `NTemp` | `TF1`

Type of S-Parameters to plot, specified as one of the following S11, S12, S21, or S22. When noise is spectral NF, NFactor, NTemp plotting is possible.

`Y Format1` — Plot format
`Angle(degrees)` (default) | `Magnitude (decibels)` | `Real` | `Imaginary`

Plot format, specified as one of the following Magnitude (decibels), Angle(degrees), Real, or Imaginary.

`Y Format2` — Plot format
`Magnitude (decibels)` (default) | `Angle(degrees)` | `Real` | `Imaginary`

Plot format, specified as one of the following Magnitude (decibels), Angle(degrees), Real, or Imaginary.

`X parameter` — X parameter
`Freq` (default)

Parameter, specified as Freq.

`X format` — Plot format
`Hz` (default) | `Auto` | `KHz` | `MHz` | `GHz` | `THz`

Plot format, specified as one of the following Hz, Auto, KHz, MHz, GHz or THz.

`Y scale` — Y-axis scale
`Linear` (default) | `Logarithmic`

Y-axis scale, specified as Linear or Logarithmic.

`X scale` — X-axis scale
`Linear` (default) | `Logarithmic`

X-axis scale, specified as Linear or Logarithmic.

`Plot` — Plot specified data
button

Plot specified data using plot button.

More About

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Stub Mode - Not a Stub

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:

$\begin{array}{l} A = \frac{e^{k d} + e^{- k d}}{2} \\ B = \frac{Z_{0} * (e^{k d} - e^{- k d})}{2} \\ C = \frac{e^{k d} - e^{- k d}}{2 * Z_{0}} \\ D = \frac{e^{k d} + e^{- k d}}{2} \end{array}$

Z₀ and k are vectors whose elements correspond to the elements of f, a vector of modeling frequencies, determined by the Output Port block. Both can be expressed in terms of the resistance (R), inductance (L), conductance (G), and capacitance (C) per unit length (meters) as follows:

$\begin{matrix} Z_{0} = \sqrt{\frac{R + j ω L}{G + j ω C}} \\ k = k_{r} + j k_{i} = \sqrt{(R + j ω L) (G + j ω C)} \end{matrix}$

where

$\begin{array}{l} R = \frac{1}{2 π σ_{c o n d} δ_{c o n d}} (\frac{1}{a} + \frac{1}{b}) \\ L = \frac{μ}{2 π} \ln (\frac{b}{a}) \\ G = \frac{2 π ω ε^{″}}{\ln (\frac{b}{a})} \\ C = \frac{2 π ε^{'}}{\ln (\frac{b}{a})} \end{array}$

In these equations:

a is the radius of the inner conductor.
b is the radius of the outer conductor.
σ_cond is the conductivity in the conductor.
μ is the permeability of the dielectric. μ = μ₀ μ_r where:
- μ₀ is the permeability in free space.
- μ_r is the Relative permeability constant parameter value.
The is a complex dielectric constant given by ε = ε′ − јε″= ε′ ( 1 − јtanδ)
ε′ is the real part of complex dielectric constant ε, ε′ = ε₀ε_r. ε″ is the imaginary part of complex dielectric constant ε, ε″ = ε₀ε_rtan δ where :
- ε₀ is the permittivity of free space.
- ε_r is the Relative permittivity constant parameter value.
- tan δ is the Loss tangent of dielectric parameter value.
δ_cond is the skin depth of the conductor, which the block calculates as $1 / \sqrt{π f μ σ_{c o n d}}$ .

References

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

Documentation

Parallel-Plate Transmission Line

Description

Parameters

`Plate width (m)` — Width of parallel-plate transmission line
`5e-3` (default) | scalar

`Plate separation (m)` — Dielectric spacing in parallel-plate transmission line
`1e-3` (default) | scalar

`Relative permeability constant` — Relative permeability of the dielectric material in the parallel-plate transmission line
`1` (default)

`Relative permittivity constant` — Relative permittivity of the dielectric material in the parallel-plate transmission line
`2.3` (default)

`Loss tangent of dielectric` — Loss tangent of dielectric in the parallel-plate transmission line
`0` (default)

`Conductivity of the conductor (S/m)` — Conductivity of the conductor in siemens per meter
`inf` (default)

`Transmission line length(m)` — Physical length of the transmission line
`0.01` (default)

`Stub mode` — Type of stub
`Not a stub` (default) | `Shunt` | `Series`

Stubless Transmission Line

Shunt and Series Stubs

`Termination of stub` — Stub termination
`Open` (default)

Dependencies

`Source of frequency data` — Frequency data source
`User-defined` (default)

`Frequency data` — Frequency data range
`[1e9:1e6:3e9]` (default) | vector | `Hz` | `kHz` | `MHz` | `GHz`

`Reference impedance(ohms)` — Reference impedance
`50` (default) | scalar

`Plot type` — Type of data plot
`X-Y plane` (default) | `Polar plane` | `Z Smith chart` | `Y Smith chart` | `ZY Smith chart`

`Y Parameter 1` — Type of S-Parameters to plot
`S21` (default) | `S11` | `S12` | `S22` | `GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` | `VSWROut` | `OIP3` | `IIP3` | `NF` | `NFactor` | `NTemp` | `TF1`

`Y Parameter 2` — Type of S-Parameters to plot
`S11` (default) | `S12` | `S21` | `S22` | `GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` | `VSWROut` | `OIP3` | `IIP3` | `NF` | `NFactor` | `NTemp` | `TF1`

`Y Format1` — Plot format
`Angle(degrees)` (default) | `Magnitude (decibels)` | `Real` | `Imaginary`

`Y Format2` — Plot format
`Magnitude (decibels)` (default) | `Angle(degrees)` | `Real` | `Imaginary`

`X parameter` — X parameter
`Freq` (default)

`X format` — Plot format
`Hz` (default) | `Auto` | `KHz` | `MHz` | `GHz` | `THz`

`Y scale` — Y-axis scale
`Linear` (default) | `Logarithmic`

`X scale` — X-axis scale
`Linear` (default) | `Logarithmic`

`Plot` — Plot specified data
button

More About

Stub Mode - Not a Stub

References

See Also

RF Blockset Documentation

Support

Documentation

Parallel-Plate Transmission Line

Description

Parameters

Plate width (m) — Width of parallel-plate transmission line 5e-3 (default) | scalar

Plate separation (m) — Dielectric spacing in parallel-plate transmission line 1e-3 (default) | scalar

Relative permeability constant — Relative permeability of the dielectric material in the parallel-plate transmission line 1 (default)

Relative permittivity constant — Relative permittivity of the dielectric material in the parallel-plate transmission line 2.3 (default)

Loss tangent of dielectric — Loss tangent of dielectric in the parallel-plate transmission line 0 (default)

Conductivity of the conductor (S/m) — Conductivity of the conductor in siemens per meter inf (default)

Transmission line length(m) — Physical length of the transmission line 0.01 (default)

Stub mode — Type of stub Not a stub (default) | Shunt | Series

Stubless Transmission Line

Shunt and Series Stubs

Termination of stub — Stub termination Open (default)

Dependencies

Source of frequency data — Frequency data source User-defined (default)

Frequency data — Frequency data range [1e9:1e6:3e9] (default) | vector | Hz | kHz | MHz | GHz

Reference impedance(ohms) — Reference impedance 50 (default) | scalar

Plot type — Type of data plot X-Y plane (default) | Polar plane | Z Smith chart | Y Smith chart | ZY Smith chart

Y Parameter 1 — Type of S-Parameters to plot S21 (default) | S11 | S12 | S22 | GroupDelay | GammaIn | GammaOut | VSWRIn | VSWROut | OIP3 | IIP3 | NF | NFactor | NTemp | TF1

Y Parameter 2 — Type of S-Parameters to plot S11 (default) | S12 | S21 | S22 | GroupDelay | GammaIn | GammaOut | VSWRIn | VSWROut | OIP3 | IIP3 | NF | NFactor | NTemp | TF1

Y Format1 — Plot format Angle(degrees) (default) | Magnitude (decibels) | Real | Imaginary

Y Format2 — Plot format Magnitude (decibels) (default) | Angle(degrees) | Real | Imaginary

X parameter — X parameter Freq (default)

X format — Plot format Hz (default) | Auto | KHz | MHz | GHz | THz

Y scale — Y-axis scale Linear (default) | Logarithmic

X scale — X-axis scale Linear (default) | Logarithmic

Plot — Plot specified data button

More About

Stub Mode - Not a Stub

References

See Also

RF Blockset Documentation

Support

`Plate width (m)` — Width of parallel-plate transmission line
`5e-3` (default) | scalar

`Plate separation (m)` — Dielectric spacing in parallel-plate transmission line
`1e-3` (default) | scalar

`Relative permeability constant` — Relative permeability of the dielectric material in the parallel-plate transmission line
`1` (default)

`Relative permittivity constant` — Relative permittivity of the dielectric material in the parallel-plate transmission line
`2.3` (default)

`Loss tangent of dielectric` — Loss tangent of dielectric in the parallel-plate transmission line
`0` (default)

`Conductivity of the conductor (S/m)` — Conductivity of the conductor in siemens per meter
`inf` (default)

`Transmission line length(m)` — Physical length of the transmission line
`0.01` (default)

`Stub mode` — Type of stub
`Not a stub` (default) | `Shunt` | `Series`

`Termination of stub` — Stub termination
`Open` (default)

`Source of frequency data` — Frequency data source
`User-defined` (default)

`Frequency data` — Frequency data range
`[1e9:1e6:3e9]` (default) | vector | `Hz` | `kHz` | `MHz` | `GHz`

`Reference impedance(ohms)` — Reference impedance
`50` (default) | scalar

`Plot type` — Type of data plot
`X-Y plane` (default) | `Polar plane` | `Z Smith chart` | `Y Smith chart` | `ZY Smith chart`

`Y Parameter 1` — Type of S-Parameters to plot
`S21` (default) | `S11` | `S12` | `S22` | `GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` | `VSWROut` | `OIP3` | `IIP3` | `NF` | `NFactor` | `NTemp` | `TF1`

`Y Parameter 2` — Type of S-Parameters to plot
`S11` (default) | `S12` | `S21` | `S22` | `GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` | `VSWROut` | `OIP3` | `IIP3` | `NF` | `NFactor` | `NTemp` | `TF1`

`Y Format1` — Plot format
`Angle(degrees)` (default) | `Magnitude (decibels)` | `Real` | `Imaginary`

`Y Format2` — Plot format
`Magnitude (decibels)` (default) | `Angle(degrees)` | `Real` | `Imaginary`

`X parameter` — X parameter
`Freq` (default)

`X format` — Plot format
`Hz` (default) | `Auto` | `KHz` | `MHz` | `GHz` | `THz`

`Y scale` — Y-axis scale
`Linear` (default) | `Logarithmic`

`X scale` — X-axis scale
`Linear` (default) | `Logarithmic`

`Plot` — Plot specified data
button