Coplanar Waveguide Transmission Line

Model coplanar waveguide transmission line

Library:
RF Blockset / Equivalent Baseband / Transmission Lines

Description

The Coplanar Waveguide Transmission Line block models the coplanar waveguide transmission line described in the block dialog box in terms of its frequency-dependent S-parameters. A coplanar waveguide transmission line is shown in cross-section in the following figure. Its physical characteristics include the conductor width (w), the conductor thickness (t), the slot width (s), the substrate height (d), and the relative permittivity constant (ε).

Parameters

expand all

Main

`Conductor width (m)` — Physical width of the conductor
`0.6e-3` (default) | scalar

Physical width of the conductor of the coplanar waveguide, specified as a scalar in meters.

`Slot width (m)` — Physical width of the slot
`0.2e-3` (default) | scalar

Physical width of the slot of the coplanar waveguide, specified as a scalar in meters.

`Substrate height (m)` — Thickness of the dielectric on which the conductor resides
`0.635e-3` (default) | scalar

Thickness of the dielectric on which the conductor resides in the coplanar waveguide, specified as a scalar in meters.

`Strip thickness (m)` — Physical thickness of the conductor
`0.005e-3` (default) | scalar

Physical thickness of the conductor in which wave propagates.

`Relative permittivity constant` — Relative permittivity of the dielectric
`9.8` (default) | scalar

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` — Dielectric loss tangent
`0` (default) | scalar

Loss tangent of dielectric, specified as a scalar.

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

Conductivity measures the ease with which current flows in the conductor.

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

Physical length of the transmission line, specified 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 coaxial transmission line as stubless line, the Coaxial 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 info, see Stub Mode- Not a stub.

Shunt Transmission Line

Shunt—This parameter provides a two-port network that consists of a stub transmission line that you can terminate with either a short circuit or an open circuit as shown in these diagrams.
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 Transmission Line

Series—This mode parameter provides a two-port network that consists of a series transmission line that you can terminate with either a short circuit or an open circuit as show in these diagrams.
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) | `Short`

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

Dependencies

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

Visualization

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

When Source of frequency data is User-specified, specify as a vector of frequencies in the Frequency data parameter.

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

Frequency data range, specified as a vector in hertz.

Dependencies

To set this parameter, first select User-specified in Source of amplifier gain. This selection activates the Visualization Tab which contains Source of frequency data

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

Reference impedance of the coaxial transmission line, specified as a scalar in ohms.

`Plot type` — Type of data plot
`X-Y plane` (default) | `Composite data` | `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 :

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.
Composite data—The composite data plot automatically generates four separate plots in one figure window, showing the frequency dependence of several parameters.
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 of your data. The block plots only the range of data corresponding to the specified frequencies.

`Y Parameter1` — Type of parameters to plot
`S21` (default) | `S11` | `S12` | `S22` | `GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` | `VSWROut` | `OIP3` | `IIP3` | `NF` | `NFactor` | `NTemp` | `TF1` | `TF2` | `TF3` | `Gt` | `Ga` | `Gp` | `Gmag` | `Gmsg` | `GammaMS` | `GammaML` | `K` | `Delta` | `Mu` | `MuPrime`

Type of parameters to plot, specified as one of the following S11, S12, S21, S22, GroupDelay, GammaIn, GammaOut, VSWRIn, VSWROut, OIP3, IIP3, TF1, TF2, TF3, Gt, Ga, Gp, Gmag, Gmsg, GammaMS, GammaML, K, Delta, Mu or MuPrime. When noise is spectral NF, NFactor and NTemp plotting is possible.

`Y Parameter2` — Type of parameters to plot
`S11` (default) | `S12` | `S21` | `S22` | `GroupDelay` | `GammaIn` | `GammaOut` | `VSWRIn` | `VSWROut` | `OIP3` | `IIP3` | `NF` | `NFactor` | `NTemp` | `TF1` | `TF2` | `TF3` | `Gt` | `Ga` | `Gp` | `Gmag` | `Gmsg` | `GammaMS` | `GammaML` | `K` | `Delta` | `Mu` | `MuPrime`

`Y Format1` — Plot format
`Angle (degrees)` (default) | `dB` | `Magnitude (decibels)` | `Abs` | `Mag` | `Magnitude (linear)` | `Angle` | `Angle (radians)` | `Real` | `Imag` | `Imaginary`

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

`Y Format2` — Plot format
`dB` (default) | `Magnitude (decibels)` | `Abs` | `Mag` | `Magnitude (linear)` | `Angle` | `Angle (degrees)` | `Angle (radians)` | `Real` | `Imag` | `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. This parameter determines the data for x-axes on the X-Y plane plot.

`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) | `Log`

Y-axis scale, specified as Linear or Log.

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

X-axis scale, specified as Linear or Log.

`Plot` — Plot specified data
button

Plot the specified data using the plot button.

More About

expand all

Stub Mode- Not a stub

This block calculates the ABCD-parameters using the physical length of the transmission line, d, and the complex propagation constant k using the 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)

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

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 of 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
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] Gupta, K. C., Ramesh Garg, Inder Bahl, and Prakash Bhartia.Microstrip Lines and Slotlines. 2nd Edition, Artech House, Inc., Norwood, MA, 1996.

Documentation

Coplanar Waveguide Transmission Line

Description

Parameters

Main

`Conductor width (m)` — Physical width of the conductor
`0.6e-3` (default) | scalar

`Slot width (m)` — Physical width of the slot
`0.2e-3` (default) | scalar

`Substrate height (m)` — Thickness of the dielectric on which the conductor resides
`0.635e-3` (default) | scalar

`Strip thickness (m)` — Physical thickness of the conductor
`0.005e-3` (default) | scalar

`Relative permittivity constant` — Relative permittivity of the dielectric
`9.8` (default) | scalar

`Loss tangent of dielectric` — Dielectric loss tangent
`0` (default) | scalar

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

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

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

Stubless Transmission Line

Shunt Transmission Line

Series Transmission Line

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

Dependencies

Visualization

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

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

Dependencies

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

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

`Y Format1` — Plot format
`Angle (degrees)` (default) | `dB` | `Magnitude (decibels)` | `Abs` | `Mag` | `Magnitude (linear)` | `Angle` | `Angle (radians)` | `Real` | `Imag` | `Imaginary`

`Y Format2` — Plot format
`dB` (default) | `Magnitude (decibels)` | `Abs` | `Mag` | `Magnitude (linear)` | `Angle` | `Angle (degrees)` | `Angle (radians)` | `Real` | `Imag` | `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) | `Log`

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

`Plot` — Plot specified data
button

More About

Stub Mode- Not a stub

References

See Also

RF Blockset Documentation

Support

Documentation

Coplanar Waveguide Transmission Line

Description

Parameters

Main

Conductor width (m) — Physical width of the conductor 0.6e-3 (default) | scalar

Slot width (m) — Physical width of the slot 0.2e-3 (default) | scalar

Substrate height (m) — Thickness of the dielectric on which the conductor resides 0.635e-3 (default) | scalar

Strip thickness (m) — Physical thickness of the conductor 0.005e-3 (default) | scalar

Relative permittivity constant — Relative permittivity of the dielectric 9.8 (default) | scalar

Loss tangent of dielectric — Dielectric loss tangent 0 (default) | scalar

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

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

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

Stubless Transmission Line

Shunt Transmission Line

Series Transmission Line

Termination of stub — Stub termination Open (default) | Short

Dependencies

Visualization

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

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

Dependencies

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

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

Y Parameter1 — Type of parameters to plot S21 (default) | S11 | S12 | S22 | GroupDelay | GammaIn | GammaOut | VSWRIn | VSWROut | OIP3 | IIP3 | NF | NFactor | NTemp | TF1 | TF2 | TF3 | Gt | Ga | Gp | Gmag | Gmsg | GammaMS | GammaML | K | Delta | Mu | MuPrime

Y Parameter2 — Type of parameters to plot S11 (default) | S12 | S21 | S22 | GroupDelay | GammaIn | GammaOut | VSWRIn | VSWROut | OIP3 | IIP3 | NF | NFactor | NTemp | TF1 | TF2 | TF3 | Gt | Ga | Gp | Gmag | Gmsg | GammaMS | GammaML | K | Delta | Mu | MuPrime

Y Format1 — Plot format Angle (degrees) (default) | dB | Magnitude (decibels) | Abs | Mag | Magnitude (linear) | Angle | Angle (radians) | Real | Imag | Imaginary

Y Format2 — Plot format dB (default) | Magnitude (decibels) | Abs | Mag | Magnitude (linear) | Angle | Angle (degrees) | Angle (radians) | Real | Imag | 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) | Log

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

Plot — Plot specified data button

More About

Stub Mode- Not a stub

References

See Also

RF Blockset Documentation

Support

`Conductor width (m)` — Physical width of the conductor
`0.6e-3` (default) | scalar

`Slot width (m)` — Physical width of the slot
`0.2e-3` (default) | scalar

`Substrate height (m)` — Thickness of the dielectric on which the conductor resides
`0.635e-3` (default) | scalar

`Strip thickness (m)` — Physical thickness of the conductor
`0.005e-3` (default) | scalar

`Relative permittivity constant` — Relative permittivity of the dielectric
`9.8` (default) | scalar

`Loss tangent of dielectric` — Dielectric loss tangent
`0` (default) | scalar

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

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

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

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

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

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

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

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

`Y Format1` — Plot format
`Angle (degrees)` (default) | `dB` | `Magnitude (decibels)` | `Abs` | `Mag` | `Magnitude (linear)` | `Angle` | `Angle (radians)` | `Real` | `Imag` | `Imaginary`

`Y Format2` — Plot format
`dB` (default) | `Magnitude (decibels)` | `Abs` | `Mag` | `Magnitude (linear)` | `Angle` | `Angle (degrees)` | `Angle (radians)` | `Real` | `Imag` | `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) | `Log`

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

`Plot` — Plot specified data
button