Coaxial Transmission Line

Model coaxial transmission line

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• RF Blockset / Equivalent Baseband / Transmission Lines

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Description

The Coaxial Transmission Line block uses S-parameters to model its frequency behavior. A cross-section of the Coaxial Transmission Line is shown in the following figure. Its physical characteristics include the radius of the inner conductor a and the radius of the outer conductor b.

Parameters

Main

Outer radius (m) — Radius of outer conductor

2.57e-3 (default) | scalar

Radius of the outer conductor of the coaxial transmission line, specified as a scalar in meters.

Inner radius(m) — Radius of Inner conductor

0.725e-3 (default) | scalar

Radius of the inner conductor of the coaxial transmission line, specified as a scalar in meters.

Relative permeability constant — Relative permeability of dielectric

1 (default) | real scalar

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

2.3 (default) | real 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) | non-negative 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) | positive scalar

Conductivity of the conductor, specified as a positive scalar.

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

0.01 (default) | positive 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 information, 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 and it is calculated as follows:

  for a short circuited transmission line

  $${\text{Z}}_{\text{in}}=j{Z}_0\tan \gamma l$$

  and for the open circuited transmission line

  $${\text{Z}}_{\text{in}}=-j{Z}_0\cot \gamma l$$

  where

  • Z₀ is the characteristic impedance and

  • $$\gamma$$ is the propagation constant

  The ABCD-parameters for the shunt stub are calculated as

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

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

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

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)

Source of frequency data is User-specified, and the vector of frequencies are specified 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

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 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-axis 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

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:

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

Z₀ and k are vectors whose elements correspond to the elements of f, 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)

$$\begin{array}{c}{Z}_0=\sqrt{\frac{R+j\omega L}{G+j\omega C}}\\ k=k_r+j{k}_i=\sqrt{(R+j\omega L)(G+j\omega C)}\end{array}$$

where

$$\begin{array}{l}R=\frac{1}{2\pi {\sigma }_{cond}{\delta }_{cond}}\left(\frac{1}{a}+\frac{1}{b}\right)\\ L=\frac{\mu }{2\pi }\ln \left(\frac{b}{a}\right)\\ G=\frac{2\pi \omega {\epsilon }^{″}}{\ln \left(\frac{b}{a}\right)}\\ C=\frac{2\pi {\epsilon }^{\prime }}{\ln \left(\frac{b}{a}\right)}\end{array}$$

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

References

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