rfckt.coaxial

Coaxial transmission line

Description

Use the rfckt.coaxial object to create a coaxial transmission line that is characterized by line dimensions, stub type, and termination.

A coaxial transmission line is shown in cross-section in the following figure. Its physical characteristics include the radius of the inner conductor of the coaxial transmission line a, and the radius of the outer conductor b.

Note

txlineCoaxial is recommended over rfckt.coaxial because it enables you to:

• Create a coaxial transmission line.

• Build a circuit object with a coaxial transmission line.

• Model a coaxial 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.coaxial

h = rfckt.coaxial(Name,Value)

Description

h = rfckt.coaxial returns a coaxial transmission line object whose properties are set to their default values.

h = rfckt.coaxial(Name,Value) sets properties using one or more name-value pairs. For example, rfckt.coaxial('OuterRadius',0.0043) creates a coaxial transmission line object with outer radius of 0.0043 meters. You can specify multiple name-value pairs. Enclose each property name in quotes. 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 an rfdata.data object. This 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 is2.3.

Data Types: double

InnerRadius — Inner conductor radius

scalar

Inner conductor radius, specified as a scalar in meters. The default value is 7.25e-4.

Data Types: double

LineLength — Physical length of transmission line

scalar

Physical length of 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

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

'Coaxial Transmission Line' (default) | 1-by-N character array

This property is read-only.

Object name, specified as a 1-by-N character array.

Data Types: char

nport — Number of ports

positive integer

This property is read-only.

Number of ports, specified as a positive integer.

Data Types: double

OuterRadius — Outer conductor radius

scalar in meters

Outer conductor radius, specified as a scalar in meters. The default value is 0.0026.

Data Types: double

SigmaCond — Conductor conductivity

scalar

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

Data Types: double

StubMode — Type of stub

'NotaStub' | '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

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

Examples

Create Coaxial Transmission Line

Create a coaxial transmission line with 0.0045 meters outer radius using rfckt.coaxial.

tx1=rfckt.coaxial('OuterRadius',0.0045)

tx1 = 
   rfckt.coaxial with properties:

       OuterRadius: 0.0045
       InnerRadius: 7.2500e-04
               MuR: 1
          EpsilonR: 2.3000
       LossTangent: 0
         SigmaCond: Inf
        LineLength: 0.0100
          StubMode: 'NotAStub'
       Termination: 'NotApplicable'
             nPort: 2
    AnalyzedResult: []
              Name: 'Coaxial Transmission Line'

Algorithms

The analyze method treats the transmission line as a 2-port linear network. It computes the AnalyzedResult property of a stub or as a stubless line using the data stored in the rfckt.coaxial object properties as follows:

• If you model the transmission line as a stubless 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

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

  In these equations:

  • a is the radius of the inner conductor.

  • b is the radius of the outer conductor.

  • σ_cond is the conductivity 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 method 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 before R2006a