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Coaxial transmission line

Use the `coaxial`

class to represent coaxial transmission
lines that are characterized by line dimensions, stub type, and
termination.

Use the `coaxial`

class to represent coaxial transmission lines that
are 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*.

`h = rfckt.coaxial`

`h = rfckt.coaxial('Property1',value1,'Property2',value2,...)`

`h = rfckt.coaxial`

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

`h = rfckt.coaxial('Property1',value1,'Property2',value2,...)`

returns a coaxial transmission line object, `h`

, with the
specified properties. Properties that you do not specify retain their
default values.

`analyze` | Analyze circuit object in frequency domain |

`calculate` | Calculate specified parameters for circuit object |

`circle` | Draw circles on Smith Chart |

`listformat` | List valid formats for specified circuit object parameter |

`getz0` | Characteristic impedance of transmission line object |

`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 specified object parameters with y-axes on both left and right sides |

`polar` | Plot specified object parameters on polar coordinates |

`semilogx` | Plot specified circuit object parameters using log scale for x-axis |

`semilogy` | Plot specified circuit object parameters using log scale for y-axis |

`smith` | Plot specified circuit object parameters on Smith chart |

`write` | Write RF data from circuit or data object to file |

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:$$\begin{array}{l}A=\frac{{e}^{kd}+{e}^{-kd}}{2}\\ B=\frac{{Z}_{0}*\left({e}^{kd}-{e}^{-kd}\right)}{2}\\ C=\frac{{e}^{kd}-{e}^{-kd}}{2*{Z}_{0}}\\ D=\frac{{e}^{kd}+{e}^{-kd}}{2}\end{array}$$

*Z*_{0}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

$$\begin{array}{c}R=\frac{1}{2\pi {\sigma}_{cond}{\delta}_{cond}}\left(\frac{1}{a}+\frac{1}{b}\right)\\ L=\frac{\mu}{2\pi}\mathrm{ln}\left(\frac{b}{a}\right)\\ G=\frac{2\pi \omega {\epsilon}^{\u2033}}{\mathrm{ln}\left(\frac{b}{a}\right)}\\ C=\frac{2\pi \epsilon}{\mathrm{ln}\left(\frac{b}{a}\right)}\end{array}$$

In these equations:

*a*is the radius of the inner conductor.*b*is the radius of the outer conductor.*σ*is the conductivity in the conductor._{cond}*μ*is the permeability of the dielectric.*ε*is the permittivity of the dielectric.*ε″*is the imaginary part of*ε*,*ε″*=*ε*_{0}*ε*tan_{r}*δ*, where:*ε*_{0}is the permittivity of free space.*ε*is the_{r}`EpsilonR`

property value.tan

*δ*is the`LossTangent`

property value.

*δ*is the skin depth of the conductor, which the method calculates as $$1/\sqrt{\pi f\mu {\sigma}_{cond}}$$._{cond}*f*is a vector of modeling frequencies determined by the Outport 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*is the input impedance of the shunt circuit. The ABCD-parameters for the shunt stub are calculated as:_{in}$$\begin{array}{c}A=1\\ B=0\\ C=1/{Z}_{in}\\ D=1\end{array}$$

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*is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as_{in}$$\begin{array}{c}A=1\\ B={Z}_{in}\\ C=0\\ D=1\end{array}$$

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

`rfckt.cpw`

| `rfckt.microstrip`

| `rfckt.parallelplate`

| `rfckt.rlcgline`

| `rfckt.txline`