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Coplanar waveguide transmission line

Use the `cpw`

object to represent coplanar waveguide
transmission lines that are characterized by line dimensions, stub type, and
termination.

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 permittivity constant
(*ε*).

`h = rfckt.cpw`

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

`h = rfckt.cpw`

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

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

sets
properties using one or more name-value pairs. For example,
`rfckt.cpw ('ConductorWidth',0.3)`

creates an RF
coplanar waveguide transmission line with a width of 0.3 . You can specify
multiple name-value pairs. Enclose each property name in a quote.

`analyze` | Analyze RFCKT object in frequency domain |

`calculate` | Calculate specified parameters for rfckt objects or rfdata objects |

`plotyy` | Plot specified parameters on X-Y plane with Y-axes on both left and right sides |

`getz0` | Get characteristic impedance of transmission line object |

`circle` | Draw circles on Smith Chart |

`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 specified circuit object parameters on X-Y plane |

`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
stub less line using the data stored in the `rfckt.cpw`

object
properties as follows:

If you model the transmission line as a stub less 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 specified conductor strip width, slot width, substrate height, conductor strip thickness, relative permittivity constant, conductivity and dielectric loss tangent of the transmission line, as described in [1].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}$$\begin{array}{c}A=1\\ B={Z}_{in}\\ C=0\\ D=1\end{array}$$

The `analyze`

method uses the S-parameters to
calculate the group delay values at the frequencies specified in the
`analyze`

input argument `freq`

, as described in
the `analyze`

reference page.

[1] [1] Gupta, K. C., R. Garg, I. Bahl, and P. Bhartia, *Microstrip Lines
and Slotlines*, 2nd Edition, Artech House, Inc., Norwood, MA,
1996.

`rfckt.coaxial`

| `rfckt.microstrip`

| `rfckt.parallelplate`

| `rfckt.rlcgline`

| `rfckt.twowire`

| `rfckt.txline`