# rfckt.rlcgline

Passive component or network

## Description

Use the rlcgline object to represent RLCG transmission lines that are characterized by line loss, line length, stub type, and termination.

## Creation

### Description

example

h = rfckt.rlcgline returns an RLCG transmission line object whose properties are set to their default values.

h = rfckt.rlcgline(Name,Value) sets properties using one or more name-value pairs. For example, rfckt.rlcgline('LineLenght',0.04) creates a RLGC transmission line with a physical length of 0.04 meters. You can specify multiple name-value pairs. Enclose each property name in a quote. Properties not specified retain their default values.

## Properties

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Computed S-parameters, noise figure, OIP3, and group delay values, specified as rfdata.data object. AnalyzedResult is a read-only property. For more information refer, .Algorithms.

Data Types: function_handle

Resistance values per length, specified as a vector in ohms per meter. The resistance values correspond to the frequency values in 'Freq' property. All values must be positive. The default value is 0.

Data Types: double

Capacitance values per length, specified as a vector in farads per meter. The capacitance values correspond to the frequency values in 'Freq' property. All values must be positive. The default value is 0.

Data Types: double

Frequency data for the RLCG values, specified as a M-element vector. The values must be positive and correspond to the order of the RLCG values. The default value is 1e9.

Data Types: double

Conductance values per length, specified as a vector in Siemens per meter. The conductance values correspond to the frequency values in 'Freq' property. All values must be positive. The default value is 0.

Data Types: double

Interpolation method used in rfckt.rlcgline, specified as one of the following values:

MethodDescription
LinearLinear interpolation
SplineCubic spline interpolation
CubicPiecewise cubic Hermite interpolation

Data Types: char

Inductance values per length, specified as vector in henries per meter. The inductance values correspond to the frequency values in 'Freq' property. All values must be positive. The default value is 0.

Data Types: double

Physical length of transmission line, specified as a scalar in meters. The default value is 0.01.

Data Types: double

Object name, specified as a 1-by-N character array. Name is a read-only property.

Data Types: char

Number of ports, specified as a positive integer. nportt is a read-only property. The default value is 2.

Data Types: double

Type of stub, specified as one of the following values: 'NotaStub', 'Series', 'Shunt'.

Data Types: double

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 X-Y 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 groupdelay Group delay of S-parameter object or RF filter object or RF Toolbox circuit object

## Examples

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Create an RLCG transmission line using rfckt.rlcgline.

rlcgtx=rfckt.rlcgline('R',0.002,'C',8.8542e-12,'L',1.2566e-6,'G',0.002')
rlcgtx =
rfckt.rlcgline with properties:

Freq: 1.0000e+09
R: 0.0020
L: 1.2566e-06
C: 8.8542e-12
G: 0.0020
IntpType: 'Linear'
LineLength: 0.0100
StubMode: 'NotAStub'
Termination: 'NotApplicable'
nPort: 2
AnalyzedResult: []
Name: 'RLCG Transmission Line'

## Algorithms

The analyze method treats the transmission line, which can be lossy or lossless, as a 2-port linear network. It uses the interpolation method you specify in the IntpType property to find the R, L, C, and G values at the frequencies you specify when you call analyze. Then, it calculates the characteristic impedance, Z0, phase velocity, PV, and loss using these interpolated values. It computes the AnalyzedResult property of a stub or as a stubless line using the data stored in the rfckt.rlcgline 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:

$\begin{array}{c}{Z}_{0}=\sqrt{\frac{R+j2\pi fL}{G+j2\pi fC}}\\ k={k}_{r}+j{k}_{i}=\sqrt{\left(R+j2\pi fL\right)\left(G+j2\pi FC\right)}\end{array}$

• 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.

Zin 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.

Zin is the input impedance of the series circuit. The ABCD-parameters for the series stub are calculated as:

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

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.

## References

[1] Ludwig, R. and P. Bretchko, RF Circuit Design: Theory and Applications, Prentice-Hall, 2000