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Short Circuited RLGC Transmitting Line with Floating Ground (Closed Form): RLGC_TxS2

Symbol

Summary

RLGC_TxO2 simulates a general short-circuited transmission line with isolated ground terminals. This model provides computation of circuit parameters for general transmission lines whose behavior in a frequency domain is governed by a user- supplied table of primary per-unit-length line parameters R, L, G, and C. Extreme care should be used with this element as it is meant to work in concert with additional elements which relate the voltages at the end of the transmission line to the global ground. Unusual and unexpected behavior can result if these additional elements are omitted. See the RLGC_Tx4 model documentation for implementation details.

Equivalent Circuit of Single Line

Parameters

Name Description Unit Type Default
ID Name Text TL1
Len Length of Line Length L[1]
F Vector of Frequencies at which L, C, R, G specified Frequency 1 GHz
R Vector of Series R per-unit-length Resistance/meter 100
L Vector of Series L per-unit-length Inductance/meter Li[1]
G Vector of Shunt G per-unit-length Conductance/meter 0
C Vector of Shunt C per-unit-length Capacitance/meter C[1]

[1] User-modifiable default. Modify by editing the DEFAULT.LPF file in the root installation directory. See “Default Values” for details.

Parameter Details

F. Vector of frequencies at which R, L, G, and C parameters are specified. Frequencies must be sequential and specified in ascending order.

R. Vector of series resistance (see Equivalent Circuit) per-unit-length specified in resistance project units per meter. Each vector entry must be specified at the corresponding frequency entry from frequency vector F.

L. Vector of series inductance (see Equivalent Circuit) per-unit-length specified in inductance project units per meter. Each vector entry must be specified at the corresponding frequency entry from frequency vector F.

G. Vector of shunt conductance (see Equivalent Circuit) per-unit-length specified in conductance project units per meter. Each vector entry must be specified at the corresponding frequency entry from frequency vector F.

C. Vector of shunt capacitance (see Equivalent Circuit) per-unit-length specified in capacitance project units per meter. Each vector entry must be specified at the corresponding frequency entry from frequency vector F.

Parameter Restrictions and Recommendations

  1. Lengths of vector parameters R, L, G, and C must be exactly equal to the length of frequency vector F.

  2. If project operational frequency is out of range of frequencies in F then R, L, G, and C parameters are extrapolated as constant values equal to the first/last entries of corresponding vectors. No warning is issued.

  3. Vector can be specified in three ways: First, it can be entered as a right side value of model parameter, e.g. R={100,102,110,113,120}; Second, vector can be specified elsewhere in equation; Third way is specification of vector in a column or row of a text file. Third way provides a convenient and flexible method of specification of all RLGC parameters in the single location. Just create, for example, file RLGC.txt containing space separated columns of R1, R2 etc. First column must represent frequency in project units (note that changing of project default frequency units will demand manual scaling of frequencies in this file). Import or link this file to your project and give it a name, say, RLGC_15. Now you can specify, say, parameter R as R = Col(datafile("RLGC_15"),1). It means that values of vector R will be copied to the model from the column 1 of file RLGC.txt imported under name RLGC_15. If you prefer to deploy your data row-wise use R = Row(datafile("RLGC_15"),1).

  4. If your project uses text file input to feed data to this model be aware what frequency, resistance, inductance or conductance units this file implies. There is a chance that default units of your project differ from those in your data file. If this happens, you must scale input values multiplying call of function Col or Row by scaling coefficient. For example, if your project uses capacitances in picofarads and data file contains data in Farads you may get capacitance data from the fifth column of data file RLGC_15 like this: C1= 1e+12*Col(datafile("RLGC_15"),5).

Implementation Details

Model implementation is based on linear interpolation of RLGC parameters at each project evaluation frequency. Interpolation uses user-supplied via parameters look-out tables. If project operational frequency is out of range of frequencies in F then R, L, G, and C parameters are extrapolated as constant values equal to the first/last entries of corresponding vectors.

The following is a Y-matrix for a grounded transmission line system:

where α+jβ represents the complex propagation constant, Z is the characteristic impedance of the line and L is the length of the line as derived from the input parameters.

Applying the equivalent circuit shown above, the Y-matrix of the floating transmission line system can be shown to be the following:

At DC, the Y-Matrix changes to a model of two wires above a ground plane:

where R is a real resistance approaching zero.

Layout

This element does not have an assigned layout cell. You can assign artwork cells to any element. See “Assigning Artwork Cells to Layout of Schematic Elements” for details.

Recommendations for Use

This model, along with additional components can be used to model transmission line baluns and transmission line transformers in which one of the conductors is shielded from ground, like a coaxial line.

NOTE: Because the model definition does not include interactions with the ground, unusual and unexpected results can occur if other components are not used to relate the voltage on both sides of the transmission line to ground.

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