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rlgc2s

Convert RLGC transmission line parameters to S-parameters

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Syntax

s_params = rlgc2s(R,L,G,C,length,freq)
s_params = rlgc2s(___,z0)

Description

s_params = rlgc2s(R,L,G,C,length,freq) transforms RLGC transmission line parameter data into S-parameters with a reference impedance of 50 Ω.

example

s_params = rlgc2s(___,z0) transforms RLGC transmission line parameter data into S-parameters with a reference impedance of z0. Use this option with the input arguments in the previous syntax.

Examples

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Open Live Script

Define the variables for a transmission line.

length = 1e-3;
freq = 1e9;
z0 = 50;
R = 50;
L = 1e-9;
G = .01;
C = 1e-12;

Calculate the s-parameters.

s_params = rlgc2s(R,L,G,C,length,freq,z0)
s_params = 2×2 complex

   0.0002 - 0.0001i   0.9993 - 0.0002i
   0.9993 - 0.0002i   0.0002 - 0.0001i

Input Arguments

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Resistance matrix, specified as an N-by-N-by-M array of distributed resistances, in units of Ω/m. The N-by-N matrices must be real symmetric, the diagonal terms must be nonnegative, and the off-diagonal terms must be nonnegative.

Inductance matrix, specified as an N-by-N-by-M array of distributed inductances, in units of H/m. The N-by-N matrices must be real symmetric, the diagonal terms must be positive, and the off-diagonal terms must be nonnegative.

Conductance Matrix, specified as an N-by-N-by-M array of distributed conductances, in units of S/m. The N-by-N matrices must be real symmetric, the diagonal terms must be nonnegative, and the off-diagonal terms must be nonpositive.

Capacitance matrix, specified as an N-by-N-by-M array of distributed capacitances, in units of F/m. The matrices must be real symmetric, the diagonal terms must be positive, and the off-diagonal terms must be nonpositive.

Length of transmission line, specified as a scalar in meters.

Frequency, Specified as a vector of M frequencies over which the transmission line parameters are defined.

Reference impedance of N-port S-Parameters, specified as positive real scalar in ohms.

Output Arguments

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S-parameters, returned as a 2N-by-2N-by-M array of complex numbers. The following figure describes the port ordering convention of the output.

Port ordering in 4-by-4 S-parameters matrix

This port ordering convention assumes that:

  • Each 2N-by-2N matrix consists of N input terminals and N output terminals.

  • The first N ports (1 through N) of the S-parameter matrix are input ports.

  • The last N ports (N + 1 through 2N) are output ports.

To reorder ports after using this function, use the snp2smp function.

More About

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RLCG Transmission Line Model

The following figure illustrates the RLGC transmission line model.RLGC transmission line

The representation consists of:

  • The distributed resistance, R, of the conductors, represented by a series resistor.

  • The distributed inductance, L, represented by a series inductor.

  • The distributed conductance, G,

  • The distributed capacitance, C, between the two conductors, represented by a shunt capacitor.

RLGC component units are all per unit length Δx.

References

[1] Bhatti, A. A. “A Computer Based Method for Computing the N-Dimensional Generalized ABCD Parameter Matrices of N-Dimensional Systems with Distributed Parameters.” [1990] Proceedings. The Twenty-Second Southeastern Symposium on System Theory, IEEE Comput. Soc. Press, 1990, pp. 590–93. DOI.org (Crossref), doi:10.1109/SSST.1990.138213.

Version History

Introduced in R2011b

See Also