rlgc2s

Convert RLGC transmission line parameters to S-parameters

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.

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

Convert RLGC Transmission Line Parameters to S-Parameters

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

R — Resistance matrix

N-by-N-by-M array

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.

L — Inductance matrix

N-by-N-by-M array

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.

G — Conductance Matrix

N-by-N-by-M array

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.

C — Capacitance matrix

N-by-N-by-M array

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 — Length of transmission line

scalar

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

freq — Frequency

M-by-1

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

z0 — Reference impedance

50 (default) | positive real scalar

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

Output Arguments

s_params — S-parameters

2N-by-2N-by-M array

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.

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

RLCG Transmission Line Model

The following figure illustrates the RLGC transmission line model.

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