Convert RLGC transmission line parameters to S-parameters
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
R — Resistance matrix
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
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
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
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
Length of transmission line, specified as a scalar in meters.
freq — Frequency
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.
s_params — S-parameters
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
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.
 Bhatti, A. A. “A Computer Based Method for Computing the N-Dimensional Generalized ABCD Parameter Matrices of N-Dimensional Systems with Distributed Parameters.”  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.
Introduced in R2011b