Convert S-parameters to RLGC transmission line parameters
Convert S-Parameters to RLGC Parameters
Define the s-parameters.
s_11 = 0.000249791883190134 - 9.42320545953709e-005i; s_12 = 0.999250283783862 - 0.000219770154524734i; s_21 = 0.999250283783863 - 0.000219770154524756i; s_22 = 0.000249791883190079 - 9.42320545953931e-005i; s_params = [s_11,s_12; s_21,s_22];
Specify the length, frequency of operation, and impedance of the transmission line.
length = 1e-3; freq = 1e9; z0 = 50;
Convert from s-parameters to rlgc-parameters.
rlgc_params = s2rlgc(s_params,length,freq,z0)
rlgc_params = struct with fields: R: 50.0000 L: 1.0000e-09 G: 0.0100 C: 1.0000e-12 alpha: 0.7265 beta: 0.2594 Zc: 63.7761 -14.1268i
s_params — Scattering parameters of transmission line
Specify a 2N-by-2N-by-M array of S-parameters to transform into RLGC transmission line parameters. The following figure describes the port ordering convention assumed by the function.
The function 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 before using this function, use the
length — Length of transmission line
Specify the length of the transmission line in meters.
freq — Frequency
Specify the vector of M frequencies over which the S-parameter
s_params is defined.
z0 — Reference impedance
50 (default) | positive real scalar
Reference impedance of N-port S-Parameters, specified as positive real scalar in ohms.
rlgc_params — Transmission line parameters
rlgc_params is structure whose fields are
N-by-N-by-M arrays of
transmission line parameters. Each of the M
N-by-N matrices correspond to a frequency in the
rlgc_params.Ris an array of distributed resistances, in units of Ω/m. The matrices are real symmetric, the diagonal terms are nonnegative, and the off-diagonal terms are nonnegative.
rlgc_params.Lis an array of distributed inductances, in units of H/m. The matrices are real symmetric, the diagonal terms are positive, and the off-diagonal terms are nonnegative.
rlgc_params.Gis an array of distributed conductances, in units of S/m. The matrices are real symmetric, the diagonal terms are nonnegative, and the off-diagonal terms are nonpositive.
rlgc_params.Cis an array of distributed capacitances, in units of F/m. The matrices are real symmetric, the diagonal terms are positive, and the off-diagonal terms are nonpositive.
rlgc_params.Zcis an array of complex characteristic line impedances, in ohms.
rlgc_params.alphais an array of real attenuation coefficients, in units of Np/m.
rlgc_params.betais an array of real phase constants, in units of rad/m.
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, of the conductors, represented by a series inductor.
The distributed conductance, G, between the two conductors, represented by a shunt resistor.
The distributed capacitance, C, between the two conductors, represented by a shunt capacitor.
RLGC component units are all per unit length Δx.
 Degerstrom, M.J., Gilbert, B.K., and Daniel, E.S . "Accurate resistance, inductance, capacitance, and conductance (RLCG) from uniform transmission line measurements."Electrical Performance of Electronic Packaging. IEEE-EPEP, 18th Conference, 27–29 October 2008, pp. 77–80.
 Sampath, M.K. "On addressing the practical issues in the extraction of RLGC parameters for lossy multi-conductor transmission lines using S-parameter models." Electrical Performance of Electronic Packaging,. IEEE-EPEP, 18th Conference, 27–29 October 2008, pp. 259–262.
 Eisenstadt, W. R., and Eo, Y. "S-parameter-based IC interconnect transmission line characterization," IEEE Transactions on Components, Hybrids, and Manufacturing Technology. Vol. 15, No. 4, August 1992, pp. 483–490.