s2rlgc - Convert S-parameters to RLGC transmission line parameters

Syntax

Description

rlgc_params = s2rlgc(s_params,length,freq,z0) transforms multi-port S-parameter data into a frequency-domain representation of an RLGC transmission line.

rlgc_params = s2rlgc(s_params,length,freq) transforms multi-port S-parameter data into RLGC transmission line parameters using a reference impedance of 50 Ω.

Input Arguments

s_params	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 snp2smp function.
length	Specify the length of the transmission line in meters.
freq	Specify the vector of M frequencies over which the S-parameter array s_params is defined.
z0	Specify the reference impedance of the S-parameters in ohms. Default: 50

Output Arguments

rlgc_params

The output 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 input vector freq. rlgc_params.R is 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.L is 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.G is 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.C is 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.Zc is an array of complex characteristic line impedances, in ohms. rlgc_params.alpha is an array of real attenuation coefficients, in units of Np/m. rlgc_params.beta is an array of real phase constants, in units of rad/m.

Definitions

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.

Examples

Convert S-parameters to RLGC transmission line 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];
length = 1e-3;
freq = 1e9;
z0 = 50;
rlgc_params = s2rlgc(s_params,length,freq,z0)

References

Degerstrom, M.J., B.K. Gilbert, and E.S. Daniel. "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 multiconductor transmission lines using S-parameter models." Electrical Performance of Electronic Packaging,. IEEE-EPEP, 18th Conference, 27–29 October 2008, pp. 259–262.

See Also

rlgc2s

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