rlgc2s - Convert RLGC transmission line parameters to S-parameters

Syntax

Description

s_params = rlgc2s(R,L,G,C,length,freq,z0) transforms RLGC transmission line parameter data into S-parameters.

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.

Input Arguments

R	Specify 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	Specify 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	Specify 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	Specify 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	Specify the length of the transmission line in meters.
freq	Specify the vector of M frequencies over which the transmission line parameters are defined.
z0	Specify the reference impedance of the resulting S-parameters in ohms. Default: 50

Output Arguments

s_params

The output is a 2N-by-2N-by-M array of S-parameters. 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.

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, 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.

Examples

Convert RLGC transmission line parameters into S-parameters:

%Define transmission line variables
length = 1e-3;
freq = 1e9;
z0 = 50;
R = 50;
L = 1e-9;
G = .01;
C = 1e-12;
% Calculate S-parameters
s_params = rlgc2s(R,L,G,C,length,freq,z0)

References

Bhatti, A. Aziz. "A computer Based Method for Computing the N-Dimensional Generalized ABCD Parameter Matrices of N-Dimensional Systems with Distributed Parameters." Southeastern Symposium on System Theory. SSST, 22nd Conference, 11–13 March 1990, pp. 590–593.

See Also

s2rlgc

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