mu_prime()

Returns the geometrically derived stability factor for the source

Syntax
y = mu_prime(S)

Arguments

Name	Description	Range	Type	Required
S	scattering matrix of a 2-port network	(-∞, ∞)	complex	yes

Examples

a = mu_prime(S)

Defined in

$HPEESOF_DIR/expressions/ael/circuit_fun.ael

See Also

mu()

Notes/Equations

This measurement gives the distance from the center of the Smith chart to the nearest unstable-input (source) stability circle. This stability factor is given by:
mu_prime = {1-|S ₂₂ | ² } / {|S ₁₁ - conj(S ₂₂ )*Delta | + |S ₂₁ *S ₁₂ | }
where Delta is the determinant of the S-parameter matrix. Having mu_prime > 1 is the single necessary and sufficient condition for unconditional stability of the 2-port network.

Reference

M. L. Edwards and J. H. Sinsky, "A new criterion for linear 2-port stability using geometrically derived parameters", IEEE Transactions on Microwave Theory and Techniques, Vol. 40, No. 12, pp. 2303-2311, Dec. 1992.