A Convex Programming Approach for Generating Guaranteed Passive Approximations to Tabulated Frequency-Data

Fast Passivity Enforcement of $S$-Parameter Macromodels by Pole Perturbation

“…In the case of scattering parameters, the exact definition of passivity stipulates that must be unitary bounded (4) such that the following equivalent condition is satisfied:…”

“…Nevertheless, passivity of the macromodel is of crucial importance since a nonpassive model may lead to unstable transient simulations in an unpredictable manner. Several techniques have been considered to address this issue, ranging from convex optimization [4] to Nevanlinna-pick interpolation [5], semidefinite programming [6], linear or quadratic programming [7], residue perturbation [8]- [10], pole perturbation [11], modal perturbation [12], waveform shaping [13], and others [14]- [17]. This paper introduces a new iterative algorithm that is able to enforce passivity by means of a fast pole perturbation scheme.…”

Compact Reduced Order Modeling for Multiple-Port Interconnects

“…But as shown in the examples, with terminal reduction technique, we can actually handle circuits with much large terminals. Also more efficient convex programming implementation in [3] can be used to further improve the capacity.…”

“…In [3] a Positive Real Lemma has been introduced to check passivity of the system. The following two statements can be proved to be equivalent.…”

“…(21) will lead to a very large number of constraints. Thus we use a more compact form [3] in our implementation.…”