A simple method for restoring passivity in S-parameters using singular value decomposition

With new high speed data standards, such as USB 3.0, data rate has increased up to 5 Gbps (a 10-fold increase from USB 2.0) creating new challenges for a design engineer. Amid these speeds, issues like crosstalk, signal integrity and bit-error rates are coming to the forefront of the design cycle, especially for consumer electronics-related devices. Therefore, there is a need of accurate methods to characterize device behavior at high frequencies. For instance, S-parameter characterization of high speed interconnect components by full wave field solvers, macromodels and physical measurement are prone to numerical, modeling, and measurement error. This error can lead to non-physical results such as passivity violations. This is a major problem in modern package design where extensive signal integrity simulations are required to validate a systems performance and passivity violations can cause such simulations to fail completely. This paper presents a new method for restoring passivity to non-passive S-parameter data by using singular value decomposition. Simulations show promising results although the method is limited to passivity violations of 1 dB.