Characterization of multiple coupled interconnection lines from time domain measurement

Measurement techniques used to characterize the uniformly and nonuniformly coupled interconnects in high-speed single-layered and multilayered structures are reported. For an N-line structure, time-domain reflectometer (TDR) measurements can be used to extract all the normal mode parameters of the coupled interconnect system. These include N×(N+1)/2 independent characteristic impedance matrix elements, N eigenvalues representing the normal mode velocities, and a voltage or current eigenvector matrix. The basic excitation response model is shown. For uniformly coupled lines N sets of linearly independent measurements can be made where step waveforms are applied at specified nodes and the response is measured at all the nodes. With a multichannel TDR system it is possible to excite more than one line at a time, e.g. the common and differential modes of a pair of coupled lines. The characteristic impedance matrix elements are evaluated in terms of the generalized reflection coefficient or the scattering matrix elements at the input end in terms of N linearly independent excitations