Dear Si-List Members, I wish all of you a beautiful Holiday season and a happy prosperous New Year! Procedures for SPICE modeling of coupled transmission lines constitute an important signal integrity topic. For case of two balanced symmetric lines, the following relations can prove useful: Z_even = sqrt[L11 + L12)/(C11- C12)] TD_even = sqrt[(L11 + L12) * (C11 - C12)] Z_odd = sqrt[(L11- L12)/(C11 + C12)] TD_odd = sqrt[(L11- L12) * (C11 + C12)] Where, Z_odd is equivalent impedance for a coupled pair of transmission lines propagating in the odd mode pattern; Z_even is impedance for the even mode pattern. similarly, TD_odd and TD_even represent equivalent delay for a coupled pair propagating in odd mode and even mode patterns respectively. Derivation of above equations are presented in reference 1. One interesting application of these formulas relates to obtaining coupled SPICE model from TDR measured data. Here, the goal being to compute the [L] and [C] matrices given the following TDR measurements: Differential impedance (i.e., Z_diff = 2 * Z_odd for a symmetric pair) Common mode impedance (i.e., Z_comm = 0.5 * Z_even) Differential delay (i.e. TD_diff = TD_odd) Common mode delay (i.e. TD_comm = TD_even) The formulas outlined in this post are sufficient for solving L11, L12, C11 and C12 from the TDR measured Z_diff, Z_comm, TD_diff and TD_comm for a coupled pair. Furthermore, for case of balanced transmission lines consisting of two identical conductors symmetrical with respect to planes: L11 = L22, L12 = L21, C11 = C22, C12=C21 Subsequently, all elements (including self and mutual inductance and capacitance values) of the [L] and [C] matrices can be ascertained to allow construction of the desired coupled SPICE model. There exist other techniques for generating coupled lines models based on TDR measurements, but the method discussed here can be appealing particularly to those who enjoy mathematics. When such a SPICE model is produced, it is in good practice to simulate it under conditions emulating TDR measurements (i.e. same source and line termination) and then correlating the simulation results with the TDR measured data. This can provide useful information for verifying the quality and accuracy of the model. Reference 1. Stephen H. Hall, Garrett W. Hall, and James A. McCall, "High-Speed Digital System Design A Handbook of Interconnect Theory and Design Practices", John Wiley & Sons, Inc., 2000, PP. 53-57. Kind Regards, Abe Riazi ServerWorks ------------------------------------------------------------------ To unsubscribe from si-list: si-list-request@xxxxxxxxxxxxx with 'unsubscribe' in the Subject field or to administer your membership from a web page, go to: //www.freelists.org/webpage/si-list For help: si-list-request@xxxxxxxxxxxxx with 'help' in the Subject field List FAQ wiki page is located at: http://si-list.org/wiki/wiki.pl?Si-List_FAQ List technical documents are available at: http://www.si-list.org List archives are viewable at: //www.freelists.org/archives/si-list or at our remote archives: http://groups.yahoo.com/group/si-list/messages Old (prior to June 6, 2001) list archives are viewable at: http://www.qsl.net/wb6tpu