Method and apparatus for representing high speed interconnects in closed forms
A simulation apparatus and method is provided for simulating complex high speed interconnects for which closed forms of the S-parameter are incorporated. Differential transmission lines are represented in a causal manner analytically using the 4-port S-parameter without concerns of passivity and stability. Difficult discontinuities of interconnect such as differential vias are represented in closed form and the present invention allows those interconnects to be characterized by 4-port S-parameter measurements or simulation. A complete method of combining causal transmission line models with discontinuities in cascade is provided.
1. A method for modeling a high speed interconnect and transmission line using closed form representations of the S-parameter comprising the steps:
providing computer program instructions to a processor, the processor operable to execute the computer program instructions;
constructing, by the processor executing the computer program instructions, a Discontinuity-Line Model which expresses the S-parameter in closed forms and allows for cascading the high speed interconnect;
deriving, by the processor executing the computer program instructions, an equation for the S-Parameter of the Discontinuity-Line Model which takes into account a propagation constant for the transmission line;
cascading, by the processor executing the computer program instructions, the Discontinuity-Line Model with at least another Discontinuity-Line Model to form a via-line-via model; and
calculating, by the processor executing the computer program instructions, a cascaded S-parameter for the cascaded Discontinuity-Line Model.
2. The method for modeling a high speed interconnect of claim 1 wherein the Discontinuity-Line Model may be applied to both single-ended and differential high speed interconnect systems.
3. The method for modeling a high speed interconnect of claim 1 wherein the step of cascading the Discontinuity-Line Model comprises using the S-parameter obtained from at least one of closed-form representation, measurement, simulation, and 3D modeling.
4. The method for modeling a high speed interconnect of claim 1 wherein the Discontinuity-Line Model is configured for use with a plurality of possible combinations of realistic and complex high speed interconnects.
5. A method for modeling a high speed interconnect comprising the steps of:
on at least one processor operable to execute computer program instructions;
establishing, by the processor executing the computer program instructions, a first set of explicit mathematical expressions for modeling causality into a computational software program running on the at least one processor to obtain dependencies for modeling causality;
loading, by the processor executing the computer program instructions, real values for all parameters in the first set of explicit mathematical expressions into the software program, and the real values obtained from a model circuit,
outputting, by the software program, a complex propagation constant that includes the effects of causality on the high speed interconnect
deriving, by the processor executing the computer program instructions, an equation for the S-Parameter which takes into account the complex propagation constant; and
modeling the high speed interconnect using a closed form expression of the derived S-parameter.
6. The method for modeling a high speed interconnect of claim 5 wherein the complex propagation constant guarantees causality.
7. A method for modeling a high speed interconnect and a transmission line using closed form representations of the S-parameter comprising the steps:
on at least one processor operable to execute computer program instructions;
defining port excitation equations with reference to all ports of a 4-port network;
deriving, by the processor executing the computer program instructions, a matrix representing a summed S-parameter of a discontinuity line model in closed form for the 4-port network and taking into account a propagation constant for the transmission line; cascading, by the processor executing the computer program instructions, the Discontinuity-Line Model with at least another Discontinuity-Line Model to form a via-line-via model; and
providing the port excitation equations and the matrix into a computational software program running on the at least one processor, wherein the software program is operable to calculate a complex propagation constant for the transmission line, and a combined 4-port S-parameter.
8. A method for modeling a high speed interconnect using closed form representations of the S-parameter comprising the steps:
providing computer program instructions to a processor, the processor operable to execute the computer program instructions;
establishing, by the processor executing the computer program instructions, a closed form representation of the S-parameter for a high speed interconnect deriving, by the processor executing the computer program instructions, an equation for the S-Parameter of a Discontinuity-Line Model which takes into account a propagation constant for the transmission line; cascading, by the processor executing the computer program instructions, the Discontinuity-Line Model with at least another Discontinuity-Line Model to form a via-line-via model; and
calculating, by the processor executing the computer program instructions, a timing impairment caused by the interconnect through an analytical treatment of the closed form representation of the S-parameter.