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The number of interconnects in any VLSI system is very large. During high speed interconnect analysis, interconnect effects like signal delay, crosstalk, ground bound noise, ringing and distortion become more significant. These interconnect effects, also known as signal integrity effects, must be taken in to account during digital circuit design. It is predicted that interconnects will be responsible for nearly 70-80% of the signal delay in high-speed systems. For high-speed electronic system design, interconnect simulation and optimization is very important. Here Back propagation Neural network is used for simulating the interconnect and the network is trained using Levenberg-Marquardt algorithm. Neural network Interconnect model captures the relationship between the Physical and signal integrity characteristics of the interconnects involved and produces the output as Capacitance, Characteristic impedance, Inductance matrices by using the training data. The network is trained to produce the results according to the required target. Hence a reasonably good model is developed for the Interconnect circuit design. Further the dimensions of interconnect can be optimized with Genetic algorithm (GA) using the trained ANN models. Here multi-objective GA have been used to design the interconnect model yielding a global optimized output which is required for signal integrity.