PRIMA: passive reduced-order interconnect macromodeling algorithm
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
Efficient model order reduction including skin effect
Proceedings of the 40th annual Design Automation Conference
Modeling skin and proximity effects with reduced realizable RL circuits
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Impact of on-chip interconnect frequency-dependent R(f)L(f) on digital and RF design
IEEE Transactions on Very Large Scale Integration (VLSI) Systems
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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With clock frequencies in the multigigahertz range, wide wires in the power and clock distribution networks suffer from prominent frequency-dependent effects. To overcome the simulation problem of such circuits, a guaranteed stable and parallelizable model order reduction technique is proposed that can handle frequency-dependent elements by construction. The basic idea is to match the output at multiple frequencies with a reduced order function. Once the reduced function is known, it becomes straightforward to calculate the time-domain response. Since this technique works in the frequency domain, it does not require replacement of frequency-dependent elements with equivalent constant RLC subcircuits, significantly reducing the size of equivalent circuits of wide power and clock distribution networks. With parallel computation, the proposed technique obtains time-domain responses in comparable time to calculate the first moment in AWE. Simulations have shown that as few as six frequency points are needed for coupled RC circuits and up to 50 frequency points are needed for complex RLC circuits. To test its ability of handling frequency-dependent elements, a sample circuit with frequency-dependent elements is used that is about 30% of the size of the equivalent circuit with constant RLC elements used in SPICE. In all cases, the proposed technique gives accurate and stable time-domain responses.