PRIMA: passive reduced-order interconnect macromodeling algorithm
ICCAD '97 Proceedings of the 1997 IEEE/ACM international conference on Computer-aided design
Phase noise in oscillators: DAEs and colored noise sources
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
Computing phase noise eigenfunctions directly from steady-state Jacobian matrices
Proceedings of the 2000 IEEE/ACM international conference on Computer-aided design
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Proceedings of the 44th annual Design Automation Conference
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We present an efficient method for automatically extracting unified amplitude/phase macromodels of arbitrary oscillators from their SPICE-level circuit descriptions. Such comprehensive oscillator macromodels are necessary for accuracy when speeding up simulation of higher-level circuits/systems, such as PLLs, in which oscillators are embedded. Standard MOR techniques for linear time invariant (LTI) and varying (LTV) systems are not applicable to oscillators on account of their fundamentally nonlinear phase behavior. By employing a cancellation technique to deflate out the phase component, we restore the validity and efficacy of Krylov-subspace-based LTV MOR techniques for macromodelling oscillator amplitude responses. The nonlinear phase response is re-incorporated into the macromodel after the amplitude components have been reduced. The resulting unified macromodels predict oscillator waveforms, in the presence of any kind of input or interference, at far lower computational cost than full SPICE-level simulation, and with far greater accuracy compared to existing macromodels. We demonstrate the proposed techniques on LC and ring oscillators, obtaining speedups of 30-120 x with no appreciable loss of accuracy, even for small circuits.