PPV phase macromodels are important for speeding up simulation of oscillator related circuits, such as PLLs, without sacrificing accuracy. Prior numerical methods for extracting PPVs face very significant robustness and accuracy problems when confronted with digitally controlled oscillators (DCOs, core building blocks in digital phase-locked loops), due to large RC time-constants from gated capacitors. In this paper, we present a hierarchical harmonic balance based technique for numerically extracting the PPV of DCOs from their SPICE-level circuit descriptions. The proposed method applies hierarchical circuit partitioning and multi-level Newton methods to achieve dramatically superior convergence and PPV accuracy in the presence of large RC time-constants. We validate the method on a large DCO with many gated capacitors and demonstrate that it can extract the PPV efficiently and robustly, succeeding when prior methods fail. The method also provides speedups of an order of magnitude for large circuits, in addition to having significantly smaller memory requirements.
Abstract-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 higherlevel 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× with no appreciable loss of accuracy, even for small circuits.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.