Joel R. Phillips’s research while affiliated with Cadence Design Systems, Inc. and other places

In one embodiment of the invention, a multi-CCC current source model is disclosed to perform statistical timing analysis of an integrated circuit design. The multi-CCC current source model includes a voltage waveform transfer function, a voltage dependent current source, and an output capacitor. The voltage waveform transfer function receives an input voltage waveform and transforms it into an intermediate voltage waveform. The voltage dependent current source generates an output current in response to the intermediate voltage waveform. The output capacitor is coupled in parallel to the voltage dependent current source to generate an output voltage waveform for computation of a timing delay.

In one embodiment of the invention, a method for electronic circuit design is disclosed. The method includes analyzing a hierarchy of a netlist of a circuit to determine primary inputs and primary outputs of the circuit at an upper level, and internal vertices of the circuit at lower levels between the primary inputs and the primary outputs; forming a timing graph of the circuit including a plurality of timing delay edges representing timing delay between the primary inputs, the internal vertices and the primary outputs to form a plurality of paths of a path space from the primary inputs to the primary outputs; and in response to the timing delay of the plurality of timing delay edges, dynamically pruning paths of the plurality of paths using branch and bound techniques on bounds of timing delay that are a function of one or more circuit parameters to reduce the path space down to one or more critical timing paths of the circuit with a worse case metric of timing delay between the primary inputs and the primary outputs. Additionally or alternatively, timing in the circuit may be analyzed to determine a bound of timing delay of the circuit for one or more parameter corners in a parameter space and if the bound of timing delay is worse than a threshold time delay then one or more parameter corners may be pruned from the parameter space using branch and bound techniques.

A system and method are disclosed for waveform based variational static timing analysis. A circuit is divided into its linear circuit parts and non-linear circuit parts and modeled together, by a combination of linear modeling techniques, into linear equations that may be represented by matrices. The linear equations in matrix form may be readily solved by a computer such that an input waveform to an input pin of the circuit can be sequentially “pushed” through the various interconnects and logic networks of the circuit to an output pin. Output voltage waveforms are obtained at each stage of the waveform pushing and may be used to perform static timing analysis.

A method is provided for use during static timing analysis of an integrated circuit design to produce an equivalent waveform model, the method comprising: using an analog model of the inner component, to simulate an inner component to produce multiple analog simulation output characterization waveforms as a function of multiple input waveforms used to characterize the design cell; using the analog model of the inner component to simulate the inner component to produce an analog simulation output waveform as a function of the complex waveform; and producing the equivalent waveform model as a function of the multiple analog simulation output characterization waveforms and the analog simulation output waveform.

In one embodiment of the invention, a method of statically analyzing an integrated circuit with process and environment variations is provided. The method includes characterizing each circuit cell of a cell library for a sensitivity to process parameter variations within a predetermined range; creating a timing graph corresponding to a netlist representing an integrated circuit design; along nodes of the timing graph, computing delay values including sensitivities to process variations; for each selected output node of the netlist, propagating a full timing value function with the sensitivities to the selected output nodes; and generating a parameterized timing report including the sensitivities to the process variations.

In one embodiment, a method of constructing an equivalent waveform model for static timing analysis of integrated circuit designs is disclosed. The method includes fitting time point coefficients (qk) and known time delay values from a delay and slew model of a receiving gate from a timing library; determining waveform values (Ikj) for input waveforms from the timing library; determining timing values (dj) from a timing table in the timing library in response to the input waveforms of the timing library; and determining coefficients (qk) by minimizing a residual of a delay equation.

In one embodiment of the invention, a multi-CCC current source model is disclosed to perform statistical timing analysis of an integrated circuit design. The multi-CCC current source model includes a voltage waveform transfer function, a voltage dependent current source, and an output capacitor. The voltage waveform transfer function receives an input voltage waveform and transforms it into an intermediate voltage waveform. The voltage dependent current source generates an output current in response to the intermediate voltage waveform. The output capacitor is coupled in parallel to the voltage dependent current source to generate an output voltage waveform for computation of a timing delay.

In one embodiment of the invention, a multi-CCC current source model is disclosed to perform statistical timing analysis of an integrated circuit design. The multi-CCC current source model includes a voltage waveform transfer function, a voltage dependent current source, and an output capacitor. The voltage waveform transfer function receives an input voltage waveform and transforms it into an intermediate voltage waveform. The voltage dependent current source generates an output current in response to the intermediate voltage waveform. The output capacitor is coupled in parallel to the voltage dependent current source to generate an output voltage waveform for computation of a timing delay.

A system and method are disclosed for waveform based variational static timing analysis. A circuit is divided into its linear circuit parts and non-linear circuit parts and modeled together, by a combination of linear modeling techniques, into linear equations that may be represented by matrices. The linear equations in matrix form may be readily solved by a computer such that an input waveform to an input pin of the circuit can be sequentially “pushed” through the various interconnects and logic networks of the circuit to an output pin. Output voltage waveforms are obtained at each stage of the waveform pushing and may be used to perform static timing analysis.

Modern deep sub-micron ultra-large scale integration designs with hundreds of millions of devices require huge grids for power distribution. Such grids, operating with decreasing power supply voltages, are a design limiting factor and accurate analysis of their behavior is of paramount importance as any voltage drops can seriously impact performance or functionality. As power grid models have millions of unknowns, highly optimized special-purpose simulation tools are required to handle the time and memory complexity of solving for their dynamic behavior. In this paper, we propose a hierarchical matrix representation of the power grid model that is both space and time efficient. With this representation, reduced storage matrix factors are efficiently computed and applied in the analysis at every time-step of the simulation. Results show an almost linear complexity growth, namely O(n loga(n)), for some small constant a, in both space and time, when using this matrix representation. Comparisons of our academic implementation with production-quality code prove this method to be very efficient when dealing with the simulation of large power grid models.