Analog and Mixed Signal Verification using Satisfiability Solver on Discretized Models

With increasing demand of performance constraints and the ever reducing size of the IC chips, analog and mixed-signal designs have become indispensable and increasingly complex in modern CMOS technologies. This has resulted in the rise of stochastic behavior in circuits, making it important to detect all the corner cases and verify the correct functionality of the design under all circumstances during the earlier stages of the design process. It can be achieved by functional or formal verification methods, which are still widely unexplored for Analog and Mixed-Signal (AMS) designs. Design Verification is a process to validate the performance of the system in accordance with desired specifications. Functional verification relies on simulating different combinations of inputs for maximum state space coverage. With the exponential increase in the complexity of circuits, traditional functional verification techniques are getting more and more inadequate in terms of exhaustiveness of the solution. Formal verification attempts to provide a mathematical proof for the correctness of the design regardless of the circumstances. Thus, it is possible to get 100% coverage using formal verification. However, it requires advanced mathematics knowledge and thus is not feasible for all applications. In this thesis, we present a technique for analog and mixed-signal verification targeting DC verification using Berkeley Short-channel Igfet Models (BSIM) for approximation. The verification problem is first defined using the state space equations for the given circuit and applying Satisfiability Modulo Theories (SMT) solver to determine a region that encloses complete DC equilibrium of the circuit. The technique is applied to an example circuit and the results are analyzed in turns of runtime effectiveness