Charge Pump Phase-Locked Loops and Full Wave Rectifiers for Reachability Analysis

Abstract

Analog-mixed signal (AMS) circuits are widely used in various mission-critical applications necessitating their formal verification prior to implementation. We consider modeling two AMS circuits as hybrid automata, particularly a charge pump phase-locked loop (CP-PLL) and a full-wave rectifier (FWR). We present executable models for the benchmarks in SpaceEx format, perform reachability analysis, and demonstrate their automatic conversion to MathWorks Simulink/Stateflow (SLSF) format using the HyST tool. Moreover, as a next step towards implementation, we present the VHDL-AMS description of a circuit based on the verified model. Category: academic Difficulty: medium Context and OriginsMany analog-mixed signal (AMS) circuits are widely used in various mission cicritical applications and require formal verification prior implementation. Formal verification methods construct a mathematical model M with precise semantics, provide extensive analysis with respect to some correctness requirement P, and verify that M |= P [2]. This can be ascertained through reachability analysis [1]. As an example of circuitry that can benefit from formal verification prior to field implementation and deployment, we provide two potential benchmarks for hybrid verification research community, i.e., charge pump phase-locked loop (CP-PLL), and full-wave rectifier (FWR).CP-PLL integrated circuits are widely used in modern mobile, radio, and wireless communication applications to synchronize a high-frequency signal with a low-frequency reference signal. In [8], the auhtors use SpaceEx model checking tool [6] to verify the global convergence with respect to phase and frequency lock for a digital PLL. An FWR converts an AC electric input signal to a DC output signal, and formal verification through reachability analysis has been reported using different model checking tools in [5], except SpaceEx. We develop hybrid automaton models of and used SpaceEx [6], a reachability analysis G