Verifying robust frequency domain properties of non linear oscillators using SMT

We present a novel mixed time and frequency domain approach to the formal verification of oscillators properties which are specified in the frequency domain. We use robust periodogram specification to specify the oscillator behaviour in the close vicinity of the limit cycle. Using SAT modulo ODE (SMO) for Bounded Model Checking (BMC) of the non-linear hybrid automata, we show that the oscillator hybrid timed traces satisfy frequency domain specifications

Workshop on Verification and Theorem Proving for Continuous Systems (NetCA Workshop 2005)

Oxford, UK, 26 August 200

Millimeter wave experiment for ATS-F

A detailed description of spaceborne equipment is provided. The equipment consists of two transmitters radiating signals at 20 and 30 GHz from either U.S. coverage horn antennas or a narrow beam parabolic antenna. Three modes of operation are provided: a continuous wave mode, a multitone mode in which nine spectral lines having 180 MHz separation and spaced symmetrically about each carrier, and a communications mode in which communications signals from the main spacecraft transponder are modulated on the two carriers. Detailed performance attained in the flight/prototype model of the equipment is presented both under laboratory conditions and under environmental extremes. Provisions made for ensuring reliability in space operation are described. Also described the bench test equipment developed for use with the experiment, and a summary of the new technology is included

Exploiting Bounds Optimization for the Semi-formal Verification of Analog Circuits

This paper proposes a semi-formal methodology for modeling and verification of analog circuits behavioral properties using multivariate optimization techniques. Analog circuit differential models are automatically extracted and their qualitative behavior is computed for interval-valued parameters, inputs and initial conditions. The method has the advantage of guaranteeing the rough enclosure of any possible dynamical behavior of analog circuits. The circuit behavioral properties are then verified on the generated transient response bounds. Experimental results show that the resulting state variable envelopes can be effectively employed for a sound verification of analog circuit properties, in an acceptable run-time

Towards the automated modelling and formal verification of analog designs

The verification of analog circuits remains a very time consuming and expensive part of the design process. Complete simulation of the state space is not possible; a line is drawn by the designer when it is deemed that enough sets of inputs and outputs have been covered and therefore the circuit is "verified". Unfortunately, bugs could still exist and for safety critical applications this is not acceptable. As well, a bug in the design could lead to costly recalls and a loss of revenue. Formal methods, which use mathematical logic to prove correctness of a design have been developed. However, available techniques for the formal verification of analog circuits are plagued by inaccuracies and a high level of user effort and interaction. We propose in this thesis a complete methodology for the modelling and formal verification of analog circuits. Bond graphs, which are based on the flow of power, are used to automatically extract the circuit's system of Ordinary Differential Equations. Subsequently, two formal verification methods, one based on automated theorem proving with MetiTarski, the other on predicate abstraction based model checking with HybridSal, are then used to verify functional properties on the extracted models. The methodology proposed is mechanical in nature and can be made completely automated. We apply this modelling and verification methodology on a set of analog designs that exhibit complex non-linear behaviour

Statistical Run-Time Verification of Analog Circuits in Presence of Noise and Process Variation

Noise and process variation present a practical limit on the performance of analog circuits. This paper proposes a methodology for modeling and verification of analog designs in the presence of shot noise, thermal noise, and process variations. The idea is to use stochastic differential equations to model noise in additive and multiplicative form and then combine process variation due to 0.18 μm technology in a statistical run-time verification environment. The efficiency of MonteCarlo and Bootstrap statistical techniques are compared for a Colpitts oscillator and a phase locked loop-based frequency synthesizer circuit

Surrogate based Optimization and Verification of Analog and Mixed Signal Circuits

Nonlinear Analog and Mixed Signal (AMS) circuits are very complex and expensive to design and verify. Deeper technology scaling has made these designs susceptible to noise and process variations which presents a growing concern due to the degradation in the circuit performances and risks of design failures. In fact, due to process parameters, AMS circuits like phase locked loops may present chaotic behavior that can be confused with noisy behavior. To design and verify circuits, current industrial designs rely heavily on simulation based verification and knowledge based optimization techniques. However, such techniques lack mathematical rigor necessary to catch up with the growing design constraints besides being computationally intractable. Given all aforementioned barriers, new techniques are needed to ensure that circuits are robust and optimized despite process variations and possible chaotic behavior. In this thesis, we develop a methodology for optimization and verification of AMS circuits advancing three frontiers in the variability-aware design flow. The first frontier is a robust circuit sizing methodology wherein a multi-level circuit optimization approach is proposed. The optimization is conducted in two phases. First, a global sizing phase powered by a regional sensitivity analysis to quickly scout the feasible design space that reduces the optimization search. Second, nominal sizing step based on space mapping of two AMS circuits models at different levels of abstraction is developed for the sake of breaking the re-design loop without performance penalties. The second frontier concerns a dynamics verification scheme of the circuit behavior (i.e., study the chaotic vs. stochastic circuit behavior). It is based on a surrogate generation approach and a statistical proof by contradiction technique using Gaussian Kernel measure in the state space domain. The last frontier focus on quantitative verification approaches to predict parametric yield for both a single and multiple circuit performance constraints. The single performance approach is based on a combination of geometrical intertwined reachability analysis and a non-parametric statistical verification scheme. On the other hand, the multiple performances approach involves process parameter reduction, state space based pattern matching, and multiple hypothesis testing procedures. The performance of the proposed methodology is demonstrated on several benchmark analog and mixed signal circuits. The optimization approach greatly improves computational efficiency while locating a comparable/better design point than other approaches. Moreover, great improvements were achieved using our verification methods with many orders of speedup compared to existing techniques

A Framework for Noise Analysis and Verification of Analog Circuits

Analog circuit design and verification face significant challenges due to circuit complexity and short market windows. In particular, the influence of technology parameters on circuits, noise modeling and verification still remain a priority for many applications. Noise could be due to unwanted interaction between the various circuit blocks or it could be inherited from the circuit elements. Current industrial designs rely heavily on simulation techniques, but ensuring the correctness of such designs under all circumstances usually becomes impractically expensive. In this PhD thesis, we propose a methodology for modeling and verification of analog designs in the presence of noise and process variation using run-time verification methods. Verification based on run-time techniques employs logical or statistical monitors to check if an execution (simulation) of the design model violates the design specifications (properties). In order to study the random behavior of noise, we propose an approach based on modeling the designs using stochastic differential equations (SDE) in the time domain. Then, we define assertion and statistical verification methods in a MATLAB SDE simulation framework for monitoring properties of interest in order to detect errors. In order to overcome some of the drawbacks associated with monitoring techniques, we define a pattern matching based verification method for qualitative estimation of the simulation traces. We illustrate the efficiency of the proposed methods on different benchmark circuits

Retention and application of Skylab experiences to future programs

The problems encountered and special techniques and procedures developed on the Skylab program are described along with the experiences and practical benefits obtained for dissemination and use on future programs. Three major topics are discussed: electrical problems, mechanical problems, and special techniques. Special techniques and procedures are identified that were either developed or refined during the Skylab program. These techniques and procedures came from all manufacturing and test phases of the Skylab program and include both flight and GSE items from component level to sophisticated spaceflight systems