Verification Of Analog Circuits Research Articles

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.

Causal reasoning mining approach to analog circuit verification

Functional errors in analog portion of mixed signal circuits become more severe and improvements in verification methods are increasingly important. Current verification methods fall into two categories, simulation-based verification and formal verification (Barke et al. [1]), focusing on verifying analog circuit function/performance. This paper proposes a novel approach verifying analog circuit design using causal reasoning. Causal reasoning is the inductive reasoning process to create a new design. The flow begins with mining the causal reasoning steps (design plan) that produced the circuit, including starting ideas, design step sequence, and their justifications (Jiao et al., 2015 [2]). Then, topological features corresponding to the starting ideas and design step sequence are verified individually by replacing the related devices with ideal behavior model. Performance is evaluated through Cadence Spectre simulation. Comparison with new circuit performance reveals incorrect functional issues and/or performance potentials for improvement. They are negative causes of certain starting ideas or design steps, which might have been omitted during the design process. The paper discusses three operational amplifier designs realized in 0.2-μm CMOS technology to illustrate the verification approach.

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 Monte-Carlo and Bootstrap statistical techniques are compared for a Colpitts oscillator and a phase locked loop-based frequency synthesizer circuit.

Simulation-based verification using Temporally Attributed Boolean Logic

We propose a specification logic called Temporally Attributed Boolean (TAB) Logic for Assertion Based Verification, which allows us to: (i) represent assertions succinctly, (ii) incorporate data-orientation and (iii) associate timing to design intentions. TAB Logic allows us to write specifications functionally linking system variables from different temporal contexts. We present examples to show the motivation for this logic especially in the context of high level modeling of complex real time systems. We formally define TAB Logic, formulate the problem of verification on a simulation trace and present efficient algorithms to check TAB assertions, both offline and online. We present results of application of TAB Logic for Instruction Semantics and Bus Transaction Verification of a bus integrated pipelined processor core implementation. We also employ TAB Logic to validate the Interrupt mode behavior of the processor core implementation. Further, we show the utility of TAB Logic in fault detection. Finally, we demonstrate the applicability of TAB Logic in the domain of simulation based verification of analog circuits like Operational Amplifiers and DC-DC Converters. We finally discuss the limitations of TAB logic and conclude.

A verification system for transient response of analog circuits

We present a method for application of formal techniques like model checking and equivalence checking for validation of the transient response of nonlinear analog circuits. We propose a temporal logic called Ana CTL (computational tree logic for analog circuit verification) which is suitable for specifying properties specific to analog circuits. The application of Ana CTL for validation of transient behavior of arbitrarily nonlinear analog circuits is presented. The transient response of a circuit under all possible input waveforms is represented as a finite state machine (FSM), by bounding and discretizing the continuous state space of an analog circuit. We have developed algorithms to run Ana CTL queries on this discretized model using search-based methods which reduce the runtime considerably by avoiding creation of the whole FSM. The application of these methods on several real-life analog circuits is presented and we show that this system is a useful aid for detecting and debugging early design errors. We also present methods for checking the equivalence of transient response of two analog circuits. The behavior of two different analog circuits can rarely be exactly similar. Hence, we introduce a notion of approximate equivalence. A query language for checking different notions of user-definable approximate equivalence is presented which extends the syntax of the Ana CTL model checking language. In its extended form, Ana CTL can be used combining model checking with equivalence checking.

Analog Circuit Verification: a State of an Art

Extending formal verification methodology toward analog circuits is a very challenging task that will occupy researchers for some time. To put this challenge in context we sketch some of the history of digital circuit verification as well as more recent attempts to adapt it to continnuous and hybrid systems.

The Case for Analog Circuit Verification

The traditional approach to validate analog circuits is to utilize extensive SPICE-level simulations. The main challenge of this approach is knowing when all important corner cases have been simulated. A new alternative is to utilize formal verification techniques. This paper utilizes a simple example to illustrate the potential flaws of a simulation-only based validation methodology and the potential benefits of formal verification of analog circuits.

Frequency Response Verification of Analog Circuits Using Global Optimization Techniques

This paper develops a new formal technique to verify the frequency response of analog circuits using global optimization techniques. Since simulation-based approaches are unable to cover the design space, there is a need for formal approaches to verify large circuits. Drawing parallels from the digital domain, the verification problem in the analog domain is modeled as a non-linear optimization problem and solved using global optimization techniques by ensuring that the implementation response is bounded within an envelope around the specification. We also address the problem of verifying frequency response under the influence of parameter variations. Direct as well as indirect techniques are illustrated using accurate frequency response models. Experimental results are presented to show the effectiveness of the proposed methodology.