Timing and Transients in Digital Circuits - Integrated Systems ...

1 What you will learnComputer science views digital circuits as ideal machines and describes their behavior using mathematicalmodels such as finite state machines and computer arithmetics. While such abstractions arevalid and useful given certain preconditions, they omit a number of effects that impact real circuits.The most important simplifications relate to transients and delays that come from the fact that noelectrical node can change its state in zero time and no physical signal can propagate in zero time.Getting the timing right is absolutely essential when designing a digital circuit, if that circuit is meant tobehave in the same way as its mathematical or computer model. Several lessons of our VLSI coursewill be devoted to data throughput, timing constraints, tradeoffs between time and energy, clockingdisciplines, sychronization, metastability, and other timing-related issues.This warm-up exercise is here to make sure you are aware of the fundamental concepts and quantitiesrequired to understand that material and to become an expert user of electronic design automation(EDA) software. More specifically, we will show you• How to capture the time-wise behavior of digital (sub)circuits.• Visual formalisms that help analyze timing issues.• The very basics of synchronous circuit operation and simulation set up.• What determines the maximum frequency at which a circuit can be clocked.• The dependencies introduced by signals entering or departing from a circuit.• Things to watch out for when designing control logic and state machines.2 Terms and Concepts2.1 Transients in digital circuitsAll circuits discussed here are digital and make use of two-valued signals. For practical reasons,the voltage levels that represent 0 and 1 respectively must be separated by some “forbidden” intervalwhere a signal has no meaningful binary interpretation and must be considered as logically undefinedor invalid. In accordance with the IEEE 1164 standard, we use the symbol X to denote situationswhere a signal is electrically driven but has no known logic value. Note that any signal that switchesfrom 0 to 1 or vice versa will transit through the forbidden interval for a brief lapse of time.Some signals may even rock back and forth a few times or exihibit short-lived voltage excursionsbefore eventually reaching their steady-state condition. As explained in appendix A.5 “Transient behaviorof logic circuits” of our textbook 1 even circuits of just a few gates must be suspected to developsuch spurious and unwanted signals, known as hazards, unless one has proof to the contrary.2.2 Combinational, sequential, and sychronous circuitsA digital circuit is qualified as combinational if its present output gets determined by its presentinput exclusively when in steady-state condition. This contrasts with sequential logic the output ofwhich depends not only on present but also on past input values. Sequential circuits must, therefore,necessarily keep their state in some kind of storage elements whereas combinational ones have no1Hubert Kaeslin, “Digital Integrated Circuit Design, from VLSI Architectures to CMOS Fabrication”, CambridgeUniversity Press, 2008.2