ELEC 326Kartik MohanramHanded out on Thursday, August 27th, 20091 ObjectivesThe circuits studied in this course are examples of electrical systems. Therefore, these notes will primarily• provide an introduction to the general properties and characteristics of electrical systems,• explain the role of system models in the analysis and synthesis of electrical systems, and• give a brief introduction to digital systems.I encourage all of you to read Chapter 1 in the textbook. This is a general introduction to the area of digital design thatshould be viewed as introductory material augmenting these notes.1.1 What is a system?A system is a collection of devices assembled to perform a useful transformation of information.• Information is presented to a system’s input terminals in the form of time-varying signals.• Changes in a system’s input signals can produce changes in its output signals after some delay (controlling thisdelay is at the core of all system design).• Systems may contain internal memory used to save information for future use.• The value of a system’s output signal is determined by the values of the system’s input signals and the informa-tion in its internal memory.• The values of the output signals are determined by some rule or algorithm that can be physically implemented.• If a system has memory, it can have two or more different output values for the same input value.1.2 System modelsA system model is a simplified description of one or more properties of a system.• Models predict how a system will react to changes in its input signals.• Models predict system behavior without building a physical instance of the system.• A single model never represents all of the physical properties of a system, and therefore cannot exactly predicta system’s behavior.• While in theory we could represent everything about a system, the result would be a model that is at least ascomplex as the system it models.• We use simple models that can answer questions about certain system properties of interest, and may have touse different types of models to answer questions about other properties.11.3 Structural vs. behavioral modelsThere are two types of models that you will encounter in this course. One is used to describe how a system is built andthe other to describe what it does.A structural model describes how a system is built (i.e., its internal structure).• It usually takes the form of a diagram showing how the component parts of the system are interconnected.• It could also take the form of one or more lists of components and connections (e.g., the input to a computersimulation program).• Structural models show how to build a system, but are not usually very good for predicting its behavior.• Even structural models leave out some detail to make them manageable (e.g., the physical positioning of wiresand components).A behavioral model describes what a system does by defining the transformation of input signals into outputsignals by the system (i.e., its external behavior).• Behavioral models usually do not provide any information about how the system is built (i.e., its internal details).• Completely different physical systems can have the same behavior, so a behavioral model does not describe aunique system.In the past, most models of physical systems were based on mathematical equations. Recall simple systems of equa-tions that you solved in your mechanics and basis EE classes. In recent years, the use of computer simulation modelshas become widespread.1.4 Analysis, synthesis, & verification of systems• Analysis: Derive a system’s behavior from a description of its physical structure, i.e., derive a behavioral modelfor the system from its structural model.• Synthesis: Build a system that has a given behavior, i.e., derive a structural model for the system from itsbehavioral model.• Usually we want to optimize one or more parameters when we synthesize a system, e.g., speed, power, cost,reliability.• Automating synthesis with computer-aided design tools (CAD) tools to map the behavioral model into a struc-tural model. Three main companies that do this – Synopsys, Mentor Graphic, Cadence.1.5 Hierarchical system organizationHierarchically organized systems have the following properties:• A hierarchical system consists of building block modules interconnected in some way.• The modules themselves are constructed from interconnected simpler modules.• Internal module design detail is hidden from and independent of systems built from them.• Without this hierarchical approach we cannot build complex systems.• For the hierarchical approach to work, the models for a module’s behavior must remain valid when they areconnected to other modules, i.e., connecting modules must not affect the behavior of those modules.22 Digital systemsSome basic characteristics of all digital systems follow• Signals can assume only a discrete number of values, usually two.• For two-valued systems, it is usual to designate the two signal voltages as L and H (for low and high) instead ofreferring to them by the actual voltages of the signals.• Advantages of two-valued signals:– Noise immunity– Unlimited precision: use multiple signals– Simple, cheap, and stable circuits– Easy to detect one of two values – using the notion of thresholds• Digital system models are based on discrete math and algorithms, e.g., Boolean algebra, graphical state transitiongraphs, algorithms (flow charts, programs).• Digital systems are behaviorally or structurally described using hardware description languages (HDLs). Exam-ples include Verilog, which we will study in reasonable depth in this course, and VHDL.2.1 Combinational vs. sequential systems• Combinational systems have no memory, so input signals uniquely determine output signals. If the inputssignals are the same at two different times, the outputs at those times will be the same.• Sequential systems have memory, so past input signals can affect current output signals. The same input signalsat different times can produce different output signals. Sequential systems are built by adding memory to com-binational systems. The memory in a sequential circuit can cause its outputs to depend on past inputs as well ascurrent ones.2.2 Exercise:For each of the following system descriptions indicate whether it can be realized as a combinational system or whethera sequential system must be used.