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At the University of Denver we have taught circuits for eighteen years to electrical (EE), mechanical (ME) and computer engineering (CpE) sophomores using a considerably different approach. Our course covers most of the traditional topics but with different emphasis and organization. We introduce design and evaluation right from the beginning with students designing circuits to meet constraints within the first several lessons. We introduce the operational amplifier as another linear circuit element early and fully integrate it throughout the course. DC circuits are designed using voltage and current dividers to deliver specified currents, voltages or power; interface circuits are designed when neither the source circuit nor the load circuit is alterable; and instrumentation systems are created to interface transducers to a particular output device. A major departure from most circuits courses occurs in our approach to dynamic circuits. We begin by introducing a separate block on signal waveforms including singularity functions, exponentials, sinusoids and their combinations. This better prepares the student for finding solutions of firstand second-order circuits using the classical differential equation approach. The most significant departure from tradition occurs when Laplace transforms are introduced immediately after the classical treatment of circuit differential equations. This arrangement allows the concepts of sinusoidal steady-state response, network functions, frequency responses, impulse response, step responses, and convolution to be treated within a common framework. We have found that beginning students achieve a real understanding of transient and steady-state responses more rapidly by this method than the classical phasor-first approach. The Laplace transform early approach actually saves classroom time because students quickly master classical phasor analysis when it is presented as a logical outgrowth of an overall theme. We spend a block of time on mastering how to design circuits to achieve a desired transfer function. Since there are often several competing solutions, learning how to choose between the various solutions depending on different constraints is another key feature of our course. Finally, we spend a block of time designing both active and passive filters (Butterworth, Chebyshev, First-order Cascade) – real applications. Students learn how to select the best filter type based on various real scenarios. Computer simulations and an accompanying lab add additional realism to the course. In sum students become highly motivated because they know how to actually design circuits. The emphasis on design and Laplace transforms prepares them well for Electronics, Signals and Systems, Controls and Instrumentation courses. This approach has been successfully applied to the circuits courses taught at the USAF Academy. P ge 991.1 Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education Introduction Linear circuits are ubiquitously taught to all electrical and computer engineers. It is also often a required course for numerous other engineering disciplines, mechanical and bio engineers most notably. Although there are numerous variants to how circuits are currently taught the most common approach is to teach linear circuits by beginning with dc circuits, introduce circuit theorems, then possibly teach dependent sources and the operational amplifier, introduce inductors and capacitors followed by first-order RL and RC circuits, then transition to ac circuits using phasor analysis. Subsequently there appears to be two major approaches. Some will teach frequency response and three-phase power using only phasor analysis, while others will introduce Laplace transforms and do ac circuits using Laplace analysis. Up to the early 1990’s essentially all circuits courses that were taught solved only analysis problems – that is, circuit problems were usually constructed so that students determined an output of a circuit given one or more inputs. There was only one acceptable solution to the problem. In the early 1990’s the Accreditation Board for Engineering and Technology (ABET) began emphasizing the importance of design in the curriculum. What ABET sought to influence were programs wherein students had some experience with design before they attempted their capstone design project. Although design was usually added to other than circuits courses, a few brave circuits instructors began to add some design content to their courses. Some circuits texts began to include some design problems. Today including design content in the first and/or second circuits course is still far from being universally adopted. Many students, especially those in non-electrical/computer engineering programs, view linear circuits as uninteresting, difficult and unrewarding. After eighteen years teaching circuits with a different approach, we believe that our methods yield a more efficient and exciting method of teaching circuits. Furthermore, students appear to like this method more than the classical approach, they learn more and are better prepared to pursue subsequent courses. Our basic philosophy The philosophy we espouse is to deliver a course that would involve students more in the learning process. We believe that students connect more with what they are learning if they can see that what they are doing is actually practical. That is, they see usefulness to what they are learning. In understanding human learning we turned to Bloom’s Taxonomy of Educational Objectives 1 . We felt that by having students master higher level thinking skills would engage them intellectually and make learning more rewarding. Coupling design skills, for example, to a laboratory program would then permit the students to see that they could actually build circuits that would perform in the manner they wanted. In addition, since different students will solve design problems differently it is natural to ask which design is the better. We felt that students should be able to determine which solution is the best considering given constraints. We added elements to the course that have students compare and evaluate designs. This effort is called Evaluation in Bloom’s Taxonomy and represents the highest level of cognitive learning. The traditional approach to linear circuits introduces phasors before Laplace transforms. This time-honored method is based using phasors to develop ac circuit analysis, frequency response, steady-state power, and polyphase circuit analysis. Laplace transform theory, if taught at all in P ge 991.2 Proceedings of the 2004 American Society for Engineering Education Annual Conference & Exposition Copyright © 2004, American Society for Engineering Education circuit courses, is often left to the last few weeks of the second course. Our experience is that students find the challenge of first learning phasor analysis about the same as learning Laplace analysis. The advantage of treating Laplace analysis first is that once mastered it makes learning phasor analysis easy – much easier than learning Laplace analysis after having first mastering phasor analysis. The basic problem with the phasor-first method is that most students never make the connection between phasor analysis and the transient and steady-state concepts developed through Laplace analysis. They rarely see that phasor analysis is just a special case of Laplace analysis and that phasors are a simplifying tool for treating the sinusoidal steady-state. Our approach to teaching linear circuits Our course begins much like traditional courses with dc circuits. However, immediately after the basic theorems we have added a lesson on signal transfer and a lesson on interface circuit design. These two lectures occur just after eight lectures on fundamentals. The lesson on signal transfer prepares students to know that circuits have limitations on how much voltage, current or power can be delivered to a load. Interface circuit design enables students to deliver to a fixed load from a fixed source a requisite voltage, current or power providing, of course, that the maximum possible signal limit is not exceeded. In this section we also begin a discussion of loading – what it is, when it is a bad thing and when it is a good thing. A suitable laboratory exercise is to have students design an interface circuit to deliver a certain voltage, current or power ±10% to a fixed load using a limited set of resistors, for example. As simple as this exercise is it begins to build confidence early that the student can design. Who has created the best design vis-à-vis a set of constraints begins providing insight into the highest level of learning – Evaluation. Since we do a lot of design in our course the Op-amp becomes an essential tool. We develop student understanding of Op-Amp behavior as follows. We begin with two lessons on dependent sources including analysis of a dependent source circuit with feedback. Then we have a lesson on the BJT transistor – using a piecewise linear model as a simple demonstration of the use of modeling active circuits with dependent sources. This prepares us to transition to studying the Op-Amp. We use four lectures in teaching about the Op-Amp. We focus on its use as a premier design tool. We cover cascading Op-Amps and raise the issue of loading again – including the use of the Follower. We have students practice interfacing transducers to Op-Amps as part of an instrumentation system. In designing instrumentation systems we begin with a desired transducer and its characteristic and finish with a working circuit that produces the desired output. We show students how to design both a weighted summer D/A and an R-2R D/A. Determining which D/A approach is better continues to introduce students to making choices. An instrumentation laboratory exercise using a strain

A Proven Different Approach To Teaching Linear Circuits