Using Threshold Functions in Teaching Electronics

Abstract

Teaching of digital electronics and the teaching of analog electronics differ significantly. The methods in use today differ in two major points: the required mathematical background and the used didactic methods. The well-known gap between the analog and the digital paradigms in teaching electronics has motivated the present study. The paper introduces a novel approach for electronics course teaching. The approach uses a concept threshold functions. Threshold functions have three remarkable properties that are suitable for the purposes of teaching an electronics course. The first property is the simplicity of the functions’ representation and implementation; the essence of a threshold function is understandable on the common sense level. The second property is the dual analog-digital nature of the threshold functions. The definition of a threshold function usually includes both Boolean and arithmetic portions and weaves together the two alternative domains: digital and analog. Since students are familiar with regular arithmetic functions from previous math courses, the addition of Boolean concepts is simple to grasp. The possibility to transform any threshold function from one domain to another, serves as a powerful tool for processes teaching. The third property we consider is the multiple representations possible for threshold functions. Besides the classical Boolean and arithmetic representations, a threshold function can be represented in the format of an electric/electronic circuit and also can be represented in a spatial form, by three-dimensional visualization for better understanding the functional properties of threshold functions. The paper discusses a problem-based learning with two main types of problems: synthesis and analysis problems of threshold elements. While the analysis problem is relatively simple, the problem of optimal synthesis is NP-complete, and equivalent to a well-known optimization problem that exists also in linear programming. Using the linear programming for teaching the synthesis of a threshold element is a challenging pedagogical task. The paper describes an approach for solving this task. A number of real-world problems may be formulated and efficiently solved by using the proposed threshold-based approach, for example the problems of event-driven control, fuzzy control, linear optimization, self-regulation. These problems formulate as students’ assignments, and are used in the lesson. These exercises convert a lesson of electronics into an interesting, challengeable and useful educational event. Introduction of the threshold approach into the electronics curriculum enables the students to acquire much deeper understanding of electronic systems.