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Notes 1 - Intro

# Notes 1 - Intro - I INTRODUCTION 1.1 Circuit Theory...

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I. INTRODUCTION 1.1 Circuit Theory Fundamentals In this course we study circuits with non-linear elements or devices (diodes and transistors). We will use circuit theory tools to analyze these circuits. However, some of tools developed in circuit theory apply only to “linear” elements (thus, linear circuit theory). Therefore, let’s first examine what we can use to analyze non-linear elements. 1.1.1 Circuit Theory Elements Circuit theory is an approximation to Maxwell’s electromagnetic equation which allows to analyze complicated circuit. There are nine fundamental circuit elements in circuit theory, denoted by their i v characteristics: Resistor: v = Ri Capacitor: i = C dv dt or V = 1 jωC I Inductor: v = L di dt or V = jωL I Independent voltage source: v = v s = const. for any current Independent current source: i = i s = const. for any voltage and four controlled sources: voltage-controlled voltage source, current-controlled voltage source (similar to independent voltage source but with source strength depending on voltage or current on another element in the circuit) and voltage-controlled current source, current- controlled current source. There are two other circuit elements that we will use and are special cases of the above elements. They are: Short Circuit: v = 0 for any current Open Circuit: i = 0 for any voltage As can be seen, “short circuit” is a special case of a resistor (with R = 0) or a special case of an independent voltage source (with v s = 0) while “open circuit” is a special case of a resistor (with R → ∞ ) or a special case of an independent current source (with i s = 0). ECE65 Lecture Notes (F. Najmabadi), Fall 2009 1

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It is essential to remember that the above circuit elements do NOT represent physical de- vices, rather they are idealized elements, “cooked” up to simplify the analysis (because their voltage-current relationship is linear). Physical elements that we encounter in the real world can only be modeled with one of these ideal elements within a certain range of parameters and within a certain accuracy. For example take a resistor in the lab. At high enough fre- quencies, it will exhibit capacitance ( i.e. its “resistance” drops as frequency increases). At high enough current, when the resistor is hot enough, the ratio of v/i is not linear anymore. So, an “ideal” resistor used in circuit theory is NOT a physical device. Rather, a “real” resistor in the lab can be approximated by an “ideal” resistor only for a range of currents or voltages (typically rated by its maximum power), a range of frequencies, and even a range of environmental conditions (temperature, humidity, etc. ). Only when the voltage across this “real” resistor is directly proportional to the current flowing through it, ı.e., the element i v characteristics equation is v/i = const = R We can take this observation one step further: Any two-terminal network (a box with two wires coming out of it) whose voltage is directly proportional to the current flowing through, i.e., the element i v characteristics equation is v = Ri
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