AnalogNotes - Lecture Notes for Analog Electronics Raymond...

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Lecture Notes for Analog Electronics Raymond E. Frey Physics Department University of Oregon Eugene, OR 97403, USA [email protected] December, 1999
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Class Notes 1 1 Basic Principles In electromagnetism, voltage is a unit of either electrical potential or EMF. In electronics, including the text, the term “voltage” refers to the physical quantity of either potential or EMF. Note that we will use SI units, as does the text. As usual, the sign convention for current I = dq/dt is that I is positive in the direction which positive electrical charge moves. We will begin by considering DC ( i.e. constant in time) voltages and currents to introduce Ohm’s Law and Kirchoff’s Laws. We will soon see, however, that these generalize to AC. 1.1 Ohm’s Law For a resistor R , as in the Fig. 1 below, the voltage drop from point a to b , V = V ab = V a - V b is given by V = IR . I R ab Figure 1: Voltage drop across a resistor. Adev ice( e.g. a resistor) which obeys Ohm’s Law is said to be ohmic. The power dissipated by the resistor is P = VI = I 2 R = V 2 /R . 1.2 Kirchoff’s Laws Consider an electrical circuit, that is a closed conductive path (for example a battery con- nected to a resistor via conductive wire), or a network of interconnected paths. 1. For any node of the circuit in I = out I . Note that the choice of “in” or “out” for any circuit segment is arbitrary, but it must remain consistent. So for the example of Fig. 2 we have I 1 = I 2 + I 3 . 2. For any closed circuit, the sum of the circuit EMFs ( e.g. batteries, generators) is equal to the sum of the circuit voltage drops: E = V . Three simple, but important, applications of these “laws” follow. 1
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II I 12 3 Figure 2: A current node. 1.2.1 Resistors in series Two resistors, R 1 and R 2 , connected in series have voltage drop V = I ( R 1 + R 2 ). That is, they have a combined resistance R s given by their sum: R s = R 1 + R 2 This generalizes for n series resistors to R s = n i =1 R i . 1.2.2 Resistors in parallel Two resistors, R 1 and R 2 , connected in parallel have voltage drop V = IR p ,where R p =[(1 /R 1 )+(1 /R 2 )] - 1 This generalizes for n parallel resistors to 1 /R p = n X i =1 1 /R i 1.2.3 Voltage Divider The circuit of Fig. 3 is called a voltage divider. It is one of the most useful and important circuit elements we will encounter. The relationship between V in = V ac and V out = V bc is given by V out = V in ± R 2 R 1 + R 2 ² 1.3 Voltage and Current Sources A voltage source delivers a constant voltage regardless of the current it produces. It is an idealization. For example a battery can be thought of as a voltage source in series with a small resistor (the “internal resistance” of the battery). When we indicate a voltage V input to a circuit, this is to be considered a voltage source unless otherwise stated.
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This note was uploaded on 08/07/2011 for the course ECE 209 taught by Professor Arif during the Summer '11 term at National Institute of Technology, Calicut.

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AnalogNotes - Lecture Notes for Analog Electronics Raymond...

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