AC Circuit Analysis
CIRCUITS LABORATORY EXPERIMENT 3 AC Circuit Analysis
3.1
Introduction
The steady-state behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the generation, transmission, distribution, and consumption of electric energy occur under essentially sinusoidal steady-state conditions. Second, an understanding of sinusoidal behavior makes possible the prediction of circuit behavior when nonsinusoidal sources are used through the use of techniques such as Fourier analysis and superposition. Finally, by specifying the performance of a circuit in terms of its steady-state sinusoidal behavior, the design of the circuit can often be simplified. Needless to say, the importance of sinusoidal steady-state behavior cannot be overemphasized, and many of the topics in future experiments are based on a thorough understanding of the techniques used to analyze circuits driven by sinusoidal sources. In this experiment, the behavior of several types of circuits will be examined to determine their behavior when excited by sinusoidal sources. First, the behavior of both RC and RLC circuits will be examined when driven by a sinusoidal source at a 3-1
given frequency. Subsequently, the frequency response of both a low-pass filter and a high-pass filter will be considered.
3.2 Objectives
At the end of this experiment, the student will be able to: (1) Determine the steady-state behavior of linear circuits driven by sinusoidal sources, (2) Use the oscilloscope to measure the phase difference between two sinusoidal signals, (3) Determine analytically the frequency response of a network, (4) Construct Bode plots relating the magnitude and phase response of the voltage ratio of a linear network as a function of frequency, and (5) Design primitive low- and high-pass filters using one resistor and one capacitor.
3.3
Theory
3.3.1 Sinusoidal Steady-State Analysis
As stated previously, the steady-state behavior of
3.1
Introduction
The steady-state behavior of circuits energized by sinusoidal sources is an important area of study for several reasons. First, the generation, transmission, distribution, and consumption of electric energy occur under essentially sinusoidal steady-state conditions. Second, an understanding of sinusoidal behavior makes possible the prediction of circuit behavior when nonsinusoidal sources are used through the use of techniques such as Fourier analysis and superposition. Finally, by specifying the performance of a circuit in terms of its steady-state sinusoidal behavior, the design of the circuit can often be simplified. Needless to say, the importance of sinusoidal steady-state behavior cannot be overemphasized, and many of the topics in future experiments are based on a thorough understanding of the techniques used to analyze circuits driven by sinusoidal sources. In this experiment, the behavior of several types of circuits will be examined to determine their behavior when excited by sinusoidal sources. First, the behavior of both RC and RLC circuits will be examined when driven by a sinusoidal source at a 3-1
given frequency. Subsequently, the frequency response of both a low-pass filter and a high-pass filter will be considered.
3.2 Objectives
At the end of this experiment, the student will be able to: (1) Determine the steady-state behavior of linear circuits driven by sinusoidal sources, (2) Use the oscilloscope to measure the phase difference between two sinusoidal signals, (3) Determine analytically the frequency response of a network, (4) Construct Bode plots relating the magnitude and phase response of the voltage ratio of a linear network as a function of frequency, and (5) Design primitive low- and high-pass filters using one resistor and one capacitor.
3.3
Theory
3.3.1 Sinusoidal Steady-State Analysis
As stated previously, the steady-state behavior of
References: 1. Nilsson, J. W., Electric Circuits, (5th ed.), Prentice Hall, Upper Saddle River, New Jersey, 2001. 2. Grinich, V. H. and Jackson, H. C., Introduction to Integrated Circuits, McGraw-Hill, New York, 1975. 3 - 28