Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Chapter 21 Decibels, Filters, and Bode Plots Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] OBJECTIVES • Develop confidence in the use of logarithms and decibels in the description of power and voltage levels. • Become familiar with the frequency response of high- and low-pass filters. Learn to calculate the cutoff frequency and describe the phase response. • Be able to calculate the cutoff frequencies and sketch the frequency response of a pass-band or stop-band filter. • Develop skills in interpreting and establishing the Bode response of any filter. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INTRODUCTION • The unit decibel (dB), defined by a logarithmic expression, is used throughout the industry to define levels of audio, voltage gain, energy, field strength, and so on. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INTRODUCTION Logarithms • Basic Relationships – Let us first examine the relationship between the variables of the logarithmic function. – The mathematical expression: Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] INTRODUCTION Logarithms • Some Areas of Application – The following are some of the most common applications of the logarithmic function: • 1. The response of a system can be plotted for a range of values that may otherwise be impossible or unwieldy with a linear scale. • 2. Levels of power, voltage, and the like can be compared without dealing with very large or very small numbers that often cloud the true impact of the difference in magnitudes. • 3. A number of systems respond to outside stimuli in a nonlinear logarithmic manner. • 4. The response of a cascaded or compound system can be rapidly determined using logarithms if the gain of each stage is known on a logarithmic basis. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PROPERTIES OF LOGARITHMS • There are a few characteristics of logarithms that should be emphasized: – The common or natural logarithm of the number 1 is 0 – The log of any number less than 1 is a negative number – The log of the product of two numbers is the sum of the logs of the numbers – The log of the quotient of two numbers is the log of the numerator minus the log of the denominator – The log of a number taken to a power is equal to the product of the power and the log of the number Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DECIBELS • Power Gain • Voltage Gain • Human Auditory Response Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DECIBELS TABLE 21.1 Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DECIBELS Pout Pin dB 10log10 ( Pout Pin ) 0.1 -10 1 0 2 3 10 10 20 13 100 20 1000 20 10000 40 Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DECIBELS TABLE 21.2 Typical sound levels and their decibel levels. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] DECIBELS FIG. 21.5 LRAD (Long Range Acoustic Device) 1000X. (Courtesy of the American Technology Corporation.) Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] FILTERS • Any combination of passive (R, L, and C) and/or active (transistors or operational amplifiers) elements designed to select or reject a band of frequencies is called a filter. • In communication systems, filters are used to pass those frequencies containing the desired information and to reject the remaining frequencies. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] FILTERS • In general, there are two classifications of filters: – Passive filters – Active filters Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] FILTERS FIG. 21.7 Defining the four broad categories of filters. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C LOW-PASS FILTER FIG. 21.8 Low-pass filter. Introductory Circuit Analysis, 12/e Boylestad FIG. 21.9 R-C low-pass filter at low frequencies. Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C LOW-PASS FILTER FIG. 21.10 R-C low-pass filter at high frequencies. Introductory Circuit Analysis, 12/e Boylestad FIG. 21.11 Vo versus frequency for a lowpass R-C filter. Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C LOW-PASS FILTER FIG. 21.12 Normalized plot of Fig. 21.11. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C LOW-PASS FILTER FIG. 21.13 Angle by which Vo leads Vi. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C LOW-PASS FILTER FIG. 21.14 Angle by which Vo lags Vi. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C LOW-PASS FILTER FIG. 21.15 Low-pass R-L filter. Introductory Circuit Analysis, 12/e Boylestad FIG. 21.16 Example 21.5. Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C LOW-PASS FILTER FIG. 21.17 Frequency response for the low-pass R-C network in Fig. 21.16. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C LOW-PASS FILTER FIG. 21.18 Normalized plot of Fig. 21.17. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C HIGH-PASS FILTER FIG. 21.19 High-pass filter. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C HIGH-PASS FILTER FIG. 21.20 R-C high-pass filter at very high frequencies. Introductory Circuit Analysis, 12/e Boylestad FIG. 21.21 R-C high-pass filter at f = 0 Hz. Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C HIGH-PASS FILTER FIG. 21.22 Vo versus frequency for a high-pass R-C filter. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C HIGH-PASS FILTER FIG. 21.23 Normalized plot of Fig. 21.22. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C HIGH-PASS FILTER FIG. 21.24 Phase-angle response for the high-pass R-C filter. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C HIGH-PASS FILTER FIG. 21.25 High-pass R-L filter. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C HIGH-PASS FILTER FIG. 21.26 Normalized plots for a low-pass and a high-pass filter using the same elements. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] R-C HIGH-PASS FILTER FIG. 21.27 Phase plots for a low-pass and a high-pass filter using the same elements. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PASS-BAND FILTERS FIG. 21.28 Series resonant pass-band filter. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PASS-BAND FILTERS FIG. 21.29 Parallel resonant pass-band filter. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PASS-BAND FILTERS FIG. 21.30 Series resonant pass-band filter for Example 21.7. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PASS-BAND FILTERS FIG. 21.31 Pass-band response for the network. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PASS-BAND FILTERS FIG. 21.32 Normalized plots for the pass-band filter in Fig. 21.30. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PASS-BAND FILTERS FIG. 21.33 Pass-band filter. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PASS-BAND FILTERS FIG. 21.34 Pass-band characteristics. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PASS-BAND FILTERS FIG. 21.35 Pass-band filter. Introductory Circuit Analysis, 12/e Boylestad FIG. 21.36 Pass-band characteristics for the filter in Fig. 21.35. Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] PASS-BAND FILTERS FIG. 21.37 Network of Fig. 21.35 at f = 994.72 kHz. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BAND-REJECT FILTERS • Since the characteristics of a bandreject filter (also called stop-band or notch filter) are the inverse of the pattern obtained for the band-pass filter, a band-reject filter can be designed by simply applying Kirchhoff’s voltage law to each circuit. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BAND-REJECT FILTERS FIG. 21.38 Demonstrating how an applied signal of fixed magnitude can be broken down into a pass-band and band-reject response curve. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BAND-REJECT FILTERS FIG. 21.39 Band-reject filter using a series resonant circuit. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BAND-REJECT FILTERS FIG. 21.40 Band-reject filter using a parallel resonant network. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BAND-REJECT FILTERS FIG. 21.41 Band-reject filter. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint] BAND-REJECT FILTERS FIG. 21.42 Band-reject characteristics. Introductory Circuit Analysis, 12/e Boylestad Copyright ©2011 by Pearson Education, Inc. publishing as Pearson [imprint]