Transcript figure 11-1
Chapter 11 Advanced Operational Amplifier applications Electronic Integration Electronic Differentiation Active Filters o o o o o o Basic Filter Concepts Active Filter Design Low-Pass and High-Pass Filters Frequency and Impedance Scaling Normalized Low-Pass and High-Pass Filters Bandpass and Band-Stop Filters Chapter 11 Advanced Operational Amplifier applications Electronic Integration Electronic Differentiation Active Filters o o o o o o Basic Filter Concepts Active Filter Design Low-Pass and High-Pass Filters Frequency and Impedance Scaling Normalized Low-Pass and High-Pass Filters Bandpass and Band-Stop Filters When the input to an integrator is a dc level, the output will rise linearly with time. FIGURE 11-1 The output of the integrator at t seconds is the area Et under the input waveform Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-2 An ideal electronic integrator iC i1 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Example 11-1 1. Find the peak value of the output of the ideal integrator. The input is vi = 0.5 sin(100t)V. 2. Repeat, when vi = 0.5 sin(103t)V Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 11-3 (Example 11-1) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-4 Bode plot of the gain of an ideal integrator for the R1C = 0.001 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-5 Allowable region of operation for an op-amp integrator Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Practical Integrators FIGURE 11-6(a) A resistor Rf connected in parallel with C causes the practical integrator to behave like an inverting amplifier to dc inputs and like an integrator to high-frequency ac inputs Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-6(b) Bode plot for the practical or ac integrator, showing that integration occurs at frequencies well above 1 / (2Rf C) Xc << Rf 1 2fC << Rf f >> Bogart/Beasley/Rico Electronic Devices and Circuits, 6e 1 2R f C = fc Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Example 11-2 Design a practical integrator that 1. Integrates signals with frequencies down to 100 Hz, 2. Produces a peak output of 0.1 V when the input is a 10-V-Peak sine wave having frequency 10 kHz, and 3. Find the dc component in the output when there is a +50-mV dc input. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 11-7 (Example 11-2) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-8 A three-input integrator Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Chapter 11 Advanced Operational Amplifier applications Electronic Integration Electronic Differentiation Active Filters o o o o o o Basic Filter Concepts Active Filter Design Low-Pass and High-Pass Filters Frequency and Impedance Scaling Normalized Low-Pass and High-Pass Filters Bandpass and Band-Stop Filters FIGURE 11-9 The ideal electronic differentiator produces an output equal to the rate of change of the input. Because the rate of change of a ramp is constant, the output in this example is a dc level. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-10 An ideal electronic differentiator if iC Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-11 A practical differentiator. Differentiation occurs at low frequencies, but resistor R1 prevent high-frequency differentiation Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-12 Bode plots for the ideal and practical differentiators. fb is the break frequency due to the input R1 - C combination and f2 is the upper cutoff frequency of the (closed-loop) amplifier. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Example 11-3 1. Design a practical differentiator that will differentiator that will differentiate signals with frequencies up to 200 Hz. The gain at 10 Hz should be 0.1. 2. If the op-amp used in the design has a unity-gain frequency of 1 MHz, what is the upper cutoff frequency of the differentiator? Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 11-13 (Example 11-3) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e FIGURE 11-14 (Example 11-3) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Chapter 11 Advanced Operational Amplifier applications Electronic Integration Electronic Differentiation Active Filters o o o o o o Basic Filter Concepts Active Filter Design Low-Pass and High-Pass Filters Frequency and Impedance Scaling Normalized Low-Pass and High-Pass Filters Bandpass and Band-Stop Filters FIGURE 11-29 Ideal and practical frequency responses of some commonly used filter types Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-30 Frequency response of low-pass and high-pass Butterworth filters with different orders Filters are classified by their order, an integer number n, also called the number of poles. In general, the higher the order of a filter, the more closely it approximates an ideal filter and the more complex the circuitry required to construct it. The frequency response outside the passband of a filter of order n has a slope that is asymptotic to 20n dB/decade. Filters are also classified as belonging to one of several specific design types that affect their response characteristics within and outside of their pass bands. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-31 Chebyshev low-pass frequency response: f2 = cutoff frequency; RW = ripple width Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-32 Comparison of the frequency responses of secondorder, low-pass Butterworth and Chebyshev filters Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-33 Comparison of the frequency responses of low-Q and high-Q bandpass filters Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-34 Block diagram of a second-order, VCVS low-pass or high-pass filter. It is also called a Sallen-Key filter. + - Low-Pass Filter High-Pass Filter Bogart/Beasley/Rico Electronic Devices and Circuits, 6e ZA ZB ZC ZD R C R C C R C R Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-35 General low-pass filter structure; even-ordered filters do not use the first stage Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-36 General high-pass filter structure; even-ordered filters do not use the first stage Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Example 11-9 Design a third-order, low-pass Butterworth filter for a cutoff frequency of 2.5 kHz. Select R = 10 kΩ. Example 11-10 Design a unity-gain, fourth-order, high-pass Chebyshev filter with 2-dB ripple for a cutoff frequency of 800 kHz. Select C = 100 nF. Example 11-11 A certain normalized low-pass filter from a handbook shows three l-ohm resistors and three capacitors with values C1 = 0.564 F, C2 = 0.222 F, andC3 = 0.0322 F. The normalized frequency is 1 Hz. Determine the new capacitor values required for a cutoff frequency of 5 kHz if we use 10-kΩ resistors. Simple Bandpass Filter FIGURE 11-37 The infinite-gain multiplefeedback (IGMF) second-order bandpass filter Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Example 11-14 Characterize the bandpass filter shown in the following Figure. FIGURE 11-38 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e (Example 11-14) Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-39 A wideband bandpass filter obtained by cascading overlapping low-pass and high-pass filters Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-40 (a) Block diagram of a band-stop filter obtained from a unity-gain bandpass filter. (b) A possible implementation using the multiple-feedback BP filter Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. FIGURE 11-41 Obtaining a wideband band-stop filter from nonoverlapping LP and HP filters Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved. Example 11-15 Design a band-stop filter with center frequency of 1 kHz and a 3-dB rejection band of 150 Hz. Use the following circuit with unity gain.