Advanced Operational Amplifier applications Chapter 11 Advanced Operational Amplifier applications Electronic Integration Electronic Differentiation Active Filters 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

Advanced Operational Amplifier applications Chapter 11 Advanced Operational Amplifier applications Electronic Integration Electronic Differentiation Active Filters 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 Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

Repeat, when vi = 0.5 sin(103t)V Example 11-1 Find the peak value of the output of the ideal integrator. The input is vi = 0.5 sin(100t)V. Repeat, when vi = 0.5 sin(103t)V FIGURE 11-3 (Example 11-1) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 11-4 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.

Xc << Rf << Rf f >> = fc FIGURE 11-6(b) Bode plot for the practical or ac integrator, showing that integration occurs at frequencies well above 1 / (2Rf C) Xc << Rf << Rf f >> = fc Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

Example 11-2 Design a practical integrator that Integrates signals with frequencies down to 100 Hz, Produces a peak output of 0.1 V when the input is a 10-V-Peak sine wave having frequency 10 kHz, and Find the dc component in the output when there is a +50-mV dc input. FIGURE 11-7 (Example 11-2) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 11-8 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.

Advanced Operational Amplifier applications Chapter 11 Advanced Operational Amplifier applications Electronic Integration Electronic Differentiation Active Filters 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 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 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 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.

Advanced Operational Amplifier applications Chapter 11 Advanced Operational Amplifier applications Electronic Integration Electronic Differentiation Active Filters 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 second-order, 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. + - ZA ZD ZC ZB Low-Pass Filter R R C C High-Pass Filter C C R R Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 11-35 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 multiple-feedback (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.

Characterize the bandpass filter shown in the following Figure. Example 11-14 Characterize the bandpass filter shown in the following Figure. FIGURE 11-38 (Example 11-14) Bogart/Beasley/Rico Electronic Devices and Circuits, 6e Copyright ©2004 by Pearson Education, Inc. Upper Saddle River, New Jersey 07458 All rights reserved.

FIGURE 11-39 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.