chapter 11 advanced operational amplifier applications electronic integration electronic...

Chapter 11 Advanced Operational Amplifier applications

Electronic Integration Electronic DifferentiationActive Filters oBasic Filter Concepts oActive Filter Design oLow-Pass and High-Pass Filters oFrequency and Impedance Scaling oNormalized Low-Pass and High-Pass Filters oBandpass and Band-Stop Filters

FIGURE 11-1 The output of the integrator at t seconds is the area Et under the input waveform

Bogart/Beasley/RicoElectronic Devices and Circuits, 6e

Copyright ©2004 by Pearson Education, Inc.Upper Saddle River, New Jersey 07458

All rights reserved.

When the input to an integrator is a dc level, the output will rise linearly with time.

FIGURE 11-2 An ideal electronic integrator




i1

iC

FIGURE 11-3 (Example 11-1)Bogart/Beasley/RicoElectronic Devices and Circuits, 6e



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

FIGURE 11-4 Bode plot of the gain of an ideal integrator for the R1C = 0.001




FIGURE 11-5 Allowable region of operation for an op-amp integrator




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




Practical Integrators

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

<< RffC2

1

f >> CR f2

1= fc

FIGURE 11-7 (Example 11-2)Bogart/Beasley/RicoElectronic Devices and Circuits, 6e



Example 11-2 Design a practical integrator that1.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, and3.Find the dc component in the output when there is a +50-mV dc input.

FIGURE 11-8 A three-input integrator




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.




FIGURE 11-10 An ideal electronic differentiator




if

iC

FIGURE 11-11 A practical differentiator. Differentiation occurs at low frequencies, but resistor R1 prevent high-frequency differentiation




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.




FIGURE 11-13 (Example 11-3) Bogart/Beasley/RicoElectronic Devices and Circuits, 6e



Example 11-31. 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?

FIGURE 11-14 (Example 11-3) Bogart/Beasley/RicoElectronic Devices and Circuits, 6e



FIGURE 11-29 Ideal and practical frequency responses of some commonly used filter types




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.

FIGURE 11-31 Chebyshev low-pass frequency response: f2 = cutoff frequency; RW = ripple width




FIGURE 11-32 Comparison of the frequency responses of second-order, low-pass Butterworth and Chebyshev filters




FIGURE 11-33 Comparison of the frequency responses of low-Q and high-Q bandpass filters




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 ZDZCZB

Low-Pass Filter R R C CHigh-Pass Filter C C R R

FIGURE 11-35 General low-pass filter structure; even-ordered filters do not use the first stage




FIGURE 11-36 General high-pass filter structure; even-ordered filters do not use the first stage




Example 11-9Design a third-order, low-pass Butterworth filter for a cutoff frequency of 2.5 kHz. Select R = 10 kΩ.

Example 11-10Design 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 11-11A 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.

FIGURE 11-37 The infinite-gain multiple-feedback (IGMF) second-order bandpass filter




Simple Bandpass Filter

FIGURE 11-38 (Example 11-14)




Example 11-14 Characterize the bandpass filter shown in the following Figure.

FIGURE 11-39 A wideband bandpass filter obtained by cascading overlapping low-pass and high-pass filters




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




FIGURE 11-41 Obtaining a wideband band-stop filter from nonoverlapping LP and HP filters




Example 11-15Design 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.

chapter 11 advanced operational amplifier applications electronic integration electronic...

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