1. 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

2. 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

3. When the input to an integrator is a dc level, the output will rise linearly with time.
FIGURE The output of the integrator at t seconds is the area Et under the input waveform
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4. FIGURE 11-2 An ideal electronic integrator
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5. 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 (Example 11-1)
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6. FIGURE 11-4 Bode plot of the gain of an ideal integrator for the R1C = 0.001
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7. FIGURE 11-5 Allowable region of operation for an op-amp integrator
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8. 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
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9. 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
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10. 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 (Example 11-2)
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11. FIGURE 11-8 A three-input integrator
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12. 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

13. FIGURE 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.
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14. FIGURE 11-10 An ideal electronic differentiator
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15. FIGURE 11-11 A practical differentiator
FIGURE A practical differentiator. Differentiation occurs at low frequencies, but resistor R1 prevent high-frequency differentiation
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16. FIGURE 11-12 Bode plots for the ideal and practical differentiators
FIGURE 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.
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17. 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 (Example 11-3)
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18. Bogart/Beasley/Rico Electronic Devices and Circuits, 6e
FIGURE (Example 11-3)
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19. 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

20. FIGURE 11-29 Ideal and practical frequency responses of some commonly used filter types
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21. 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.
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22. FIGURE 11-31 Chebyshev low-pass frequency response: f2 = cutoff frequency; RW = ripple width
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23. FIGURE Comparison of the frequency responses of second-order, low-pass Butterworth and Chebyshev filters
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24. FIGURE 11-33 Comparison of the frequency responses of low-Q and high-Q bandpass filters
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25. FIGURE 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
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26. FIGURE 11-35 General low-pass filter structure; even-ordered filters do not use the first stage
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27. FIGURE 11-36 General high-pass filter structure; even-ordered filters do not use the first stage
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28. 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 = F, C2 = F, andC3 = 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.

29. Simple Bandpass Filter
FIGURE The infinite-gain multiple-feedback (IGMF) second-order bandpass filter
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30. Characterize the bandpass filter shown in the following Figure.
Example 11-14
Characterize the bandpass filter shown in the following Figure.
FIGURE (Example 11-14)
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31. FIGURE A wideband bandpass filter obtained by cascading overlapping low-pass and high-pass filters
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32. FIGURE (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
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33. FIGURE 11-41 Obtaining a wideband band-stop filter from nonoverlapping LP and HP filters
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34. 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.