Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN: 9780133923605
Author: Robert L. Boylestad
Publisher: PEARSON
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Please help solve the problems shown in the photo. Any help at all will be much appreciated! Picture 1 is the data, and Picture 2 has the problem statements. Thank you!

 

Design Objective: To design a filter whose output signal will exhibit a desired signal to noise ratio. Data: A corrupted input signal x(t) consists of a clean component (from now on referred to as "signal") s(t) plus a noise component 1(1), and it exhibits a signal to noise ratio (S / N) x = 5 / 1. The signal has an amplitude of A.=5 Volts and a frequency f, =1 KHz. The noise component has a frequency of f, = 20KHZ. We will consider two filter circuits implemented with operational amplifiers. Figure 1 shows a first-order filter plus an inverting amplifier, and Figure 2 shows a second-order filter C1 R R R x(t) • R y(t) Figure 1: First-order filter plus inverting amplifier C R R R x(t). R y(t) Figure 2: Second-order filter
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Transcribed Image Text:Design Objective: To design a filter whose output signal will exhibit a desired signal to noise ratio. Data: A corrupted input signal x(t) consists of a clean component (from now on referred to as "signal") s(t) plus a noise component 1(1), and it exhibits a signal to noise ratio (S / N) x = 5 / 1. The signal has an amplitude of A.=5 Volts and a frequency f, =1 KHz. The noise component has a frequency of f, = 20KHZ. We will consider two filter circuits implemented with operational amplifiers. Figure 1 shows a first-order filter plus an inverting amplifier, and Figure 2 shows a second-order filter C1 R R R x(t) • R y(t) Figure 1: First-order filter plus inverting amplifier C R R R x(t). R y(t) Figure 2: Second-order filter
Design Specifications: Design a filter so that it attenuates the noise component n(t) by a factor of 10, while the signal component s(t) remains almost unchanged. In other words, our ideal target is an output signal with a signal to noise ratio of (S / N) y = 50 / 1. 1. First-Order Filter Y(@) la) Find the transfer function H(@) = X(@) lb) Design the filter so that it attenuates the noise by a factor of 10 lc) The filter affects the noise severely. Unfortunately, it has a “side effect", as it also affects the signal (though slightly). With your design from part lb): Calculate the undesired attenuation experienced by the signal. What is the resulting signal to noise ratio (S/N) y at the output? How close is it to the ideal target of (S/ N) y = 50 / 1? Calculate the undesired phase shift experienced by the signal. ld) Using MATLAB, devise simulation experiments to corroborate all your mathematical predictions in parts 1b) and lc). All simulation experiments should include: The computer code (MATLAB) The plot (s), with the most noticeable features labeled. A comment underneath each plot, explaining how the plot verifies the predicted design performance.
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Transcribed Image Text:Design Specifications: Design a filter so that it attenuates the noise component n(t) by a factor of 10, while the signal component s(t) remains almost unchanged. In other words, our ideal target is an output signal with a signal to noise ratio of (S / N) y = 50 / 1. 1. First-Order Filter Y(@) la) Find the transfer function H(@) = X(@) lb) Design the filter so that it attenuates the noise by a factor of 10 lc) The filter affects the noise severely. Unfortunately, it has a “side effect", as it also affects the signal (though slightly). With your design from part lb): Calculate the undesired attenuation experienced by the signal. What is the resulting signal to noise ratio (S/N) y at the output? How close is it to the ideal target of (S/ N) y = 50 / 1? Calculate the undesired phase shift experienced by the signal. ld) Using MATLAB, devise simulation experiments to corroborate all your mathematical predictions in parts 1b) and lc). All simulation experiments should include: The computer code (MATLAB) The plot (s), with the most noticeable features labeled. A comment underneath each plot, explaining how the plot verifies the predicted design performance.
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