EE 212 - Spring 2017

EE 212: Circuits and Signals II

(this page will be updated throughout the semester)

Instructor: Kevin Wedeward (Workman 221, 835-5708, kevin.wedeward@nmt.edu, https://sites.google.com/nmt.edu/kevin-wedeward/)

Class Syllabus/Webpage: https://sites.google.com/nmt.edu/kevin-wedeward/courses/ee-212-spring-2017

Lab Shedule: http://www.ee.nmt.edu/~wedeward/EE212L/SP17/ee212l.html

Class Time/Place: MWF 09:00am-09:50am in Workman Center 113

Office Hours: MWF 10:00am-12:00pm

Textbook:

• Elementary Linear Circuit Analysis, 2nd Ed., by Leonard S. Bobrow, Oxford University Press, ISBN 9780195113723
• Author's website and errata

Prerequisite: EE 211 (Circuits and Signals I)

Corequisite: None

Course Description from Catalog: Continuation of EE 211, Laplace transform techniques, transient response, power, steady‐state sinusoidal response, and frequency response of RLC circuits.

Topics: Selected from chapters 9-14 of textbook.

• AC power (average power, reactive power, complex power, power triangle, power factor, power factor correction)
• Effective values of voltage and current
• Three-phase circuits, wye and delta connections
• Frequency response (transfer functions, magnitude responses, phase responses, Bode Plots, resonance, filters)
• Laplace Transform (properties, table, inverse via partial-fraction expansion, application to circuits)
• Mutual inductance and ideal transformers
• Fourier Series (trigonometric form, complex form, response of circuit)
• Fourier Transform

Course Outcomes: Students will be able to

1. calculate and understand voltage, current and power in sinusoidal circuits;
2. analyze sinusoidal circuits in the frequency-domain to find transfer functions and frequency responses;
3. apply Laplace Transforms to solve for time-domain responses without writing differential equations; and
4. find the Fourier Series representation of periodic signals and in turn the response of circuits to periodic sources.

Grading:

• A passing grade is required for both the class and lab. You must pass each individually with a D or better to get a combined passing grade.
• Class
  • Homework: 10%
    • Typically assigned every other class.
    • Collaboration is encouraged, but the work turned in must be your own.
    • Homework should be neatly written with all steps clearly shown, single-sided and stapled when multiple pages.
    • Late homework is not accepted.
  • Four exams (including final exam): 65%
• Laboratory: 25%

Reading Assignments:

• Chapter 9 (01/18/2016)
• Sections 10.1, 10.2 (02/03/2017)
• Section 10.3 focusing on resonance and bandwidth (02/27/2017)
• Sections 11.1 - 11.3 (03/01/2017)
• Chapter 13 with focus on 13.1, 13.3 (03/29/2017)
• Section 14.1 (04/19/2017)
• Sections 12.1, 12.2 (04/24/2017)

Homework:

1. Due Beginning of Class (BoC) M 01/23/2017: Problem 9.2 sketching circuit in frequency-domain, finding average power absorbed by all elements including source, finding reactive power absorbed by all elements including source, confirming average power and reactive power are conserved, and finding equivalent impedance seen by (connected to) the source.
2. Due BoC M 01/30/2017: Problems 9.21, 9.22, 9.23, 9.28 (note pf is for circuit connected to source)
3. Due BoC F 02/03/2017: Problems 9.27 (power refers to average power, provide value of reactive element), 9.32
4. Due BoC W 02/08/2017: Problems 9.35, 9.36, 9.37 noting line voltage given is line-to-line and per phase impedance is that of line and load combined
5. Due BoC F 02/17/2017: Problems 10.5, 10.7; for both sketch amplitude and phase responses, and plot via Matlab as well using R = C = 1 as needed
6. Due BoC W 02/22/2017 F 02/24/2017: Problems 10.12, 10.16; for both problems sketch the Bode plots (gain and phase) using line approximations and then plot with Matlab
7. Due BoC W 03/01/2017: Problem 10.19, H(jw) = 1000(jw)/((jw + 1)((jw)^2 + 20(jw) + 10000)); for both sketch the Bode Plots (gain and phase) using line approximations (noting key "true values") and plot with Matlab
8. Due BoC M 03/06/2017: Problems 10.20, 10.21 also plotting magnitude and phase of impedance with Matlab on which resonant frequency and other interesting behaviors are noted
9. Due BoC W 03/22/2017 F 03/24/2017: Problems 11.1 b, c; 11.3 d; 11.11 b; 11.13 a; 11.14 b; 11.15; and DE 11.12
10. Due BoC W 03/29/2017: Problems 11.22, 11.23, 11.40
11. Due BoC M 04/03/2017:
    • Fig. P7.26 on page 345 - find the s-domain and frequency-domain (AC) transfer functions H(s) = V₁(s)/V_s(s) and H(jw) = V₁/V_s
    • Fig. P11.47 on page 548 - find the s-domain and frequency-domain (AC) transfer functions H(s) = V(s)/V_s(s) and H(jw) = V/V_s
    • Given the transfer function H(s) = -5s/(s^2 + 15s + 50), find the output when (a) the input is u(t) and (b) the input is 10cos(4t) applied for a long time
    • Given the transfer function H(s) = 20/(s^2 + 4s + 20), find the output when (a) the input is u(t) and (b) the input is 10cos(4t) applied for a long time
12. Due BoC W 04/12/2017: Problems 13.3, 13.5, 13.8; for each (a) find the the trigonometric Fourier Series representation of the signal, (b) plot (via Matlab) the Fourier Series representation of the signal using 100 terms, and (c) plot (via Matlab acceptable) the frequency (amplitude and phase) spectrum taking the first six harmonics
    1. Due BoC F 04/21/2017: Problems 13.25, 13.27, 13.30; for each plot complex frequency spectrum (amplitude and phase) taking terms from -6 to 6 as well as the series approximation of the original function for 50 positive and 50 negative terms
13. Due BoC F 04/28/2017: Problems 14.2, 12.4, 12.5; Drill Exercise 12.1
14. Due BoC W 05/03/2017: Problems 12.24 also finding the impedance Z(s) labelled, 12.25 b

Examples:

1. Frequency Response - using Matlab to plot frequency responses of three circuits analyzed in class.
2. Frequency Response/Bode Plot - using Matlab to plot frequency responses of three circuits analyzed in class. Here amplitudes/magnitudes are shown in dB and logarithmic axes are used for angular frequency.
3. Frequency Response/Bode Plot - using Matlab to generate Bode Plots for examples sketched in class.
4. Trigonometric Fourier Series - using Matlab to generate plots of Trigonometric Fourier Series for even square wave used in class example.
5. Frequency Spectrum of Trigonometric Fourier Series - using Matlab to generate plots of Frequency Spectrum via a Trigonometric Fourier Series of an even square wave used in class example.
6. Trigonometric Fourier Series and Frequency Spectrum of odd square wave - using Matlab to generate plots of Trigonometric Fourier Series of odd square wave used in class example along with its Frequency Spectrum.
7. Trigonometric Fourier Series and Frequency Spectrum of even triangle wave - using Matlab to generate plots of Trigonometric Fourier Series of even triangle wave used in class example along with its Frequency Spectrum.
8. Complex Fourier Series and Frequency Spectrum of Odd Square Wave - using Matlab to generate plots of Complex Fourier Series of odd square wave used in class example along with its Complex Frequency Spectrum.
9. Complex Fourier Series and Frequency Spectrum of Even Triangle Wave - using Matlab to generate plots of Complex Fourier Series of odd square wave used in class example along with its Complex Frequency Spectrum.

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