{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HW3soln - PHYS3360/AEP3630 Electronic Circuits Spring 2011...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
PHYS3360/AEP3630 Electronic Circuits, Spring 2011, HW3 Solutions 1 AC Circuits Solutions 1. a. Choose any convenient value for 𝑡 0 and perform integration of one period. 𝑉 𝑖𝑛 , 𝑛 = 2 𝑗𝑛𝜋 (1 ( 1) 𝑛 ), 𝑛 > 0, 𝑉 𝑖𝑛 , 0 = 0, 𝑛 = 0. Units of 𝑉 𝑖𝑛 , 𝑛 are volts. Note: all even harmonics are 0. This is true for any half-wave (odd) symmetric shape, e.g. a shape for which each half-cycle is the mirror image of the next half-cycle. b. through d. The new Fourier coefficients corresponding to the output are given by 𝑉 𝑜𝑢𝑡 , 𝑛 = 𝑉 𝑖𝑛 , 𝑛 𝑗𝑛𝜔 / 𝜔 𝑐 1 + 𝑗𝑛𝜔 / 𝜔 𝑐 . Here 𝜔 = 2 𝜋 /1ms = 6.28 kHz is the fundamental angular frequency, and 𝜔 𝑐 = 1/0.1ms = 10 kHz is the corner frequency of the high-pass filter. The corresponding plots are shown above. It is seen that with 𝑛 𝑚𝑎𝑥 = 19 the most salient features of the shapes (both input and output) are being reproduced with truncated Fourier series. There are some artifacts, such as ringing and overshoot (undershoot) near abrupt steps. The latter is known as Gibbs phenomenon, which
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern