ECE 202 (Talavage) Exam #3

Transcription

1 ECE 202 (Talavage) Exam #3 23 November 2015 Name: INSTRUCTIONS This is a closed book, closed notes exam. The exam consists of 8 thematic problems (19 parts) worth a total of 100 points. No computers, cell phones or scrap paper are permitted. Only slide rules or your TI 30X IIS calculator is permitted. When you are requested to stop writing, continued work on the exam will be construed as cheating, and you will be given a score of 0 for the exam. All students are expected to abide by the customary ethical standards of the University i.e., your answers must reflect only your own knowledge and reasoning ability. As a reminder, at the very minimum, cheating will result in a 0 on the exam and possibly an F for your course grade. Communicating with any of your classmates, in any language, by any means, for any reason, at any time between the official start of the exam and the official end of the exam is grounds for immediate ejection from the exam site and loss of all credit for this exam. Covert discussions with yourself are acceptable, but may be a sign of deeper issues. Good luck! 1

2 ECE 202 Fall 2015 Exam #3 (Talavage) 2 Problem 1 (3 parts; 10 points total) You are asked to design a maximally-flat (Butterworth) lowpass filter for which the passband has A max = 3 db with ω p = 2π100 rad/s, and the stopband has A min = 70 db with ω s = 2π10000 rad/s. (a) [4 pts] Compute the minimum order of the filter, n. (b) [4 pts] What is the minimum cutoff frequency, ω c,min, for this filter? (c) [2 pts] If a normalized Butterworth LP filter circuit is used to realize this design, what values of K f is required to convert the design to meet the specifications?

3 ECE 202 Fall 2015 Exam #3 (Talavage) 3 Problem 2 (2 parts; 10 points total) You have been asked to design a 3rd-order Butterworth lowpass filter for which the passband has A max = 2 db with ω p = 100 rad/s, and the stopband has A min = 50 db with ω s = 1000 rad/s. The normalized filter configuration can look like the following: (a) [4 pts] What is the minimum cutoff frequency, ω c,min, allowed for the specified filter? (b) [6 pts] Compute the values required for the reactive components in the given configuration to achieve the filter specification.

4 ECE 202 Fall 2015 Exam #3 (Talavage) 4 Problem 3 (4 parts; 25 points total) You are asked to design a maximally-flat highpass filter for which the passband has A max = 2 db with ω p = 5000 rad/s, and the stopband has A min = 30 db with ω s = 500 rad/s. (a) [5 pts] Draw the brickwall specification representing the corresponding (normalized) lowpass filter (note that this is in terms of Ω). (b) [5 pts] Compute the minimum order, n, for the LPF in part (a). (c) [5 pts] What is the minimum cutoff frequency, Ω c,min, for this LP filter?

5 ECE 202 Fall 2015 Exam #3 (Talavage) 5 (d) [10 pts] The following is a circuit configured as a 2nd-order normalized Butterworth LPF. Redraw this circuit as a highpass filter meeting your cutoff frequency specification from part (c).

6 ECE 202 Fall 2015 Exam #3 (Talavage) 6 Problem 4 (2 parts; 10 points total) Use the active filter stage implementation at right for all parts of this problem. Do not worry about using realistic component values! (a) [5 pts] If R1 corresponds to a 0.5 Ω resistor, determine values for R2, X1, and X2, given that H(s) = 4s+8 3s+5.

7 ECE 202 Fall 2015 Exam #3 (Talavage) 7 (b) [5 pts] Derive and draw a 2nd-order multistage active filter implemen-. Note that the poles remain real. tation for H(s) = 10 s+2 (3s+5)(4s+1)

8 ECE 202 Fall 2015 Exam #3 (Talavage) 8 Problem 5 (1 part; 10 points) The following circuit is a Sallen and Key active filter representation of a normalized Butterworth LP filter with A max = 3 db. [10 pts] Convert this circuit to a highpass filter having ω p = 200 rad/s.

9 ECE 202 Fall 2015 Exam #3 (Talavage) 9 Problem 6 (2 parts; 10 points total) Solve for the requested quantity or quantities in each problem, below. (a) [5 pts] Solve for the input impedance, Z in. (b) [5 pts] Solve for the mutual inductance, M.

10 ECE 202 Fall 2015 Exam #3 (Talavage) 10 Problem 7 (3 parts; 15 points total) Use the following circuit for all parts of this problem. (a) [5 pts] Solve for the input impedance looking into the transformer from the left, Z in. (b) [5 pts] Compute the relationship between the two indicated currents.

11 ECE 202 Fall 2015 Exam #3 (Talavage) 11 (c) [5 pts] Solve for the transfer function, H(s) = V out(s) V in (s).

12 ECE 202 Fall 2015 Exam #3 (Talavage) 12 Problem 8 (2 parts; 10 points total) (a) [5 pts] What value of turns ratio is required to achieve maximum power transfer in the circuit below? (b) [5 pts] For the circuit below, draw an equivalent circuit permitting use of ideal transformer equations to solve for v out (but do not do so!).