ECE 333 Green Electric Energy

Homework 1 Solutions

Problem 1: Determine the r.m.s. value of the waveform 𝑥(∙) shown below:

Solution to the Problem 1: We compute the r.m.s. value of 𝑥 𝑡 by evaluating the average value over a cycle:

𝑋 =15 𝑥 𝑡 +𝑑𝑡

-

.

/+=

𝑎2 𝑡+𝑑𝑡+

. + 𝑎 +𝑑𝑡3+ + 𝑎(−𝑡 + 5) +𝑑𝑡-

3

5

/+

𝑋 =23𝑎

+ + 2𝑎+ + 13 𝑎+

5

/+

= 0.6𝑎

Fall 2017 Prof. George Gross Room 4052 ECEB

0

0.5

1

1.5

2

2.5

1 2 3 4 5 6 7 8 9 10 11

𝒂

𝒕 0 1 2 3 4 5 6 7 8 9 10