Electrical and Electronic Principles

COMPLEX
WAVEFORMS &
TRANSIENTS IN R-
L-C CIRCUITS
[Course title]ELECTRICAL AND ELECTRONIC PRINCIPLES
8/27/19
ELECTRICAL AND ELECTRONIC PRINCIPLES

ELECTRICAL AND ELECTRONIC PRINCIPLES
Contents
Q1.a)................................................................................................................................................................... 4
i) Even function........................................................................................................................................... 4
Odd function................................................................................................................................................... 5
i) half-wave symmetry................................................................................................................................. 6
b)........................................................................................................................................................................ 8
Question 2.......................................................................................................................................................... 9
a).................................................................................................................................................................... 9
b).................................................................................................................................................................. 10
c)................................................................................................................................................................... 11
Q3. Preamble................................................................................................................................................... 13
i) Obtain the Fourier transform..................................................................................................................13
i).................................................................................................................................................................... 14
ii)................................................................................................................................................................... 14
iv).................................................................................................................................................................. 16
Q4.................................................................................................................................................................... 17
a) = 1×103 rad s-1............................................................................................................................ 17
b) = 2×103 rad s-1.......................................................................................................................... 17
c)  = 1×103 rad s-1............................................................................................................................. 17
Q5.................................................................................................................................................................... 18
a)...................................................................................................................................................................... 18
a) 10 + 3t2 + sin4t......................................................................................................................................... 19
b) 4e-3t sin2t................................................................................................................................................. 19
b)...................................................................................................................................................................... 19
a).................................................................................................................................................................. 19
b).................................................................................................................................................................. 20
Q6.................................................................................................................................................................... 21
a).................................................................................................................................................................. 21
b).................................................................................................................................................................. 22
c)................................................................................................................................................................... 23
d).................................................................................................................................................................. 24

ELECTRICAL AND ELECTRONIC PRINCIPLES

ELECTRICAL AND ELECTRONIC PRINCIPLES
Q1.a)
i) Even function
The even function is the function which is symmetric about y axis that is when we take the
mirror image about the y axis, the positive and negative x axis function looks same.
The even function is written as f(x) = f (-x)
The following figure shows f(x) =x2, it is even function.

ELECTRICAL AND ELECTRONIC PRINCIPLES
Odd function
It Satisfies the property
F(x) =-f (-x), so it is symmetric about x axis.
Below is graph of odd function, f(x) =x3

ELECTRICAL AND ELECTRONIC PRINCIPLES
In consist of Fourier series, the integral property in the Fourier series for the even and odd
function gets simplifies or even cancelled out.
Some properties of odd and even functions are
1. The sum of two even functions is even, and of two odd ones odd.
2. The product of two even or two odd functions is even.
3. The product of an even and an odd function is odd.
For even function Fourier series will have only cos term, as the cos is even function.