contains solved problems on fourier series applications in electrical circuits and derivation of fourier transform equations with its properties, description and usage

1. Fourier Analysis Techniques
Part II

2. Contents
• Applying Fourier series concept to general electric circuits
• Finding DC and AC dissipations
• Fourier Transforms Concept
• Fourier Transform Pairs
• Examples of Fourier Transform
• Application to circuits and systems
(Please not that Fourier transforms in not in HEC Approved curriculum so it will not be part of final exams)

3. Applying Fourier series concept to general electric circuits
As we know that
thus
And total power is given by

5. Example 15.7
The DC term is not given so the Average DC power voltage is 0v.
The v1, v2, v3 and v4 can be calculated by putting n=1, 2, 3 and 4 in above equation. We get;
And the total voltage for first 4 terms is then expressed as;
1ꙍ=2, 3ꙍ=6, 5ꙍ=10, 7ꙍ=14

7. Example 15.8

8. Fourier Transforms (Derivation for aperiodic signal)

9. Inverse Fourier Transforms (Derivation for aperiodic signal)
Multiply and divide by T and the apply condition for T
Fourier Transform Pair

10. Fourier Transform Usage
• Fourier transform is used to represent a general, nonperiodic function
by a continuous superposition or integral of complex exponentials.
The function is continuous w.r.t frequency and is defined for every
instant.
• The Fourier transform can be viewed as the limit of the Fourier series
of a function with the period approaches to infinity, so the limits of
integration change from one period to (−∞,∞).

11. Fourier Transformation Facts
• Just like Laplace transformation, the Fourier
Transform (FT) pairs are used for quick
conversion and reducing mathematical steps
• The end result of FT results an equation that
contains frequency component ꙍ
• Inverse Fourier Transform (IFT) converts all
the terms to the time domain relations,
containing a variable (t)
• There is no concept of fundamental
frequency and its harmonics for an aperiodic
signal
• The aperiodic signal contains frequencies as
real numbers and may have both rational as
well as irrational values, concluding a real
valued set,

12. Fourier Transformation Pairs

13. Example 15.12

14. Thanks
• http://eedmd.weebly.com/ca2/
• MS Teams: EE-201 Circuit Analysis II (Code: kv0slqu)
• http://slideshare.com/jazzofizia/