Question
Asked Nov 26, 2019
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What is the Norton equivalent of the circuit if input voltage is a periodic function as shown. Use Fourier Series.

2H
- A
1 e
- B
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2H - A 1 e - B

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Sawtooth function, period-T
T2
T2
-T
Time,
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Sawtooth function, period-T T2 T2 -T Time,

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Expert Answer

Step 1

Assuming the given voltage source as a function x(t).

Referring the given sawtooth graph with period T, it is odd function.

Fourier constant for the odd functions are zero.

Sawtooth function, perled-T
-T2
T2
Time
f(x) (x)
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Sawtooth function, perled-T -T2 T2 Time f(x) (x)

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Step 2

Solving the Fourier series:

X
72
Pper ( 1)x J=
2.A
-t-2A
T
2A2dt
te
T
-j2anf dt
H
On solving this
24e
X
72
JACosTnsin zn
( sin zn 0
JA(-1)'"
j.A
72
.1)
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X 72 Pper ( 1)x J= 2.A -t-2A T 2A2dt te T -j2anf dt H On solving this 24e X 72 JACosTnsin zn ( sin zn 0 JA(-1)'" j.A 72 .1)

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Step 3

Comparing the equation 1 with the gene...

j.A
(-1)
jbg
ajb
X
2
2
2
2
jA
х,
(-1)
jb - jA(-1)
(a, = 0 )
2
2
24
(-1)"
b
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j.A (-1) jbg ajb X 2 2 2 2 jA х, (-1) jb - jA(-1) (a, = 0 ) 2 2 24 (-1)" b

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