Howclosethesimilarityisdependson

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Unformatted text preview: the
peak
amplitude
of
the
saw­tooth
waveform.

 
 The
coefficient
of
proportionality
is
found
from
integration
and
depends
on

 n
=
the
number
of
the
harmonic
component.

 
 Analytical
formula:
 
 Saw-tooth wave of peak amplitude A = = n = integer ∑ ⎢( −1) ⎣ = + ⎡ n +1 ⎤ 2A ⋅ sin( 2π ⋅ n ⋅ f0 ⋅ t ) ⎥ = π ⋅n ⎦ 2A ⋅ sin( 2π ⋅ f0 ⋅ t ) + π 
 According
to
this
formula,
the
amplitude
of
the
2nd
harmonic
is
half
of
the
amplitude
 of
the
fundamental;
the
amplitude
of
the
3rd
harmonic
equals
to
one‐third
of
the
 amplitude
of
the
fundamental,
etc.

 ©
2010
Alexander
Ganago

 Page
2
of
4

 File:
Saw‐tooth
harmonics
 2A ⋅ sin( 2π ⋅ 2 ⋅ f0 ⋅ t + 180o ) + π ⋅2 2A + ⋅ sin( 2π ⋅ 3 ⋅ f0 ⋅ t ) + π ⋅3 2A + ⋅ sin( 2π ⋅ 4 ⋅ f0 ⋅ t + 180o ) + ... π ⋅4 [equation 5] EECS
314
Winter
2010

 
 Homework
2

 Required
reading
for
Problem
2
 
 Note
tha...
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This note was uploaded on 12/06/2010 for the course EECS 314 taught by Professor Ganago during the Spring '07 term at University of Michigan.

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