Environmental Engineering Reference
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Figure 4.54 Idealized Current of a Half-controlled B2 Bridge Connection
A 2
π
periodical function f (
ω
t ) in the interval -
π ω
t
+
π
can be
decomposed in a convergent series:
(4.113)
The coefficients a n and b n can be estimated as:
(n = 0, 1, 2, ...)
(4.114)
(n = 1, 2, ...).
(4.115)
For the square-wave current of the B2 bridge connection with amplitude â and
control angle
α
, harmonic analysis results in:
(4.116)
Besides the desired sinusoidal first harmonic (order 1), this function consists of
various oscillations with different periods (order ≥ 2). They are called
harmonics. Figure 4.55 shows the first seven harmonics The square-shape is
already recognizable when adding these harmonics. A perfect reproduction of
the square shape needs all existing harmonics. In practice, harmonic analysis
can be carried out with an oscilloscope and computer-based analysis.
Proprietary devices can estimate the harmonic content independently.
According to harmonic analysis, the current i ( t ) is composed of the first
harmonic with the amplitude î 1 and further harmonics with the amplitudes î 2 ,
î 3 and so on:
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