Environmental Engineering Reference
In-Depth Information
1 and 3 active
2 and 4 active
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: