Digital Signal Processing Reference
In-Depth Information
Power-supply periodic signals
EXAMPLE 2.6
Power supplies that convert an ac voltage (sinusoidal voltage) into a dc voltage (constant
voltage) are required in almost all electronic equipment that doesn't use batteries. Shown in
Figure 2.10 are voltages that commonly appear in certain power supplies. (See Section 1.2.)
The voltage in Figure 2.10(a) is called a
half-wave rectified signal
. This signal is gener-
ated from a sinusoidal signal by replacing the negative half cycles of the sinusoid with a volt-
age of zero. The positive half cycles are unchanged.
The signal in Figure 2.10(b) is called a
full-wave rectified signal
. This signal is generat-
ed from a sinusoidal signal by the amplitude reversal of each negative half cycle. The positive
half cycles are unchanged. Note that the period of this signal is one-half that of the sinusoid
and, hence, one-half that of the half-wave rectified signal.
It is necessary in the analysis and design of these power supplies to express these sig-
nals as mathematical functions. These mathematical functions will be written after the defin-
itions of some additional signals are presented.
v(t
)
V
m
T
0
T
0
/2
T
0
2
T
0
t
0
(a)
v
(
t
)
V
m
T
0
T
0
2
T
0
3
T
0
4
T
0
t
2
T
0
0
Figure 2.10
(a) Half-wave and (b) full-
wave rectified signals.
(b)
■
The sum of continuous-time periodic signals is periodic if and only if the ratios
of the periods of the individual signals are ratios of integers. If a sum of
N
periodic
signals is periodic, the fundamental period can be found as follows [1]:
T
01
1.
Convert each period ratio, to a ratio of integers, where
is the period of the first signal considered and is the period of one of
the other
N
-1 signals. If one or more of these ratios is not rational, then the
sum of signals is not periodic.
T
0i
, 2 … i … N,
T
01
T
0i
2.
Eliminate common factors from the numerator and denominator of each
ratio of integers.
