Crest Factor - Hameg Instruments HM8115-2 Manual De Instrucciones

Basics of Power Measurement
Abbreviations and symbols used:
W active, true power P
VA apparent power S
var reactiv power Q
u(t) voltage as a variable of time
u²(t) voltage squared as a variable of time
IÛI rectifi ed voltage
V rms value of voltage
rms
û peak value of voltage
I rms value of current
rms
î peak value of current
ϕ
phase angle between voltage and current
cos ϕ power factor, valid only for sine waveform
PF power factor in general for arbitrary waveforms
Arithmetic mean value (average)
_
∫
T
1
x = — x | · dt
(t) (t)
T
0
The arithmetic mean value of a periodic signal is the average
calculated for a full period T, it is identical to its DC content.
– If the average = 0 it is a pure AC signal
– If all instantaneous values are equal to the average it is
pure DC
– Otherwise the average will constitute the DC content of the
signal
Rectifi ed mean value
I_
∫
T
1
IxI = — Ix I · dt
(t) (t)
T
0
The rectifi ed mean is the average of the absolute values. The
absolute values are derived by rectifying the signal. In gene-
ral the rectifi ed mean is calculated by integrating the absolute
values for a period T.
û
0
IuI
0
In case of a sine wave u(t) = û sin
amount to 2/π = 0.637 of the peak value according to:
I_
∫
T
1
Iû sin ωtI
IuI = —
T
0
t
t
ω
t the rectifi ed mean will
2
dt = — û = 0,637û
π
B a s i c s o f P o w e r M e a s u r e m e n t
Root-Mean-Square Value (RMS)
The quadratic mean value of a signal is equal to the mean of
the signal squared integrated for a full period
_
∫
T
1
(t) 2 (t) 2
x = x
— |
T
0
The rms value is derived by calculating the square root
∫
T
1
(t) 2
x = x
—
eff
T
0
The purpose of the rms value was to create a value which al-
lows the use of the same formulas as with DC for resistance,
power etc. The rms value of an AC signal generates the same
effect as a DC signal of the same numerical value.
Example:
If an AC rms signal of 230 V is applied to an incandescent lamp
(purely resistive at 50/60 Hz) the lamp will be as bright as po-
wered by 230 V DC.
For a sine wave u(t) = û sin ωt the rms value will be 1/√2 = 0.707
of the peak value:
∫
T
1
(û sin ωt)
U =
—
T
0
V
U
rm
s
eff
0
Form factor
The form factor multiplied by the rectifi ed value equals the rms
value. The form factor is derived by:
V
rms
F = —— = — — — — — — — — — —
IûI
For a sine wave the form factor is
π
— — = 1,11
2
2
HINT

Crest factor

The crest factor is derived by dividing the peak value by the rms
value of a signal. It is very important for the correct measure-
ment of pulse signals and a vital specifi cation of a measuring
instrument.
û
C = —— = — — — — — — — — — —
V
rms
For sinusoidal signals the crest factor is
√2 = 1,414
HINT
· dt
| · dt
û
2
= 0,707û
dt = —
2
u (t) 2
u(t)
rms value
rectifi ed value
peak value
rms value
Subject to change without notice
t
29