Rohde & Schwarz Hameg HM8115-2G Handbuch Seite 32

B a s i c s o f P o w e r M e a s u r e m e n t
Please note that erroneous results will show if the
crest factor of a signal is higher than that of the
measuring instrument because it will be overdri-
ven.
STOP
Hence the accuracy of the rms value measurement will depend
on the crest factor of the signal, the higher the crest factor the
less the accuracy. Please note also that the crest factor speci-
fi cation relates to the full scale value, if the signal is below full
scale its crest factor may be proportionally higher.
Form factors
Power
With DC power is simply derived by multiplying voltage and
current.
With AC the waveform and the phase angle resp. time relati-
onship between voltage and current have also to be taken into
account. For sine waves the calculation is fairly simple, as the
sine is the only waveform without harmonics. For all other wa-
veforms the calculation will be more complex.
As long as the instrument specifi cations for frequency and crest
factor are observed the power meter will accurately measure
the average of the instantaneous power.
Active, true Power (unit W, designation P)
As soon as either the source or the load or both contain induc-
tive or capacitive components there will be a phase angle or
time difference between voltage and current. The active power
u
i
û
î
ϕ
30
Subject to change without notice
Crest- Form-
factor factor
C F
π
2 = 1,11
2 2
π
2 = 1,11
2 2
π
2 = 1,57
2
3 = 1,15
2
3
ω
ϕ
Icos ϕ
ωt
I
is calculated from the rms voltage and the real component of
the current as shown in the vector diagram above.
Defi ning: P = active power
V = rms value of voltage
rms
I = rms value of current
rms
ϕ
= phase angle
the active power is derived as follows:
P = V · I
rms
cosϕ is the socalled power factor (valid for sine waves only).
The instantaneous power is the power at time t
equal to the product of voltage and current both at
HINT
time t.
p = i · u
(t) (t) (t)
For sine waves the instantaneous power is given by:
= û sin (ωt + ϕ) · î sin ωt
p
(t)
The active power or true power is equal to the arithmetic mean
of the instantaneous power. The active power is derived by inte-
grating for a period T and dividing by the period T as folllows:
1
P =
—
T
î · û · cosϕ
= ———————
= U
eff
The power factor will be maximum cos
phase shift. This is only the case with a purely resi-
stive circuit.
In an ac circuit which contains only reactances the
phase shift will be
HINT hence cos
Reactive Power (unit VAr, designation Q)
Reactive power equals rms voltage times reactive current.
With the designations:
Q = reactive Power
V = rms voltage
rms
I = rms current
rms
ϕ
= phase angle between
voltage and current
a vector diagramm
can be drawn as follows:
The reactive power is derived by:
Q = V · I
rms rms
Reactive currents constitute a load on the public
U
mains. In order to reduce the reactive power the
phase angle ϕ must be made smaller. For most of
the reactive power transformers, motors etc. are
responsible, therefore capacitors in parallel to
these loads must be added to compensate for their
inductive currents.
HINT
· cosϕ
rms
∫
T
î sin ωt û sin ( ωt + ϕ) dt
·
0
2
· cos ϕ
· I
eff
ϕ
= 90° and the power factor
ϕ
= 0. The active power will be also zero.
· sinϕ
ϕ
= 1 at zero