Hioki Power HiTester 3193, Instruction Manual

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14.4 Internal Block Diagram
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14.4.2 MEAN Value (MEAN rectification effective value for
display)
Averaging value =
|e|dt
T
T
e
RMS value =
Averaging value =
RMS value
─────── =
Averaging value
A
A
MEAN value =
×
Averaging value
14.4.3 Active Power
E RMS value of voltage
I RMS value of current
ω
angular frequency
t time
θ
phase difference between voltage
waveform and current waveform
+
e
i
E
ω
t
I
ω
t
θ
For MEAN values, the input signal waveform is converted to a DC voltage
by an absolute value detecting circuit and a smoothing circuit Since this is
an analog process, all signals within the frequency range of the specification
are converted precisely.
This is found using an absolute value detecting circuit and a smoothing
circuit. The theoretical expression used here for the MEAN value is as
follows:
However, using this expression as it is for a sine wave of amplitude A and
period 2
π
, results in RMS and average values as follows:
And thus for the same measured sine wave the figures do not agree. For this
reason, to make the figures agree when a sine wave signal is input, the
average value defined above is multiplied by a coefficient to give the MEAN
value (mean rectification effective value for display).
If the sine wave voltage and sine wave current are e and i respectively, then
this can be expressed as follows:
The instantaneous power p is the product of e and i , as follows:
p = e
・
i
= 2 EI cos
ω
t
･
cos (
ω
t +
θ
)
= EI cos(2
ω
t +
θ
)+ EI cos
θ
The DC component in this expression is the active power P :
P = EI cos
θ
In the internal circuit, the instantaneous power p is computed by a multiplier
IC, and the active power P is obtained by smoothing to give a DC voltage
proportional to the active power P .