MR8740T_user_manual_eng_20191016H.pdf - 第176页
171 Operators of W aveform Calculation and Calculation Results b i : i th data point of calculation results, d i : i th data point acquired across the source channel W aveform calculation type Description 1st-order integ…
170
Operators of Waveform Calculation and Calculation Results
b
i
:
i
th data point of calculation results,
d
i
:
i
th data point acquired across the source channel
Waveform calculation
type
Description
Arc sine (ASIN)
With
d
i
> 1 b
i
= π / 2
With
−1 ≤ d
i
≤ 1 b
i
= arcsin(d
i
)
With
d
i
< −1 b
i
= −π / 2 (i = 1, 2, . . . , n)
For the trigonometric and inverse trigonometric functions, specify numbers in radians
(rad).
Arc cosine (ACOS)
With
d
i
> 1 b
i
= 0
With
−1 ≤ d
i
≤ 1 b
i
= arccos(d
i
)
With
d
i
< −1 b
i
= π (i = 1, 2, . . . , n)
For the trigonometric and inverse trigonometric functions, specify numbers in radians
(rad).
Arc tangent (ATAN)
b
i
= arctan(d
i
) (i = 1, 2, . . . , n)
For the trigonometric and inverse trigonometric functions, specify numbers in radians
(rad).
Arc tangent 2
(ATAN2(y, x))
Responses arc tangent of (
y / x
) in the range of [
−π
,
π
]. Specify numbers in radians (rad).
ATAN2(y, x) =
With
x ≥ 0 ATAN( y / x )
With
x < 0
and
y ≥ 0 ATAN( y / x ) + π
With
x < 0
and
y < 0 ATAN( y / x ) − π
1st-order differential
(DIF)
2nd-order differential
(DIF2)
The instrument makes 1st-order differential and 2nd-order differential calculations using
5th-order Lagrange interpolation formula to obtain 1-point data from 5-point values that
includes before and after the point.
The instrument differentiates data
d
1
to
d
n
considering them as the corresponding data
for the sampling time
t
1
to
t
1
.
Note If the instrument differentiates a waveform that oscillates slowly, calculation results
vary signicantly.
In such a case, raise the second parameter of the function.
The following expressions hold provided the second parameter equals one.
Arithmetic expressions of 1st-order differential
Point
t
1
b
1
= (−25d
1
+ 48d
2
− 36d
3
+ 16d
4
− 3d
5
) / 12h
Point
t
2
b
2
= (−3d
1
− 10d
2
+ 18d
3
− 6d
4
+ d
5
) / 12h
Point
t
3
b
3
= (d
1
− 8d
2
+ 8d
4
− d
5
) / 12h
↓
Point
t
i
b
i
= (d
i−2
− 8d
i−1
+ 8d
i+1
− d
i+2
) / 12h
↓
Point
t
n−2
b
n−2
= (d
n−4
− 8d
n−3
+ 8d
n−1
− d
n
) / 12h
Point
t
n−1
b
n−1
= (−d
n−4
+ 6d
n−3
− 18d
n−2
+ 10d
n−1
+ 3d
n
) / 12h
Point
t
n
b
n
= (3d
n−4
− 16d
n−3
+ 36d
n−2
− 48d
n−1
+ 25d
n
) / 12h
b
1
through
b
n
: Calculation result data
h = Δt
: Sampling interval
Arithmetic expressions of 2nd-order differential
Point
t
1
b
1
= (35d
1
− 104d
2
+ 114d
3
− 56d
4
+ 11d
5
) / 12h
2
Point
t
2
b
2
= (11d
1
− 20d
2
+ 6d
3
+ 4d
4
− d
5
) / 12h
2
Point
t
3
b
3
= (−d
1
+ 16d
2
− 30d
3
+ 16d
4
− d
5
) / 12h
2
↓
Point
t
i
b
i
= (−d
i-2
+ 16d
i−1
− 30d
i
+ 16d
i+1
− d
i+2
) / 12h
2
↓
Point
t
n−2
b
n−2
= (−d
n−4
+ 16d
n−3
− 30d
n−2
+ 16d
n−1
− d
n
) / 12h
2
Point
t
n−1
b
n−1
= (−d
n−4
+ 4d
n−3
+ 6d
n−2
− 20d
n−1
+ 11d
n
) / 12h
2
Point
t
n
b
n
= (11d
n−4
− 56d
n−3
+ 114d
n−2
− 104d
n−1
+ 35d
n
) / 12h
2
171
Operators of Waveform Calculation and Calculation Results
b
i
:
i
th data point of calculation results,
d
i
:
i
th data point acquired across the source channel
Waveform calculation
type
Description
1st-order integration
(INT)
2nd-order integration
(INT2)
To calculate values of 1st-order and 2nd-order integration, the instrument uses the
trapezoidal formula.
The instrument integrates data
d
1
to
d
n
considering them as the corresponding data for
the sampling time
t
1
to
t
n
.
Arithmetic expressions of 1st-order integration
Point
t
1
I
1
= 0
Point
t
2
I
2
= (d
1
+ d
2
) h / 2
Point
t
3
I
3
= (d
1
+ d
2
) h / 2 + (d
2
+ d
3
) h / 2 = I
2
+ (d
2
+ d
3
) h / 2
↓
Point
t
n
I
n
= I
n-1
+ (d
n-1
+ d
n
) h / 2
I
1
through
I
n
: Calculation result data
h
=
Δt
: Sampling period
Arithmetic expressions of 2nd-order integration
Point
t
1
II
1
= 0
Point
t
2
II
2
= (I
1
+ I
2
) h / 2
Point
t
3
II
3
= (I
1
+ I
2
) h / 2 + (I
2
+ I
3
) h / 2 = II
2
+ (I
2
+ I
3
) h / 2
↓
Point
t
n
II
n
= II
n−1
+ (I
n−1
+ I
n
) h / 2
II
1
through
II
n
: Calculation result data
Note Integration is susceptible to minor deviation of the zero-position. Be sure to
execute zero-adjustment before performing a measurement. In addition, zero-
point offset correction may be required.
Example: To adjust the zero point by 0.124 mV
Z1 = INT (CH1-0.000124)
Waveform shifting
by PLC delay time
specied in digital
voltmeter module
(PLCS)
The instrument shifts a waveform by a frequency (PLC) specied in a digital voltmeter
module and a delay time of PLCS.
Since digital voltmeter modules calculate averages during periods specied in the
NPLC setting, observed waveforms will lag behind waveforms acquired with Model
8966 Analog Unit by a half of the NPLC setting.
The PLCS calculation advances the waveforms acquired with the digital voltmeter
module by the delay time and thus compensates the results for the lag behind the
waveforms acquired with Model 8966.
Note If the end of the calculation result contains no data, this part measures a voltage
of 0 V.
Average value (PAVE)
Calculates an average value of waveform data to use this numerical calculation result
for waveform calculations.
=
∑
AVE
n
n
d
AVE
: Average
n
: Number of data points
d
i
:
i
th data point acquired across
the channel
Maximum value
(PMAX)
Calculates the maximum value of waveform
data to use this numerical calculation result
for waveform calculations.
Maximum
Minimum value (PMIN)
Calculates the minimum value of waveform
data to use this numerical calculation result
for waveform calculations.
Minimum
8
Waveform Calculation Function
172
Operators of Waveform Calculation and Calculation Results
b
i
:
i
th data point of calculation results,
d
i
:
i
th data point acquired across the source channel
Waveform calculation
type
Description
Level at time
(PLEVEL)
Calculates a measured value at a time a
specied time has elapsed from a trigger
point to use this numerical calculation
result for waveform calculations.
Level
0 V