MR8740T_user_manual_eng_20191016H.pdf - 第175页

170 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 Arc sine (ASIN)…

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169
Operators of Waveform Calculation and Calculation Results
8.3 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
Four arithmetic
operations (+, −, ×, ÷)
Makes calculations using operators specied from the four arithmetic operations, which
consists of addition (+), subtraction (−), multiplication (×), and division (÷). Multiplication
signs (×) and division signs (÷) are represented as asterisks (*) and slashed (/),
respectively.
Absolute value (ABS)
b
i
= | d
i
| (i = 1, 2, . . . , n)
Exponent (EXP)
b
i
= exp (d
i
) (i = 1, 2, . . . , n)
Common logarithm
(LOG)
With
d
i
> 0 b
i
= log
10
d
i
With
d
i
= 0 b
i
= −∞
(Outputs overowing values)
With
d
i
< 0 b
i
= log
10
| d
i
| (i = 1, 2, . . . , n)
Note: The following expressions can convert common logarithms into natural
logarithms.
InX = log
e
X = log
10
X / log
10
e
1 / log
10
e ≈ 2.30
Square root
For
d
i
≥ 0 b
i
= √d
-
i
With
d
i
< 0 b
i
= −√
|
d
-
i
| (
i = 1, 2, . . . , n)
Cube root (CBR)
=
√
3
Moving average (MOV)
For this function, specify the number of moving points at the second parameter
k
.
When
k
is an odd number When
k
is an even number

−1

−1
∑
d
t
( = 1, 2, . . . , n)




d
t
  . . . , 
d
t
:
t
th data point acquired across the source channel
k
: Number of moving point (1 to 5000)
Specify the constant
k
following a comma. Example: To calculate 100-point moving
averages of the Z1 data. MOV(Z1,100)
For each
k
/2 points of data at the beginning and end of the calculation interval, the
instrument makes calculations by plugging in zero for data-missing parts
Parallel move in the
time axis direction
(SLI)
For this function, specify the number of moving points at the second parameter k.
The instrument yields waveforms parallel moving in the time axis direction by the
specied number of points.
b
i
= d
i−k
(i = 1, 2, . . . , n)
k
: Number of moving point (−5000 to 5000)
Specify the constant
k
following a comma. Example: To move data Z1 by 100 points
SLI(Z1,100)
Note When waveforms are parallelly moved, the non-data parts at the beginning or
end of the calculation interval measure a voltage of 0 V.
Sine (SIN)
b
i
= sin(d
i
) (i = 1, 2, . . . , n)
For the trigonometric and inverse trigonometric functions, specify numbers in radians
(rad).
Cosine (COS)
b
i
= cos(d
i
) (i = 1, 2, . . . , n)
For the trigonometric and inverse trigonometric functions, specify numbers in radians
(rad).
Tangent (TAN)
b
i
= tan(d
i
) (i = 1, 2, . . . , n)
For the trigonometric and inverse trigonometric functions, specify numbers in radians
(rad).
8
Waveform Calculation Function
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 signicantly.
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
specied in digital
voltmeter module
(PLCS)
The instrument shifts a waveform by a frequency (PLC) specied in a digital voltmeter
module and a delay time of PLCS.
Since digital voltmeter modules calculate averages during periods specied 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