AD538
THEORY OF OPERATION
RE-EXAMINATION OF MULTIPLIER/DIVIDER ACCURACY
total error calculations for both grades over the 100:1 input
Traditionally, the accuracy (actually the errors) of analog
multipliers and dividers has been specified in terms of percent
of full scale. Thus specified, a 1% multiplier error with a 10 V
full-scale output would mean a worst-case error of +100 mV at
any level within its designated output range. While this type of
error specification is easy to test evaluate, and interpret, it can
leave the user guessing as to how useful the multiplier actually
is at low output levels, those approaching the specified error
limit (in this case) 100 mV.
range are illustrated in Table 4. This error specification format
is a familiar one to designers and users of digital voltmeters
where error is specified as a percent of reading ± a certain
number of digits on the meter readout.
For operation as a multiplier or divider over a wider dynamic
range (>100:1), the AD538 has a more detailed error specification
that is the sum of three components: a percent of reading term,
an output offset term, and an input offset term for the VY/VX log
ratio section. A sample application of this specification, taken
from Table 4, for the AD538AD with VY = 1 V, VZ = 100 mV
and VX = 10 mV would yield a maximum error of ±±.0% of
reading ±500 ꢀV ± (1 V + 100 mV)/10 mV × ±50 ꢀV or ±±.0%
of reading ±500 ꢀV ± ±2.5 mV. This example illustrates that
with very low level inputs the AD538’s incremental gain (VY +
VZ)/VX has increased to make the input offset contribution to
error substantial.
The error sources of the AD538 do not follow the percent of
full-scale approach to specification, thus it more optimally
fits the needs of the very wide dynamic range applications
for which it is best suited. Rather than as a percent of full
scale, the AD538’s error as a multiplier or divider for a 100:1
(100 mV to 10 V) input range is specified as the sum of two
error components: a percent of reading (ideal output) term
plus a fixed output offset. Following this format, the AD538AD,
operating as a multiplier or divider with inputs down to 100 mV,
has a maximum error of ±1% of reading ±500 ꢀV. Some sample
Table 4. Sample Error Calculation Chart (Worst Case)
Total Error
VY
Input
(V)
VZ
Input
(V)
VX
Input
(V)
Ideal
Output
(V)
% of Reading
Total Offset Error Error Term
Total Error
Summation
(mV)
Summation as a
% of the Ideal
Output
Term (mV)
(mV)
100
50
100:1 INPUT
RANGE
10
10
10
10
0.5
(AD)
(BD)
(AD)
(BD)
100.5
50.25
(AD)
(BD)
1.0
0.5
(AD)
(BD)
0.25
Total Error =
±± rdg
±ꢀutput VꢀS
10
0.1
0.1
10
0.5
0.25
(AD)
(BD)
100
50
(AD)
(BD)
100.5
50.25
(AD)
(BD)
1.0
0.5
(AD)
(BD)
1
1
1
1
0.5
0.25
0.5
0.25
28
16.75
(AD)
(BD)
(AD)
(BD)
(AD)
(BD)
10 )
5
1
0.5
200
100
(AD
10.5
5.25
1.5
0.75
228
(AD)
(BD)
(AD)
(BD)
(AD)
(BD)
1.05
0.5
1.5
0.75
2.28
1.17
(AD)
(BD)
(AD)
(BD)
(AD)
(BD)
(BD)
(AD)
(BD)
(AD)
(BD)
0.1
1
0.1
0.10
0.1
0.01
0.1
10
WIDE
DYNAMIC
RANGE
116.75
Total Error =
±± rdg ±
10
0.05
2
0.25
1.76
1
(AD)
(BD)
5
2.5
(AD)
(BD)
6.76
3.5
(AD)
(BD)
2.7
1.4
(AD)
(BD)
ꢀutput VꢀS
Input VꢀS
(VY + VZ)/VX
±
×
5
0.01
0.01
0.01
0.1
5
1
125.75
75.4
25.53
15.27
(AD)
(BD)
(AD)
(BD)
100
50
20
(AD)
(BD)
(AD)
(BD)
225.75
125.4
45.53
25.27
(AD)
(BD)
(AD)
(BD)
4.52
2.51
4.55
2.53
(AD)
(BD)
(AD)
(BD)
10
10
Rev. E | Page 9 of 16
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