CN0385 Datasheet, PDF (3/13 Pages) Analog Devices – Devices Connected

Circuit Note
CN-0385
The AD8475 funnel amplifier provides high precision attenuation
(0.4×), accurate common-mode level shifting, and single-ended
to differential conversion. Its low output noise spectral density
(10 nV/√Hz) and fast settling time (50 ns to 0.001% for a 2 V
output step) make it well suited to drive the AD4003.
The AD4003 is a fully-differential, 2 MSPS, 18-bit precision SAR
ADC that features a typical signal-to-noise ratio (SNR) of 98 dB
when using a 4.096 V reference. The AD4003 is also low power,
and only consumes approximately 17 mW at full throughput. Its
power consumption scales with throughput, and can operate at
lower sample rates to cut its power use (for example, 0.17 mW
at 100 kSPS).
System DC Accuracy Errors
Figure 2 shows the ideal transfer function of the data acquisition
system.
011...111
011...110
011...101
and the average offset error of all of the channels. Offset error
match is calculated using the following equation:
7
∑ ^ε_{b, j}
∆ε_{b, MAX}
= (max(ε_b,i
−
j=0
8
) | i = 0, 1, ..., 7)
where εb,i and εb,j are the offset errors for the i and j channels,
respectively.
This offset error match can be found for each of the gain
configurations. Note that offset error can be expressed either in
codes or volts.
Gain Error Measurement
Error in the gain of the system also contributes to overall system
inaccuracy. The ideal transfer function of the AD4003 is shown in
Figure 2, where the −2¹⁷ and 2¹⁷ − 1 output codes correspond to
a negative full-scale input voltage (−FS) and a positive full-scale
input voltage (+FS), respectively; however, the combination of
offset error (εb) and gain error (εm) results in a deviation from
this relationship.
100...010
100...001
100...000
–FSR
–FSR + 1 LSB
–FSR + 0.5 LSB
+FSR – 1 LSB
+FSR – 1.5 LSB
ANALOG INPUT
Figure 2. ADC Ideal Transfer Function
Each of the components in the data acquisition signal chain
adds its own offset error and gain error that cause the real
transfer function of the system to deviate from the ideal transfer
function shown in Figure 2. The cumulative effects of these
errors can be measured at a system level by comparing known
dc inputs near zero and full scale at the input to the ADG5207
(RC filter if it is present) and the resulting output codes from
the AD4003 to obtain a system calibration factor.
Gain error can be expressed as a percentage error between the
actual system gain and the ideal system gain. The more common
expression is in percent full-scale error (%FS), which is a measure
of the error between the ideal and actual input voltages that
produces the 2¹⁷ − 1 code.
The ideal full-scale input voltage (VFS, ) IDEAL is a function of the
resolution of the ADC (18-bits for the AD4003) and the
accuracy of the reference voltage (VREF). Errors in the voltage
reference translate to gain errors in the ADC. To decouple
reference errors from ADC gain error, VREF is measured using a
precision multimeter. The ideal full-scale input voltage can then
be calculated using
V_{FS, IDEAL}
=
2¹⁸
2 × V_{REF, MEAS}
= ²¹⁷
V_{REF , MEAS}
The actual system gain can be found by calculating the slope of
the linear regression of a group of several input voltages (mLR)
and the resulting output codes:
Offset Error Measurement
YREAL = mLR × VIN
For ideal bipolar, differential ADCs, a 0 V differential input
results in an output code of 0. Real ADCs typically exhibit some
offset error (εb), which is defined as the deviation between the
ideal output code and the measured output code for a 0 V input.
The offset error for the data acquisition system can be found by
grounding its input and observing the resulting output code. This
error varies between each of the gain settings of the AD8251 and
between each of the channels of the ADG5207. Offset error is
therefore measured for each of the channels in all four gain
configurations.
The real full-scale input voltage (VFS, ) REAL can then be calculated
using
V_{FS, REAL}
= ^YREAL
m_LR
= ²¹⁷
m_LR
The gain error (expressed in %FS error) can then be calculated
using
ε_m
= ^{VFS, IDEAL − VFS, REAL}
V_{FS, IDEAL}
× 100%
Because the system monitors multiple channels, it is also important
The gain error of the system varies with the gain of the AD8251,
to quantify the amount by which the offset error deviates between
but is channel independent. Therefore, gain error is measured
channels. Offset error match (Δεb, MAX) is a measure of the max-
for each of the four gain configurations, but only using one of
imum deviation between the offset error of each of the channels
the ADG5207 channels in this system.
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