# Texas Instruments | Reduce Effects of Ext RC Filter on Gain Error and Drift in SAR ADC w/Int AFE (Rev. A) | Application notes | Texas Instruments Reduce Effects of Ext RC Filter on Gain Error and Drift in SAR ADC w/Int AFE (Rev. A) Application notes

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Reducing Effects of External RC Filter on Gain Error and
Drift in SAR ADC with Integrated AFE
For applications using SAR ADCs with integrated
analog front ends (AFE), such as theADS8588S, an
external resistor-capacitor (RC) filter at the input may
be necessary to eliminate noise pickup and to protect
the input from electrical overstress. However, this filter
introduces gain error and gain error drift. The purpose
of this TechNote is to show how to calculate the gain
error and gain error drift added by the external RC
filter. Figure 1 shows the integrated AFE in the
ADS8588S and the external balanced RC filter. It is
very important to understand that the external filter
requires a resistor on both the positive and negative
inputs as shown; matching the input impedances is
required for good common mode and noise rejection.
The selection of the external resistor is designed to
limit the input current from an overstress event. A
typical value for this resistance is 10k ohms, and for
maximum protection an external TVS diode is
recommended. The capacitor is selected to set the
filter cutoff frequency. For this example the cutoff
frequency is set to 320Hz for a system monitoring 50
or 60 Hz power signals. The cutoff frequency can be
adjusted according to the design requirements.
Adding the external resistor will affect the room
temperature gain of the data converter as the
resistance is directly in series with the 1M ohm input
impedance of the AFE. Assuming the internal input
impedance and external resistors are known, this gain
error can be mathematically accounted for. However,
the ADS8588S internal impendence has a range of
0.85 Mohm to 1.15 Mohm, which will minimize the
effectiveness of this correction. In this example, the
corrected gain error would be approximately ±0.15%
from internal impedance variation, whereas the
uncorrected gain error would be about 1%±0.15%.
Depending on the magnitude of the external resistor
used, this gain error will differ but for many
applications calibration is used to significantly reduce
this error.
The room temperature gain error added to the system
by the external resistor is given by the equation below.
This gain error equation is based on a voltage divider
relationship and is the additional uncorrected error
from the external resistor. For this example, the
uncorrected gain error due to the external resistor is
0.9901%. For comparison, the ADS8588S internal
maximum gain error is 64 least significant bits which
translates to 0.098% [100*64/(2^16)=0.098%].
GainError(REXT )RoomTemp=
GainError(REXT )RoomTemp=
1
R
1+ IN
REXT
1
= 0.009901 or 0.9901%
1MŸ
1+
10kŸ
A simple two point calibration is typically used to
correct for gain error in a data converter system. This
method will eliminate both the gain error introduced by
the external resistor as well as internal device gain
error. In this calibration method two test signals are
applied and measured at 10% and 90% of the linear
range of the input voltage range. These
measurements are then used to calculate the slope
(m) and offset (b) of the linear transfer function, shown
in the equations below.
Code = PÂVin +b
m=
Code_ max - Code_min
Vmax-Vmin
b = Code_ min - m·Vmin
Vin
REXT
REXT
AIN_xP
RIN
1MŸ
CEXT
PGA
RIN
3rd
2nd
Order
Order
Low-Pass
Driver
1MŸ
16-B
16-Bit SAR
SAR
CHx_OUT
AIN_xGND
Figure 1. ADS8588S Integrated Analog Front End with external RC filter
SBAA232A – July 2017 – Revised July 2017
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Reducing Effects of External RC Filter on Gain Error and Drift in SAR ADC
with Integrated AFE
1
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Once the calibration coefficients are determined, they
are used to correct for the gain and offset of the data
converter and external components, using the
equation below. Mathematically, this is done by solving
the straight line equation for the input signal. Usually
the calibration method is executed during a factory
automated test, once the coefficients are calculated,
they are stored in memory and used in all subsequent
measurements to minimize the error.
VinCALIBRATE =
Code - b
m
Using calibration can reduce gain and offset errors to
almost negligible levels. After calibration, most of the
residual error is due to noise and drift. Both the
internal 1Mohm resistor and the external filter resistor
will contribute to the system drift. From the ADS8588S
datasheet, the electrical characteristic lists the input
impedance maximum drift at ±25ppm/°C. For this
example a precision low drift external resistor (0.1%
±25ppm/°C) was used. Using a precision low drift
resistor for the filter will achieve best results. To
calculate the effect of the external resistor on drift, first
find the gain error at high temperature. This is done by
calculating the internal and external effective
resistance at high temperature as is shown in the
equations below. For worst case analysis, the signs of
the drift term of the internal and external impedances
must be different. If the signs were to be the same, the
drift errors from the internal and external impedances
would cancel.
RIN(-25ppm¤() =1MQ|€-25ppm/°C·:125°C-25°C; + 1]
RIN(-25ppm¤() = 0.9975 MŸ
REXT(+25ppm¤() =10kQ|€25ppm/°C·:125°C - 25°C;+1]
REXT(+25ppm¤() = 10.025kŸ
Next, to calculate gain error drift, calculate the gain
error at 25⁰C, and at125⁰C.
GainError(REXT)RoomTemp=
1
= 0.009901 or 0.9901%
1MŸ
1+
10kŸ
1
GainError(REXT )125°C =
1+
0Ÿ
NŸ
GainErrorDrift (REXT )=
ûGainError
Â106
ûTemperature
.009950-.009901
Â106 ppm
:125°C-25°C ;
GainErrorDrift (REXT ) = -0.49ppm/°C
In the ADS8588s datasheet the gain error temperature
drift is listed at a maximum ±14ppm/°C when using an
external reference. This is orders of magnitude larger
than the calculated additional drift error introduced by
the external resistor (-0.49ppm/°C), making the
introduced error insignificant. The minimal drift error
introduced by the external components is possible
because both the internal 1Mohm resistance and the
external resistance have low drift. This same
calculation can be done using different external
resistor values. The absolute worst case drift can be
kept relatively low if low drift external resistors (e.g.
±25ppm/⁰C or better) are used. For example, the worst
case drift introduced by a 1Mohm ±25ppm/⁰C external
In summary, an external RC filter is a common way to
reduce noise as well as protect the input circuit. This
circuit will have some impact on the gain error and drift
of the system. This paper demonstrated a method for
calculating gain error and drift. For best accuracy,
calibration can be used. The drift error can be
minimized by using precision low drift external
resistors; this drift will generally be significantly lower
than the device’s drift.
Table 1. Alternative Device Recommendations
Device
Optimized Parameters
Input Impedance Max
Drift ±25ppm/°C
Simultaneous Sampling,
16 Bit, 200-kSPS
Input Impedance Max
Drift ±25ppm/°C
MUX, 16 Bit, 500-kSPS
Input Impedance Max
Drift ±25ppm/°C
Single Channel, 16 Bit, 1MSPS
= 0.009950 or 0.995%
Finally, take the difference of the errors over
temperature, divide by the temperature range used
and multiply by one million to convert to ppm.
2
GainErrorDrift (REXT ) =
Table 2. Related Documentation
TI Recision Labs ACD 3.2:Understanding
and Calibrating the Offset and Gain for ADC
Systems
TIDUCO9
High-Accuracy Analog Front End Reference
Design Using 16-Bit SAR ADC With ±10-V
Measurement Range
TIDU540A
High-Accuracy AC Voltage and Current
Measurement AFE for Feeder Terminal Unit
Reference Design
TIDU427B
Phase-Compensated, 8-Ch, Multiplexed
Data Acquisition System for Power
Automation Reference Design
Reducing Effects of External RC Filter on Gain Error and Drift in SAR ADC
with Integrated AFE
SBAA232A – July 2017 – Revised July 2017
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