AN2226 PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise.pdf

AN2226
PSoC® 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low
Frequency Noise
Author: Dennis Seguine
Associated Project: Yes
Associated Part Family: CY8C24/27/28/29xxx
Software Version: PSoC ® Designer™ 5.4 SP1
Related Application Notes For a complete list of the application notes, click here.
AN2226 presents low noise signal processing in PSoC® 1 through the use of Correlated Double Sampling (CDS) to
reduce errors due to offset, drift, and low frequency noise. An analog front end for a type K thermocouple is used as a
design example. For equivalent implementation in PSoC 3 or PSoC 5, see AN66444. For complete thermocouple
system design see in PSoC 3 or PSoC 5, see AN75511. A project for analog front end for type K thermocouple is
provided in the associated download.
Introduction
The thermocouple (TC) is a voltage output device that
measures the temperature difference between the sensor
tip and a reference junction (called the cold junction). This
is a relative measurement and to be accurate, the
reference lead temperature must also be known. Type K
thermocouples have an average output of approximately
40.7 µV/°C. This output is approximately linear. For
complete linearization, see AN75511.
Correlated Double Sampling (CDS) provides a means to
efficiently subtract offset and remove drift, and low
frequency noise from this sensitive measurement. This
technique works just as well for differential measurements
such as pressure sensors and load cells.
The thermocouple’s output is absolute (not ratiometric), so
the reference for the ADCINC14 is selected to be an
absolute voltage referenced to the PSoC’s internal
bandgap. The lowest ADC scale is 0 to 2*Vbg or 2.6 V.
For the ADCINC14, the resolution is 2.6 V/2^14 or 159 µV
per bit. This is four degrees per bit and is not useful for
one degree accuracy.
Simple Approach
With insufficient ADC resolution, DC gain is required to
make the measurement useful. A PGA is added to boost
the input signal.
Figure 2. Thermocouple Amplifier with Gain
Too Simple Approach
The "too simple" approach to thermocouple measurement
is to connect the reference lead of the thermocouple to
ground and the output to a high resolution ADC. In this
case, the PSoC 1 ADC with the highest resolution is
ADCINC14.
Figure 1. Too Simple Thermocouple Circuit
ADCINC14
ADCINC14
Type K
The highest nominal PGA gain available is 48. This yields
a PGA output of 48*40.7 µV = 1.95 mV per degree or
0.08 degrees per bit. This is a good start, but the circuit
still has problems with low frequency noise, drift, minimum
operating voltage, and accuracy.
Type K
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PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
Figure 5. Sequential Offset Subtraction
Accommodating Offset and Drift
The thermocouple output is relative to the temperature of
the reference lead (the grounded terminal in Figure 2). If
the reference lead is at room temperature and the
thermocouple is colder, then the output voltage is
negative. The PSoC does not handle negative voltages.
Therefore, the input must be biased above ground by an
amount sufficient to accommodate the negative
temperature limit of the thermocouple. A practical
measurement limit is -100 °C. This is only -4 mV.
Next, the opamps in the PGA and the ADCINC14 have
input offset voltages. The opamp specification limit is
±10 mV with a 1.6 mV typical. The offset of the ADCINC14
is reflected to the PGA input divided by the gain. The
worst case offset compensation required is the sum of
PGA offset, ADC offset, and negative signal range, a total
of 14.2 mV.
Vdd (5.0V)
49.9 kΩ
Type K
ADCINC14
(+15 mV)
150 Ω
Vdd (5.0V)
49.9 kΩ
Type K
ADCINC14
(+15 mV)
150 Ω
The offset is achieved using a resistive divider from the
Vdd supply.
The stored offset value is subtracted from the
thermocouple output measurement. Problems with this
technique arise from opamp input noise and offset voltage
drift.
Figure 3. Accounting for Circuit Offset
Vdd (5.0V)
49.9 kΩ
ADCINC14
Type K
The PGA has input noise dominated by a 1/f term. The flat
band noise level is 65 nV/rtHz, with the 1/f corner at
4.5 kHz.
(+15 mV)
Figure 6. Opamp Noise Characteristic
150 Ω
nV/rtHz
1.0E+04
The ±10 mV offset voltage is equal to ±250 °C and must
be calculated. This is done by measuring both sides of the
thermocouple and then taking the difference. The
multiplexer is the standard PSoC port 0 input mux.
Voltage noise
1.0E+03
Figure 4. Thermocouple Offset Compensation
1.0E+02
Vdd (5.0V)
49.9 kΩ
1.0E+01
Type K
(+15 mV)
0
1
10
100
Hz
1000
10000
100000
ADCINC14
This is from a model
characterization data.
150 Ω
in
AN2224,
taken
from
The total PGA noise is given by:
The easy thing to do is to measure the offset at the
reference side of the thermocouple at startup and store
the digitized value. The mux is switched to the
thermocouple output and the value digitized.
1

 f  2
v nt = n0  f u − f l + f c ln u 
 f l 

Equation 1
In this equation:
n0 is the flat band noise
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PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
The offset measurement is:
fC is the 1/f corner frequency
VTC _ OFFSET = V N + VOFFSET
fU is the upper frequency limit
(~fSAMPLE/2=60 Hz/2)
Equation 3
The offset is measured at the previous sample time:
fL is the lower frequency limit (0.01 Hz)
VTC _ OFFSET _ DELAY = (VN + VOFFSET ) * Z −1 Equation 4
vnt = 12.4 µV RMS
The noise bandwidth is limited by the sin(x)/x noise
shaping of the incremental ADC. The -3 dB point of the
filter is at 0.44 * fSAMPLE.
Figure 7. ADC sin(x)/x Response
Z-1 is the delay operator, so VN* Z-1 represents the value of
VN at the previous sample time.
The difference is:
VSIGNAL = (VTC + V N + VOFFSET ) − (V N + VOFFSET ) * Z −1
1

VSIGNAL = VTC − (VN + VOFFSET ) * 1 −  Equation 5
 Z
VOFFSET is static and its value on the current sample is the
same as the value on the previous sample. By subtracting
one time sample from the next with VOFFSET remaining
unchanged, VOFFSET is simply subtracted out. VN is not
static; this is the noise and drift term to be eliminated.
 1
VSIGNAL = VTC − VN * 1 − 
 Z
The ADC rejects noise above the sample rate, but it has
no effect on offset or low frequency noise.
The indicated temperature is the difference between the
stored value and the most recent reading. The noise
contributions from the two measurements add in RMS, so
the noise on the reading is 17.5 µV RMS. ADC opamp
noise and quantization error (=1 LSB/sqrt(12)) add an
amount of error small in comparison to the PGA's noise.
With this noise level, an indicated temperature wander of
approximately ±1.5 degrees for a three sigma variation is
expected. This is worse than the desired specification and
does not account for drift or measurement scale accuracy.
The Vos drift for PSoC 1 is 5 µV/ºC typical and 35 µV/ºC
worst case. A one degree shift in die temperature
indicates as much as 0.9 ºC change in the indicated
thermocouple reading. A degree or two of chip
temperature variation (not unreasonable in any warm up
situation) dominates the error from the noise. To resolve
this problem, measure and subtract the offset and noise in
real time. This technique is called CDS.
Equation 6
Using the bilinear transform:
sT
2
Z=
sT
1−
2
1+
Equation 7
In this equation, T = 1/fSAMPLE. With a little algebraic
manipulation:

2s
VSIGNAL = VTC − V N * 
 s + 2 f SAMPLE



Equation 8
The combination of the correlated double sample and the
ADC's sinc (sin(x)/x) filter creates a frequency response
that significantly reduces the low frequency components of
the noise, as shown in Figure 8. The sinc function has its
first null at the sample rate, in this case at 60 samples per
second. This is also useful for rejecting AC line noise.
Correlated Double Sampling
Using the last circuit above, alternating measurements are
taken of the zero-referenced offset and the thermocouple
signal.
The direct thermocouple measurement is:
VTC _ SAMPLE = VTC + V N + VOFFSET
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Equation 2
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PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
Figure 8. CDS Frequency Response
The noise power of the PSoC input opamp increases as
frequency decreases, i.e., proportional to 1/f. Thus, the
noise voltage increases as square root of 1/f. The doublesampling and filtering process results in attenuation of the
noise voltage that increases as at the rate of 1/f. As the
frequency is reduced, the resulting filtered noise level
continues to drop. In the limit, (DC or f=0, as in offset
voltage), there is no noise contribution and the offset
voltage is completely cancelled. The resulting noise curve
is shown in Figure 10.
CDS + sinc
dB
10
0
-10
-20
-30
-40
-50
Figure 10. Thermocouple and CDS Noise Response
CDS
sin(x)/x
-60
Noise Response
-70
0
1
10
100
Hz
1000
10000
100000
Noise Reduction
100000
nV/rtHz
10000
The sinc filter has the low pass characteristic and the
correlated double sample has a high pass characteristic.
However, the high pass only affects the noise. The
product of the two functions results in a few dB bump in
the transfer function just below the sample rate, but overall
dramatic reduction in the total noise.
The difference of the ADC thermocouple and offset
measurement is filtered with a binary-weighted first order
IIR filter, implemented in software (see the AN2276), with
a coefficient of 16. The corner frequency of this filter is
less than 1 Hz. This is still adequate, because
thermocouple signals are very slow compared to the
measurement speed. When faster response is required,
the corner frequency of the IIR filter is easily adjusted by
changing the coefficient. This also increases the noise
bandwidth.
The correlated double sampling process results in two
effective filters, one for the signal, and one for the noise,
as shown in Figure 9. The signal is affected only by the IIR
filter's response (in RED). The noise is affected by the
combination of the IIR and the correlated double sample
(in BLUE).
Figure 9. Thermocouple Noise Characteristic
IIR Filter
dB
10
0
-10
-20
-30
-40
-50
IIR
SUM_Filt
-60
-70
0
1
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10
100
Hz 1000
10000
100000
1000
100
10
1
PGA Noise
Net TC Noise
0.1
0.01
0
1
10
100
Hz 1000
10000
100000
The very low frequency noise is reduced by a factor of
100. The offset drift, dependent on the rate of change of
the die temperature, is reduced to near zero. The
integrated total noise voltage is approximately 3 mV RMS.
This is adequate to make the worst case noise sufficient
for resolution of thermocouple temperature down to one
quarter of a degree Celsius.
Project
The PSoC project was built on a PSoC Eval 1 board using
CY8C27443. The project is limited to measuring both
terminals of a "simulated thermocouple," each respective
to ground (Vss), then shipping the data to the onboard
LCD and through UART to a PC terminal program. The
output is in counts of a 14 bit converter, resulting in 3.4 µV
per bit equivalent to 0.083 degrees per bit. Thermocouples
are approximately linear. This project does not include
linearization, and does not include conversion from counts
to degrees. It also does not include scale compensation
using measurement of a calibrated reference source. The
simulated thermocouple is a resistive divider from Vdd to
the offset reference. The voltage across the simulated
thermocouple is measured as 44 mV average with 2 mV of
"flicker" using an Agilent 34410 DMM with 1.0 µV
resolution.
The block layout is shown in Figure 11. It can be
implemented in any PSoC with continuous time and
switched capacitor blocks: CY8C24x23, CY8C24x94,
CY8C27x43, or CY8C29x66. It cannot be implemented in
CY8C21xxx or CY8C20xxx.
Document No. 001-45198 Rev. *H
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PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
The Tx8 is used only to transfer data to the terminal
program of the PC; if the Tx8 is not used (data shipped
through I2C or USB), then the project fits in CY8C24x23 or
CY8C24x94.
Connections
Table 1. Pin Connections
Signal
Figure 11. CDS PSoC Block and Connection Layout
Pin
Thermocouple input high side
P0[1] (AMUX4_1(0))
Thermocouple input low side
P0[3] (AMUX4_1(1))
TX8
P1[2]
LCD
Port 2
To understand how to make these connections, refer to
the application note AN2094 - PSoC 1 - Getting Started
with GPIO.
Results
The data is captured to a text file through a 9600 baud
UART with an RS232 connection. Eight seconds of data is
captured at 60 samples per second, totaling about 480
samples. The data analysis and plotting is done with
Microsoft Excel.
Code
The associated example project streams the data to the
LCD in hex integer form and the data to the UART in
floating point. The code is written in C. The IIR filter on the
correlated double sample difference uses 1/16 times the
new data plus 15/16 times the last output data:
1 V

VRESULT [n] = VRESULT [n − 1] * 1 −  + DIFF Equation 9
16
16


Multiplications are executed much faster in the PSoC than
divisions, so the equation is rewritten:
The output data is in counts of the 14 bit ADC. One bit
represents 3.4 µV. The average reference output is 2470
counts. When the PGA gain is 46.5 (from nominal gain of
48) and 14 bit ADC using 2.6 V full scale, this average
reference voltage is 7.5 mV. This is a reasonable level,
offset from the designed 15 mV compensation voltage by
the PGA's input offset voltage. The raw thermocouple data
is first evaluated by subtracting the AVERAGE reference
voltage from the TC reading.
Figure 12. Raw Thermocouple Data
Raw Measured - Average Ref
20
19
18
17
16
15
14
13
12
1

VRESULT [n] = (VRESULT [n − 1] − VDIFF ) * 1 −  + VDIFF
16


Equation 10
11
10
9
8
7
6
The calculations are executed in floating point to display
the simplicity of the algorithms. Conversion to fixed point
involves fractional arithmetic to avoid truncation errors.
Using a coefficient that is a power of two (e.g., 1/4, 1/8, or
1/16) results in very simple calculations, thus an
implementation in assembler is easily done.
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Meas-Avg(Ref)
The peak to peak noise is 12 counts, or roughly one
degree C. This can be averaged with an IIR filter
(coefficient 1/16) to reduce the noise.
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PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
Figure 13. Filtered Thermocouple Data
Compared to the filtered CDS data to the filtered raw data,
the performance improvement of the CDS technique is
obvious. The standard deviation of the noise is
reduced from 7.6 µV to 0.66 µV. When the bandwidth of
the IIR filter is reduced, it results in the corresponding
reduction of standard deviation of the noise. This indicates
that the noise is broadband compared to the IIR filter
bandwidth.
Raw Measured, Filtered Raw
20
19
18
17
16
15
14
13
12
11
System Errors
10
9
8
For the specific example of a thermocouple, errors (not
just noises) can accumulate from the PGA, the ADC, and
the sensor itself.
Meas-Avg(Ref)
7
Filt(Meas-Avg(Ref))
6
This reduces the peak-to-peak noise to four counts. Even
at this filtered level, a general negative drift is seen. There
is no guarantee that the offset measured at the start of the
scan is the correct value in the long run.
Correlated double sampling takes the difference between
the measured value and the reference at every sample.
This removes the offset voltage of the amplifier and much
of the low frequency and the peak-to-peak variation.
Figure 14. Correlated Double Sample on TC Data
PGA Gain Accuracy
The PGA has a gain of the form of:
G PGA = 1 +
CDS
20
Type K (and all other) thermocouples are slightly
nonlinear, deviating from the nominal by about one quarter
of a degree over a 50 °C range. Correcting this curvature
is a matter of more algebra in the code, a spline fit in the
code, or the use of a lookup table. Examples of
linearization are contained in AN75511.
19
18
17
16
Equation 11
R2 and R1 are large value resistors, selected by a
multiplex tap from a single tapped string. Including
contributions from the open loop gain and switches, the
gain is:
15
14
13
12
11
10
9
8
7
R2
R1
CDS
6
Comparison the unfiltered CDS data in Figure 14 with the
raw data of Figure 12 shows that peak to peak range of
the signal is reduced. The raw data is characterized by
large low frequency jumps, which do not appear in the
CDS data. This means that the dominant low frequency
the noise is common to the reference and signal terminals.
Overlaying the averaged CDS data (averaged with the
same 1/16 coefficient filter used on raw data in Figure 13)
shows a measurement with about 1.2 counts peak-to-peak
noise.
Figure 15. Thermocouple Output with CDS Compensation
CDS Comparison
20
19
18
17
G PGA

R + RSWU

1+ 2

R1 + RSWL
=
 1 + 1 1 + R2 + RSWU

A 
R1 + RSWL









Equation 12
RSWU represents the resistance of the switch between the
opamp output and the upper end of R2. RSWL represents
the resistance of the switch between the lower end of R1
and ground. This is detailed in the block schematic in the
PSoC Technical Reference Manual. A is the open loop
gain of the opamp in the PGA.
The total resistance (sum of R1 and R2) is fixed. For a
nominal gain of 48, the value of R1 is the unit value,
approximately 15 kΩ. The value of R2 is 47 times the unit
value, total of 705 kΩ. If the switches were ideal and open
loop gain infinite, the gain would be:
16
15
G PGA = 1 +
14
13
12
11
47 *15k
= 48
1 *15k
Equation 13
10
9
8
CDS
7
Filt(CDS)
6
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PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
Tolerance matching on these resistors is approximately
0.5 percent. As a practical matter, the switches do not
have zero resistance; their value is about 300 Ω at Vdd =
5.0 V and 450 Ω at 3.3 V.
The nominal output of the PGA is 40.7 µV*46.5 =
1.908 mV/°C. The PGA has a further gain inaccuracy as a
function of output signal level. The resistance of the lower
switch (RSWL) is quite constant. The resistance of the
upper switch (RSWU) however varies with the signal level
and can add as much as 0.6% nonlinearity when the
opamp output is near Vdd -1.0 V. This problem can be
limited to 0.1% of reading if the opamp output is kept
below 3.0 V. For the scale factor of 1.9 mV/°C, this means
that this error is small as long as the temperature to be
measured with the type K thermocouple is less than
1600 °C. This provides adequate margin for accurate
measurements even for most furnaces.
The DC open loop gain of the opamp is finite (typically
equal to 10000 in PSoC). The opamp contributes 0.47% to
the total error at guaranteed minimum gain of 10000. The
expected maximum gain for a "typical" PSoC opamp is
100000, reducing the opamp-induced gain reduction to
0.047% percent.
The mean gain is calculated as 46.8, or 2.3 percent below
the nominal of 48.0. It is accurate to describe the PGA
(nominal gain 48) as Gain = of 46.8 ±1.8% at Vdd = 5.0 V.
This tolerance accounts for variations due to internal
component matching and opamp gain to a three sigma
limit.
ADC Gain Accuracy
The PGA uses up part of the error budget. The ADC is a
lot worse. The ADCINC14 accuracy specification (and all
other ADCs) is ±3% on the internal reference. Of this
error, 0.1% is from the ADC, the dominant portion is from
the reference. Using an external signal for analog ground
and reference reduces this slightly, but there are still offset
and gain errors in the reference block.
The solution to gain error in ADC and PGA problems is
calibration: add an external reference source.
Figure 16. Thermocouple Scale Compensation
Vdd (5.0V)
49.9 kΩ
LM4140A
1.2V+/-0.1%
(+15 mV)
121 kΩ
0.1%
412 Ω
0.1%
Type K
The LM4140A provides a 1.2 V ±1% reference above the
offset point. The resistive divider provides a 4.07 mV
reference above the offset point. This is equal to a 100 °C
calibration point. The scale reference point, offset point,
and thermocouple output can be measured sequentially.
The scale is 100 degrees over the difference between the
reference point and the offset point. Correlated double
sampling on the scale along with the input removes any
noise on the reference. The calibration is now as accurate
as the external semiconductor reference and the resistors
selected. Note that error in scale is a function of reading.
Therefore, at reduced temperatures such as room
temperature range, the scale error is less than that at full
scale calibration point (100 °C). Two point calibration can
be implemented by dividing the 121 kΩ resistor to provide
a second calibration point.
The cost of the LM4140A and the precision resistors is
about $1 from Digikey. More precision is possible with
more expensive precision resistors. The money is worth
spending until the scale factor no longer dominates the
error budget.
Reference Temperature
The last problem is measurement and of cold junction
temperature. This can be done by embedding the
connections for the thermocouple terminals in a thermally
isolated block with a measurement thermistor. Reference
temperature accuracies of better than 0.5 °C can be
achieved using the methods detailed in AN2017. Better
resistor tolerance and more precise calculation methods
may yield slightly lower error.
Caveats
Sufficient resources are available in CY8C27x43 or
CY8C29x66 to implement thermocouple and reference
junction measurements simultaneously. In CY8C24x23,
with half of the analog block count, the PGA must be
reconfigured and analog mux bus connections must be
reconnected to make the reference measurement. This is
easy to do with dynamic reconfiguration.
The project can be implemented in CY8C24x23 if the ADC
is switched to a 13 bit version, ADCINCVR. CY8C24x23
has a PGA offset voltage induced by a known problem in
the Vss routing of the reference block. It results in an
additional PGA offset voltage of up to 7.5 mV, depending
on reference block power setting. This is automatically
compensated through the correlated double sample, but
the voltage must be accommodated by raising the offset
reference point by 7.5 mV.
ADCINC14
75 Ω
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Document No. 001-45198 Rev. *H
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PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
Summary

AN2276 - Binary Weighted Single-Pole IIR Low-Pass
Filters in PSoC® 1
A straightforward method of implementing a Type K
thermocouple measurement using correlated doubling
sampling in PSoC 1 is outlined.

AN2099 - PSoC® 1, PSoC 3, and PSoC 5 - SinglePole Infinite Impulse Response (IIR) Filters
Scale adjustments necessary to accommodate the ±4%
error from PGA gain and ADC range are not demonstrated
but are simple to implement. Compensation for reference
lead temperature using a thermistor is straightforward.

AN66444 - PSoC® 3 and PSoC 5 Correlated Double
Sampling
The signal processing techniques used to extract the TC
data from offset and 1/f noise are simple, proven, and
applicable to any DC or low frequency sensor, whether
single-ended or differential.
About the Author
Related Application Notes


Name:
Dennis Seguine
Title:
Member of Technical Staff
Cypress Semiconductor
Contact:
[email protected]
®
AN2017 - PSoC 1 Thermistor-Based Thermometer
AN2224 - PSoC® 1 - Lower Noise Continuous Time
Signal Processing
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Document No. 001-45198 Rev. *H
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PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
Document History
Document Title: AN2226 - PSoC® 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
Document Number: 001-45198
Revision
ECN
Orig. of
Change
Submission
Date
Description of Change
**
2274691
SHEA/PYRS
04/06/2008
New application note.
*A
2631863
YARA/PYRS
01/20/2009
Corrected Figure 7.
*B
2718255
FKL
06/12/2009
Included ‘Thermocouple Measurement’ in title and updated software version.
*C
3176918
SEG
02/18/2011
Updated title and abstract, moved code to example project.
*D
3358004
SEG
09/08/2011
Updated title, corrected schematic error.
*E
3665985
SEG
09/12/2012
Re-ordered, clarified text for linearity.
*F
4074369
AMKA
07/22/2013
Provided pin connection details.
*G
4356059
SEG
04/23/2014
Sunset update
*H
4736111
DIMA
04/22/2015
Updated Software Version as “PSoC Designer™ 5.4 SP1” in page 1.
Updated template.
®
Updated attached Associated Project to PSoC Designer 5.4 SP1.
Completing Sunset Review.
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Document No. 001-45198 Rev. *H
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PSoC 1 - Using Correlated Double Sampling to Reduce Offset, Drift, and Low Frequency Noise
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