Dealing with Noise on ZoomingADC

TN8000.32
ADVANCED COMMUNICATIONS & SENSING
Technical Note
PRELIMINARY
Dealing with noise on ZoomingADC
1. Introduction
3. Linearity
With its three amplification stages, the ZoomingADC is able
to amplify the input signal up to 1000 times. What are the
benefits of this big amplification? How can I improve the
linearity?
The total gain is calculated by multiplying the gain of the 3
stages. If a PGA is not used it should be disabled: the
current consumption is decreased and no noise is added to
the signal.
This Technical Note discusses the Programmable Gain
Amplifier (PGA) of the ZoomingADC. It gives some advice
to best use it.
The gain depends on the full scale input voltage. It is
recommended to take margin for temperature drift then the
maximal gain should be around:
2. Input circuit
FullScaleInputVoltage
gain = ------------------------------------------------------------- × 0.8
VBATT
MUX
PGA
The first PGA is designed for millivolts full scale signal. If
the total gain is less than 100, it should not be enabled. Its
transfer function is very linear while its output is in the range
±VBATT/5.
PGA2 has an offset cancelling block to recenter the signal
around 0. It is possible to add or subtract an offset up to
VBATT. The output should not be more than ±VBATT/2
after offset cancelation to preserve the good INL of the
circuit.
MODULATOR
(Analog part of
the ADC)
PGA3 is directly connected to the ADC. It is linear on all the
range. PGA3 output range should match ±Vref/2 which is
the ADC input range.
Vout
Figure 1. The PGA before the ADC
Vout
Vout
+VBATT
+VBATT/2
+VREF/2
+VBATT/5
The Zooming ADC has an architecture composed of 3
amplifiers with 2 offset cancellation stages.
Vin
Vin
ADC
input
range
-VBATT/5
-VBATT/2
PGA1 transfer function
+
PGA2 transfer function
Vin
-VREF/2
-VBATT
PGA3 transfer function
ADC
Figure 3. PGA transfer functions
PGA1
PGA2 OFFSET 2 PGA3
-
+
-
+
-
Linearity is an important characteristic when sensor are
used because a good linearity gives a good accuracy on
the measurement.
OFFSET 3
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Figure 2. ZoomingADC architecture
The offset cancellation permits to recenter the signal and
not saturate the amplifier. By this way a high gain setting is
possible even if the signal has a DC component.
1TN8000.32,
Revision 1.0 / September 2008
©2008
1.
Semtech Corp.
To make the amplification optimized in linearity, output of
the first stages (PGA1, PGA2) should be as little as
possible and less than ±VBATT/5 and ±VBATT/2
respectively. That is the case when the strongest gain is set
on the stage closest of the ADC. The gain is set first on
PGA3 then PGA2 and at last on PGA1 if needed.
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The ZoomingADC is used in many Semtech sensing
products from the simple SX8725 to the more complex
XE8000. It always integrates a multiplexer and a PGA
before the Sigma-Delta modulator.
TN8000.32
Dealing with noise on ZoomingADC
ADVANCED COMMUNICATIONS & SENSING
PRELIMINARY
Technical Note
For example, a total gain of 50 is set with PGA3=10,
PGA2=5 and PGA1 disabled.
Therefore, a noise requirement should give a noise
threshold to not be exceed with a probability.
For more explanation on the way to set the gain, see the
application note AN8725: Understanding pressure
measuring with SX8725.
For a given percentage of good reading, the standard
deviation has to be multiplied by a number given in table 1.
The quantization noise of the ADC is different than the PGA
thermal noise. The quantization noise comes from the
rounding error between the analog input voltage to the ADC
and the output digitized value. This noise is signaldependent and varies with the ADC resolution.
Probability that a Width of
reading is in the
the
specification(%) interval
68.2
2
80
2.56
90
3.28
95
3.92
98
4.66
99
5.16
99.9
6.58
The quantization noise of an ADC with a full scale input
q
signal is n q = ---------- where q is the LSB size in volt.
12
Thermal noise comes from the thermal agitation of
electrons. It varies with temperature. The thermal noise of a
resistor R at temperature T measured on the bandwidth B is
given by the following equation:
Vn =
Table 1. Confidence intervals
4kTRB (k is the Boltzmann’s constant)
We can predict that a cold circuit with narrow band signal
will produce less noise than a circuit in a hot environment
with large band signal.
The noise in the ZoomingADC is random and follow a
Gaussian distribution. Consequently, the probability that an
output code is in a certain range is computable. The
standard deviation of the data set is the RMS noise level.
σ = RMSnoise
A little bit more than 68% of the output code value are
located around ±σ of the data set mean as shown in
figure 4.
.
5. Noise on ZoomingADC
In the ZoomingADC, enabling a PGA add a certain amount
of noise to the input signal.
The noise measured at the output of PGA3 is the sum of the
noise made by PGA1, PGA2 and PGA3. But noise signals
are random and uncorrelated. The equivalent RMS is the
square root of the sum of the squares.
When PGA1 is turned on, the noise generated at the output
of PGA1 is amplified by PGA2 and PGA3. As it can be the
dominant noise source, it has been designed carefully to
minimise the noise.
The noise measured at the output is often given in volt rms.
Mathematically, it is the root of the mean squared voltage.
The output noise can be brought back at the input by being
dividing by the gain. It is then called input referred noise.
The input referred noise formula of the ZoomingADC is
given below:
InputNoise =
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Figure 4. Gaussian curve
2
Vn3 - 2  ------------------Vn2  2  Vn1
 ----------------------------------------
 G3 ⋅ G2 ⋅ G1 +  G2 ⋅ G1 +  G1 
--------------------------------------------------------------------------------------------------OSR ⋅ NELCONV
We could think that a noise voltage superior to 4σ couldn’t
occur. In fact, it can occur but because the probability is
very low the observation time to see this evenement is high.
TN8000.32 Revision 1.0/September 2008
©2008 Semtech Corp.
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4. Noise
The multiplication factor of 6.6 is often use to compute a
peak-peak noise from a rms value. It is a conservative value
which implies that 99.9% of the reading are in the noise
specification.
TN8000.32
Dealing with noise on ZoomingADC
PRELIMINARY
Technical Note
Figure 5. SX8724 Input and output noise
fs=500 kHz, OSR=1024, NELCONV=8, Update Rate = 60.97 Hz
OSR and NELCONV are two parameters of the Zooming
ADC which set the resolution.
setting change. The various setting are indicated with
arrows.
Vn3, Vn2 and Vn1 are respectively the equivalent noise
voltage source created by PGA3, PGA2 and PGA1.
Vn3=696uV, Vn2=271uV and Vn1=189uV on the SX8724.
The blue solid line curve shows the noise for an application
optimized in noise. Actually, the noise is lower especially
when the gain is around 10 and 100 but the linearity can be
degraded.
The variable Over Sampling Ratio (OSR) and Number of
Elementary Conversion (NELCONV) allows noise reduction
by averaging.
It is easy to show that for a given gain, the noise could be
reduced if the bigger gain is set on the first stages. For
example a gain of 500 could be set with PGA1=10,
PGA2=10 and PGA3=5 to minimize the noise but be
cautious that the output voltage of each amplifier is on the
correct linear range.
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It is in contradiction with the previous section on linearity
which states the biggest gain on the last stage. depending
on the application, a trade-off has to be done between noise
and linearity.
On the graph of figure 6, from the point OSR=1024,
NELCONV=8 to the point OSR=64, NELCONV=1, each
successive point is reached by decreasing OSR or
NELCONV by a factor of 2.
One can conclude that multiplying OSR or NELCONV by 2
decreases the noise and the data rate by a factor of
The effective bandwidth is also decreased by
2.
2.
As a resistor, decreasing the bandwidth lowers the noise.
The curve on figure 5 shows the output and input noise
when the SX8724 is set with the maximun of resolution
(OSR=1024, NELCONV=8). The red dotted line curve (
shows the noise when the application is optimized in
linearity. It presents unsteadiness corresponding to the gain
TN8000.32 Revision 1.0/September 2008
©2008 Semtech Corp.
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ADVANCED COMMUNICATIONS & SENSING
TN8000.32
Dealing with noise on ZoomingADC
ADVANCED COMMUNICATIONS & SENSING
Technical Note
PRELIMINARY
LSB
InputResolution = ----------gain
One could say: the maximum gain you set, the better input
resolution you get.
But in fact, it’s not as simple because as seen previously the
amplifier adds noise to the signal. Enabling PGA3 for
example add 5.9 µVrms of noise which is 36µVpp at the
output of the amplifier. The LSB size (when gain=1) of a 16
bit ADC with a 3.3V supply is 50µV. It is bigger than PGA3
noise. Therefore enabling PGA3 to match the amplifier’s
output range to the input range of the ADC is always
efficient.
Figure 6. Speed vs. PGA RMS noise
for fs=500kHz
6. ADC resolution
The ADC resolution is also set by setting OSR and
NELCONV. The resolution can be set from 6 to 16 bits. The
update rate varies with the resolution.
Because of the noise shaping features of the Sigma Delta
ADC quantization noise is 2 times better filtered when OSR
is doubled than when NELCONV is doubled. That is why
the ADC theoretical resolution n up to 16 bits is given by the
following equation:
n = 2 × log 2( OSR ) + log 2( NELCONV )
Even though the resolution is truncated to 16 bit by the
output register size, it may make sense to set OSR and
NELCONV to higher values in order to lower the bandwith
thus to reduce the influence of the thermal noise in the
PGA.
ST0002_01_US
Amplifier
output RMS
Noise (µV)
Input referred
RMS noise
(µV)
10
20
50
100
200
500
1000
5.91
32.3
33.1
33.9
53.7
111
208
0.591
1.615
0.662
0.339
0.2685
0.222
0.208
Table 2 SX8724 in 16bits mode (VBATT=3.3V)
Update Rate = 60.97 Hz
The noise free code resolution of an ADC is the number of
bits of resolution beyond which it is impossible to distinctly
resolve individual codes. When the gain increase, the noise
free counts decrease because of the noise effect. This can
be seen on table 3.
7. Input resolution
The primary benefits of having a PGA is that the equivalent
input noise decreases when the gain is increased. In other
terms, the Signal to Noise Ratio (SNR) increase. In the ideal
case, with a gain of 2, the input resolution is doubled. With a
gain of 1000, the input resolution is divided by 1000 then it’s
like the ADC has increased its resolution by almost 10 bits.
That is why amplifying a small signal is necessary to gain in
resolution.
The input referred resolution is given by the following
equation:
TN8000.32 Revision 1.0/September 2008
©2008 Semtech Corp.
Gain
Gain
Output noise
(LSB)
Noise
free
counts
Noise free
code
resolution
10
20
50
100
200
500
1000
>1
4.2
4.3
4.4
7
14.5
27.3
65536
15604
15241
14895
9362
4520
2401
16
13.9
13.9
13.9
13.2
12.1
11.2
Table 3 Noise free counts and code resolution
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The typical output and input noise of a SX8724 set up with
NELCONV=8, OSR=1024 and various gain is shown on
table 2.
TN8000.32
Dealing with noise on ZoomingADC
ADVANCED COMMUNICATIONS & SENSING
However the input referred resolution does improve with
gain. For example, a 20 mV full-scale input signal can be
converted with 50uVpp noise resolution which corresponds
to the quantization noise when the ADC is supplied in 3.3V
and the gain is set to 1. If the same signal is converted with
a gain of 100, the noise resolution is (4.4x50/100)=2.2uVpp.
Technical Note
PRELIMINARY
Resolution
Pressure
resolution (Pa)
Average
size
16 bit
17 bit
18 bit
19 bit
20 bit
1
0.5
0.25
0.125
0.0625
1
4
16
64
256
Right shift
>>1
>>2
>>3
>>4
Maximun
bandwith (Hz)
500
125
31.25
7.8
1.95
Table 4 Average to increase resolution
8. Increasing the resolution
Dividing the data rate by 2 decreases the noise voltage level
by 2 and increase the resolution of the measurement by
0.5 bit.
In a more general way, for each additional bit of resolution n
added, the signal must be oversampled four times. This
technique uses the theory of oversampling and decimation.
It assumes that:
The signal-component of interest should not vary
significantly during a conversion
The amplitude of the noise should be at least 1 LSB.
9. Measuring noise
The SX8724 evaluation kit (ref. XE8000EV121) can be
used to measure the noise on the ZoomingADC.
The input should be grounded or connected to a DC source.
The software permits to set the various parameter of the
ADC (Gain, Sample rate) and collect a data set. The
standard deviation gives the RMS noise level of the circuit
and the histogram permit to check that the noise is
Gaussian. If the noise is not Gaussian, it could indicate
either a bad PC board layout, poor grounding techniques or
improper power supply decoupling.
The following figure show a measure of the noise taken with
10000 output codes on a SX8724 set with a gain of 500.
To show the efficiency of the method, we can take an
example. The measurement of a hyperbaric chamber must
be done with a great resolution. The range of the pressure
is 0-65535 Pa. The pressure is stable for several hours but
has to be measured accurately.
A resolution of 0.1 Pa must be resolved for this application.
Therefore an ADC with a noise free count of at least 650k
samples is required which means a 20 bit ADC is needed.
The ZoomingADC is used for its ability to interface easily a
pressure sensor. It is set to 16 bit with an update rate of
1000 samples per second. One set of 256 samples are
taken.
The pressure input range is the exact resolution of the 16 bit
ADC, therefore the resolution is 1 Pa. To achieve 20 bit of
resolution, 256 samples must be averaged. The trade-off is
the output rate (or the bandwidth) has been divided by 256
and the CPU usage has increased.
Figure 7. SX8724 noise with OSR=1024, NELCONV=8
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In concordance with table 2, you can find in appendix the
noise histogram for various gain settings for the SX8724.
Appendix: Noise histogram
TN8000.32 Revision 1.0/September 2008
©2008 Semtech Corp.
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Digital filtering permits to increase the resolution to the
detriment of the data rate.
TN8000.32
Dealing with noise on ZoomingADC
PRELIMINARY
Technical Note
ST0002_01_US
DRAFT - FOR INTERNAL USE
ADVANCED COMMUNICATIONS & SENSING
TN8000.32 Revision 1.0/September 2008
©2008 Semtech Corp.
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Dealing with noise on ZoomingADC
DIVISION
DOC STATUS
Technical Note
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