CN0385 Datasheet, PDF (4/13 Pages) Analog Devices – Devices Connected

CN-0385
System Noise Analysis
One of the key design goals in precision data acquisition
systems is achieving a high SNR, which can be achieved by
increasing the full-scale signal amplitude and/or by decreasing
the noise power generated by the components in the system.
The total noise power present in the system can be found by
taking the root sum square (rss) of the noise power contributed
by its individual components, referred to the input of the
AD4003:
v_{n, TOTAL} =
v2
n, ADG5207
+
v_n,
2
AD8251
+ v_{n, AD8475} ²
+ v_{n, AD4003}²
The expected SNR of the system (SNREXPECTED) can then be
found using
SNR_EXPECTED
=
20
log_{}

VREF 2
v_{n, TOTAL}



The expected noise contributions for each component in the
system and the resulting expected SNR performance of the
whole system is shown in Table 2. The total system noise
calculation ignores thermal noise contributed by the passive
components in the system.
Noise Due to the AD4003 ADC
The noise of the AD4003 ADC is a function of both its inherent
quantization error and noise caused by internal components
(such as passive components producing thermal noise).
The rms input voltage noise of the AD4003 can be calculated
from its specified SNR using
v_{n, AD4003}
= ^VREF
2
 ^{SNRAD 4003} 
× 10^{ 20 }
The SNR for the AD4003 (SNRAD4003) is specified as approximately
98 dB for a 4.096 V reference.
The single-pole RC filter at the input of the AD4003 limits the
wideband noise from the upstream components. A smaller filter
bandwidth improves SNR by further limiting noise power;
however, its time constant must also be sufficiently short to
settle voltage kickbacks due to charge injections that occur as
the AD4003 inputs reconnect to the front-end circuitry during
the acquisition phase. The appropriate bandwidth for the system
is at least 5 MHz (for more information, see the Analog
Dialogue article, Front-End Amplifier and RC Filter Design for a
Precision SAR Analog-to-Digital Converter).
Circuit Note
Noise Due to the AD8475 Funnel Amplifier
The rms noise contributed by the AD8475 (vn, ) AD8475 is a function
of its referred to output noise spectral density (NSD) (eAD8475) and
the RC filter bandwidth at the input to the AD4003 (BWRC):
v_{n, AD8475} = e_AD8475 ×
π
2
×
BW_RC
where eAD8475 = 10 nV/√Hz.
Noise Due to the AD8251 Instrumentation Amplifier
The AD8251 functions as a gain stage that improves SNR for
small amplitude signals by boosting their amplitude to more
closely fill the ±VREF range at the input to the AD4003. Ideally, if
the system gain increases by a factor of G, the SNR (in dB) of
the input signal improves by
ΔSNR = log10(G)
This level of improvement is not achievable in reality, however,
because wideband noise is also amplified by the noise gain of
the circuit. Fortunately, this degradation is not as large as the
improvement due to signal gain.
The rms noise contributed by the AD8251 is a function of its
referred to input NSD (eAD8251), its gain setting (GAD8251), the
attenuation factor of the AD8475 (GAD8475), and the noise filter
bandwidth at the input of the AD4003:
v_{n, AD8251} = e_AD8251 × G_AD8251 × G_AD8475 ×
π
2
×
BW_RC
The value of eAD8251 is also dependent on the AD8251 gain; the
value of eAD8251 can be found in the AD8251 data sheet.
Noise Due to the ADG5207 Multiplexer
The NSD and resulting rms noise contributed by the ADG5207
can be found by using the Johnson/Nyquist noise equation,
because the device acts like a series resistance between the
source and the rest of the analog front end:
e_{n, ADG5207} = 4 × k_B × T × R_ON
and
v_{n, ADG5207} = e_{n, ADG5207} × G_AD8251 × G_AD8475 ×
π
2
×
BW_RC
The resistance of each channel (RON) can be found in the
ADG5207 data sheet.
A summary of the calculated noise performance of the system is
shown in Table 2. The largest contributors to the total noise are
the AD8251 in-amp and the AD4003 ADC.
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