For related images and graphs see:
http://www.datx.com/white_papers/Understanding-SFDR-Spec.pdf
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As A/D converters (ADC) and data acquisition boards increase
their bandwidth, more and more are including the spurious free
dynamic range (SFDR) specification as an indicator of their
fidelity. The converter is not the only source of spurious
signals; however, because of complex interactions between the ADC
and the signal conditioning circuits that invariably precede it.
The key to properly interpreting this specification lies in
understanding the sources of spurious signals and how SFDR is
measured. Like everything else in the world of electronics, the
speed and bandwidth of data acquisition (DAQ) systems and their
key components, the ADCs, are increasing. And they don't show any
signs of stopping. The need for speed in applications such as
high-speed data acquisition is continually pushing the limits of
ADCs. At the same time, the need for precision and accuracy in
the DAQs and ADCs remains high. One of the specifications that
ADC and DAQ board vendors have begun touting is the spurious free
dynamic range (SFDR). They often quote the SFDR specification as
an indicator of the digital output's fidelity to the original
signal. While there is an element of truth in that implication,
the SFDR specification can be misleading if not properly
interpreted. The basic definition of the SFDR specification is
simple. It is the strength ratio of the fundamental signal to the
strongest spurious signal in the output. In many cases, the
spurious signal is the result of non-linearity in the A/D
conversion, hence the interpretation of SFDR as an indicator of
fidelity. But a number of other sources of strong spurious
signals may be present in the DAQ system, so the SFDR
specification requires a closer look.
Because ADCs are never used as the only element between the input
signal and the digital output, the place to begin this closer
look is by considering all of the elements in a DAQ system. As
shown in Figure 1, a DAQ module contains several key functions,
including a signal-conditioning filter, a sample-and-hold
circuit, and in many cases an analog multiplexer to make one ADC
handle multiple input signals. Non-linearity in any of these
elements can generate spurious signals that can affect the
achievable SFDR.
Another source of spurious signals occurs within the anti-
aliasing filter as a result of the high signal bandwidth
available in today's ADCs. The purpose of an anti-aliasing filter
is to limit the input signal's bandwidth to eliminate high-
frequency components. A rule of sampled data systems is that the
input signal's spectrum gets folded around a frequency one-half
that of the sample clock. An ideal anti-aliasing filter would
pass all signals in the band of interest and block all signals
outside of that band.
The reality is, however, that filters are not perfect. As shown
in Figure 2, the roll-off characteristics of a practical filter
mean that it will still pass some of the signals above the
filter's cutoff frequency. Depending on where that cutoff occurs
relative to the sampling frequency, the folded signal spectrum
may overlap the input signal spectrum. If the filtered signal
contains any energy in this overlap band, that energy appears as
spurious signals in the output, affecting the SFDR.
As a result of these numerous spurious sources, the significance
of SFDR in many systems is not the converted signal's fidelity,
but the impact of the spurious signal as a noise source. In
effect, SFDR indicates the lowest-energy input signal that can be
distinguished from spurious signals. Any signal below the SFDR
cannot be reliably identified as a true signal instead of as a
spurious one. The practical ramification of this ambiguity is
that the spurious signals can mask desired signals.
In a motor maintenance application, for example, the DAQ is
looking for harmonics of the motor rotation rate in the motor's
vibration spectrum. The presence of growing harmonics is an
indication of motor wear and the need for replacement. When the
DAQ itself creates spurious signals, those harmonics may be
masked until they become stronger, reducing the system's ability
to make an early prediction of motor failure. In another example,
the presence of spurious signals in digitized audio reduces a
system's effectiveness. In the audio case, these signals manifest
as "hiss" in the audio signal, reducing the signal quality.
The anti-aliasing filter is only one example of spurious signal
sources. A more complete list includes:
* Sample-hold non-linearity
* ADC non-linearity
* Signal multiplexing
* System clock noise
* DC/DC converter noise
* Adjacent channel noise
* Channel overload (driving op-amp to rails)
Because of the many sources of spurious signals, SFDR of the ADC
alone is not a sufficient measurement of the achievable signal
dynamic range. The measurement must be made in the context of a
full DAQ system.
The test setup for measuring SFDR, shown in Figure 3, involves
generating a pure sinusoidal input signal (accurate to at least
0.001%) with strength within 1 dB of the DAQ system's maximum
input range. Then, perform an FFT (Fast Fourier Transform) on the
output. The frequency spectrum that the FFT produces allows
direct measurement of the SFDR. In addition, performing the FFT
on the output of an adjacent channel, which has its input
grounded, provides a measure of the spurious signals coming from
the rest of the system as well as coupling of signals from other
inputs.
Comparing the two measurements will also provide a metric known
as the effective number of bits (ENOB). The ENOB tells users how
many of the system's output bits will contain useful information,
typically a value lower than the resolution of the ADC. It is a
particularly useful metric, as it measures the performance of the
entire DAQ system, not just the ADC, and it does so under
dynamic, real-world conditions.
As a metric, the ENOB is a more useful measure of a DAQ system's
performance. For the analog front end, for instance, it will
detect such things as interactions between the over-voltage
protection circuits and EMI filters. Noise from gain-setting
resistors within the instrumentation amplifier, amplifier and
sample-and-hold bandwidth errors, and the effects of acquisition
time, channel-to-channel offset, and channel crosstalk in the
input multiplexer all contribute to ENOB. So do system electrical
noise, distortions that the ADC introduces (a component of SFDR)
and the effects of over-driving the filter opamps when the input
signal is over-range.
The ENOB metric includes the effects of SFDR, but provides a more
accurate overall picture of a DAQ system's potential performance.
This does not mean that the SFDR specification has no value,
however. Because it focuses specifically on spurious signals
rather than random noise, it provides some guidance as to where
improvements can be made to the DAQ system.
When spurious signals are large relative to random noise, the
frequency of the spurious signal helps identify the source. Pure
harmonics of the input frequency, for instance, can be due to
non-linearity in the signal conditioning chain as well as the
ADC. If the ADC's specified linearity does not account for all of
the harmonic energy, the front-end should be checked.
The spurious signals introduced by folding of the anti-aliasing
filter's output around the frequency at half the sample clock
rate can be identified by their concentration at the high end of
the filter bandwidth. When those signals set the SFDR limit, they
can be reduced in two ways. One is to use a filter with a sharper
roll-off, which generally implies a more complex filter. The
other is to increase the sample clock frequency, so that the
folding involves signal components further out in the filter's
roll-off curve.
When the spurious appear tied to the channel switching frequency
of a multiple-input ADC, designers can look for noise in the
multiplexer. They can also look at the slew rate and settling
time of the sample-hold circuit, making sure that converted
signals are not being affected by the values on adjacent
channels. An alternative, increasingly available due to
semiconductor process improvements, is to eliminate the use of a
multiplexer and use one ADC for each channel. This allows a
simultaneous sample-and-hold for each input signal, eliminating
cross-talk and switching noise, and ensures that those signals
can utilize the full sample rate of the ADCs rather than just a
fraction. This increase also helps move the folding point for the
anti-aliasing filter.
Thus, the SFDR specification has value for the DAQ system
designer and user, but as a metric of data fidelity it has
limits. In its place, the ENOB metric provides a more complete
picture of a DAQ system's performance. The ENOB value
incorporates the effects that SFDR aims to measure, as well as
virtually every other noise source and distortion in the system.
To properly utilize the SFDR specification, designers need to
consider how SFDR has been measured, and whether it applies to an
entire DAQ module or just the ADC. If it is just the ADC, they
should realize that the analog front-end design may degrade the
achievable DAQ performance below the values indicated by SFDR.
The SFDR specification can then serve as a pointer to problems
within the front-end, and help designers maximize the fidelity of
their DAQ system.
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