IEEE Solid-State Circuits Magazine - Summer 2015 - 49
(based on the signal-to-quantization
noise ratio). The resolution (in bits)
and data rate (in samples/second)
set the size of the "Shannon's box"
doorway (see Figure 1). While there
are unconventional signal processing approaches that bend some of
the classic assumptions (see the
article in this issue "Where Analog
Meets Digital"), these laws still hold.
To put a bit of intuition behind
these dimensions, consider an example from everyday life: the FM radio
band. A single radio station occupies
200 kHz of bandwidth, so we would
require a data converter of at least
400 thousand samples per second
(Ks/s) to unambiguously digitize a
single station. To capture the entire
20 MHz FM band in the United States,
we would need a data converter sampling at 40 million samples per second (Ms/s) or greater.
Dynamic range requirements can
be a bit trickier to determine. Say
that a single station required eight
bits to recover a high fidelity signal-as we start adding stations,
how much more dynamic range
would be required? If all stations
are at the same power level, we
would need 3 dB more dynamic
range for every doubling of the
number of stations (if you have two
stations, each cannot be at the full
scale of the A/D because that could
cause clipping when the stations
were in phase-you have to "back
off" of full scale). However, in most
real world situations, the different
signals (or stations) may reach the
data converter at different power
levels (called a "near/far" problem
in communications). If one is to recover a weak signal in the presence
of a strong signal, the dynamic
range requirements can increase
dramatically. This is true across all
applications, from audio (the faint
orchestra instrument in the presence of a loud drum beat) to imaging (resolving the activity going on
in the shadows in the presence of a
bright object).
With these key performance dimensions identified, any advance
Largest
"Capture-Able" Signal "The Ceiling"
Useable Bandwidth
"The Walls"
Smallest
Detectable Signal
"The Floor"
Figure 1: "Shannon's box": bandwidth
(sampling rate) and dynamic
range (resolution).
in technology may be traced as an
advance in these two dimensions.
Faster conversion rates provide
converters that can capture larger
bandwidths; higher resolutions provide more dynamic range, as well as
the ability to handle more signal information. It is satisfying to realize
that these same dimensions capture
performance advance in digital processor technology.
At this point, it is worth noting
that in most cases the data converter is moving the signal across
another very important boundary-that between the continuoustime and discrete-time domains.
In many applications, the analog-to-digital converter (ADC) is
presumed to provide both the
sampling function (which moves
the signal from continuous time to
the sampled signal can remain
in the analog domain: switched
capacitor circuits are a well known
example of discrete-time analog
signal processing.
Nevertheless, by the time the
signal is taken into the digital
domain, it is going to be treated
as discrete in both amplitude and
time. Mentally separating the sampling and the quantization actions
can be important in some analyses
because the two operations create
very different artifacts: sampling
produces aliasing in ADCs, or zeroorder-hold or sinx/x artifacts in
the simple reconstruction found in
most digital-to-analog converters
(DACs). Quantization errors produce
clipping for signals that exceed the
full scale of the resolution word,
and quantization noise that forms
a sensitivity floor. These errors
exist even in a theoretically perfect
converter, but, because converters
are implemented with real circuits,
they are also subjected to a host of
nonlinearities and other sources of
error [1]-[7].
DaCs and aDCs:
Which is more important?
We should not forget that signals
need to commute between the analog
and digital domains in both directions: the ADC must capture the signal, while the DAC must reconstruct
it. Much of the literature (this special
issue included) seems to pay particular attention to the A/D function:
Shannon's theory suggests that the theoretical
limit of a channel's information capacity is a
function of its dynamic range and its bandwidth.
discrete time) and the quantization
function (which moves the signal
from analog to digital). It is for the
sampling function that the Nyquist
theorem is applied to describe the
maximum signal bandwidth that
can be unambiguously represented
(one half the sampling rate), but
ADC papers in the circuits' conferences often outnumber the DAC
papers by 3:1 or more. Are ADCs
more commercially important? Is the
ADC function more difficult?
Let us consider the question of
commercial significance first. Initially, we might think that most
IEEE SOLID-STATE CIRCUITS MAGAZINE
su m m e r 2 0 15
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