Since bits (and their errors) switch in and out
throughout the transfer curve, their effect is sig-
nal dependent. That is, harmonic and
intermodulation distortion, as well as noise, can
vary with different input conditions. Designing a
system around characterization data is risky since
transfer curves can differ drastically unit-to-unit
and lot-to-lot.
The CS5012A/14/16 achieves repeatable signal-
to-noise and harmonic distortion performance
using an on-chip self-calibration scheme. The
CS5012A calibrates its bit weight errors to a
small fraction of an LSB at 12-bits yielding peak
distortion below the noise floor (see Figure 19).
The CS5014 calibrates its bit weights to within
±
1/16 LSB at 14-bits (
±
0.0004% FS) yielding
peak distortion as low as -105 dB (see Fig-
ure 22). The CS5016 calibrates its bit weights to
within
±
1/4 LSB at 16-bits (
±
0.0004% FS) yield-
ing peak distortion as low as -105 dB (see
Figure 24). Unlike traditional ADC’s, the linear-
ity of the CS5012A/14/16 are not limited by
bit-weight errors; their performance is therefore
extremely repeatable and independent of input
signal conditions.
Quantization Noise
The error due to quantization of the analog input
ultimately dictates the accuracy of any A/D con-
verter. The continuous analog input must be
represented by one of a finite number of digital
codes, so the best accuracy to which an analog
input can be known from its digital code is
±
1/2 LSB. Under circumstances commonly en-
countered in signal processing applications, this
quantization error can be treated as a random
variable. The magnitude of the error is limited to
±
1/2 LSB, but any value within this range has
equal probability of occurrence. Such a prob-
ability distribution leads to an error "signal" with
an rms value of 1 LSB/
√
12. Using an rms signal
value of FS/
√
8 (amplitude = FS/2), this relates to
ideal 12, 14 and 16-bit signal-to-noise ratios of
74, 86 and 98 dB respectively.
Equally important is the spectral content of this
error signal. It can be shown to be approximately
white, with its energy spread uniformly over the
band from dc to one-half the sampling rate. Ad-
vantage of this characteristic can be made by
judicious use of filtering. If the signal is ban-
dlimited, much of the quantization error can be
filtered out, and improved system performance
can be attained.
FFT Tests and Windowing
In the factory, the CS5012A/14/16 are tested us-
ing Fast Fourier Transform (FFT) techniques to
analyze the converter’s dynamic performance. A
pure sinewave is applied to the CS5012A/14/16,
and a "time record" of 1024 samples is captured
and processed. The FFT algorithm analyzes the
spectral content of the digital waveform and dis-
tributes its energy among 512 "frequency bins."
Assuming an ideal sinewave, distribution of en-
ergy in bins outside of the fundamental and dc
can only be due to quantization effects and errors
in the CS5012A/14/16.
If sampling is not synchronized to the input sine-
wave, it is highly unlikely that the time record
will contain an integer number of periods of the
input signal. However, the FFT assumes that the
signal is periodic, and will calculate the spectrum
of a signal that appears to have large discontinui-
ties, thereby yielding a severely distorted
spectrum. To avoid this problem, the time record
is multiplied by a window function prior to per-
forming the FFT. The window function smoothly
forces the endpoints of the time record to zero,
thereby removing the discontinuities. The effect
of the window in the frequency-domain is to con-
volute the spectrum of the window with that of
the actual input.
Figure 18 shows an FFT computed from an ideal
12-bit sinewave. The quality of the window used
for harmonic analysis is typically judged by its
highest side-lobe level. The Blackman-Harris
window used for testing the CS5014 and CS5016
has a maximum side-lobe level of -92 dB. Fig-
CS5012A, CS5014, CS5016
DS14F6 2-31
