Download Input-referred noise improves A/D converter resolution

A/D Converters
Input-referred noise improves A/D
converter resolution
By Walter Kester,
Staff Applications Engineer,
Analog Devices, Inc.
All analogue-to-digital converters (ADCs) have a certain amount
of input-referred noise. In most
cases, less input noise is better.
There are some cases, however,
where input noise can actually
be helpful in achieving higher
resolution.
In precision, low-frequency
measurement applications, the
effects of this noise can be reduced by digitally averaging the
ADC output data, using lower
sampling rates and additional
hardware. While the resolution of
the ADC can be increased by this
averaging process, integral nonlinearity errors are not reduced.
In certain high-speed applications, adding some out-of-band
noise dither can improve the
differential nonlinearity (DNL)
of the ADC (see Figure 1, below)
and increase its spurious-free
dynamic range (SFDR). The effectiveness of this method depends
highly on the characteristics of
the ADC being considered.
As the analogue input voltage
to an “ideal” ADC is increased, the
output remains constant until a
transition region is reached. At
that point, it instantly jumps to
the next value, remaining there
until the next transition region is
reached. A theoretically perfect
ADC has zero code-transition
quantization noise and a transition region width equal to zero.
A real-world ADC has a certain
amount of code transition noise,
and thus, a finite transition
region width. All ADC circuits
produce a certain amount of rms
noise because of resistor noise
and “kT/C” noise.
This input-referred noise is
characterized by examining
the histogram of many output
samples taken with constant DC
input. The output is typically a
distribution of codes centred on
the nominal value of the DC input. The noise is approximately
Gaussian, so the standard deviation of the histogram corresponds to the effective input
rms noise.
The DNL of the ADC will
cause deviations from an ideal
Gaussian distribution. A code
distribution that is significantly
non-Gaussian usually indicates
a bad printed circuit board
(PCB) layout, poor grounding
techniques or improper powersupply decoupling. Another
indication of trouble is when
the width of the distribution
changes drastically as the DC input is swept over the ADC input
voltage range.
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. Multiplying the
rms noise by 6.6 converts it to
peak-to-peak noise.
The term “effective resolution” is used if the root mean
square (RMS) noise (rather than
peak-to-peak noise) is used
to calculate resolution. Under
identical conditions, effective
resolution is larger than noisefree code resolution by approximately 2.7bits.
The effects of input-referred
noise can be reduced by digital
averaging. Consider a 16bit ADC
that has 15 noise-free bits at a
sampling rate of 100 ksps (samples per second). Averaging two
measurements of an unchanging
signal for each output sample
reduces the effective sampling
rate to 50Ksps—and increases
the signal to noise ratio (SNR) by
3dB (decibels) and the number of
noise-free bits to 15.5. Averaging
four measurements per output
Figure 1: Noise enhances A/D signals. Staying outside of the band is key.
sample reduces the sampling
rate to 25ksps, and increases the
SNR by 6dB and the number of
noise-free bits to 16.
Averaging
process
The averaging process also helps
smooth out the differential nonlinearity (DNL) errors. This can
be illustrated for the simple case
where the ADC has a missing
code at quantization level k.
Even though code k is missing
because of the large DNL error,
the average of the two adjacent
codes, k-1 and k+1, is equal to k.
Averaging can increase the
dynamic range of the ADC at the
expense of the sampling rate
and extra digital hardware. But it
will not correct the ADC’s inherent integral nonlinearity.
Maximizing SFDR requires
minimizing both the distortion
produced by the front-end amplifier and the sample-and-hold
circuit, and that produced by
nonlinearity in the encoder.
Nothing can be done to significantly reduce the front-end
distortion. But distortion caused
by DNL can often be reduced
by using dither, defined as external noise that is intentionally
summed with the analogue input signal.
One approach is to add a
large amount of dither to randomize the ADC’s transfer function. Here, a pseudorandom
number generator drives a DAC.
The analogue signal is subtracted from the ADC input and
its digital equivalent is added to
the ADC output, so no significant SNR degradation occurs. A
disadvantage of this technique,
however, is that the input signal
swing must be reduced to prevent overdriving the ADC.
Another way to increase SFDR
is to inject a narrowband dither
signal outside the signal band of
interest. Signal components are
not typically located near DC, so
this low-frequency region is often used for such a dither signal.
Another possible location for
the dither signal is slightly below
fs/2. The dither signal occupies
only a small bandwidth relative
to the signal bandwidth, hence
no significant degradation in
SNR occurs. Dither noise can be
generated in many ways. Noise
diodes can be used, but simply
amplifying the input voltage
noise of a wideband bipolar op
amp provides a more economical solution.
EE Times-India | November 2006 | eetindia.com