Page 1187 - The Mechatronics Handbook

is missing, the step size at that point in the transfer function is doubled, effectively cutting the local
resolution of the ADC in half. Therefore, ADC datasheets will specify if the ADC has no missing codes.
Another way to capture the same information included in INL is a measurement called relative
accuracy. Relative accuracy indicates how far away from the ideal the code transitions are (which is INL),
but also includes how far any part of the transfer function, including quantization “staircase” error,
deviates from ideal. In an ideal noiseless ADC, the worse case relative accuracy is always greater than the
INL. However, if an ADC has some inherent noise and has noise (referred to a dither) added to the input,
then the relative accuracy actually improves. The addition of noise to a quantizer tends to smooth the
average transfer function that results in less of a “staircase” effect. This improvement in the transfer
functions linearity comes at the expense of conversion errors caused by the added noise.

Aperture Errors
Aperture errors deal with the timing of the conversions themselves. All ADCs require some signal,
generally a pulse train clock, to tell the ADC when to start a conversion. Inherently, some small amount of
time will elapse when the ADC receives this convert signal and when the sample is held. This amount
of time that lapses is called the aperture delay. Most ADCs have an aperture delay of just a few nanosec-
onds. However, most measurement devices have some other circuitry in front of the ADC, such as
amplifiers, which have the effect of negating the aperture delay caused by the ADC. For example, if the
ADC has a delay of 10 ns and the amplifier has a delay of 160 ns, the effective aperture delay of the
system is -150 ns.
Another important time specification is jitter. Jitter (or aperture jitter) measures the difference in the
amount of time between each sample. If a signal is sampled at 1 million samples per second (1 MS/s),
the expected period between each sample would be exactly 1 µs. The actual time between samples could
vary from 1 µs by as much as a few picoseconds to a nanosecond from cycle to cycle. Jitter can be caused
by the clock source, digital clock circuitry, or S/H circuitry. The most common effect of jitter is to add
interference at frequencies very close to the signal of interest.

Noise
Noise limits the ADC resolution because an interfering waveform is present in the input signal as it is
being converted. The most common source of noise in a signal is thermal noise. Thermal noise is caused
by the random nature of electrical components. With higher temperatures and resistances in components,
the thermal noise will increase. Other common sources of noise are electromagnetically coupled to nearby
circuitry, such as logic circuits and clocks. Generally, noise is specified in volts peak-to-peak or rms, or
LSBs rms or peak-to-peak.
Quantization error, previously discussed, is sometimes referred to as quantization noise. Although
quantization error is perfectly predictable with respect to the input signal, when a signal is fairly “busy”
(meaning that each consecutive conversions do not result in many common bits of data) the quantization
error becomes chaotic. When this occurs, the quantization error can be thought of as another source of
random noise, whose statistical distribution is uniform from –0.5 to 0.5 LSB and whose standard deviation
is 1/ 12 LSB. In spectral analysis, this is sometimes the dominant source of noise.
Once noise reaches the ADC, there are ways to process the noise out of the signal, provided that the
noise is an independent signal. One of the most common ways to decrease noise in a DC measurement
is to acquire a number of points and average the values. If the noise is white random noise, which has
equal energy density at all frequencies, averaging will reduce the amount of noise by the square root of
the number of samples averaged. If the noise is interfering with a repetitive waveform, the noise can be
reduced by measuring a number of waveforms, using a level trigger and then averaging the waveforms.
Most digital oscilloscopes have waveform averaging.
Most noise specifications for an ADC are for quiet, low-impedance signals. To preserve the noise
performance of the ADC, the user must connect signals to the inputs with shielded cabling that keeps
signals away from any electromagnetic interference.

©2002 CRC Press LLC