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1 Example of a simple analog to digital converter, the Flash ADC
Analog to digital converter
(1,0,0), (1,1,0), (1,1,1). If the reference voltage is 1.0 V, we can then detect 3 transition
levels of input voltage, 1/4, 2/4, 3/4 V and four possible intervals (0-0.25, 0.25-0.5, 0.50.75 and >0.75) corresponding to the numbers 0-3 (Table 4.1). In the two’s complement
binary code, this corresponds to the numbers 00, 01, 10, 11. Since the data values are
contained in a 2 bit word, using the whole range available, we call this a 2 bit converter.
The number out of an ADC is commonly called counts.
In the above example, only positive voltages were digitized, but our signals also contain
negative voltages. We can get the negative signals by adding another ADC with a
negative reference voltage so one ADC would give out counts for the negative signals
and the other for the positive signals. The other alternative is to add a voltage of half the
reference voltage, to the input signal so that the voltages reaching the ADC never
become negative. The ADC now should have the output range +2 to -2 counts instead of
the 0-3 counts (when the offset of 2 has been subtracted). But this would be five states,
not four! With 2 bit representing positive and negative values, we only have the values
+2 to –1 to use (as defined in the two’s complement code). Actually, in bipolar
converters, since the binary full scale is not exactly symmetric, the offset subtracted is
not exactly half of the scale, but half a count less, to avoid this bias. Table 4.1 gives the
input and output levels for this case.
For high resolution (many bit) converters, one can simply subtract half of the full scale
without significant error.
-3/8 to –1/8
-1/8 to +1/8
+1/8 to +3/8
+3/8 to +5/8
V input to ADC
0.00 to 0.25
0.25 to 0.5
0.5 to 0.75
0.75 to 1
Table 4.1 Input and output to flash ADC. First column gives the voltage in; second column, the
center voltage of each interval; third, the voltage input into the converter itself after adding (0.5 V 0.125 V) (half the full scale minus half a count); third column, the numbers out and the last column
the two’s complement code and its decimal value in parenthesis. Numbers in column 3 and 4
correspond to the example with input of only positive numbers.
Flash ADC’s are extremely fast and very expensive if a high resolution is needed since
one comparator is needed for each level, so if the signal is going to be resolved with
10000 levels, 9999 comparators and precision references are needed. Flash ADC’s are
not much used in seismology but illustrate some of the characteristics of the ADC.
4.2 Basic ADC properties
We will now define some of the basic properties of ADC’s to have in mind when
continuing the description of common ADC’s :
Resolution. The smallest step that can be detected. In the above example, the smallest
step was 0.25 V, which is then the resolution corresponding to one change of the least
significant bit (LSB, the rightmost bit). For a high dynamic range digitizer, this could be
0.1 to 1 µV. ADC resolution is also labeled ADC sensitivity. The higher the resolution,
the smaller a number is given. As it was described in the section on sensors, the output
from a passive sensor can be in the nV range in which case many digitizers will need a
preamplifier. The number of bit is also often referred to as resolution. Most ADC’s have
an internal noise higher than one count: In this case, the number of noise-free bits,
rather than the total bit number, limits the effective resolution. For instance, one count
corresponds to 0.3µV in a 24 bit ADC with full-scale of ±2.5V, but it may have a noise
of 2µV peak-to-peak, and signals under this level may not be resolved in practice.
Gain. The sensitivity expressed in counts/V. It can be derived from resolution. If e.g.
the resolution is 10 µV, the gain would be 1count/(10-5V) = 105 counts/V.
Sample rate. Number of samples acquired per second. For seismology, the usual rates
are in the range 1 to 200 Hz (or, more specifically, samples per second – sps) while for
exploration seismology, sample rates can be more than 1000 Hz. In general, the
performance of the ADC degrades with increasing sample rate.
Maximum input or full-scale (FS). The maximum input for the ADC. Using any higher
input will result in the same output. In the example above, the maximum input is 1.0 V
or in the bipolar mode ±0.5V. Typical values are ±1 to ±30 V.
Dynamic range. Defined as the ratio between the largest and smallest value the ADC
can give. In the above example, the dynamic range = 4/1 = 4, or in dB, 20·log(4) = 12
dB. This can be a bit misleading since both negative and positive numbers are input and
the ADC has to work in bipolar mode. So the real dynamic range is only half, in this
case 6 dB. However, dynamic ranges given in dB for ADC’s are sometimes given for
the full range. For some digitizers, the lowest bits only contain noise, so the dynamic
range is defined as the ratio between the largest input voltage and the noise level of the
digitizer. This number can be substantially smaller than the theoretical largest dynamic
range of a digitizer and may depend on the data rate or sampling frequency. So, to give
one number for the dynamic range, a frequency bandwidth should ideally also be given.
Dynamic range in terms of bit. The dynamic range can also be given as number of bits
available in the output data sample. An n-bit converter then gives the numbers 0-2n or in
bipolar mode ±2n-1. In the example in Table 4.1, we have a 2-bit converter. This way of
giving the ADC dynamic range is the most common and there is no confusion about
what the meaning is. In seismology we mostly use 12, 16 and 24 bit converters. As seen
later, the 24 bit converters give out 3 bytes, but in many cases only the 17-22 more
significant bits are noise free. So, like for dynamic range, the usable dynamic range for
a 24-bit converter could be given as e.g. 18 bit.
Accuracy. The absolute accuracy is a measure of all error sources. It is defined as the
difference between the input voltage and the voltage representing the output. Ideally this
error should be ±LSB/2 and this is achieved by several low and medium-resolution
Analog to digital converter
commercial ADC’s (it is more difficult for higher resolution ones). The error only due
to the digitization steps (±LSB/2) is also called the quantization error.
Noise level. Number of counts out if the input is zero (subtracting DC offset). Ideally,
an ADC should give out 0 counts if the input is zero. This is usually the case for low
dynamic range digitizers 12-14 bit, but rarely the case for high dynamic range digitizers
(see section on 24 bit digitizers). The noise level is most often given as an average in
terms of RMS noise measured over many samples. A good 24-bit digitizer typically has
an RMS noise level of 2 counts.
Conversion time. The minimum time required for a complete conversion. Often it is
expressed by the maximum data rate or sampling frequency. Due to the finite time
required to complete a conversion, many converters use as input stage a sample and
hold circuit, whose function is to sample the analog signal before the start of a
conversion and hold the converter input constant until it is complete to avoid conversion
errors. This is not required with sigma-delta converters (see later), as they track the
signal continuously and their output represents an average of the input signal value
during the conversion interval.
Cross talk. If several channels are available in the same digitizer, a signal recorded with
one channel might be seen in another channel. Ideally this should not happen, but it is
always present in practice. The specification is given in dB meaning how much lower
the level is in the neighboring channel. A 24 bit digitizer might have cross talk damping
of 80 dB or a factor of 10 000 damping. If the input in channel 1 is at the maximum
giving ±223 counts out and channel 2 has no signal, the output of channel 2 caused by
cross talk would still be ±223 /10000=839 counts. This is well above the noise level for
most 24-bit digitizers, so cross talk creates a clear artificial signal in this case. In
practice, the signal shape and level is often similar in the different channels (e.g. for a 3
component station), so the problem might not be as bad as it sounds, but it certainly
should not be ignored. A good 24-bit digitizer has 120 dB of damping or better (see
Table 4.6). Cheaper multichannel digitizers use a single ADC and an analog
multiplexer, which connects different inputs sequentially to the ADC input. This limits
the cross-talk separation because analog multiplexers have limited performances. For
high resolution digitizers, one digitizer per channel is preferred.
Non-linearity. If the analog input is a linear ramp, this parameter is the relative
deviation of the converter output from the ideal value. It is expressed with relation to
full scale (FS), e.g. 0.01% of FS. For high dynamic range converters, it is important
because a poor linearity may cause two different signals at the input to be
intermodulated (the amplitude of one depends on the other) at the output. Usually it is
not a problem with modern sigma-delta converters.
Input impedance. The input impedance (ohm). Ideally it should be as high as possible in
order to have little influence on the sensor or other connected equipment. A typical
value is 1 Mohm.
Offset. If the input is zero, the offset is the DC level (the average) of the output. This
could also be called the DC shift of the ADC. There is nearly always some offset, either
caused by the ADC itself or caused by the components connected to the ADC. The
ADC might have a possibility of adjusting the offset by changing some reference
voltage. A small offset is of no importance, but any offset will limit the dynamic range
since the ADC will reach its maximum value (positive or negative) for smaller input
values than its nominal full-scale. Figure 4.3 shows an example where the effect of the
offset is to reduce the dynamic range by a factor of 2. The offset will be temperature
dependent, but usually this is a small problem with a drift of typically less than 1 µV/ºC.
Figure 4.3 Effect on dynamic range when a large offset is present. The range of the ADC is ±V.
The large amplitude signal (left) has no offset and amplitude is ±V. The smaller amplitude signal
(right) has an offset of V/2 and the input signal that can be recorded by the ADC is now limited to
+V/2 to –3V/2.
Now that the properties of ADC’s have been given, we can continue to describe
4.3 A typical ADC, the Ramp ADC
One of the simplest approaches of implementing an ADC is the ramp ADC. Figure 4.4
shows a simplified diagram. The control logic sends a signal to the ramp generator to
start a conversion. The ramp generator then generates a ramp signal starting from level
0 (seen on left). The ramp signal enters the comparator and once the ramp signal is
larger than or equal to the input signal, the output from the comparator switches from
zero to 1. At the same time as the ramp generator starts, the counter will start to count
the number of levels on the ramp. When the comparator switches to level 1, the control
logic will stop the counter and the number reached by the counter is then a measure of
the input voltage. After some time, the counter is reset and a new sample can be taken.
A cheaper variant of this type of digitizer generates a ramp by integrating a reference
voltage while a clock signal drives a counter. When the ramp voltage reaches the input
voltage, the digitizer just reads the time elapsed as the counter output. The counter and
integrator are then reset for a new conversion.
Analog to digital converter
Figure 4.4 Ramp ADC, see text.
The Ramp ADC is relatively slow and even slower if a high resolution is required. It
also becomes slower as the number increase in size since the counter has to count longer
for large amplitudes. An improvement of the ramp ADC is the successive
approximation ADC, which is almost identical to the ramp ADC except that it has a
more sophisticated control circuit. The converter does not test all levels, but first tests if
the input level is below or above half the full scale, thus the possible range has been
halved. It then tests if the input level is above or below the middle of this new range etc.
The conversion time is much smaller than for the ramp ADC and constant. This design
is the most popular of the classical type of ADC’s. A typical 16 bit digitizer of this type
may have a conversion time of 20µs, which is fast enough for multichannel seismic data
acquisition. Nevertheless, it requires a sample and hold circuit.
We have all used a digital multimeter. It contains a digitizer sampling a few times a
second which can be seen by how often the numbers change on the display. Most
multimeters have a range of ±2000 (V, mV etc). Why 2000 and not ±10 000 which
would be a more convenient range? Simply because a cheap 12 bit converter is used,
which has a range of ±2048 counts.
4.4 Multi channel ADC
We usually have more than one channel to digitize. For three component stations there
are 3, while for telemetric networks or small arrays, there might be up to 100 channels.
The simplest approach is to have one ADC for each channel. However, this might be
overkill depending on the application and in addition quite expensive. There are several
ADC cards for PC’s (and other computers) on the market that have up to 64 channels