Perhaps an alternative analogy would be helpful here...
Each of the many signals can be imagined as its own phasor. One end of
the phasor is anchored on the origin (0 V) and the other is spinning
around the origin at the frequency of the signal with a length equal to
its amplitude. Since the ADC responds to instantaneous voltage, what
matters is the vector sum of all those many phasors. A large number of
the phasors must align perfectly to add up to extreme voltages that
overload the ADC. As you might imagine, this happens very, very rarely
under most circumstances. Even when it does happen, it only happens for
a fleeting instant because of the semi-random phase and frequency
relationships between the phasors. Thus, Jim's bell curve in which the
extreme voltage probability is very low.
One caution about circumstances: if there are truly large signals
present (such as at a multi-multi station or near an AM or SW broadcast
station) many fewer phasors must align to create the overload voltage
and so the overload happens more frequently. Still, the alignment is
quite brief and after the raw sample set is decimated, overloads lasting
for just a few samples or less don't have a lot of effect.
73, Ward N0AX
On 10/14/2015 11:00 AM, topband-request@contesting.com wrote:
My example considered an SDR transceiver that received two signals, each with
instantaneous RF voltage that varied from +3V to -3V, and for simplicity I
assumed each signal could have only seven values spanning this range. I didn't
make it clear that these are independent signals on different frequencies. Thus
every time the ADC in an SDR samples the voltage sum of the two signals at its
input, it will get a different result. For example, with one sample the SDR may
see a voltage of +1V, which comes from +2V from one signal and -1V from the
other signal. A later sample might produce a voltage of -2V, which could come
from +1V from one signal and -3V from the other. In other words, with each
sample, the SDR will measure a different voltage, because the signals have
different frequencies and are not in phase with each other.
Suppose now that we let the SDR sample the voltage a million times, one after
another. Then the Central Limit Theorem tells us how those million measurements
will be distributed, in other words how many times the SDR will measure 6V, 5V,
4V...0...-4V,-5V,and -6V. What the CLT tells us is that the distribution of
these measurements generally follow a bell-shaped curve, with the peak at 0V.
This means that most of the time, the SDR will measure approximately 0V at its
input. Only infrequently will it measure the large +6V and -6V voltages,
because those large voltages are at the extreme edges of the bell-shaped
distribution.
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