Topband: ADC Overload

[Ward Silver]

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 at 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.