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Re: Topband: ADC Overload

To: topband@contesting.com
Subject: Re: Topband: ADC Overload
From: Ward Silver <hwardsil@gmail.com>
Date: Wed, 14 Oct 2015 14:43:45 -0500
List-post: <topband@contesting.com">mailto:topband@contesting.com>
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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