ADC overload myths debunked

I've received some feedback that there is some confusion circulating on other ham radio reflectors regarding how analog to digital converters (ADCs) work in radio applications.  Specifically, some of the comments tend to say that direct sampling ADCs just won't work in strong signal environments so I'd like to explain why this is not factual for those who are interested. I have a few points to illustrate this.

As hams we tend to think of strong signals in terms of their total power, how many total Watts they are.  When you think of signals in this way, you can add their power in your head and think: two -10dBm signals add to -7dBm total power (3dB increase).  In fact, you can take multiple signals and add them together in a power meter and the power meter will show the total power of all signals.  But this is the average and not instantaneous power.

An ADC, on the other hand, is really a discrete signal device.  All of the signals get chopped into samples and so the real question is: how do the signals add together in the discrete time domain?  To answer this, we have to look at the signals and how they interact.  An RF carrier is like any AC signal -- it is a sine wave that varies from negative to positive voltage along the curve of a sine wave.  If we add two sine waves of exactly the same amplitude, frequency and phase, the peak voltage will be doubled (6 dB).

But two signals of the same amplitude and phase on the same frequency isn't reality.  Reality is signals all across the bands that are totally unrelated (uncorrelated) -- for example one at 14.100374 and another at 21.102392, etc.  The variance of the algebraic sum of these signals will decrease with the square root of the number of signals present.  As more signals are added, there is a decreasingly small probability that these signals will add (precise alignment of the highest voltage peak of the signals) and the algebraic sum of the signals will degenerate into a quasi-Gaussian distribution.  To get a fabled 6dB voltage rise, they would have to already be exactly the same voltage, frequency and phase (this is what is done in a power combiner in an amplifier and it’s hard to make that happen).  If one is stronger, the addition of a weaker signal will not add much to the total level.  

If we're talking about a large number of signals across a wide spectrum, it's the same situation.  They would virtually never all add at the same time so they will not combine at just the point where the peak of all signals occurs.  It just doesn't ever happen.  As a mathematician friend of mine pointed out, the two primary principles involved are the Law of Large Numbers (https://en.wikipedia.org/wiki/Law_of_large_numbers) and the Central Limit Theorem (https://en.wikipedia.org/wiki/Central_limit_theorem) which you can peruse for more insight.

As an intuitive analogy, we could look at our solar system.  Let's discuss the likelihood that the planets will cause the ocean to rise and cover up the state of Hawai'i. The planets all have their own period around the sun (frequency).  They are all different amplitudes as well (gravitational influence on the Earth if we're thinking about rising tides).  The questions are:

1) How often do all the planets align?
2) When they do align, will the ocean cover Hawai'i (overload)

There was a book published on this in the 70's called The Jupiter Effect (https://en.wikipedia.org/wiki/The_Jupiter_Effect) which proclaimed death and destruction when this was to occur.  The book was, of course, proved wrong but not before it became a bestseller.  First, the planets almost never come into alignment -- even in the book the planets were only going to be on the same side of the sun, within a 95-degree arc.  Second, when they do align, the amplitude from the outer planets is so low, it just doesn't matter.  My college physics professor was asked about this problem and worked the equations and showed that even if they were all in precise alignment, the ocean would rise by an additional 1/4" briefly... just not worth worrying about.  It is the same situation in ADCs.  The real truth is that more and stronger signals actually make an ADC work better through a process called linearization.  Everyone that has studied ADCs knows this -- the irony here is that lots of strong signals are a benefit, not a detractor like they are in old technology superheterodyne transceivers where IMD dynamic range degrades rapidly with signal strength.  Translation: Strong signals -- Bring it!

Another point to make is that all overloads are not created equal.  Overload sounds like an undesirable situation, but a momentary overload has no significant effect on a direct sampling radio.  Why is this so?  The individual data points that make up a signal you are listening to are almost never going to fall in the same time as the overload, statistically.  With a noise blanker, we remove thousands of samples with no negative effects to the signal being monitored and a momentary overload from the addition of many signals summing up will have a much lower effect.  This effect is called "soft overload" because momentary overloads just don't have an impact on the radio.  It takes much more significant and sustained overloads to cause a real problem.  The overload that folks are talking about is a non-event.  Even if it did happen, it's not going to affect the radio's performance.

Finally, there's often confusion about dynamic range from wideband ADCs.  The confusion generally works like this -- someone will lookup a data converter that runs at 100MHz and see that it has a dynamic range of 70dB and assume that it could never beat a radio with an 85dB dynamic range.  The problem is that this is an apples and oranges comparison.  You cannot talk about instantaneous dynamic range without talking about detection bandwidth.  For ham radio, this is the width of the actual receiver.  We use a standard 500Hz bandwidth receiver for comparison purposes but it could be 2700Hz for sideband or 50Hz for CW, for example.  

What really happens is that we use a process called decimation ( https://en.wikipedia.org/wiki/Decimation_(signal_processing) ) which takes the data collected at an oversampled rate (100MHz for example) and then systematically reduce the sampling rate down to the bandwidth of interest.  In this process dynamic range is increased in what is called "processing gain" (http://www.dsprelated.com/freebooks/sasp/Processing_Gain.html).  In the FLEX-6500 and FLEX-6700, we operate the ADCs at 245.76 Msps so that the typical processing gain is on the order of 56dB.  When added to the 75.5dB quoted spec of the ADC, the calculated instantaneous dynamic range is on the order of 132dB.  This far exceeds the dynamic range of ALL superheterodyne receivers (Don’t believe what you read about blocking dynamic range as it is irrelevant if the radio falls apart due to phase noise before this level).

In reality, it is impossible for any receiver to have blocking dynamic range or IMD dynamic range greater than its phase noise dynamic range (PNDR) otherwise known as reciprocal mixing dynamic range (RMDR).  In all cases and no matter the architecture, if RMDR is less than BDR or IMD DR for a given tone spacing, the phase noise will cover the signal of interest before blocking or IMD will be a factor.  In fact there is not a single transceiver from any manufacturer on the market that would not have its blocking dynamic range limited by its internal phase noise much less first by the noise from the transmitted signal.  

Most of the old technology superheterodyne transceivers on the market have horrible RMDR numbers.  When a strong signal is heard by them, their oscillators spread the signal all around the band as noise covering up signals you are trying to hear.  Here's the simple test: Take two of your favorite legacy radios and transmit in one while listening in the other and watch what happens to the noise floor at 2, 10, 20, 50 and 100kHz from that signal.  You will see that these receivers show significant noise floor increases that prevent operation near each other.  This is the practical concern -- there's no reason to talk about a number of mythical strong signals of all the same power that might correlate to cause an overload in a new type of receiver... the real problem is the superheterodyne receiver that folds under a single strong signal in the vicinity of small signals you are trying to copy.  Most contesters have experienced this first hand when two radios are being used.  If you have to tell your operating buddy in the same band to stay so many kHz away from you, you know the problem well.  This is also a classic Field Day problem.

We have thousands of radios in the field and if any of these issues were real, we (and you) would have heard about it.  You should have confidence that you have the best transceiver on the market -- experienced and knowledgeable people have said so.  They have said so because it is proven out in test after test and it is simply mathematically true.  FlexRadio Systems makes the best amateur transceivers available.