[TenTec] OT: Dynamic range of SDR Radios with 16-bit DAC

[Gary J FollettDukes HiFi]

I know all of the Rick. 

It still does not explain how you can digitize a signal with amplitude that is 140 dB signal above one LSB using a 16 bit A to D.

Gary



> On Sep 11, 2016, at 3:59 AM, rick at dj0ip.de <Rick at DJ0IP.de> wrote:
> 
> Response to Gary's comment:
> 
> 
> 
> " How is it that a 16 bit A to D can now handle a dynamic range of 132 dB
> (in band)? "
> 
> 
> 
> ANSWER:
> 
> 
> 
> There are two parts to this, the first dealing directly with dynamic range,
> the second is a paper on "ADC Overload Myths Debunked."
> 
> 
> 
> PART I:  Dynamic Range with 16-bit ADC
> 
> 
> 
> This is explained By Gerald, K5SDR (founder of FLEX) in a news letter.  I
> will paste it below in its entirety.
> 
> 
> 
> by Gerald Youngblood, K5SDR
> 
> 
> 
> A number of people have asked how you can get more than 96 dB of
> instantaneous dynamic range out of a 16-bit A/D converter.  You may think
> that one can only achieve 6 dB per bit, which would be 96 dB.  Technically
> the theoretical maximum limit is 6.02n +1.67 dB (where n is the number of
> bits).[1,2] What many people fail to understand is that dynamic range is a
> meaningless term without knowing the final detection bandwidth (i.e. 500 Hz
> CW filter).
> 
> Instantaneous dynamic range increases with decreasing bandwidth by a factor
> of 10*log*(bandwidth change).  That means that a 50 Hz filter will provide
> 10 dB higher dynamic range than a 500 Hz filter.  That is why you hear less
> noise in the smaller filter.  The actual receiver noise figure (NF) of the
> radio has not changed but the detection bandwidth has.  Thus the SNR and
> dynamic range improves accordingly.
> 
> 
> 
> The dynamic range of any ADC is normally assumed to be specified over the
> Nyquist bandwidth, which is equal to 1/2 of the converter's sampling rate.
> With the ADC used in the FLEX-6000 series, the Nyquist bandwidth is 122.88
> MHz.  To calculate instantaneous dynamic range, one needs to know the
> converter's specified signal to noise ratio (SNR), maximum peak signal
> handling capability, sampling rate, and final detection bandwidth.  There
> are many application notes available from Analog Devices, Linear Technology,
> Texas Instruments, etc. that aid in these calculations.  It is beyond the
> scope of this newsletter to provide the detailed education and analysis.
> 
> 
> 
> The bottom line is that the FLEX-6000 ADC running at 245.76 Msps provides a
> nominal instantaneous dynamic range on the order of 130 dB in a 500 Hz
> bandwidth or about 140 dB in a 50 Hz bandwidth.  How much do you need in
> practice?  Let's look at that question next.
> 
> 
> 
> References:
> 
> 
> 
> 1. "Quantization Noise: An Expanded Derivation of the Equation, SNR= 6.02 N
> + 1.76 dB", Ching Man, Analog Devices,Inc.
> 
> http:www.analog.com/static/imported-files/tutorials/MT-229.pdf
> 
> 
> 
> 2. "15.3.2 Quantization - Digitization in Amplitude; DSP and Software Radio
> Design", The 2013 ARRL Handbook, American Radio Relay League.
> 
> 
> 
> 
> 
> PART II:  ADC Overload Myths Debunked
> 
> By Steve Hicks, N5AC; VP Engiineering, FLEX Radio
> 
> 
> 
> 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>
> https://en.wikipedia.org/wiki/Law_of_large_numbers) and the Central Limit
> Theorem ( <https://en.wikipedia.org/wiki/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>
> 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)>
> 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)>
> 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 super heterodyne  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 super heterodyne 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.
> 
> 
> 
> End
> 
> 
> 
> 
> 
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