An A to D converts an analog voltage into a digital word.
Each LSB (Least Significant Bit) bit in that A to D represents a voltage, for
example, 1 mV/LSB.
The next significant bit contains TWO LSB units, or 2 mV in this example.
Going on up the scale, you run out of bits in a 16 bit A to D when you have
collected 65,536 “bits", each representing 1 mV for a grand total of 65,563 mV.
Thus the voltage ratio between the smallest signal the A to D can measure and
the largest is 65536/1=65,536.
From the ARRL publication "A Tutorial on the Decibel”:
dB= 20 * log(reference/voltage reference)
In this case, that voltage ratio is 65,536.
dB = 20 * log (65536) = 96.3 dB
What Flex is talking about is NOISE dynamic range, and what they say is
absolutely correct, I never said it was not correct. When you digitize a
complex waveform (whether is is an audio sampling with 16 bits, sampled at 44.1
KHz, just above the Nyquist frequency, or whether it is a full RF span from 100
KHz to 30 MHz with 16 bits, sampled at even 200 MHz, well above the Nyquist
frequency) the principles are the same. When you narrow the output bandpass
with digital filters, the noise drops accordingly, and that is exactly what
Flex says in it literature. They refer to this as “instantaneous dynamic range”.
This has NOTHING to do with whether or not a given A to D can handle a signal
140 dB above its LSB value. Even with some “enhancements”, no one I have seen
can explain just exactly how anybody could digitize 140 dB signal range with 16
bits without serious compression of the analog signal going into that A to D.
I do not claim to know the answer to the question “How can you exceed 96 dB (or
even 106 dB, the most claimed by any audio digitization system) with 16 bits?”.
I clearly asked anyone who DOES know the answer to post it. It can’t be that
hard for a good EE to explain.
I am an applied physicist, not an electrical engineer. I know what I can get
away with when digitizing analog signals and when converting digital
spectrometer energy to analog drive signals. All I can get from a 16 bit DAC is
1 part in 65,536, or 96.3 dB. The same limit applies to ADC signals coming into
my signal averager.
That is why I am trying to learn how this apparent disagreement can be resolved
because I would LOVE to learn how to get more resolution out of some of m older
apparatus without scrapping the DAC’s and ADC’s, their expensive interface
cards and so on.
It will also help me when I am ready to buy an SDR. I want to know how it works
before I buy it.
Please note that I am well aware of “double precision” which is simply
parsing, for example, a 32 bit word into two 16 bit words, and clocking them
into the computing device, keeping track of which 16 bit word is least
significant and most significant.
All audio CD’s actually get their 16 bit resolution using this double precision
methodology. These 18 bit words are first parsed into 8 bit symbols, encoded
via the complex Reed Soloman code, which disperses the bits over many actual
recorded symbols and these symbols contain merge bits on each end of the words,
all in an effort to mistake proof the digitization and playback process. At no
time is a single 16 bit audio sample ever recorded onto an audio CD, only the
pair of 8 bit “halves” of a given 16 bit word is recorded 9and decoded in the
CD player).
If manufacturers are indeed using double precision digitization, that would be
great since the resolution using 32 bits would be more than adequate for Ham
radio as the signal dynamic range would then be 192.7 dB.
The use of double precision would resolve the question but no one has offered
that this is what manufacturers are doing in radios.
Gary
> On Sep 11, 2016, at 4:06 PM, rick@dj0ip.de <Rick@DJ0IP.de> wrote:
>
> Well there are those who disagree with you Gary.
> Specifically the engineers at FLEX.
>
> I have never used a FLEX but there are guys I highly respect here (N1EU,
> N4PY) who have and assure us their radios are not crunching at 96 dB.
>
> I would say the onus is on you to show us it's wrong.
>
> 73 - Rick, DJ0IP
> (Nr. Frankfurt, Germany)
>
>
>
> -----Original Message-----
> From: TenTec [mailto:tentec-bounces@contesting.com] On Behalf Of Gary J
> FollettDukes HiFi
> Sent: Sunday, September 11, 2016 11:07 PM
> To: Discussion of Ten-Tec Equipment
> Subject: Re: [TenTec] OT: Dynamic range of SDR Radios with 16-bit DAC
>
> 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@dj0ip.de <Rick@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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