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
_______________________________________________
TenTec mailing list
TenTec@contesting.com
http://lists.contesting.com/mailman/listinfo/tentec
|