[Elecraft] Analog vs. Digital Front Ends

[Joe Subich, W4TV]

On 9/16/2015 2:02 PM, Alan wrote:
> The amplitude distribution of a large number of signals of different
> frequencies and amplitudes closely approximates Gaussian noise (see
> note 1 below). As a rule of thumb the peak to RMS voltage ratio of
> Gaussian noise is about 5 or 6. Of course, theoretically it is
> infinity, but peaks over about 5-6 are statistically rare (note 2),
> so that's a good practical rule of thumb.

We know N > 3 based on NC0B's test with the Flex-6700.  5-6 may be
reasonable if all signals are the same strength but what happens when
a very strong signal (that neighbor half mile away) preloads the ADC?

 > A voltage ratio of 5-6 is 14-15.6 dB.  ADC overload should be rare as
 > long as you keep the RMS power 15 dB or so below the ADC full-scale.

Unfortunately, with practical DDC transceivers like the Flex-6000
series, that 15 dB below ADC full scale does very bad things to
sensitivity.  Based on ARRL's April 2015 test, turning off +20 dB
preammp reduces sensitivity (MDS) from -135 dBm to -119 dBm while
the 20 KHz IMDDR3 goes from 94 dB (preamp on) to 103 dB (preamp off).
In practice, the user is faced with a choice between sensitivity and
IMD.

The real issue is that the -10 to -17 dBm clip point for the current
class of DDC devices is simply too low for full performance from MDS
to clipping.  Considering that K9ZOA's Norton pre-amplifiers are rated
for *+19 dBm* at the 1 dB compression point, a well designed "analog"
transceiver has nearly 30 dB more headroom (while maintaining full
sensitivity) than the DDC products.  This is the issue that the DDC
proponents can't escape (and don't want to address).

73,

    ... Joe, W4TV


On 9/16/2015 2:02 PM, Alan wrote:
> On 09/16/2015 05:25 AM, Joe Subich, W4TV wrote:
> ...
>>       N      "S"
>> ----------------------------------
>>       1     S9 +63 dB (-10 dBm)
>>       3     S9 +53 dB
>>      10     S9 +43 dB
>>      32     S9 +33 dB
>>     100     S9 +23 dB
>>     316     S9 +13 dB
>>    ~450     S9 +10 dB
>>    1000     S9  +3 dB
>>   ~1400     S9  +0 dB (-73 dBm)
>>
>> Since it is the instantaneous peaks that cause problems, increasing the
>> number of signals decreases the frequency of the ADC overflows.  There
>> is certainly analysis that can be done to compute the probability of a
>> peak given a specific number of signals and frequency distribution but
>> my best guess is that the number of signals involved will be somewhere
>> between 10 and 100.
>
> The amplitude distribution of a large number of signals of different
> frequencies and amplitudes closely approximates Gaussian noise (see note
> 1 below).  As a rule of thumb the peak to RMS voltage ratio of Gaussian
> noise is about 5 or 6.  Of course, theoretically it is infinity, but
> peaks over about 5-6 are statistically rare (note 2), so that's a good
> practical rule of thumb.
>
> A voltage ratio of 5-6 is 14-15.6 dB.  ADC overload should be rare as
> long as you keep the RMS power 15 dB or so below the ADC full-scale.
>
> A lot depends on what happens when the ADC overloads.  If it simply
> clips the signal, an occasional brief overload would not be
> objectionable.  That's how the ADC in the P3 works.  On the other hand,
> if it "wraps around" (for example, 0x7FFF = 32767 wraps to 0x8000 =
> minus 32768) then it's obviously much more of a problem.  In that case,
> you would need an external analog clipper to keep the ADC from overloading.
>
> Alan N1AL
>
>
> Note 1:
>
> The Central Limit Theorem:
> https://en.wikipedia.org/wiki/Central_limit_theorem
>
> Note 2:
>
> The cumulative Gaussian probability density function is given in the
> Wikipedia article:
>
> https://en.wikipedia.org/wiki/Normal_distribution#Numerical_approximations_for_the_normal_CDF
>
>
> If I calculated right then for x=5, CDF = (1 - 3*10^-8).  If the ADC
> sample rate is 100 Msps, then on average there would be 3 overloaded
> samples per second. For x=6, CDF = (1 - 2.8*10^-11) so there would be
> one overload about every 360 seconds.
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