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.
______________________________________________________________
Elecraft mailing list
Home: http://mailman.qth.net/mailman/listinfo/elecraft
Help: http://mailman.qth.net/mmfaq.htm
Post: mailto:[email protected]
This list hosted by: http://www.qsl.net
Please help support this email list: http://www.qsl.net/donate.html
Message delivered to [email protected]
