[hpsdr] Interesting math, etc.

[Robert McGwier]

I recently had called into question my statements concerning A/D and 
blocking dynamic range results on systems where you have a fairly wide 
front end since people I have an immense amount of respect for (N8VB and 
VK6APH) were getting results contrary to my beliefs based on measurements.

I was given some older opinions on the subject by Bill Sabin in some QEX 
articles by Rick Campbell and others.   Their opinions (or experience) 
are right but the reasoning given there is all wrong.  After Phil Harman 
pointed out these articles and opinions to me and Phil Covington gave me 
his recent results,  it dawned on me that I had seen applicable results 
before but with a mathematical treatment that leads to understanding 
rather than opinions which can leave one in doubt.

For years I have known about the work of Karl Meinzer, DJ4ZC, on the 
additive sum  of multiple signals in a wide band.  He used this work to 
derive his arguments for doing High Efficiency Linear Amplification by 
Parametric Synthesis (HELAPS) which we have used for multiple decades in 
AMSAT projects.  I will not bore you with the mathematical details here 
but let me give you the "Bob synopsis" of the "standard  understanding 
of multiple signals being added in an A/D".  THEY ARE COMPLETELY FULL OF 
IT.   The thing that you should think of if you have any mathematical 
training at all is that sums of independent random variables (a bunch of 
uncorrelated signals being added up) approaches a Gaussian (white noise) 
distribution and it does it pretty rapidly.  Meinzer's thesis even 
derives results for this when the signals are a random mixture of tones, 
ssb signals, digital signals, etc.  The envelopes rapidly approach a 
well known statistical distribution that is well understood.   The 
amount of time that one can spend above an A/D's clipping limit is so 
small that it will have a very small impact on the performance so long 
as it is accompanied by a reasonable BPF.  This is planned for the HPSDR 
and Mercury / ATLAS system.

Back to practical from the land of Mathematical Bliss:  The "collective 
understanding" about blocking dynamic range and A/D's which I have been 
a party  to until recently, is largely off the mark.   I am now 
expecting Mercury and QS1R to have excellent single and dual tone 
results and much better than I expected before behavior on random large 
signals over fairly wide bandwidths.

My apologies for taking the party line and not thinking.  I must be 
getting old and tired since I used to question if 2+2 was 4 without a 
proof just for the sake of having an argument which could then be 
settled over a brewski!

73's
Bob
N4HY

-- 
AMSAT Director and VP Engineering. Member: ARRL, AMSAT-DL,
TAPR, Packrats, NJQRP, QRP ARCI, QCWA, FRC. ARRL SDR WG Chair
"Taking fun as simply fun and earnestness in earnest shows
how thoroughly thou none of the two discernest." - Piet Hine