John Ackermann N8UR skrev:

Because they WILL drift appart.

Interlocking them force them to a common frequency and average phase.

Cheers,
Magnus

On Tue, 23 Dec 2008 17:27:28 +0100, Magnus Danielson
magnus@rubidium.dyndns.org wrote:

I got the hunting thing out of my blood when I was still a teenager.  I'm now
a precision shooter and a shooting nerd.  Shooting can be very exciting to the
type that populate this list.  Internal ballistics, external ballistics,
statistics, precision mechanics, precision electronics, etc.

Ballistics timing is fast enough that you get to play with the things that
concern time-nuts.  I have, for example, drilled an old barrel and inserted
conductive probes every inch.  The bullet passing by makes up the circuit. The
probes were arranged in an R/2R D/A converter circuit so that I could digitize
them all with one fast A/D converter.  I wanted to watch the acceleration of
the bullet down the barrel and compare it to chamber pressure.

I learned that what I suspected was true, that with some powder loads, the
acceleration process is over before the bullet exits the muzzle and that
during the last few inches, the bullet was actually slowing from friction.

It also explained why I could get almost as much velocity out of my .308 bolt
action silhouette pistol with the 14" barrel as I could from my M-14,
optimized power and powder weight for the pistol, of course.

Finally, of course, there is the pride of accomplishment of achieving results
that few others in the world can do.  Similar to achieving the best amateurs
have done with time measurements.

There are lots and lots of things a nerd can do with a firearm other than just
shoot at things.

John

John De Armond
See my website for my current email address
http://www.neon-john.com
http://www.johndearmond.com <-- best little blog on the net!
Tellico Plains, Occupied TN
Some people are like a Slinky .. not really good for anything
but you still smile
when you shove them down the stairs.

John,

When you add two (statistically independent) 5 MHz signals and get a 10MHz
signal, the 10 MHz signal's relative noise and drift will be the average
of the relative noise and drift of the two 5 MHz signals. So as when you
average n signals, the noise and drift are reduced by sq.rt of n, in this
case, 1.4, or about 2dB (if I am correct), a modest improvement.

Combining more than 2 signals that way (to get more than 2dB improvement)
gets complicated in a hurry.

I guess the idea behind differential locking was to simplify the circuit so
that a large n could be used to get meaningful improvement without too much
additional circuitry.

Didier KO4BB

Didier skrev:

Not to ruin your analogy here, but what I was discussing on interlocking
was intended as means to phase-lock the two oscillators (say 5 MHz but I
was thinking 10 MHz) and you could then just add their sines, not mix
them up. Thus, you do not get the sum frequency, you get the average
frequency. Of course you could go for the frequency multiplication
variant if you want.

Square root of 2 is about 1,414 or about 3,01 dB.

Actually no. Not really. You can build pairs and then interconnect them
together the same way to form a quad, and so you go on. The neat thing
is that the combined oscillators behave as a new oscillator. This is a
very traditional way of combining sources to reduce noise. It is
certainly not new.

Indeed.

Cheers,
Magnus

John,

Just so won't feel alone on this list; I, also am a 'shooter' and
have many things that go BANG, besides reverse polarity
electrolytics. I'm a handgun target and combat nut. Of corse I load
all own ammo.

Hadley
K7MLR

At 04:43 PM 12/23/2008, you wrote:

2008/12/24 Had had@to-way.com:

I only shoot in the shower and load my own ammo.

I've always found that NTC resistors, or electrolytics, go really well
across 240Vac and make a decent enough sound of a shotgun when let off
indoors. I wonder if I should measure just how fast people can be made
to move when encouraged by one of these going off.

Bah Humbug, Steve

Steve Rooke - ZL3TUV & G8KVD & JAKDTTNW
Omnium finis imminet

Specifically, John was suggesting adding the two 5MHz signals, instead of
locking them, that's why I added "statistically independent".

I am always confused when considering noise, is it 10log(p1/p0) or
20log(p1/p0)?

First of all, that only works for a number of oscillators that is a power of
two. Then I suppose that as you increase the number of pairs, it will become
harder for individual oscillators to lock themselves to the output (unless
you add circuitry), so you move away from an interlocked system and closer
to a purely added system. Adding the outputs from a bunch of independent
oscillators does not give you one clean output, it gives you a narrow band
of noise. I must be missing something?

Didier

On 12/24/08 6:04 AM, "Didier" didier@cox.net wrote:

If you're talking noise POWER (or variance..) 10 log10(p1/p0)
If you're talking noise voltage (or standard deviations) 20 log10(v1/vo)

Didier wrote:

A moment's reflection on why the 10 log  vs. 20 log, might help.

The conversion from a power ratio to dB is:

dB = 10 log (P1/P2)

Remember that Power = VxV/R, so:

P1/P2 = (V1xV1)/(V2xV2), the R's cancelling.

So,

dB = 10 log [(V1^2)/V2^2)] or, 10 log[(V1/V2)^2]

If we want to express this as a ratio of voltages, rather than a
ratio of powers (there's a pun in there somewhere ;-),
we need to take the square root of (V1/V2)^2 outside of the log.

To do this, we need to remember that log[X^2] = 2 log X, so:

dB = 10 log[(V1/V2)^2] = 20 log[V1/V2]

A couple of things to note:

1. dB's are dB's.  3dB represents the doubling of a power ratio,
   6dB represents the doubling of a voltage ratio.
2. Convention says that if -dB's are loss, and +dB's are gain, but that
   is just convention.

-Chuck Harris

Didier skrev:

They are statistically independent regardless, except for within (or in
the vincinity of) the PLL bandwidth.

It is very simple. bel is a power ratio in base 10 logarithm, thus
log10(P/Pref) where P is the power (in watts) and Pref is the reference
Power by which we normalize. A decibel is the same thing but scaled to a
tenth of the scale, thus 10log10(P/Pref). For voltage we recall that
P=UI and Ohm's law gives us U=RI giving I=U/R and thus P=U^/R. Inserting
this gives 10log10(U^2/R/Pref). Since log(x^2)=2log(x) we can shift the
2 out and form 20log10(U/sqrt(RPref)) which we can simplify to
20log10(U/Uref) by letting Uref = sqrt(RPref).

So 10log... is for powers and 20log is for voltages.

Double power gives 10log10(2) = 100.301 = 3,01 dB.
Double voltage gives 20log10(2) = 200.301 = 6,02 dB.

If you look at the grouping that I described you will see that for
combining N oscillators it takes N-1 diffrential locking loops, meaning
N-1 phase comparators and N-1 loopfilters etc. I was also giving the
specific hint that this was a simplified description in that I assumed
non-weighed result, where as you could fairly easily create a weighed
form. Consider want to lock one oscillator two a pair. Then weigth 2/3
of the signal to the pair input and 4/3 of the signal to the single
oscillator, thus slightly less to the pair and slightly more to the
single oscillator.

The actual trick here is that the signal and the noise will add
differently together. Recall, that for uncorrelated signals we add
powers, so Ptot = P1 + P2 or from a voltage perspective Utot^2 = U1^2 +
U2^2, assuing U1 = U2 gives Utot = U1 * sqrt(2) or Ptot = P1 * 2 thus
giving +3,01 dB. For correlated signals we add amplitude (in voltage)
such that Utot = U1 + U2 which for U1=U2 gives Utot = U1 * 2 thus giving
+6,02 dB. Now, for two frequency-locked 10 MHz sines which is also
phase-locked to be nominally at 0 degrees from each other we have two
correlated signals and the phase-alignment ensures that their amplitudes
adds correctly to the maximum value, thus giving us a +6,02 dB gain. The
noise of the two oscillators is uncorrelated to each other, and thus
giving us a +3,01 dB gain, assuming more or less equalent oscillators.
The net gain in S/N ratio is 6,02-3,01 = 3,01 dB.

You can combine the two sines through a mixer rather than through
additive combination, but that was not what was originally described.

This technique have been used for ages for low-noise amplifiers etc. I
have only adapted it to the fields of oscillators. It is a crude
approximation which gives some improvement (if done correctly) but does
not really comes THAT cheaply.

Cheers,
Magnus