[Laser] Fundamental energy in square wave

[Charles Pooley]

James:

For understanding of the square wave, refer to any math book discussing Fourier transform.

You mentioned impossibility of negative light.  Not so, in a sense.  If you were to use coherent transmission, shifting the phase 180 degrees is essentially negative light with respect ot the first phase.

But as a practical manner, the application will determine whether this is needed.  OOK, pulse position are but a few modulation schemes available.  For an OOK application see:

 http://www.microlaunchers.com/7816/L3/laser/laser-link.html

Here, on/off keying is appropriate as the count of photons is the limiting factor and using CW LEDs make that the choice.

Charles Pooley             Microlaunchers

--- On Mon, 1/19/09, James Whitfield <n5gui at cox.net> wrote:
From: James Whitfield <n5gui at cox.net>
Subject: [Laser] Fundamental energy in square wave
To: "Free Space LASER Communications" <laser at mailman.qth.net>
Date: Monday, January 19, 2009, 2:58 PM

I have a question that is more math theory than practical experimentation.

What is the spectrum energy in a on off pulsed beam?

To explain the problem a little better, this is what I was doing:

I took the idea that a 50/50 square wave is (theoretically) made up of the 
sum of the fundamental and all of its odd harmonics, each multiplied by the 
reciprocal of its harmonic number.  To get a better "feel" for the
situation 
I wrote a spreadsheet to calculate 250 steps of a full cycle of a sine 
function and to add to it the odd harmonics, adjusted in amplitude, to the 
19th.

The resulting graph looked as though it would converge to a square wave with 
whose height would be about 87.63 percent of the height of the fundamental.

That being the case it would seem that a square wave would then contain the 
spectrum energy of fundamental sine wave with an amplitude more than 14 
percent higher than the measured height of the square wave.

Trying to relate that to light communication gets a little complicated since 
what we send out is a modulated wave, which in effect is adding a bias to 
the sine or square wave so that the light gets brighter and dimmer, but 
never goes negative.  Even on-off keying represents a bias condition.  Off 
is the negative rail, on is full brightness.

In practical terms, let's say that I have a light communication transmitter

with a peak instantaneous output of one watt.  I bias its output to half 
power and modulate it with either a sine wave or a square wave, both at the 
same frequency.  Both signals have the same average power, although the sine 
wave may take a linear amplifier that is less efficient at controlling the 
supplied power.  The square wave would seem to have an advantage in 
simplicity and efficiency.

Does it also provide a stronger signal at the receiver?  If so, how much? 
And does that translate into a benefit for detecting and decoding the 
signal?

I know this is a math question.  And since I already got onto the subject, 
what would be the pros and cons from a signal detection (at the computer 
sound card ) of sending pulses that were not 50/50?  Keying ON for 1/3 of 
the time and OFF for 2/3 would translate into lower average power for the 
same peak.  So for the same average power, does that mean a stronger signal 
even if the spectrum is not obvious?


James
 n5gui 


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