[Laser] RE : Re: Fundamental energy in square wave more details

[James Whitfield]

My thanks for the responses to my question.

I confess that I had trouble understanding the answers.  That must mean that 
at least in part I did not understand the situation I was considering well 
enough to form a clearly asked question.  It was also humbling ( or perhaps 
generating feelings of humiliation ) to "hear" words much like I undoubtedly 
said when I was an aspiring teacher ( mercifully, for the students as well 
as myself, only a short detour from my career path as an aerospace 
engineer ).

I did absorb enough to take a second look at the problem.  The questions 
that I posed had come from a spark of an idea that resulted from a 
spreadsheet to model, or at least approximate, a square wave as the sum of 
sine waves.  I realized that the power in a square wave would also be the 
sum of the power from the constituent sine waves, and that I might be able 
to understand better an approximation made from a similar spreadsheet.

I started with a fundamental sine wave with a power of one watt (RMS).  I 
reasoned that the third harmonic, being one third the amplitude would have 
one ninth the power.  Fifth harmonic would have one twenty-fifth the power; 
seventh harmonic, one forty-ninth; and so on.  The sum of the first through 
the two hundred first harmonic was 1.23123 watt, which yields the 
fundamental should therefore have 81.22 percent of the power in a square 
wave.  If some of the experiementers out there can verify this by running an 
audio square wave through a spectrum analyzer, I would like to know.

The limited conclusion that I can reach from this is that if I had 
equipement that was power limited on the output beam, then the emitted 
signal, and presumably the received signal, from sine wave should only be 
0.90 dB stronger than the fundamental contained in an equal power square 
wave.  That suggests to me that there is limited benefit in trying to form a 
sine wave.

Without going into how in this email, I calculated the relative merits of 
square versus sine wave output in the situation where the two have the same 
peak amplitude ( not limited to the power of the beam but its peak 
intensity ).  In that case the square wave should hold a meager 0.24 dB 
advantage.

I had been thinking of a digital scheme, perhaps DominoEX or BPSK31.  Both 
would seem to be able to use sine or square wave emissions at the 
transmitter.  On the receive end I would expect differences in performance 
to be similar to what I have "calculated" here, though experimental error 
would likely be greater.

Again my thanks for the response.  As always, I hope this will have some 
benefit to the group.


Best wishes,


James
 n5gui