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

[Garnier Yves]

>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.

James,
If your two signals have the same peak amplitude TX
side they will have the same peak amplitude output the
photo detector :-)
The problem is the available SNR versus the associated
circuits and demodulator you use.
Is your signal integrated and averaged?
Is your signal applied to a high Q LC circuit adjusted
to the fundamental frequency?
Is your signal switched and integrated into two
compared channels via a synchronic detection?
Is your signal modulated in phase for demodulation?
In each case the square wave seems better because the
energy ratio between each half period is maximal.
If a peak detector is used the crest factor of a
sq-wave is 1 (0 dB). The crest factor of a sine-wave
is 1.414 (3 dB).
http://en.wikipedia.org/wiki/Crest_factor
The question is very more complex it seems.
73 Yves F1AVY

--- James Whitfield <n5gui at cox.net> a écrit :

> 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
> 
> 
> 
> 
> 
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Yves F1AVY
http://f1avyopto.wifeo.com