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amfmrad
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I have a spectrum analyzer and pulse generator. I decided to see what the spectrum of a sequence of pulses was and found some surprises. The pulses have very fast rise and fall times (5 nanoseconds) with a pulse width of 30 nanoseconds. As a result I obtained the classical (Sinx/x)^2 power spectrum when the pulse period was long (>> 100 nanoseconds). However, as I increased the frequency of the pulse generator to up to 10 MHz (100 nanosecond pulse period) I saw discrete lines peaking at the envelope of the (Sinx/x)^2 spectrum. I then decided to model the spectrum and obtained the following equation which I would like to verify;
P(f)=(VT)^2 * [Sin(x)/x]^2 * [1/(1+y^2)] * [Sin(Nz)/Sin(z)]^2
P(f)=Power Spectrum at frequency f
V=Peak pulse voltage
T=Pulse Width (30 nanoseconds)
Tau=Exponential pulse rise time and fall time (5 nanoseconds)
Tp=Pulse Period (Pulse frequency=1/Tp) (40 nanoseconds minimum)
N= The number of pulses in the sequence (not critical but I use a number like 10 or 100)
x=pie*f*T with pie=3.14196...
y=2*pie*f*Tau
z=pie*f*Tp
I rechecked the equation and believe it to be correct. The calculated spectrum looks like what I see on the spectrum analyzer (discrete lines peaking at the single pulse spectrum) due to the last term in the equation [Sin(Nz)/Sin(z)]^2 which becomes unity at f = m/(2NTp) with m=0,1,2,.. However, this function does crazy things for other frequencies, which I can't explain?.
Incidentally, I have details of my calculations as well as graphs and pictures of the calculated and measured spectra but I don't know how to attach it?
Thanks to those interested.
Norman
P(f)=(VT)^2 * [Sin(x)/x]^2 * [1/(1+y^2)] * [Sin(Nz)/Sin(z)]^2
P(f)=Power Spectrum at frequency f
V=Peak pulse voltage
T=Pulse Width (30 nanoseconds)
Tau=Exponential pulse rise time and fall time (5 nanoseconds)
Tp=Pulse Period (Pulse frequency=1/Tp) (40 nanoseconds minimum)
N= The number of pulses in the sequence (not critical but I use a number like 10 or 100)
x=pie*f*T with pie=3.14196...
y=2*pie*f*Tau
z=pie*f*Tp
I rechecked the equation and believe it to be correct. The calculated spectrum looks like what I see on the spectrum analyzer (discrete lines peaking at the single pulse spectrum) due to the last term in the equation [Sin(Nz)/Sin(z)]^2 which becomes unity at f = m/(2NTp) with m=0,1,2,.. However, this function does crazy things for other frequencies, which I can't explain?.
Incidentally, I have details of my calculations as well as graphs and pictures of the calculated and measured spectra but I don't know how to attach it?
Thanks to those interested.
Norman
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