of several time domain functions.
Ref -7.06 dBm
3. The frequency spectrum is the product of the Fourier transforms of the time domain functions. 4.0 EXAMPLE DATA Figure 4 shows an example of a spectrum analyzer measurement of a data signal with a PRBS7 (27-1 pseudorandom bit stream) data pattern. Figure 5 is a magnified sweep of the same data.
Start: 6.500 GHz #Res BW 1.0MHz
#VBW 3.0 MHz
Stop 10.000 GHz Sweep 5.87 ms (1001 pts)
while convolution is calculated using x(t) and x(T-t), and thus has the two waveforms in the integral go in opposite directions. The only reason the math above works out so neatly is because the square pulse is symmetrical in time, and therefore looks the same going forwards or backwards. Other frequency spectra can be calculated using the same techniques: 1. Identify the structure of the autocorrelation function. 2. Express the autocorrelation function as the convolution
The first thing to notice in Figure 4 is that there are numerous uniformly spaced spectral components that seem to contain most of the energy. The spacing is a little over 80 MHz, or exactly the data rate divided by 127. That is to be expected for a PRBS7 pattern (length = 127). Consider thxat the autocorrelation function of this data pattern is exactly like that of Figure 3, except that the triangle is repeated every 127 bits when the data patternr repeats. The autocorrelation function is therefore the convolution of the triangle with a series of impulses in the time domain spaced 127 bits apart. When the Fourier transform is applied, the series of impulses in the time domain beecomes a series of impulses in the frequency domain.
sin2 ( ωτ2 0 ) comb((27 − 1)ωτ0 ) S(ω) = ( ωτ2 0 ) 27 − 1 Figure 6 also suggests several other phenomena. First of all, note that the spectral density rises a bit above
COMP Interface - PRBS7 data pattern -30.0 -40.0 -50.0
Volts (V)
Hz s)
TECH ARTICLE
-60.0
Power Supply Noise??
Clock Leakage??
x1: (5034.0M) x2: (5115.0M) dx: 81.090M
Transmit Reference Clock Phase Noise
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5100.0
5150.0
5200.0
Hertz (MHz) Figure 6: Analysis of magnified frequency sweep data (Figure 5)
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