Thursday, February 20, 2014

A Board Noise and IF Harmonic Response

Given that the software has been consolidated, LO half harmonics resolved, and wide synthesizer lines addressed it seemed like a good spot to use the B-C board as a signal source at 10.75MHz and revisit the noise floor and peaks present.  The B-C combination produces at least 4 harmonics (see previous post). To understand what artifacts in the baseline are from the IF harmonics versus ADC generated, a capture of 10.75MHz is taken, a minimum PLL frequency step taken, and that compared to baseline.  During the frequency shift the direction and amount of the frequency shift is noted.  The following data was taken with ADC unit #2 (low gain) using the lowest gain settings g0=0;g1=0.

H
Peak ID Number
Level (dBFS16)
10,747,863 kHz IF
10,744,810 kHz IF
Delta kHz with 3053Hz IF delta
dBc

1
1
-29
252
255
3
0
Fundamental ~10.75MHz
2
3
-68
496
490
6
-39
Second harmonic at ~21.5MHz
3
2
-70
244
235
9
-41
Third harmonic at ~32.25MHz
4
7
-88
7.5
19.5
12
-49
Fourth harmonic at ~53.75MHz


Note that the peak at #6 in the figure does not appear to move, nor do the -100dB ones at +475kHz and +45kHz.   

The following tables capture the calculated peaks.  The columns are the harmonic, its frequency, the number of sampling frequency intervals it represents, the integer number of 2x Nyquist intervals, the frequency within a sampling interval and the frequency within the final Nyquist interval.  (As the signal frequency is increased it reaches half the sampling rate and then wraps and begins “descending” in frequency.  Once it hits a sampling interval or pair of Nyquist intervals it begins ascending).


H
Fo(Hz)
Fs ratio
2NyInt
FsFrac
Fd(Hz)
1
10,744,810
10.74481
10
744810
255,190
2
21,489,620
21.48962
21
489620
489,620
3
32,234,430
32.23443
32
234430
234,430
4
42,979,240
42.97924
42
979240
20,760

H
Fo(Hz)
Fs ratio
2NyInt
FsFrac
Fd(Hz)
1
10,747,863
10.747863
10
747863
252,137
2
21,495,726
21.495726
21
495726
495,726
3
32,243,589
32.243589
32
243589
243,589
4
42,991,452
42.991452
42
991452
8,548

To evaluate the ADC and amplifiers the gain is changed to maximum.  The following figure illustrates a g=11 with a history of g=00.
 


Previous measurements indicated that for Unit #2 A board the small signal minimum gain is 18dB while the maximum is 35dB. Comparing the last two figure’s fundamental values of -13.9dBFS16 and -27.1dBFS16 we see a change 13.2dB while we would have expected 17dB.  This is actually quite good since we will experience gain compression given that we are almost at the full swing value of 3.3V at the amplifiers and the full scale range on the ADC.  Note that a couple of frequencies not previously present now are (i.e the signal just below 200kHz and the ones around 450kHz).
 
Lastly the noise floor is evaluated by setting the IF to ~11MHz to get it and all its harmonics on the "low" end of the ADC response. The following figure captures the spectra at an FFT of 128 (gold) and 32k (blue).
Recall that the display is in dB relative to a 16 bit value.  The rational is to keep things simple regarding who shifts what bits where and masks off the 4 bits of zeros – to keep things sane, it is all treated as a 16 bit value.  The upshot of this is that we really have a 14 bit value (which can never achieve its maximum due to leading two bits of zero) which is shifted up 2 bit (or multiplied by 4).  The noise is calculated as taking a 14 bit number (6.02*14+1.76 = 86dB) and shifting this value up by the multiplication by 4 in amplitude (or adding 20*log10( 4 ) = 12 dB) to any noise floor calculation.  The FFT processing gain is 10*log(M/2) where M is the number of FFT points.  M=128 =>18dB of gain, M=32k=>42dB of gain.  So the 128 point FFT should see a noise floor of -86dB – 18dB + 12dB = -92dBFS16 while the 32k FFT should have a noise floor of -86dB – 42dB + 12dB = 116dBFS16.  The cases in the above figure show 128point=>-87 and 32k=>-112.  In both cases we are a couple of dB too high.  For our purposes this is quite good and within expectations.

In general, I am very pleased with the results and the ability to account for everything observed.  The AD7276 has worked out extremely well in this application.


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