[evlatests] Slow Wobbles -- Barry's conjecture supported!

[Rick Perley]

    Barry has suggested that the origin of our 'slow wobbles', seen on 
some baselines at Ku and K bands (at least) while in 'A' configuration, 
may lie with offset spurs in the LO system.   Such a 'false' LO would 
add an image frequency with an offset equal to that of the offset of the 
LO spur.  The two frequencies would beat, giving a  sinusoidal-like 
oscillation in amplitude and phase with period given by:

    T = 1/(omega.u.cos(dec))  seconds

    where omega is the earth's rotation rate (Hz), u = the E-W baseline, 
measured in wavelengths of the offset frequency, and dec is the 
declination of the source. 

    If this mechanism (or one like it) is at play here, then the period 
of the 'beat' will be inversely proportional to the E-W baseline length 
(in any units).  And, as the offset spur(s) should be a multiple of 128 
MHz, we can predict the period of the beat. 

    I have checked both predictions.  Things look good for Barry's 
theory ...

    1) The baseline with the strongest effect, by far, is ea02 x ea23.  
This was an adjacent pair way out on the north arm.  For the 6-hour 
observation taken, the u-coordinate for this baseline started large 
(-100 klambda at 26 GHz), went through zero, and ended up at +80 
klambda.  The period of the phenomenon is exactly inversely related to 
these lengths.  For our K-band observation, when u = 100 kilolambda (at 
26 GHz), T ~ 19 seconds.  When u = 23 kilolambda, T = 88 seconds.  When 
u = 53 kilolambda, T = 37 seconds.  And T went to infinity when u went 
to zero. 

    2) The prediction for the offset frequency works quite well -- but 
not perfectly.   I chose the time when the u-baseline was 100 kilolambda 
at 26.2 GHz.  If the offset spur is 128 MHz, then the 'effective' 
baseline length is 510 lambda.  If the offset spur is 256 MHz, then u = 
1020 lambda.  For the former case, the beat period should be 36 
seconds.  The observed period *at Ku band* is 35 seconds.  Close 
enough!   The beat period at K-band, at this same time, is observed to 
be 20 seconds, while the prediction -- for a 256 kHz spur -- would be 18 
seconds. 

    3) One other observation supports Barry's theory:  If the beats are 
caused by an LO offset, the beat period will be independent of the 
actual sky frequency, depending only on the LO spur offset.  Hence, a 
'waterfall' plot of visibility amplitudes (or phases) with frequency on 
one axis and time on the other should show the 'beats' horizontally 
arranged.  This is what is observed. 

    But the theory does not explain two of the details:

    1) Since the same LO drives RCP and LCP, we should see the same 
beats in both.  But we don't -- there are only in LCP (at both Ku and K 
bands). 
    2) The suggested mechanism should cause equal sized beats across the 
entire bandpass.  But this is not seen -- although the beats are seen in 
most of the subbands, they are, by far, most visible in the lowest two 
(of eight). 
    3) In addition, we recall that a special test ran two weeks ago to 
reproduce the problem shortly after it was first detected, -- but this 
test showed no 'wobbles' at all.  So, the problem seems sporadic -- does 
this suggest mechanical devices are involved (like switches)?

   
    A first check into whether this mechanism is operating (as opposed 
to a more complicated one) is to see if there are indeed LO spurs in the 
L301-1, and L301-2, when the system is set up at Ku and K bands.  Since 
antennas 2 and 23 are by far the worst, I suggest starting with these.