[mmaimcal]Phase Repeatability of the Attenuators

[Mark Holdaway]

Phase Repeatability of the Attenuators:
Requirements for Fast Switching

M.A. Holdaway
7 Aug 2002


For fast switching phase calibration, a calibrator source will be
observed for about a second at 90 GHz, then the antennas will all slew
over to the target source (at the target frequency) about 1 degree
away, and the target source will be observed for several seconds.
Then, the cycle repeats, returning to the calibrator.  The phases
determined on the calibrator will be scaled to the target frequency
and interpolated in time (and perhaps position) to estimate the
atmospheric phase on the target source.

To achieve efficient digitization, different attenuator settings will
be used at the different frequency bands.  There can be phase jumps
due to the attenuators across the frequency bands, and even phase
drifts with frequency within each band.  If stable with time, these
effects can be removed by performing a bandpass calibration at the two
different bands.

How stable must the phases of the attenuators be?

Lets consider the worst case:  calibrator observations at 90 GHz
and target observations at 950 GHz.  

For fast switching phase calibration, we are aiming for residual phase
errors of about 15 - 20 degrees rms.  Lets take 20 for this argument
(at 950 GHz it will be exceedingly difficult to get 15 degrees rms
with fast switching).  This 20 degrees rms comes from two sources:
thermal noise manifesting as an imperfectly determined phase on the
calibrator scaled up to the target frequency, and the residual
atmospheric phase which differs from the calibrator and target source
observation times and positions.  Let's arbitrarily say we'll permit
one more degree of phase from the electronics:

    electronics = sqrt( 21^2 - 20^2 ) = 6.4 degrees

Now, we will be differencing two noisy numbers, so there WOULD be
a sqrt(2) in there, but the phase from the attenuator will be dominated
by the 90 GHz phase scaled up to 950 GHz, so we ignore the sqrt(2).

If the attenuators' phases are repeatable to about

    6.4 deg * ( 90/950 ) = 0.6 deg

then the effect on the fast switching residual phase will be minimal.