[evlatests] Some Small Nonlinearity in the T304?

[Rick Perley]

    Bob Hayward and I performed some tests on the T304 module on May 12, 
which I've now had the chance to properly reduce. 

    The experiment reported on here inserted noise power from a noise 
diode into the C-band front end of ea24.  The inserted noise was varied 
over a range of ~22 dB through a selectable attenuator.  The maximum 
noise added was about a factor of 3
.5 greater than the 'cold sky' noise -- a useful range over which to do 
the tests. 
    The normal calibration noise diode was modified to increase its 
value by a factor of a few -- to a level about 28% of the cold sky noise 
power.  This was done to make its contribution more easily visible in 
our analog power meter.   We manually switched the noise diode on to 
measure its contribution. 
    A 2-channel analog power meter was employed to measure the input 
power to the T304 within a 100 MHz-wide bandpass, and at the same time 
the output power from the T304, also within a 100 MHz-wide bandpass.  
(RF filters were employed to define these bandpasses, and the LOs were 
selected to ensure that both power meter channels were measuring the 
same RF frequency). 

    With the antenna pointed at the zenith (= 'cold sky'), and operating 
at a frequency of 4.9 GHz, we recorded how four quantities varied as the 
noise attenuator was varied in steps of 1 dB over a range of 22 dB:

    o  The input power to the T304
    o  The (input + cal) power to the T304
    o  The output power from the T304
    o  The (output + cal) power to the T304

    All data were recorded in logarithmic units ('dBm'), which were 
converted to linear units for the analysis below. 

    Analysis:

    A)  The noise diode power measured at the input to the T304 was 
determined by subtracting the first two quantities listed above.  The 
result showed a small but significant decline as a function of input 
power.  A linear fit gives:
   
    Cal Power = 0.0557 - .0022*Pin    microwatts. 

    The input power ranged from 0.2 to 0.85 microwatts -- hence, the 
calibration signal apparently declines by about 2.5% over the input 
power range.  I can imagine two scenarios leading to this result:
   
       a) The noise diode power actually does decrease by this value 
over that range (perhaps due to some interaction between the input noise 
source and the calibration noise diode), or

       b)  The amplifier gain (either in the front ends, or in the T302) 
declines linearly with input power by ~2.5% over the power range. 

    B)  We can determine the T304's gain by subtracting the last two 
quantities in the list above.  This gives the output calibration power, 
after the T304 module.  This power also is seen to decline with 
increasing input power.  The relation is now:

    Output Cal Power = .08981 - .0021*Pin  microwatts.

    The slope is exactly the same (within the errors), and the power 
level is higher.  The T304 gain is the ratio of these:  Gain(T304) = 
1.612. 
    This gain is independent of the actual input power -- evidence that 
the T304 is very linear over the 4:1 ratio of input powers employed. 

    C)  Another measure of the gain is obtained by plotting the output 
power as a function of the input power.  This gives:

    Pout = -.0798 + 1.575*Pin    microwatts. 

    The negative offset is physically impossible, and indicates that (at 
least) one of the two power channels has an offset.   This *should* only 
be an offset, and should not affect measures of the gain. 
    The curious result here is that the slope of this relation -- which 
defines the T304 gain -- is significantly less than the gain  determined 
by the ratio of the calibration signals.  Yet this plot is linear, with 
no sign of curvature.  Perhaps the difference is some  manifestation of 
different sensitivities of the two channels, although it is not obvious 
to me how this could explain the different measures of the gain. 

    Despite the uncertainties given above, the changes in the 
calibration power as a function of the input power are nowhere near the 
values recorded by the switched power system, where a decrease in PDif 
is typically 10 to 20% over input power ranges varying by a factor of 
four -- such as in our experiment.  Our calibration power reduction is 
by only ~2%.  And for this particularly antenna (ea24) at C-band in RCP, 
the decrease in PDif claimed by the switched power system due to  a mere 
doubling of the input noise is by nearly 30% -- about 20 times higher 
than measured in this analog experiment.