Norman's email notes about the Quick Dipper and SQUID
15-Nov-2020


I looked at Pratt's notebooks yesterday morning, and also looked for
my own notes in my office.  I'll start with the latter:

Although I couldn't find anything in my old lab books (shame on me!),
I finally found a file in the "experimental techniques" drawer of my
filing cabinet, called "SQUID".  It included the attached calculation,
undated.  I defined the gain of the entire SQUID chain, including the
transformer, as a transconductance g.  It is equal to TTR/Range in
your notation.  Since R_fb is many order of magnitude larger than
R_ref, I wrote the feedback circuit as a current source with
I_fb = V_fb/R_fb.  If you look at the bottom right-hand corner of the
page, the upper equation in the box is identical to your big equation
on your Drawing 32, if I replace (R_fb+R_ref) with R_fb in your
expression.

But now, what's interesting is that Pratt's SQUID instruction booklet
include the correction term to the voltage in the numerator, but not
the correction to the sample current in the denominator.  Clearly he
thought the latter could be completely ignored.  That was true for
his sample resistances of 1 microOhm or so, but is less true for my
group's sample resistances of 20 mOhms.  I think the correction is
still only on the few percent level, but I'll check again when I have
more time.

Finally, I believe that Pratt's correction term in the numerator was
equal to 0.06%, when N=1 on the front panel of the SQUID controller
box and using his original value or R_fb = 10 kOhms.  (Is that correct
-- I don't have the instruction booklet in front of me?)  That should
be equal to R_fb/g in my notation.  With R_fb=10 kOhms, that gives
g = 16 MOhms.  (If you can derive that value from all the other
parameters in the circuit, that would be great.)

Now regarding Pratt's notebooks, I think it would be best for you to
look at them before you write to Bill, but I've try to summarize the
main points in the attached file called  "Pratt_QD-1_notebook1_
selected_summary".   A few important points:

1. Although the turns ratio of the transformer is greater than 17
   (primary = 532 turns, secondary = 30 turns), he only got a current
   gain of 2.66.  I guess the flux coupling is rather poor, probably
   due to the copper Faraday shield placed between the primary and
   secondary.

2. The modulation coil and input coil to the SQUID have very
   different current-to-flux coupling constants.

3. Bill models the internal SQUID feedback as though it were through
   a resistor rather than an inductance coupling flux into the SQUID.
   I'm not sure why he did that.  He claims that the internal feedback
   is 1 Volt -> 1 microAmp,  but I don't think that corresponds to
   1 microAmp of current in the input coil, due to the previous point
   about the coils being different.

4. Book #2 is mostly about building QD-II, but it shows where he tried
   to increase the value of R_ref to 1.55 mOhms to optimize the system
   for our higher-resistance samples.  Unfortunately, the system was
   not stable, so he went back to the old R_ref of about 100
   microOhms.

For your amusement: Inserted between pages 146 and 147 of book #1
is a sheet showing the frequency dependence of the system response.
Then look on page 147: He laments too much current through solenoid
magnet and burned out the persistent switch!

Finally, I am pretty sure that the answer to your proposed second
question to Bill is "yes": the extra probe hanging in room B112 has an
extra Quantum Design SQUID sensor that Bill bought in case he might
ever want to build a new Quick Dipper.

That's all for now.  We may have to meet in person again if you want
to go deeper than this.

Thanks!  Norman

P.S.  I think I just found a mistake on page 3 of my notes.
      Did I write R_fb in the numerator instead of V_SQ?