[R-390] R-390 VFO Question

[David Wise]

Following up my previous post.  My original C702/C703 are N600 and N1000 respectively, so it's clear that Collins meant those caps to temp-compensate the PTO.
I misspoke about the trimmers I put in; given the original TC's, I bet I used something like 2-20pF, N750 and N1500.

If I were doing it over, I would still modify caps rather than cut turns off L701, but you do have to handle TC, and that takes some math.

Les Locklear asked if this worked well.  Yes, it did, but since I assumed the coil/core TC had drifted over the years, I set TC by trial and error, and I only survived because I was obsessed.  At the time.  Today I would just duplicate the original TC.

I did some math.  Not for TC but to investigate the effect of changing C on endpoint spread.  I'll ignore L701.

In general, f = 1/(2*pi*sqr(L*C)) .
If you make L = 1/(x**2), you get a linear control law, f = x/(2*pi*sqr(C)) .  (Where x is core lifting out of the coil, and I'm ignoring scale.)
This is the kind of coil Collins wound.

As the core ages, its permeability falls.  This does two things.  First, you have to push the core deeper in to get the same frequency.
Second, the frequency changes slower as you push it in, which compresses the endpoint frequencies.  Collins included L701 so this could be trimmed, but some PTO's have run out of trim range - the endpoint frequencies are closer than 1MHz per ten turns, even when L701 is at minimum.

The slope of the control law, f/x, is simply 1/(2*pi*sqr(C)), so you can change it, and therefore endpoint spread, by changing C.
C is in the denominator, so reducing C makes it steeper, spreading the endpoint frequencies.

Let's figure out what you get when you change C.
Assume that f is 2455 when x is 1.  x = f*2*pi*sqr(C)/k, where k is a scale factor.
f = kx/(2*pi*sqr(C)), where k is 2455*(2*pi*(sqr(C)).  If C is 390pF, k is about 304.5e-3, and x at 3455 is about 1.407, so ten turns is 0.407 delta-x.

Change C to 380pF.  Now x at 2455 is 0.987 and f at (0.987 + 0.407) is 3467 so removing one 10pF cap expands the endpoints by 3467-3455 = 12kHz .
In this simple case, you'd replace the other cap with 10pF but twice the average TC of the original pair.  In my case I'd use N1500 and call it good.

You want to set C for 1MHz endpoint spread with L701 at maximum so you have full trim range in the future.

When you reduce C or L701, you have to push the core deeper to get back down to 2455.  My Cosmos spare is 17 turns lock to lock so I don't think we have to worry about running out of depth.

I hope this made sense.  If someone can express it better, please write it up.

Dave Wise