[R-390] Theory Question - RF Transformer Alignment

[David Wise]

So close...

Collins coils are wound in a nonlinear fashion (Variable-Pitch Progressive),
such that the resonant frequency is linear - exactly proportional
to core position.  (In tuning caps, this plate profile is called
Straight Line Frequency.)  Therefore, when you adjust a slug, the
entire band is shifted without changing its shape.  (This permits
use of spiral-cut cams; easy to manufacture, and a small error in
cam angle can be trimmed out by adjusting the core.)

On the other hand, even though the variable reactance is an
inductor not a capacitor, the trim cap still affects the high end
more than the low end.  f = 1 / (2 pi sqrt(L C)), so changing C
has the effect of multiplying the resonant frequency by a constant
K (close to 1).  Think of it as changing the frequency by K percent.
This radio tunes octave bands, so the frequency at the top of
the dial is twice that at the bottom of the dial, so at the top,
K % is twice as many Hz as at the bottom.  Meanwhile, moving the
core affects top and bottom equally.  To converge, at each end
you trim the item that has the most effect at that end, so here
you want to move the cap at the top and the core at the bottom.
When you set the top, you throw off the bottom by half.  When
you reset the bottom, you throw off the top by the same amount,
so like Zeno's Paradox, each L-C cycle gets you halfway closer.

Trimming L in an octave-band conventional tuning-capacitor radio
changes the top twice as much as the bottom, but moving the
trimmer cap changes the top four times as much, so you still
adjust C at the top and L at the bottom.

The most interesting case is inductance tuning with a
conventionally-wound coil.  f is still proportional to 1 / sqrt(L),
but L is proportional to theta (tuning dial angle).  When L is
small, a given change in theta has a large effect on f, while
when L is large, the same change in theta has a smaller effect.
In a medium-wave radio (about 3:1 ratio), a given change in
theta (i.e. core position) is 9 times more effective at the top.
Meanwhile, the cap is only 3 times as effective at the top, so
if you want to converge, you adjust L at the top and C at the bottom!
(This is not speculation; I have exactly such a radio
and indeed it converges only if you align it backwards.)

I think a profile exists for which convergence is
impossible, but it makes my head hurt to think about it.

Dave Wise

> -----Original Message-----
> From: r-390-bounces at mailman.qth.net
> [mailto:r-390-bounces at mailman.qth.net]On Behalf Of Dan Merz
> Sent: Monday, September 15, 2008 9:20 AM
> To: 'Mike Hardie'; 'R-390 at mailman.qth.net'
> Subject: RE: [R-390] Theory Question - RF Transformer Alignment
>
>
>  Mike,  it seems you answered your own question. But not in
> detail. Your
> adjustments chase after the right amounts of inductance and
> capacitance
> until you find that magic combo where both are right at the
> two frequencies.