[R-390] Theory Question - RF Transformer Alignment

[Dan Merz]

Dave,  thanks for coming in with specific info about the coil design in the
390.  It all makes sense.  I didn't realize the cams were spirals and
thought they were trial and error shaped  to linearize the inductance change
to a linear frequency change.  Makes much more sense that the coil would be
designed to be frequency linear with displacement and the cam a spiral to
couple core displacement linearly with the dial rotation. The linear
frequency dependence of core position more than ensures that the change of
inductance at the high freq position is sufficiently smaller than the change
at the low freq. position to make convergence occur.  I think the inductance
change is about 1/8  ( = 1/2^3) smaller at the higher freq than it is at the
lower freq for the progressive type core.  To get convergence it would only
have to be less than 1/4.  You like to talk in terms of frequency change,
while I chose inductance.

I was glad to hear that your radio with a conventionally wound coil and
inductance tuning is adjusted just the opposite, L adjusted at high freq and
C at low. This was what my spreadsheet calculation indicated when I tried to
reach convergence with a coil that had a linear inductance profile.  I have
no doubt an inductance profile could be imagined that would defy adjustment
with either combination of L and C adjustments.   but might mean assuming a
strange combination of the trimmer cap with the main cap.   This also makes
my head hurt;  maybe when that stops I'll think about it more  Dan.   

-----Original Message-----
From: David Wise [mailto:David_Wise at Phoenix.com] 
Sent: Monday, September 15, 2008 10:51 AM
To: 'Dan Merz'; 'Mike Hardie'; 'R-390 at mailman.qth.net'
Subject: RE: [R-390] Theory Question - RF Transformer Alignment

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.