Why Do Some VFOs Tune More Linearly Than Others?

This has been one of the major complaints about our beloved analog LC VFOs:   The frequency tuning on these circuits is often not linear.  For given amount of VFO frequency dial turn you can get vastly different changes in frequency.  At one end of the tuning range the frequencies are nicely spaced and tuning is easy.  But at the other end of the tuning range all of the frequencies are bunched together.  This is one of the problems that leads some homebrewers to defect to the sad land of "digital VFOs." 

But wait.  It appears that the old designers found a solution to this problem.  Just look at the tuning dial of my HT-37.  The frequencies are all spaced out evenly.  How did they do that? 

I had been thinking that this success may have resulted from Hallicrafters' engineers using the series-tuned Clapp circuit.  Here the main frequency determining element is a series-tuned LC circuit and not the parallel tuned LC circuit that we see in the more commonly used Colpitts circuit.  

But hold on -- how could that be?  The frequency bunching problem that we attributed to the Colpitts circuit must also exist in the Clapp, right?  I went back to SSDRA where there was a good discussion of Colpitts and Clapp VFOs.  The advantage of the Clapp was said to be in its use of a larger value coil which helped minimize the effects of stray inductances.  But there was no mention of the Clapp offering improved linearity in tuning.  

I have in front of me two transceivers:  The Mythbuster uses a 9 MHz Clapp circuit (see below).  The 17-12 rig uses a Colpitts Circuit.  I checked the tuning linearity of both.  Both appeared quite linear in tuning, with no real difference between the two.  

Then I looked at the tuning capacitor in the Mythbuster 17-12 rig.  It came out of an old Hallicrafters transmitter, probably the HT-44.  I looked closely at the stator and the rotor plates.  Both are curved.  I'm guessing that this may yield a more constant change in capacitance for a given movement of the main tuning dial.  

Next I opened up the VFO on the Mythbuster.  (It is the VFO from an old Yaesu FT-101.)  I couldn't see the stators very well but it appears that their shape is different from the square shape we often see in variable capacitors.  Could it be that this variable capacitor was also made to provide linear tuning?  

Back in 2013 Norm Johnson wrote about all this in the Antique Radios.com forum: 

A capacitor that has uniform increase in capacitance with rotation will have the stations at the high end of the band squeezed together. Another type known as the straight-line frequency variable capacitor has, as you might guess, a characteristic that gives even spacing of frequencies with shaft rotation. These were popular in the 1920's but weren't very good for superhets where you needed to have a dual section capacitor that would tune both the RF and local oscillator, and have them track each other properly. The midline variable capacitor is more compatible with a superhet, and easier to make both sections track properly. This is the type that you see in most receivers from the late 1930's to the end of the tube era. They don't have quite the equal spacing between stations across the band that the old straight-line frequency caps had, but they're much better than the variables that change capacitance linearly with rotation.

I wrote an online calculator that helps in the design of the tuning. It shows what frequency range you'll get with a specific type of variable capacitor, including the effects of padder and trimmer capacitors. It also displays a dial scale that shows how the frequencies are lined up accross the dial.
http://electronbunker.ca/eb/BandspreadCalc.html

Steve W6SSP also provided some really good info back in 2013: 

There are three types of open, variable plate caps;
SLC= straight line capacitance where the capacitance varies linearly,
these are the most common and have half-circle plates
SLF= straight line frequency where the plates are tapered to allow
for linear tuning of the frequency
SLW= straight line wavelength, you get the idea...

SLF and SLW caps have oblong plates.

The effect on tuning a receiver can be dramatic. One example is the
Hammarlund SP series of receivers where the ham bands are very
compressed at one end of the tuning range. They used SLC caps
in the VFO. On the other hand rigs like the Kenwood TS-520
and FT-101 series have linear tuning across each band. These use
SLF variable caps. Most old 1920's battery radios used SLW
where stations were identified by their wavelength.
Steve W6SSP

These two variable caps came out of my junkbox.  Both are Eddystones, made in England.  My guess is that the one on the left is SLF.  But could the one on the right (out of an old regen) be SLW?   

The Drake 2-B also has perfectly linear tuning.  I looked at the manual:  "The tuning condenser is of special design..."   I'm guessing that they used an SLF variable capacitor. The 2-B had no need for ganged capacitors -- the "preselector" was tuned via a separate front panel control. 

I looked at the tuning dials on my Hammarlund HQ-100 receiver.   It is fairly linear in its tuning, but not as linear as the HT-37 or the Drake 2-B; on all of the tuning ranges the frequencies seem to spread out a bit at the lower end.  My guess is that Hammarlund used the midline variable described above by Norm Johnson.  The HQ-100 did use a ganged variable cap, with one section tuning the RF amplifier and the other tuning the local oscillator. 

Mythbuster on the bottom.  17-12 rig on the top