There are not many hits for cmos gate LC oscillators!
In 74HC4060 data sheet ( Nexperia) Fig 13, the crystal oscillator feedback is via a 2k2 limiting resistor, which might be OK for a crystal,
but I think will reduce the Q factor (and hence accuracy) of an LC, unless C2 can be increased to be >> C_variable.
I would add a jfet and make a standard colpitts of which there are lots of examples.
The aim is to get it oscillating in the linear range without too much over-drive,
across the C_Variable's range, with a pure fundamental
by adjusting the feedback side capacitor C2 (maybe the cause of the distortion you mention)
Looks '4060 need to be safely below 20MHZ.
The 74HC4060 should work as an LC oscillator. The link I posted above shows the crusty old CD4007/4069 working fine as an LC oscillator. It's not on the data sheet because it isn't something one would normally do, because an inductor is no cheaper than a crystal, or ceramic resonator, which will have far superior stability and accuracy.
https://wiki.analog.com/university/courses/electronics/electronics-lab-21Overdrive is only an issue for a fragile crystal, which can easily be damaged by too much power. The 74HC4060 can whack an LC circuit as hard as it can without any damage. In this case a squarewave is the desired outcome so it's no problem if it goes into clipping, which is good and to be expected. The only potential issue I can see is high current draw. If the 74HC4060 draws more than 10mA or so, add a resistor between the output and LC circuit, try 100R to 1k first, to dial down the drive a little.
Try a discrete JFET if you like, but I don't see anything wrong with the MOSFETs inside the 74HC4060.
The circuit on the left is a Colpitts oscillator and the one on the right Hartley. U1 is an unbuffered CMOS inverter IC, i.e. pins 9 & 10 on the '4060.
https://assets.nexperia.com/documents/data-sheet/74HC_HCT4060.pdf
In the Hartley oscillator, vary C1 and make C2 much greater, than the minimum value of C1.
In the Colpitts oscillator either C1 or C2 can variable.
Thanks! That looks similar to the oscillator based on CD4069 linked by Zero999 (https://wiki.analog.com/university/courses/electronics/electronics-lab-21). I have ordered the CD74HCT4060 now so I will try your circuit out once it arrives.
Anyways, what inductor type and value do you suggest for combining with my 14-680pF varcap? And are regular old ceramic caps okay, or are any other type preferable?
The inductance depends on what output frequency you desire and will be divided by the counter inside the 74HC4060 (you've got the choice of 2
n, where n can be from 4 to 10, or 12 to 14) which is only guaranteed to work up to 25MHz at 5V, over the full temperature range. The inductor can't be too higher value because the resistance will be too high and its parasitic capacitance will dominate too much. You could try a common more choke, in which case the inductors will be coupled, so can be smaller, but it might be too lossy over a few MHz.
The formula to calculate the frequency for the Colpitts and Hartley oscillators can be found on Wikipedia:
https://en.wikipedia.org/wiki/Colpitts_oscillatorhttps://en.wikipedia.org/wiki/Hartley_oscillatorFor the Colpitts oscillator, the variable capacitor can be either C1 or C2, with the fixed capacitor being around 330pF, around the middle value of the variable capacitor.
As I said, for the Hartley oscillator, C1 is the variable capacitor and C2 much greater, than the maximum value of C1, so 10nF will do, as it's much higher than 10nF.
I think the Hartley oscillator might be the better option, for this application, but try both.