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Quartz crystal oscillators have better frequency stability than tuned circuits of capacitors and inductors. However, they are used only as components with a fixed resonant frequency. Variable-frequency oscillators use variable capacitors and inductors even though the resulting frequency is less stable than it would be if variable crystal oscillator existed.

Why there is no a variable-frequency crystal oscillator? Something like this:

enter image description here

The resonant frequency of a crystal is determined by its size and shape. This is similar to capacitors and inductors: their parameters are determined by their geometries in addition to the materials they are made of.

Is it possible to make a quartz crystal with a thickness varying in one dimension, and a sliding elecrtodes to make its resonant frequency vary?

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  • \$\begingroup\$ Might be possible (I wouldn't know, I know very little about crystals cutting or their physics) but it's hardly worth even investigating even if it was theoretically possible. A crystal is not solid-state and already one of the largest and most fragile common components on an PCB. Now you're talking about adding even more precision moving parts and feedback loops which increases greatly increases size, complexity, expense, and power consumption. \$\endgroup\$
    – DKNguyen
    May 27, 2019 at 4:55
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    \$\begingroup\$ Your proposal is contradictory and doesn't make much sense. Crystal electromechanical properties are choosen precisely to get a stable (non-variable) frequency. There are other methods how to make a variable oscillator, VCO for example. \$\endgroup\$ May 27, 2019 at 4:55

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No such product exists, so far as I know. But there are many ways to make a tunable resonant element or tunable oscillator, so there isn't any apparent need for it in the marketplace.

There is a product called a voltage-controlled crystal oscillator (VCXO) which is tunable by perhaps a few hundred ppm by adjusting (under voltage control) the capacitance placed in parallel with the crystal, rather than by changing any properties of the crystal itself.

The main benefit of a crystal resonator is its frequency accuracy and temperature stability. Anything you do to make it tunable is likely to reduce these important qualities (because accuracy isn't critical once you make a tunable device, and any tuning circuit is likely to be subject to thermal variations that will disturb the oscillator frequency).

If you want a variable frequency oscillator with quartz-crystal accuracy and stability, the usual method is to make a phase-locked loop (PLL). Use a quartz oscillator as the reference frequency for a circuit that controls a tunable oscillator to a multiple of the quartz oscillator's frequency. If you adjust the multiplication factor, you then have a variable frequency oscillator. But since you are controlling it with reference to the quartz oscillator you get good accuracy and temperature stability.

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The variable frequency crystals are supplied as oscillators. They come in many flavours.

However, they can not function as you suggest. To fine tune a crystal, one uses variable capacitance.

Quartz crystal frequencies and temperature properties depend on the set angle, and orientation with a precision of a < 0.0001 degree with silver electrodes.

Here is an example of the process, starting with a Quartz wafer "blank" that has been cut from a crystal rod at some precise angle. enter image description here

Here is a variable frequency MEMS crystal Oscillator. It is programmed like flash memory in a "Time Machine" before placement.

enter image description here

SiT8008BI-71-XXX-000.FP0000 is a field programmable device in the low power family. It comes in the2.0 x 1.6 mm package, and can be programmed to support different combinations of the following:
Frequency: 1 MHz to 110 MHz with 6 decimal places of accuracy
Frequency stability: ±20 ppm, ±25 ppm, ±50 ppm
Temperature range: -20°C to 70°C, -40°C to 85°C
Supply voltages: 1.8V or 2.5V to 3.3V
Output drive strength: 8 different options for different rise/fall time

Cost < $1 in volume

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