Why there is no a variable-frequency crystal oscillator?

Question

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:

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?

Answer 1

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.

Answer 2

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.

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

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