# Crystal oscillator frequency Vs size?

What is the relationship between crystal oscillator frequency Vs Die size?

Why it is smaller Die size over the high frequency ranges and bigger Die size in lower frequency ranges?

• remotely related thread: Standard packages for compact SMT crystals Commented Jun 30, 2015 at 4:35
• hi Nick thanks for your link, but its not completely clarify my doubt. I would like to know about the internal structure modification about its size Vs frequency of crystal, in-depth technical aspects Commented Jun 30, 2015 at 4:40
• Are you after numbers and equations? Otherwise, it would seem obvious that the smaller the crystal, the faster a wave can propagate and bounce i.e. resonate. The faster it can bounce back and forth, the higher the frequency will be given a constant speed of a wave given a material (quartz or otherwise). Commented Jun 30, 2015 at 4:43
• The package size has nothing to do with the frequency, there are many 32.768 kHz crystals (1 Hz * 2^15) for use in watches and clocks, these can have very small packages. The resonance frequency also depends on the way the crystal is cut. I think that the available package size and frequencies are more related to the demands from the market rather than physical limitations. Commented Jun 30, 2015 at 7:19
• i am also surfing google to find in depth about Crystal internal architecture, its more over depends on its internal architecture. sorry above i mentioned package size is wrong that is crystal die size.thanks for you kind reply Commented Jun 30, 2015 at 7:24

## 1 Answer

Broadly speaking, the resonant frequency (fr) depends on size, shape, elasticity of the material. The heart of Crystal Oscillator is a Quartz Crystal, which operates on the principle of inverse piezoelectricity.

The book "Principles of Electronics" by Mr. V. K. Mehta says,

A Quarts Crystal can be made to distort in an electric field by applying a voltage to an electrode near or on the crystal. It needs to be properly cut and mounted in order to have stabilized Resonant Frequencies.

The resonating frequency nothing but the rate of expansion and contraction of the quartz. The geometry of the crystal changes depending on the polarity of an applied voltage, which is more like a mechanical deformation. The deformation of the crystal is proportional to square of electric field strength applied. And, conversely, when it is subjected to mechanical pressure, it develops charges on its surface.

Refer the equivalent circuit shown below:

(I don't know how to add a formula in the editor so I opted to take a screenshot of the formulae and upload it as an image, hope that its not a problem)

The inductance(L) depends size of the cut and firing pin. I am considering only the inductance here since it would vary in a comparatively higher variation range. Ultimately the resonant frequency depends on the size of the Cut.

Though I didn't comprehend it completely, both, due to lack of interest in minute detailing and lack of wisdom, this radio-electronics article and an article on crystal techonolgy should be a good read if you are looking to dig deeper.

• Those formulas look fine to me :-) Commented Jun 30, 2015 at 7:38