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?
Electronic – Crystal oscillator frequency Vs size
crystaloscillator
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With the details provided, it does seem like the crystal may be damaged - it's the most sensitive component on the board, and there's a good chance the pulser has been dropped a few times during it's long life.
The circuit seems reasonable and if it was originally designed with the resistor (rather than the capacitor), then I'd leave it like that. There are similar circuits out there that do use a capacitor as you say:
I'd go for replacing the crystal - choose a crystal designed for series operation such as the FOXLF160 (as opposed to the FOXLF160-20) While you're grabbing the crystal, getting a couple of 74LS38s wouldn't be a bad idea either, given they are only around 50 pence/cents each.
Also, given the price of decent CMOS oscillators nowadays, the other option is just to buy a 16MHz CMOS oscillator (5V supply tolerant) and replace the first stage with that.
Crystal, or quartz crystal. Crystal resonator is not at all incorrect but they have been called just crystals for over 50 years to no harm...
Ceramic resonator; maybe just resonator, but certainly not crystal or oscillator.
Basically yes. (The middle terminal will be ground). However there are also ceramic filters with this configuration, so be careful and double check the datasheet. (Especially if they are marked with common radio IF frequencies, 455 kHz or 10.7 MHz!)
I don't know; most likely no.2 in different packaging, I have never seen quartz crystals packaged this way.
Yes.
No, though connected to the right pins on an IC it might be. A crystal oscillator is either:
a. something like package (1) with 4 pins; it takes 3.3V or 5V in, and puts out a clean signal (making it dead easy to use), or
b. a circuit involving these components, possibly a resistor, and some kind of amplifier (inside the IC, or a separate transistor) or a misused logic gate, to drive the crystal. In the latter case you can usually substitute a ceramic resonator, but you may have to change the capacitors and a gain setting resistor (or drive limiting resistor) to make it work at all, or work reliably.
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Best 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,
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.