4. Description of terminology

5. Useful formulas for crystal unit

6. Crystal unit and load capacitance

7. Change of load capacitance and pullability

For many applications there are requirements to pull the crystal frequency by using a load reactive element. This may be necessary in order to trim out the manufacturing tolerance or in phase locked loop and frequency modulation applications. In most applications the load reactive element in capacitive and therefore only this case is now considered. The fractional difference in frequency between the load resonance frequency (FL) and the resonance frequency(Fr) is known as the load resonance frequency offset(LO).

In many applications a variable capacitor(trimmer) is used as the load reactive element to adjust the frequency. The fractional frequency range available between specified values of this load reactive element is called the pulling range(PR) and it can be calculated by using the following formula :

A useful parameter to the design engineer is the pulling sensitivity(S) at a specified value of load capacitance. It is defined as the incremental fractional frequency change for an incremental change in the load capacitance. It is normally expressed in 10-6/pF and can be calculated from the formula :

The equivalent circuit of the crystal has one other important parameter : this is R1, the motional resistance. This parameter controls the Q of the crystal unit and will define the level of oscillation in any maintaining circuit. The load resonance resistance for a given crystal unit depends upon the load capacitance with which that unit is intended to operate the crystal manufacturer has equipment to measure these quantities. The frequency of oscillation is the same in either a series or parallel connection of the load capacitnce. If the external capacitance is designed the load resonance resistance(RL) may be calculated as follows :

8. Illustrated flow chart for quartz crystal unit

specification

Process	Process Drawing	Description of process
Slicing		With the r-surface of a lumbered crystal used as the reference, wafer-shaped pieces are cut out at the prescribed angle.
Measurement of angle		To confirm that the crystal is cut at the prescribed angle, the angle is measured by means of an X-ray angle checker.
An outward form processing		To prevent joining with other vibration modes and from being influenced by sub-vibrations, the external shape is properly corrected by profiling.
Lapping		Since frequency of AT-cut crystals is determined by the thickness of the crystal piece, the thickness of the crystal pieces is made uniform by means of a surface lapping machine to raise the surface accuracy.
Etching & cleanin		After removing the worked laver produced by precision lapping and beveling by etching, cleaning is carried out
Electrode metal evaporation		The electrode used for applying a electric field to the crystal piece is formed by vacuum metal evaporation (Ag. etc.) on surface of the crystal piece.
Fine frequency adjustment		Final fine adjustment of the frequency is carried out by vacuum metal evaporation or ion gun etching while letting the crystal oscillate.
Assembly		The crystal piece is secured to the base by such means as Agpaste.
Sealing		To suppress aging of the crystal piece, the inside of the holder is first made vacuum, or filled with such inactive gas N2 and then sealed with a cap.
Inspection		The crystal pieces are inspected for their specifications including frequency deviation, frequency vs temperature characteristics, equivalent resistance, hermetic of seal and insulating properties.

9. Crystal holders

• Solder Seal : This method is cost effective and accepted for military and commercial applications. (Mil-C-3098) Nickel-Silver cans and bases are soldered together with a tin-lead alloy.
• Resistance Weld : Resistance welded enclosures are sealed together by melting the metal for a very short time with a large predeter mined electrical pulse, thus welding the crystal cover to the base. No fluxes are used in this process. The resistance-weld method has the advantages of approaching the long term stability of the coldweld method. Typical aging per year for resistance weld is <5ppm.
• Coldweld : In the coldweld method a nickel plated copper can and base are sealed together under a concentrated high pressure bonding technique. The enclosure is evacuated using a cryogenic vacuum and backfilled with a mixture of helium and nitrogen. The coldweld method is exclusively used when long term stability is required (low aging characteristics). Typical aging per year for coldweld is <3ppm. Coldweld sealed crystals are slightly higher cost.