Before beginning a design or purchase of a crystal there are system parameters, which must be considered. Below are questions, which need to be determined by your system. These parameters will determine the crystal specifications.
The quartz crystal may be represented by the L, C, R circuit (below).
C0 is the capacitance formed by the crystal electrodes plus any holder
capacitance. The L1, C1, R1 branch is called the "motional arm". The motional
capacitance, C1, controls the "pullability" of the crystal. The shift of a
crystal can be calculated by the following formula...
ppm fr Series = C1/2 (C0+CL)
Knowing two different loads on the crystal, we can look at the differences between each shift from series to calculate total trim range.
Example: given a 0.020 pF C1 and a C0 of 4.26 pF the shift from series of a 20pF load is 412.2 ppm and the shift of a 27pF load is 319.9 ppm. This gives us a tune range of 92.3 ppm between 20pF and 27pF loads.
C1 and R1 can be specified on any crystal. Typical values of R1 are 10 to 25 ohms on the fundamental mode and higher on overtones. Typical motional capacitance values are between 0.016 pF and 0.034 pF for a fundamental crystal. Motional capacitance is divided by the overtone squared. Static capacitance (C0) is about 213 times C1 on the fundamental mode.
The quartz crystal can be made on frequencies between 70 kHz and 200 MHz. The quartz crystal is designed to operate on its fundamental frequency or one of its overtones. The overtones are related to the fundamental frequency and occur at odd harmonic intervals. (1, 3, 5, 7, etc.) This becomes important between the 15 MHz to 30 MHz Range. Crystals in that frequency range can be made as either a fundamental or 3rd overtone. Fundamental mode crystals at these frequencies become very expensive as the quartz blank is extremely thin and difficult to handle, and therefore causing a higher rate of breakage in processing. If you specify an overtone mode instead of the fundamental, the cost savings may be significant.
Crystals are the key components in an oscillator circuit and they are affected by ambient conditions, particularly the temperature.
The most common calibration specification is ±10 ppm or ±.001% at + 25°C and your specific load, it is also the least expensive.
The chart to the right shows the change in frequency with respect to temperature. The various curves are dependent on the angle at which the quartz is cut from the original crystal. The angle of cut is controlled by x-ray diffraction techniques. The curves in this chart show that as the tolerance becomes tighter. The operation temperature range is reduced.
When a crystal is operating at series resonance (fs), it looks resistive in the circuit. Thus, its impedance at fs is near zero. In a well-designed series resonant circuit, correlation is not a problem and load capacitance does not have to be specified.
The crystal's impedance values will have the effect of pulling the frequency of the crystal. If the crystal is to be used at parallel resonance, the load capacity (in picofarads) should always be specified. Load capacity is the dynamic capacity of the total circuit measured or computed across the crystal terminals. It is selected to operate the crystal at a stable point on fs-fa reactance curve (10pf to close to fs). For more information on computing the load capacity of a circuit see our Oscillator Data sheets.