Theory of Operation   Equivalent Crystal Circuit   Quality Factor   Series Resonance   Parallel Resonance   Frequency Tolerance   Stability Tolerance   Drive Level   Aging   Overtone Crystals   Specify Load Capacitance   Frequency V's Temperature   Pullability   Resistance Characteristics  

Theory of Operation

Crystal resonators derive their basic frequency selective capability from a mechanical vibration resulting from a piezoelectric effect in the material. Although the theoretical analysis of this piezoelectric effect is a relatively complex electro-mechanical function,it can be shown as a simple equivalent circuit. (see Figure 1)

Figure 1.

Equivalent Crystal Circuit

The equivalent crystal circuit is useful in explaining the electrical characteristics of a crystal operating near its fundamental resonant frequency. The (Co) static capacitance, is the capacitance measured from pin to pin which includes the crystal electrode, mounting structure and holder. R1, C1, and L1 are known as the motional arm of the circuit. C1 represents the motional capacitance of the quartz; L1 is the motional inductance, a function of the mass; and R1 represents the equivalent motional arm resistance. (see Figure 1)

Quality Factor (Q)

The "Q" of a crystal unit is the Quality Factor of the motional arm at resonance. The maximum stability that can be attained by the crystal is directly related to Q. The higher the Q the smaller the band-width (#f) and the steeper the reactance slope (fs-fs). External circuit reactance value changes have less effect on a high Q crystal (less pullability) than lower Q devices. (see Figure 2)

Figure 2.

Series Resonance

When a crystal is operating at series resonance (fs), it looks resistive in the circuit. This, 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.

Figure 3.

Parallel Resonance (Anti-resonance)

When a crystal is operating at parallel resonance (fa), it will look inductive in the circuit. The crystals impedance reaches its peak at fa. A change in circuit reactance 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 should always be specified. Load capacity is the dynamic capacity of the total circuit measured or computed across the crystal terminals. In parallel circuit design, the load capacity should be selected to operate the crystal at a stable point on the fs-fa reactance curve (as close to fs as possible).

Figure 4.

Frequency Tolerance

The frequency tolerance is the maximum allowable deviation from the nominal frequency at the specified temperature. It is normally specified in the parts per million (ppm) or % of the nominal frequency.

Stability Tolerance

The stability tolerance is the maximum allowable deviation from the frequency at room temperature over a specified temperature range and is expressed in terms of PPM or % of nominal frequency. This factor is dependant upon the angle of cut (AT, BT, etc..)

Drive level

Drive level is the amount of power dissipation experienced by the crystal in a given operating circuit. Drive level is expressed in milliwatts or microwatts. Excessive drive level will result in possible fracture of the quartz resonator or excessive long-term drift. An indication of excessive drive level is a constant frequency drift.

Aging

Quartz crystal aging applies to the cumulative change in frequency which results in a permanent change in operating frequency of the crystal unit. The rate of change of frequency is fastest during the first fourty-five(45) days of operation. Many interrelated factors are involved in aging, some of the most common being; internal contamination, excessive drive level, surface change of the crystal, various thermal effects, wire fatigue and frictional wear. Proper circuit design incorporating low operating ambients, minimum drivel level, and static pre-aging will greatly reduce all but the most severe aging problems.

Overtone Crystals

The crystal is usually operated at its fundamental frequency, but can be operated on its 3rd, 5th, 7th and 9th harmonics with slight adjustments to the circuit. Overtone crystals are specially processed for plane parallelism and surface finish to enhance its performance at the desired overtone.

How to specify load capacitance

If the oscillator design recommended by the microprocessor manufacturer is as shown in figure 5, then the crystal is expected to run in its parallel mode. If a series crystal is put in this circuit, the resultant frequency will be high by about 0.02%.

Figure 5.
The load capacitance can be calculated by the following formula :

Cstray includes pin to pin, input and output capacitance of the microprocessor at the crystal 1 and crystal 2 pins plus any additional parasitics. A rule of thumb figure for Cstray is 5pf; therefore, if C1=C2=50pf, Cl would be 30pf. The effect of the load capacitance on frequency is shown in Figure 6.

Figure 6.

Relation of frequency and temperature to angle of cut

Pullability

Typical resistance Characteristics "AT" Cut Crystals