Making the piezo effect as clear as crystal

The piezoelectic effect is defined that pressure applied on quartz crystal generates voltage and voltage applied across crystal quartz produces mechanical vibration.

The frequency of the vibrations is determined by several factors:

1. The physical dimensions of the piece of quartz crystal wafer;
2. The plane or 'cut' of the piece in relation to the crystalline axes of the quartz;
3. The ambient temperature;
4. The operating circuit

Equivalent circuit

Although the theoretical analysis of the piezoelectric effect is a relatively complex electro-mechanical function, it can be shown as a simple equivalent circuit.

The equivalent crystal circuit is useful in explaining the electrical characteristics of a quartz crystal unit operating near its fundamental resonant frequency.

The series circuit consists of L1, C1 and R1 is related to elastic vibration, while the element Co is connected in parallel to the series arm as a capacitance attributable to the dielectric body of a quartz crystal wafer.

The R1 is a resonance resistance of the crystal unit at the series resonance frequency.

Operating modes

A crystal unit can be used in a circuit to operate in either of two modes - series or parallel mode.

Series resonance

Crystal units operating at series resonance appear resistive in the circuit and the value of the crystal is nearly equal to the motional resistance R1. Most crystals are manufactured at series resonance unless a load capacitance is specified.

Parallel resonance

Crystals operating at parallel resonance appear inductive in the circuit.

The crystal frequency will be determined by the equivalent electrical parameters of the crystal and the load capacitance CL which is a factor for determining the 'conditions' of a crystal unit when used in the oscillator circuit.

In an ordinary oscillation circuit, the crystal unit is used in a range where it functions as an inductive reactance.

In other words, when the oscillation circuit is seen from both terminals of the crystal unit, this oscillation circuit can be expressed as a series circuit of a negative resistance -R and a capacitance CL.

At that time this capacitance is called the load capacitance.

The relationship between load capacitance is small, the amount of frequency variation is large, and when the load capacitance is increased, frequency variation lowers. If the load capacitance is lessened in the circuit to secure a large allowance for the oscillation frequency, the frequency stability will be greatly influenced even by a small change in the circuit.

Most manufacturers have standard load capacitance values.

Shunt capacitance

Shunt capacitance (Co) is the capacitance between the crystal terminals. It varies with the package styles, usually 2-4 pF in SMD crystal units and 6-7 pF in leaded crystal units.

Frequency v temperature characteristics

To use a crystal unit as an oscillator, its oscillating frequency is required to be stable against temperature variations.

A quartz crystal has crystallographic axis, and the crystal cut is defined according to the cutting angle against a crystallographic axis and its associated mode of vibration.

The frequency v temperature characteristics of an 'AT-CUT' unit are most commonly used and are expressed by the cubic curves.

A quartz crystal wafer is cut at an angle at which a required frequency tolerance is obtained in the given operating temperature range. Actually, however, there can be some dispersion in apparent cutting angle due to the result of cutting and polishing accuracy in the successive process.

Calibration tolerance

The calibration tolerance is the maximum allowable deviation from nominal frequency at a specified temperature, typically 25°C. It is normally specified as parts per million (ppm) or a percentage of nominal frequency.

Stability

The stability is the maximum allowable deviation from nominal frequency, referencing as 0 at 25°C over a specified temperature range, usually specified in parts per million or a percentage of nominal frequency.

This parameter depends on the angle of quartz wafer cut, as explained in frequency v temperature characteristics.

Overall frequency tolerance

The overall frequency tolerance is the maximum allowable deviation from nominal frequency due to change in temperature, time and other environmental conditions.

Aging

Quartz crystal aging applies to the cumulative change in frequency which results in a parameter change in operating frequency of the crystal unit.

The rate of change of frequency is fastest during the first 30 days of operation. Many interrelated factors are involved in aging, some of the most common factors are:

1. Internal contamination;
2. Excessive drive level;
3. Crystal surface change;
4. Various thermal effects;
5. Wire fatigue;
6. Frictional wear.

Proper circuit design incorporating low ambient temperature, minimum drive level and static aging will greatly reduce, not all, but most, severe aging problems.

Typical aging figures for resistance welded crystal units operating in the 10 MHz range are two parts per million (ppm) per year.

Pullability

The pullability of a crystal refers to a crystal operating in the parallel mode and is a measure of the frequency change as a function of lad capacitance.

Pullability is important to the circuit designer who wishes to achieve several operating frequencies with a single crystal by means of changing the value of load capacitance.

Overtone crystals

The crystal is usually operated at its fundamental but can be operated on its 3rd, 5th, 7th and 9th harmonics with an adjustment to the circuit.

Overtone crystals are specially processed for the plane parallelism and surface finish to enhance its performance at the desired overtone harmonics vibration.

Spurious response

It is possible for a crystal to vibrate at a frequency that is not related to its fundamental or overtone frequencies. Such unwanted frequencies are referred to as spurious.

The circuit designer should protect the circuit from the spurious by ensuring that the oscillation feedback circuit achieves its highest gain at the desired operating frequency.

Drive level

Since a crystal unit performs mechanical vibration, too much vibration may lead to unstable oscillation frequency, and may result in severe damage to the quartz wafer in the worst case scenario.

When designing an oscillation circuit, the drive level should be below the maximum recommended drive level for the appropriate crystal unit.