Technical Support

Introduction

The word piezoelectricity literaIly means “pressure electricity” the prefix piezo (pronounced pi-e-zo) is derived from the Greek word piezein, “to press.” The word has been generally defined by Cady as follows: “piezoelectricity is electric polarization produced by mechanical strain in crystals belonging to certain classes,the polari-zation being proportional to the strain and changing direction with it.” The production of an electric polarization by mechanically ln-ducing a strain in a crystal is called the direct piezoelectric effect. The converse effect where by a mechanical strain is produced in a crystal by a polarizing electric field,also exists. The converse piezoelectric effect has sometimes been confused with the electrostrictive effect which occurs in solid dielectrics such as glass. The two effects differ in two important respects.

The piezoelectric strain is usually larger by several orders of magnitude than the electrostrictive strain,and the piezoelectric strain is proportionaI to the electric-field intensity and changes sign with it,whereas the electrostrictive strain is proportional to the square of the field intensity and therefore independent of its direction.The electrostrictive effect occurs simultaneously with the piezoelectric effect but (at least in quartz) may be ignored for practical purposes.
In some crystaIs,electric polarization is produced by simply squeezing the crystal along a certain axis,for example, by clamping it in a vice.Other types of strain such as bending, shearing, and torsion also produce polarization in crystals of certain types.often several effects occur simultaneously.Conversely,the application of polarizing electric fields may cause the crystal to experience a longitudinal or shearing stress and under certain conditions bending,torsion,and flexure may be produced.This is called the converse piezoelectric effect. The term piezoeIectricity is also used with reference to materials such as barium titanate in which electric fields produce mechanical strains.These materials are polycrystalline,however, and have a permanent dipole moment induced in them during manufacture. They also exhibit a domain structure.Their behavior is analogous to that of ferromagnetic materials in which magnetic fields produce mechanical contraction called magnetostriction. These materials are not considered in this book.

1. Vibration Mode

2. Overtones

Quartz crystals naturally vibrate in several simultaneous resonance modes referred to the fundamental or overtone modes. Usually, one of these modes is designed to be dominant at the desired operating frequency. The fundamental frequency of vibration is a function of the resonator physical dimension and angle of cut. The overtone modes occur at odd numbered harmonics of the fundamental mode and include the 3rd, 5th, 7th, 9th, and 11th. The maximum bandwidth obtainable in a filter and the maximum tuning range in an oscillator are inversely proportional to the capacitance ratio, r = Co/C1, and r increases as the square of the overtone. Consequently, a wider bandwidth or larger tuning range can be obtained with a fundamental mode resonator than with a third or higher overtones. Fundamental mode resonators are used for most filters, temperature compensated oscillators (TCXOs) and voltage controlled oscillators (VCXOs), where the required bandwidth or tuning range makes overtone devices undesirable.

Fundamentals are also used in many simple oscillators, such as clock oscillators at frequencies up to approximately 35MHz. At higher frequencies overtones are more economical for this application.
Current crystal manufacturing processes limit the lapping of the quartz plate so that the highest fundamental mode frequency that may be reliably achieved is typically around 45 MHz. At this frequency, the AT-cut quartz plate is less than 0.037 mm thick and further lapping using conventional techniques is not practical. Several methods have been developed to increase the fundamental mode frequency achievable by removing some quartz mass from the center of the plate. This so-called “inverted mesa” provides for an active area that is much thinner and is usually achieved by chemical or plasma/ion etching. These processes can produce superior quality high frequency fundamental (HFF) mode crystal to 170 MHz and beyond. Fundamental mode crystals typically have larger values of C1 than overtone mode crystals of the same frequency; therefore they are useful for applications such as VCXOs where greater pullability is required. High frequency fundamental quartz blanks are also used extensively in filter applications where they provide better spurious mode response than overtone crystals of the same frequency.
At a given operating frequency, quartz crystals aging and Q improve with higher overtone. For this reason, ovenized oscillators (OCXOs) often use overtone resonators. Usually the 3rd or 5th overtone is used. The range of tuning required to accommodate the resonator frequency tolerance and aging characteristics limits the maximum useful overtone.