THE PIEZO ELECTRIC EFFECT A BRIEF HISTORY THE PIEZO ELECTRIC EFFECT A BRIEF HISTORY

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1 THE PIEO ELECTRIC EFFECT A BRIEF HISTOR THE PIEO ELECTRIC EFFECT A BRIEF HISTOR Although the Piezo electric property of quartz and other crystalline materials was discovered by Pierre and Jacques Curie in 1880 it was not until 1917 that this property was utilized in a practical application. Professor Langevin in France and A.M. Nicolson at Western Electric independently designed sonar transceivers for the detection of submarines at sea. Nicolson later went on to file a number of patents for applications using quartz and Rochelle Salt. This latter material responded strongly to sound waves and electrical stimulus and was incorporated by Nicolson into designs for Microphones, Loudspeakers and Phonograph pick-ups. While Nicolson has proposed the use of Piezo electric materials for controlling the frequency of a vacuum tube oscillator it was Dr. Walter Cady of Wesleyan University who filed the first patents for crystal controlled oscillators in Prof. G. W. Pierce of Harvard University carried out further work on crystal oscillator development at about this time. Pierce s main achievement was the design of a crystal controlled oscillator using only one vacuum tube and no tuned circuits other than the crystal itself. During the early 1920 s crystal oscillator development and radio technology progressed steadily side by side. The major applications for crystal oscillators during these early days was for use as time standards and it wan not until around 1926 that crystal oscillators were used to control the frequency of a radio transmitter. This was done at radio station WEAF in New ork which was owned by AT and T. Bell Telephone Labs who were part of AT&T along with The Marconi mpany in the U.K. and S.E.L. Germany achieved many significant developments in crystal technology during the 1930 s. In 1934 Messrs. Lack and Willard at Bell Labs discovered the AT and BT-Cut crystals which gave the communications industry good frequency temperature performance crystals. Developments during World War II and in the years since have continued to improve the "Crystal Art" right up to the present day. Improved sealing and production techniques along with the discovery of a new family of Stress mpensated cuts are among some of the advances that have been made during the last decade. INTRODUCTION The quartz crystal element is a vibrating resonant plate, which relies upon the Piezo electric effect to couple it to electrical circuits. The inherent properties of quartz make it a uniquely simple device for highly accurate and stable frequency control and selection. Crystals are not a primary frequency standard but with care can provide stabilization far in excess of most requirements of the Electronics Industry. This note is a simple guide to the correct use of crystal elements. The quartz crystal element is cut from crystalline quartz with precise orientation to the axis as shown in Fig. 1. Fig. 1. X AT This figure shows a block of natural quartz. However, most manufacturers now use synthetic material as shown in Fig. 2. Techniques of manufacture have advanced to the point where synthetic quartz is almost indistinguishable from natural material with regard to electrical performance.

2 2 Lap-Tech Report: THE PIEO ELECTRIC EFFECT Fig. 2. Although the properties of quartz are very stable, the ultimate performance of the element is largely dependent on the way in which it is used IT IS NOT AN ABSOLUTE FREQUEN- C DETERMINING DEVICE. Its performance will largely depend upon the environment and the associated electrical circuits; we strongly advise any customer to discuss his particular application with the crystal manufacturer at the earliest stage in any design. While there are a variety of crystal cuts which will achieve near zero temperature coefficients, the following notes will be confined to the AT-Cut crystal which is the most common type employed over the frequency range 1 MHz to 300 MHz. ELECTRICAL PARAMETERS The properties of any mode of a lightly damped mechanical vibrator Piezo-electrically excited by means of electrodes can be represented, close to resonance, by an equivalent circuit (Fig. 3) which consists of a capacitance C1, inductance L1 and resistance R1 in series, shunted by a second capacitance, the parallel capacitance. These four parameters are constant and independent of frequency and amplitude, providing the crystal unit is operated in the correct way. Fig.3 L1 +X -X AT CUT 35 1 fs L1C1 The first three parameters C1, L1 and R1 are termed the "motional parameters" of the crystal +X unit. The network has two main resonances. The series -X mode Fs and the parallel mode Fa. As in all vibrating systems there are many possible modes of motion. Each particular crystal cut has a preferred mode and generally this mode is sufficiently isolated from other modes to permit the assumptions shown in Fig. 3 to be valid, providing that the unit is operated in the correct circuit and at the correct drive level. At a given frequency the parameters of the equivalent circuit generally approach constant values as the amplitude of vibration approaches zero. The amplitude, which can be tolerated before the parameters are appreciably affected, varies widely between vibrators of various types. Frequency-temperature characteristics are, to a first approximation, determined by the temperature coefficients of density and the dimensions and elastic modulii of the stability of the quartz plate. When the resultant of these three properties becomes zero, the stability of the frequency with respect to temperature will be optimum A major part of design consists of achieving this optimum condition over a specified range of temperature. The stability of the parameters for the equivalent circuit and also the frequency and temperature characteristic CAN BE ADVERSEL AFFECTED B HIGH DRIVE LEVELS, which can also excite unwanted modes. These unwanted modes can seriously modify the equivalent circuit and distort the frequency/temperature characteristics. It is therefore vitally important that recommended drive levels are not exceeded. C1 R1 fa 2 1 C1 L1 C1...2 The dependence of the resultant frequency with respect to differing input circuit conditions is determined largely by the capacitance ratio of the crystal unit (/C1). A large capacitance ratio allows better frequency stability against circuit changes; a large /C1 ratio will also make it difficult to

3 report 3 "trim" the crystal frequency in the circuit. It can be seen from Fig. 3 that there are two major resonance points associated with any mode of vibration. Fig. 4 shows the simplified form of the reactance clearly indicating these two points. These two points are very important to both the oscillator and filter designers and make the crystal element a particularly interesting device. This Technical Note will deal only with the oscillator applications. + In Fig. 6 the crystal is shown with a parallel load of Clp. In this condition the crystal is operated at maximum impedance in parallel resonance. It can be shown that: L1 C1 R1 Fig 6 Clp C1 Frp fs1 2 Clp f 1 C1 fs 2 CLs Where f = frp-fs REACTANCE - fs fa Fig. 4 FREQ From these simple equations most calculations and predictions of operating frequency can be obtained. It should be noted that in the conditions shown in Fig. 5, the resonance curve of Fig. 4 has been modified by moving the point Fs upwards in frequency with only a small change in the frequency of Fa. In the conditions of Fig. 6 the point Fa has been moved downwards in frequency with only a small change in the frequency of Fs. Typical frequency changes to be expected are given in Table 1. LOAD CAPACITANCE AND FREQUENC PULLING During manufacture definable limits are set on the accuracy of frequency. To enable the crystal to be trimmed to working frequency, it is necessary to insert a load capacitance. Where the load capacity is zero then the frequency is Fr = Fa, see Fig. 3. This condition is never achieved and is always modified by load capacitance, which will change the point of Fa or Fs depending on how the load is introduced into the circuit. In Fig. 5 the crystal is shown with a series load of Cls. In this condition the crystal is operated on a minimum impedance condition or at series resonance. It can be shown that: Table 1 F (PPM) per Pf change in Load Capacitance (Ca) Crystal Mode Mean 10 PF Mean 20 PF Mean 30 PF Mean 50 PF Fundamental rd Overtone th Overtone th Overtone (PPM is used throughout to denote pp 10 6) It is very important to define the mean load capacitance to enable the actual crystal frequency to fall within the tolerances placed on the nominal frequency in the specifications. It is also important to use, wherever possible, standard values of load capacitance; for example: 10 PF, 20 PF, 30 PF or 50 PF. Frs C1 fs1 2 CLs Or It should be noted that a tolerance of +/-1/2 20 PF load capacitance could lead to a frequency error of +/10 PPM. MODE OF VIBRATION Cls L1 C1 R1 Fig 5 f 1 C1 fs 2 CLs Where f = frs-fs The mode of vibration of the AT-Cut crystal is in thickness shear (see Fig. 7.). From these sketches it is easy to see that the critical dimension is in "y" i.e. the thickness of the plate. This dimension controls the frequency of vibration. The vibrations

4 4 Lap-Tech Report: THE PIEO ELECTRIC EFFECT are shown extending to the edge of the plate; in practice the quartz plate design ensures that the vibrations are confined to the center of the plate. X X Fig rd OT must be used in specifying frequency / temperature performance. In fact a useful guide is to add +/-1 to the theoretical tolerance in order to product a practical manufacturing tolerance. In using these curves it should be noted that the frequency deviation must be checked not only at the extremes of the temperature range but also at intermediate points to allow for the + - inflection points of the cubic curve. The optimum performance over a wide temperature range will generally result in a quite steep - + 5th OT temperature coefficient at Room Temperature. Nodial Planes This is done by controlling the ration of plate width (or diameter) to thickness. Where it is impractical to maintain the optimum ratio at lower frequencies then special measures are taken to shape the plate surface to restrict the motion. There also exists other sophisticated techniques to ensure that the motion is restricted to the area of the exciting electrodes by controlling the area and thickness of the electrode, i.e. by means of energy trapping. These techniques are also closely related to control of spurious responses and crystal parameters. All of these are of vital interest to the crystal user. Therefore, before specifying crystals for the more stringent applications, it is essential to consult the crystal manufacturer. FREQUENC / TEMPERATURE CHARACTERISTICS The Frequency / Temperature characteristics of the AT-Cut Resonator are shown in Fig. 8. These characteristics are shown for 2 intervals of angle of cut and follow very closely a cubic law combined with a linear law, which varies with this angle of cut. From this it is clear that the angle is the main controlling factor. The normal angle will vary with plate shape and mode of operation, (fundamental or overtone) and method of mounting. Therefore the crystal designer has to obtain, by empirical methods, the reference point to make these curves usable. It also must be realized that effective angle tolerances of closer than +/-1 of arc are very difficult to achieve, therefore care CRSTAL UNIT ACTIVIT Fig 8 The equivalent circuit of the crystal has one other important parameter; this is the R1, the motional resistance. This factor controls the Q or "Activity" of the crystal and will define the

5 report 5 level of oscillation in any maintaining circuit. For most oscillators, it is the ESR (Equivalent Series Resistance) of the crystal which defines its activity; the lower the ESR the greater the amplitude of oscillations. It should be noted that the ESR 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. As can be seen from Section 1.2. the frequency of oscillation is the same in either a series or parallel connection of the load capacitance. If the external capacitance is designated Ca i.e. Ca = Cls or Ca Clp, then the equivalent loss resistance may be calculated as follows: 2 ESR R1 1 Ohms In most cases, the activity of a particular unit cannot be predicated Ca during manufacture; it is only possible to ensure that it is greater that the minimum laid down in the specification. In fact, a spread in this parameter of two or three-to-one is not uncommon in the production of some types of crystals. It will be realized that such variations in activity should be allowed for in oscillator design. The lowest activity crystal, defined in the specification, should operate satisfactorily, whilst those of the highest activity should not give rise to excessive drive levels. For certainty of starting the oscillator circuit should be so designed that it will oscillate with crystal units having approximately five times the maximum ESR of the crystal unit. The necessity for this arises from the fact that the activity of the crystal units at levels of drive approaching noise level may be less than the activity measured under the specified test conditions. AGING (LONG TERM FREQUENC VARIATIONS) This is an important factor of vital concern to the user. A quartz crystal, as a mechanically moving system is very dependent on the environment in which it is operating. The encapsulation will therefore critically affect the long-term stability and in fact is a major cause of crystal aging. Therefore, the choice of crystal holder is important. There are three main forms of encapsulation: Glass sealed units. ~ Resistance weld enclosures. ~ ld-weld enclosures. It is useful to discuss the construction of each type to illustrate the aging effect. GLASS SEAL UNITS The Glass Sealed unit is usually a Glass bulb with a Kovar ringed glass seal base. Listed are the features for Glass Resonators. HIGH VACUUM SEALING: The use of high vacuum sealing provides lower damping thus giving higher Q factors, resulting in lower noise oscillators. LOW LONG TERM AGING: The combination of high vacuum, high sealing temperature and glass construction results in optimum aging trends attained quicker than metal units. This reduces the factory conditioning time required for the resonator to meet the customers aging specification. This allows the customer to be "quicker to market" with their product. HIGH TEMPERATURE OPERATION: The carefully selected bonding cements and curing processes enable the crystal to withstand continuous operation up to 200 C without any mechanical degradation and intermittent temperatures up to 300 C. RESISTANCE WELD Many crystal manufacturers as the primary method of sealing have adopted this sealing method for all of the standard type crystal enclosures. This method is also used to all the D.I.P. type clock oscillator packages. Using electroless nickel plated steel bases and can, these two parts are welded together by the passage of carefully controlled pulses of DC current across the seam formed at the junction of the base and can. This sealing method is vastly superior to solder seal and provides a clean sealing process that results in acceptable low crystal aging characteristics. COLD WELD The enclosure utilizes a welding action under very high pressure over a localized area; it results in an extremely clean process as no significant heating takes place (certain metals flow together when subjected to high pressures forming a homogeneous bond between them). These process enables a nickel or copper can to be used, usually with a copper clad kovar glass-to-metal seal base supporting pins and crystal mounting structure. This process is now generally being adopted in the crystal industry for improved aging.

6 6 Lap-Tech Report: THE PIEO ELECTRIC EFFECT Table 2 Type of Seal Ultimate Aging Notes Glass Seal PPM / year Initial aging over first 30 days - +/-1 PPM 1 PPM over first 6 months Resistance Weld1 3 PPM/year 2 PPM over 6 12 months ld Weld 0.5to 2 PPM/year 1.5 PPM over first 6 months 2 PPM over 6 12 months LEVEL OF DRIVE The most common problem in the correct use of crystals is to define the level of drive to optimize the user s requirement. The importance of drive level has been emphasized in the Section on Frequency / Temperature Characteristics. Further factors are also important since excessive drive causes the frequency to change and in some cases can lead to a permanent shift. The equipment designer should therefore; take care that variations in his circuit conditions do not result in rated drive levels being exceeded. It is also important (to ensure correct operation within the specified frequency limits) that the user is operating at the same drive level as that at which the crystal has been tested. The following summarizes the effects of drive level: - HIGH DRIVE LEVEL a) Excitation of unwanted modes causing serious deformation (Perturbation) of the Frequency / Temperature and Activity / Temperature characteristics. b) Frequency shifts due to crystal heating, usually reversible. c) Frequency shifts due to overstress usually irreversible. LOW DRIVE LEVEL This condition occurs when the drive level in the oscillator circuit is in the region of a few microwatts or less. When operating at this level the crystal ESR appears to be very much higher than under normal operating levels. This effect is known as "Second Level of Drive" (S.L.D.). It is particularly serious because of a tendency for ESR to increase after a period of non-operating storage; this can lead to a complete failure to oscillate. It is recommended that oscillator designs should allow for a much lower activity than the specified minimum, i.e. the loop gain of the circuit should be high and capable of operating a crystal with an activity of one-third the specified limit. The correct drive level for any particular application is the result of a number of compromises, which will result from a consideration of the requirements. The general advice is to always operate at the lowest possible levels taking account of the problem of S.L.D. effect. Usually any application has one of two main requirements: a) Highest possible stability. b) Adequate output signal from the oscillator. In the case of (a) it is always best to allow the oscillator, to operate at its lowest level, with adequate amplification. If however, there is a particular requirement such as (b) where, for either economy of components or a need to raise the crystal signal above the inherent noise in the system, it will be necessary to operate the crystal at a higher level than that which gives optimum frequency stability. The recommended maximum levels are given in Table 3 below. Frequency Range Mode Max Drive (mw) 1 3 MHz 3 20 MHz Above 20 MHz MHz Fundamental Fundamental Fundamental Overtone ENVIRONMENTAL CONSIDERATIONS The environment in which a crystal operates can exert a major influence on that crystal s performance and operation, The effects of temperature variation have already been described, however this is not the only environmental factor that will affect the crystal. Shock and vibration are often present in varying degrees and must be considered at the design definition stage. It follows that under conditions of severe shock and vibration the crystal may be damaged irreversibly. High levels of acceleration and deceleration can also react adversely on crystal performance. In every case, details of the application should be discussed with the crystal manufacturer in order that all of the environmental factors can be taken into account and allowed for in the design. It is of interest to note that some of the most severe environmental conditions do not always occur in military or space applications. It is generally accepted that commercial portable radios and paging receivers operate under very severe environmental conditions. Thus crystals and other components used in these equipment are designed to be particularly rugged.

7 report 7 Since 1972 Lap-Tech has been supplying high quality products to the frequency control industry. Specializing in high reliability resonators, Lap-Tech also produces sensor elements for QCM / Thin Film applications and a wide range of Lapping and Polishing services. Three ways Lap-Tech will help your business: 1. We offer a growing collection of White Papers and other helpful materials online at our web site. Be sure to visit: 2. Lap-Tech also offers free technical reviews of current or proposed specifications. This can save time and money for your company. Be sure to visit: Lap-Tech Focused on Frequency Lap-Tech Inc. 230 Simpson Ave. South Bowmanville, ON L1C 2J3 Phone Lap-Tech offers low cost sample runs to test scenarios and design possibilities. Some samples of current or past production are available at no cost to you. Be sure to visit:

Characteristics of Crystal. Piezoelectric effect of Quartz Crystal

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