Introduction to quartz crystals and natural quartz

Quartz is a crystalline form of silicon dioxide (SiO2) which is abundant in nature, forming about 12% ofthe Earth's crust. A combination of the limited supply of natural quartz along with its high cost has resultedin the development of cultured quartz.Crystals of quartz are grown by dissolving SiO2 in an alkaline solution at high temperature and pressure.This process takes place in auto cleaves which are built to withstand the extreme conditions required. Seedcrystals are mounted in frames in the cooler part of the autoclave whilst a solution of sodium carbonate orhydroxide and fragments of SiO2 are placed in the warmer portion. The solution moves from the hotter tothe cooler region and in doing so, dissolves the nutrient and deposits on the seed crystal. Temperatures arecontrolled throughout this process.Large bars of crystal can be grown in about ten weeks. The quality of the quartz depends on the conditionsof growth. Crystals are grown in shapes and sizes that minimize wastage of time and material.The bars of crystal are cut into wafers. The angle at which these wafers are cut is crucial in determining thefrequency and temperature stability of the final crystal. The most common cut is the AT-cut where theblank is cut from the bar of crystal at approximately 35°, allowing a frequency range of 1MHz to 300MHz.

Piezoelectric properties of QuartzSince the discovery of the piezoelectric properties of quartz in 1880 by Pierre Curie, quartz has become asignificant factor in the growth of the electronics industry. By stretching or compressing a piezoelectricmaterial a voltage is generated. The reverse is also true: a voltage applied to the material causes it tobecome mechanically stressed. In the case of crystals, the pressure resulting from a voltage being applied isdisplayed in the form of oscillations at a particular resonant frequency. This frequency is a function of thethickness of the crystal. By carefully preparing a crystal, it can be made to oscillate at any frequency. Thelowest frequency is called the fundamental frequency and can be supplied up to about 45MHz. Higherfrequencies (to over 300 MHz) are achieved by operating the crystal at odd overtones; 3rd, 5th, 7th, 9th and11th etc. and tuning the circuit so that the crystal oscillates at its designed overtone frequency.Overtone crystals are specially processed for plane parallelism and surface finish in order to enhance theirperformance at the required overtone frequency. The overtone frequency is higher than the equivalentharmonic multiple of the fundamental by approximately 25KHz per overtone.

Glossary of Terms for CrystalsQuartz Crystal: A circuit element having a very stable oscillation characteristic composed of quartz.

Holder: The package that the crystal is enclosed within.

Calibration Tolerance: The frequency of the crystal at a specified temperature (typically +25°C).

Temperature Stability: The frequency deviation of the crystal over the operating temperature range.

Load Capacitance: The specified capacitance of a crystal that a circuit must be for the crystal to be onfrequency.

Crystal Cut: The properties of a crystal are very dependent upon the way that the crystal is cut withreference to its internal crystalline planes

Center Frequency: The specified reference frequency of the crystal and is typically specified in megahertz(MHz) or kilohertz (kHz).

Frequency Tolerance or Calibration Accuracy: The amount of frequency deviation from a specifiedcenter frequency at ambient temperature (referenced at 25°C). This parameter is specified with a maximumand minimum frequency deviation, expressed in percent (%) or parts per million (PPM). This deviation isassociated with a set of operating conditions including load capacitance and drive level.

Frequency Stability: The amount of frequency deviation from the ambient temperature frequency over theoperating temperature range. This deviation is associated with a set of operating conditions including:Operating Temperature Range, Load Capacitance, and Drive Level. This parameter is specified with amaximum and minimum frequency deviation, expressed in percent (%) or parts per million (PPM). Thefrequency stability is determined by the following primary factors: Type of quartz cut and angle of thequartz cut. Some of the secondary factors include - mode of operation, drive level, load capacitance, andmechanical design.

Type/Angle of Quartz Cut : The type and angle of a quartz cut effects the crystal device operatingparameters, the most significant being frequency stability. The frequency stability is dependent upon theplane or the angle of the crystal element in relation to the crystalline axes of the crystal. The plane or angleis referred to as the crystal "cut". As shown in Figure 1, a common type of thickness shear crystalfabricated from Y bar quartz is the "AT" cut. In Figure 2, the frequency stability versus operatingtemperature range is plotted as a function of "AT" cut angle (0). Note the inflection point at approximately25°C and the location of the adjacent upper and lower turning points for each cut angle. The frequencystability and operating temperature range required by the customer determine the angle of cut utilized.

Figure 1 Figure 2

Operating Temperature Rate: The maximum and minimum temperatures that the crystal device can beexposed to during oscillation. Over this temperature range, all of the specified devices operating parametersare guaranteed.

Crystal Equivalent Circuit : A crystal device consists of a quartz resonator with metal plating. Thisplating, as shown in Figure 3, is located on both sides of the crystal and is connected to insulated leads onthe crystal package. The device exhibits a piezoelectric response between the two crystal electrodes asexpressed in the equivalent circuit shown in Figure 4.

Figure 3 Figure 4

Motional Capacitance and Motional Inductance: The motional capacitance and inductance aredesignated by C1 and L1, respectively, in the equivalent circuit (Figure 4). For a "Series" resonant crystal,the value of C1 resonates with the value of L1 at a frequency (FS) expressed in Equation 1. Typically, L1 isnot mentioned when working with most crystals. Due to this absolute equation, it is only necessary tospecify one motional component or the other. The industry standard is to specify a proper value of C1 only.The actual value of C1 has physical limitations when it is realized in a quartz crystal design. Theseconstraints include the mode of operation, the quartz cut, the mechanical design, and the nominal frequencyof the crystal.

Equation 1

Shunt Capacitance (C0)The static capacitance between the crystal terminals. Measured in Pico Farads (pF), Shunt Capacitance ispresent whether the device is oscillating or not (unrelated to the piezoelectric effect of the quartz). ShuntCapacitance is derived from the dielectric of the quartz, the area of the crystal electrodes, and thecapacitance presented by the crystal holder.

Equivalent Series Resistance (ESR): The resistance of the crystal with a series load capacitance.The resistive element measured in ohms, of a crystal device. At the frequency found in Equation 1, themotional inductance (L1) and motional capacitance (C1) are of equal ohmic value but are exactly oppositein phase. The net result is that they cancel one another and only a resistance remains in the series leg of theequivalent circuit (Figure 4). The ESR measurement is made only at the series resonant frequency (FS), notat some predetermined parallel resonant frequency (FL). Crystal resistance measured at some parallel loadresonant frequency is often called the "effective" resistance.

Series Vs Parallel Load Resonance: A crystal can be used in an oscillator circuit to operate in either oftwo resonant modes: Series Resonance or Parallel Load Resonance (also known as anti-resonance). Thecrystals used in these two types of modes are physically the same crystals, but are calibrated to slightlydifferent frequencies. The crystal reactance curve is shown in Figure 5. When a crystal is placed into anoscillator circuit, they oscillate together at a tuned frequency. This frequency is dependent upon the crystaldesign and the amount of Load Capacitance, if any, the oscillator circuit presents to the crystal. Specified inpicofarads (pF), Load Capacitance is comprised of a combination of the circuits discrete load capacitance,stray board capacitance, and capacitance from semiconductor miller effects. When an oscillator circuitpresents some amount of load capacitance to a crystal, the crystal is termed "Parallel Load Resonant", and avalue of Load Capacitance must be specified. If the circuit does not exhibit any capacitive loading, thecrystal is termed "Series Resonant", and no value of Load Capacitance is specified. The "Parallel LoadResonant" operating frequency of a quartz crystal is based on Equation 2.

Figure 5

Where: FS = Series Resonant Frequency (MHz)FL = Parallel Load Resonant Frequency (MHz)CL = Crystal Load Capacitance (pF)C0 = Crystal Shunt Capacitance (pF)C1 = Crystal Motional Capacitance (pF)

Equation 2

Mode of OperationThe Mode of Operation of a quartz device is one of the factors that will determine the frequency ofoscillation. For "AT" cut quartz crystals, over tone modes are at odd frequency harmonics. For example, acrystal may operate at its fundamental frequency of 10 MHz, or at odd harmonics of approximately 30MHz(Third Overtone), 50MHz (Fifth Overtone), and 70 MHz (Seventh Overtone). The equivalent circuit of anovertone mode is not shown in the above model (Figure 4), but each over tone mode would simply be anadditional parallel R1, L1, C1 branch (no additional C0 branches) equivalent to the fundamental circuitshown.

Drive Level: The measure of power dissipated within the crystal.A function of the driving or excitation current, flowing through the crystal. The Drive Level is the amountof power dissipation in the crystal, expressed in microwatts or milliwatts. Maximum power is the mostpower the device can dissipate while still maintaining operation with all electrical parameters guaranteed.Drive level should be maintained at the minimum levels necessary to initiate proper start-up and assuresteady state oscillation. Excessive drive level can cause poor aging characteristics and crystal damage.

Aging: The frequency change, which results from permanent changes in the crystal over time.The systematic change in frequency with time due to internal changes in the crystal and/or oscillator. Agingis often expressed as a maximum value in parts per million per year [ppm/year]. The rate of aging istypically greatest during the first 30 to 60 days after which time the aging rate decreases. The followingfactors effect crystal aging: Contamination on the surfaces of the quartz, stress relief of the mounting andbonding structures, material outgassing, and seal integrity.

Storage temperature Range: The minimum and maximum temperatures that the device can be stored orexposed to when in a non-oscillation state. After exposing or storing the device at the minimum ormaximum temperatures for a length of time, all of the operating specifications are guaranteed over thespecified Operating Temperature Range.

Pullability: A specification for the change in the parallel load resonant frequency as a function of changein crystal load capacitance. As expressed graphically in Figure 6, Equation 3 is used to calculate thefrequency difference, expressed in ppm, between two parallel load resonant frequencies (FCL1 and FCL2) as adirect result of a given change in crystal load capacitance (CL1 and CL2). Because there are several methodsto express crystal Pullability, please consult the factory for product specifications.

Capacitive Ratio : In applications (i.e. VCXO) where variations in the crystal parallel resonant frequencyare desired, the capacitive ratio (r) may be specified. Derived from Equation 1 and rearranged, thecapacitive ratio is a component of Equation 4. This ratio is an indicator of the change in a parallel loadresonant frequency as a direct result of a given change in crystal load capacitance. Because the value of thisratio has physical limitations when it is realized in a quartz crystal design, please consult the factory forproduct specifications.

Figure 6

Equation 3

Equation 4

Tutorials on Quartz Crystals and OscillatorsWe are pleased to present links to two separate tutorials, both authored by Dr. John Vig, who hasgraciously granted us permission to reference them here.We want to emphasize that Dr. Vig did not write these tutorials on our behalf. They were written by Dr.Vig in his capacity as an employee of the Federal Government. Providing links to these tutorials does notconstitute Dr. Vig's endorsement of our site.The first, "Introduction to Quartz Frequency Standards," has been in use throughout the frequency controlindustry for quite some time. It is an excellent tutorial.The second, "Quartz Crystal Resonators and Oscillators For Frequency Control & Timing Applications," isa much more in-depth tutorial. This tutorial is a Microsoft Power Point presentation. If you do not havePower Point, Microsoft offers a free Power Point Viewer.