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AMATEUR RADIO BY GARRY CRATT, VK2YBX How quartz crystals work One of the most common components encountered in amateur radio, yet possibly the least understood, is the quartz crystal. This article sets out to explain some of the mysteries behind the quartz crystal. Quartz is a piezoelectric material. Piezoelectricity is literally "pressure electricity", the prefix piezo being derived from the Greek "to press". The direct piezoelectric effect was discovered in 1880 by the Curie brothers and refers to the electric polarisation of these materials brought about by applying mechanical strain. Conversely, piezoelectric materials can be deformed by applying voltage to them. Many different substances have been investigated as possible piezoelectric resonators. Compared to other resonators - eg, LC circuits, mechanical resonators such as tuning forks, and piezoelectric resonators based on ceramics or other single crystal mat- erials - the quartz resonator has a unique combination of properties. The material properties of single crystal quartz are both extremely stable and highly repeatable from one specimen to another. The acoustic loss or internal friction of quartz is particularly low, leading to one of the key properties of a quartz resonator: its extremely high Q factor. The intrinsic Q of quartz is around 107 at 1MHz. Quartz crystals typically have Q factors ranging fro~ tens of thousands, to hundreds of thousands; ie, thousands of times better than the best LC circuits. Because of their inherently high Q, quartz crystals are also very stable. Quartz is a crystalline form of silicon dioxide, SiOz·. It is a hard, brittle, transparent material, with a density of 2649kg/m3 and a melting point of 1750dC. Quartz is insoluble in ordinary acids but soluble in hydrofluoric acid and in hot alkalis. Despite the natural abundance of quartz (sand is largely made up of grains of quartz), it is surprising that quartz crystals of sufficient size and purity for processing are very rare. Cultured quartz For all but exceptional requirements, natural quartz has now been superseded by cultured quartz for the manufacture of resonators. Cultured quartz is now routinely grown from aqueous alkaline solution, under conditions of high pressure and temperature in massive underground steel autoclaves. The lower part of the auto- z y -10 A, B, C constant T : Temp, Fig.1: this diagram shows how the various blanks may be cut from a quartz crystal. The AT cut is the most common but other cuts can also be used, depending on the characteristics required for the cystal. 66 SILICON CHIP To : Reference Temp. Fig.2: temperature vs frequency characteristics for various cystal cuts. As can be seen, the AT cut is the most stable. +18 ABCDE F J GH K +60 +50 L FREQ. +40 CHANGE PPM +30 M +20 N 0 -10 - 20 0 - 30 - 40 -50 -60 - 54 -44 -34 -24 - 14 -4 +6 +16 +26 +36 +46 +56 +66 +76 +86 +96 +106 +116 +126 +136 TEMPERATURE °C Fig.3: the temperature performance of a quartz crystal is governed by the angle at which the blank is cut from the crystal. These "S" curves show the expected frequency vs temperature variation for AT cut crystals. clave is maintained at a temperature of about 400°C and contains nutrient in the form of pure silica. At this temperature and at pressures in the order of a thousand atmospheres, the solubility of silica is relatively high and a saturated solution is formed. Convection currents transport the saturated solution to the upper part of the autoclave, which is maintained at a slightly lower temperature-of aociut 350°C. At this lower temperature, the solution is supersaturated and the quartz is deposited on seed crystals suspended in the cooler region of the autoclave. Over periods of many days or weeks, crystals of substantial size can be grown for use in the manufacture of resonators. By slicing the raw crystal at various angles with respect to its axis, it is possible to obtain a variety of blanks having different vibration modes and different temperature characteristics. The most commonly used type of resonator is the "AT" cut, where the quartz blank is in the form of a thin plate cut at an angle of about 35 degrees to the optic axis of the crystal. The AT cut has a frequency/temperature coefficient which can be precisely controlled by small variations in the angle of the cut. Various cuts Fig.1 shows how various blanks are cut from a quartz crystal, while Fig.2 · shows the variation of temperature/ frequency characteristics of various cuts. As you might expect, the performance of a quartz crystal over a temperature range is governed by the angle at which the blank is cut versus the axis of the quartz. The "S" curves shown in Fig.3 form a useful guide to the expected variation of frequency versus temperature for the commonly usEd "AT" cut. For crystals falling in the range 1MHz to 150MHz, a frequency tolerance of ±0.0005% over a temperature range of-55 to +105°C is readily achievable. The final essential characteristic of the quartz resonator is related to the stability of its mechanical properties. Short and long term frequency drifts of only a few parts per million per year are readily available from commercial units. The highest degree of "ageing" occurs in the first week after manufacture. After this time, the ageing process decreases logarithmically. Precision crystal units manufactured under closely controlled conditions are second only to atomic standards in their frequency stability. The first step in manufacturing a crystal resonator involves processes similar to those involved in the manufacture of optical lenses. Initially, the crystal "bar" is oriented using x-ray diffraction techniques, to determine the precise angle at which the blank must be cut. The crystal bar is then cut into wafers by a precision sawing machine, using a lapping technique, where the bar of quartz is cut by a series of steel blades driven in a reciprocating motion, while being continuously flooded with an oil based slurry. After the wafers have been sawn from the quartz bar, they are lapped JANUARY 1991 67 Co ---,I .---------i - ( ~~ c, R, L, Fig.4: the crystal equivalent circuit. Co represents the static (shunt) capacitance & is the sum of the capacitance between the electrodes plus that added by the wire leads & holder. The Rl, Ll, Cl branch is · known as the "motional arm" (see text). and polished, as any irregularities in the surface of the wafer must be reduced to a small fraction of a wavelength to keep losses to a minimum. The thickness of a typical AT blank can range from 2mm down to 33µm , with the required tolerance being 0 .1 % , so a high degree of polishing is necessary, just like an optical lens. After the mechanical processes are complete, the blank must be carefully cleaned. This is achieved by a combination of ultrasonic washing, rinsing in de-ionised water, etching in ammonium biflouride solution, then radiating the blank with ultraviolet light in the presence of oxygen. This final process is known as UV-ozone cleaning, as ozone is produced by the action of ultraviolet light on oxygen. trade is defined by using photo-etched plating masks. The electrodes are normally made from gold, silver, or aluminium, and this material is deposited using an evaporation technique. The crystal is now ready to be mounted. There are several methods of mounting the crystal which allow good electrical connection, as well as adequate mechanical support. The most commonly encountered system is the "spring mount", which uses two gold plated springs similar in appearance to a watch hairspring, which hold the blank at the electrical connection points. These springs are secured with a small amount of silver loaded epoxy resin, which is applied by a syringe. After the cleaning stage, the blank frequency is typically left 1 % higher than the desired frequency, which is compensated for by the loading effect of the electrodes. After mounting, the crystal will typically be within ±0.2% of the desired frequency. The final adjustment can be made either by plating additional electrode material onto the blank in order to bring the frequency down or by etching away some of the previously deposited electrode material, in order to take the frequency higher. Other more complex mechanical systems have also been developed for mass production. The equivalent circuit of a crystal, shown in Fig.4, can be used to explain the basic concepts governing the performance. "Co" represents the static (shunt) capacitance and is the total of the capacitance between the electrodes and the capacitance added by the wire leads and the holder. The Rl, Ll, Cl branch is known as the "motional arm". Cl represents the "motional capacitance", or the elasticity of the quartz. L1, the "motional inductance", corresponds to the oscillating mass of the quartz, and Rl is the sum of the bulk crystal losses. The values of "motional capacitance" are very small compared to the values of capacitance normally used in oscillator circuits in amateur radio, and can be calculated for the "AT" cut as follows: Cl (pF) = 0.22 x Ax F/1670 where A = the area of the electrode in square metres and F = the resonant frequency (Hz). The value of Cl can be changed for a particular resonant frequency, by varying the electrode area. This, in turn , is determined by the diameter of the quartz element. For AT cut crystals, this value is normally 10 to 30 femtofarads. The static parallel capacitance, Co, is the capacitance between the vacuum deposited metal electrodes and the quartz material as a dielectric. The Attaching electrodes At this stage the blank is ready for the attachment of electrodes. This is done using vacuum deposition techniques, where the shape of the elec- +iX I I f, ~Dr-° lp -iX f o-!HOf-o +;X ~ +jx I : fp CL / I -jX - jx i Fig. 2 fs: f p: Series Resonance anti Resonance t 0i;x , / v' fL ~ ,I / I I I CL < Fig.5: the impedance graph for a quartz crystal. There are two resonant frequencies: the series resonant frequency fs at impedance = 0 & the parallel resonant frequency fp at impedance = =. 68 SILICON CHIP Fig.6: the quartz crystal may be connected.in either series resonant mode (centre) or parallel resonant mode (bottom). In practice, the capacitor (CL) is used for fine adjustment of the crystal frequency. Fundamental Mode Oscillator 15 E 0. 10 0. ~ 5 --- •-10MH,: "I 0 I0~ 20MH1 -5 'C1: 560PF C1, JOO pF C,; 270pF C1; C 1' 1 C.~ -10 ,1 C,+C2 + 5 (pF) - --·-+ -- C, +C, C, C2 CJ<<C2 -15 0.1 0.01 1 10 lOOrnw Overtone Mode Oscillator 1 Nq--~ Fig. 7: the effect of high drive level on the resonant frequency of a crystal. The resonant frequency changes prior to destruction due to heating of the quartz. f, value of Co and Ll are as follows: Co(pF) = 40.4 x Ax F/1670 + 0.8pF For typical AT crystals, this value ranges from 1-7pF. Ll(H) = 4.22 x 104 x (1670)3/[P x A] Fig.5 shows the impedance graph for a typical quartz crystal. Neglecting losses, two resonant frequencies result, namely the series resonant frequency (Fs) at impedance = 0, and the parallel resonant frequency (Fp) at impedance = infinity. The mathematical formulae for calculating those two resonant frequencies are as follows: Fs = 1/21t✓L1.C1 = 1/21t✓L1.C1.Co/(C1 + Co) The parallel and series resonant frequencies are related by the equation: Fp = Fs✓ l + Cl/Co and the relative frequency interval between the two resonant points is equal to half of the ratio of Cl to Co, as shown by the equation: (Fp - Fs)/f = C1/2Co By series connection of a load capacitor with the crystal, the series resonance mode occurs. By connecting the capacitor across the crystal, the parallel resonance mode occurs. = 2 ir ✓ L,C, ex . Fig.6 shows the result from the connection of either a series or parallel capacitor. In practice, this capacitor is used to provide a means of adjusting the crystal frequency. It can either be a fixed capacitor, with or without a trimmer, for fine frequency adjustment. One of the important points when using a crystal oscillator is the amount of drive signal applied across the crystal itself. The amplitude of the mechanical vibrations of the crystal is proportional to the amplitude of the current flowing through it. If sufficiently high current is allowed to flow, the tensile strength of the quartz will be exceeded, causing it to fail. Fig. 7 shows how, just prior to destruction, the resonant frequency of the crystal changes due to heating of the quartz. Suffice to say, the drive level (normally expressed in milliwatts) should be kept to the minimum necessary to ensure stable oscillation. Excessive drive can result in excessive frequency drift and poor ageing. Typical levels used with AT cut crystals are in the order of 1-ZmW. Crystals are made in a large variety of shapes and sizes, depending upon the application. To meet these applications, a range of standard case sizes has been developed. Each case houses a crystal of a particular blank size, which then determines the lower end < f. ' CJ< <C. f0 ;47MHz C,; 150pF C,; 1 00pF C3; 5pF L,; 0,56µ H L,; NON L, Fig.8 (right): typical circuits for fundfamental & overtone crystal oscillators. In overtone operation, the crystal is made to oscillate at an odd harmonic (3rd, 5th, 7th etc). Fp ~ C .1 6 MHz JOpF J. 6 - 20 MHi 20 pF 150 pF C,; C,; 1 0pF 20pF of the frequency range for each type. The cases are sealed using .the resistance welding technique which has replaced the earlier solder seal and cold weld methods. While a discussion on the merits of various oscillator circuits is beyond the scope of this article, we will just briefly mention the two modes of oscillation, fundamental and overtone. Fundamental operation is self explanatory - the crystal is made to oscillate at its fundamental frequency. In overtone operation (3rd, 5th, 7th), the crystal is driven to oscillate at the overtone frequency, while still within the drive limitations previously mentioned. Either series or parallel resonance modes can be used for fundamental or overtone crystals, but a crystal designed for fundamental operation cannot be used sucessfully for overtone operation. Fig.8 shows circuits for fundamental and overtone operation. References (1). Hy-QHandbook of Quartz Crystal Devices by David Salt, 1987. (2). Kookje Electrical Industrial Co Ltd, Korea - data sheets. (3). Harmony Electronics Corp., Taiwan - data sheets and catalog. (4). Ilshin Communication Co Ltd Korea - data sheets and catalog. (5). Hy-Q Crystals Pty Ltd - Quartz Crystal Product Guide. SC JANUARY1991 69