Making it Crystal Clear: Crystal Oscillators in Communications

A crystal can be made for every stability need. Due to their incomparable cost/performance relationships, crystals have comfortably remained in use for many of the same critical functions they have always performed, despite the introduction of many newer technologies in communications.

By Rob Howald

Crystals have been around for a very long time and represent one of the few items that continue to be the best choice for the same functions that they were used for some 60 years ago. It’s almost impossible to design hardware for communication systems and not run across a crystal oscillator. Digital, analog, and RF designers use them. There is arguably no better example of inexpensive yet very high performance than a crystal resonator. This has much to do with the fact that the source material (quartz) is naturally abundant, is easily grown, and has piezoelectric characteristics. The ease of fabrication and nonstop demand has created a glut of vendors offering nearly identically performing components, often with only cost distinguishing them. This is particularly the case in the commercial world. Crystal production is being fueled by the needs of the wireless and broadband communication industries. And while communication systems design centers on communication, crystals have applications in a lot more places than in our little universe. According to the handiest market reference I have (early 1990s) commercial production is over a billion crystal devices per year. ¹

Now, as for that piezoelectric thing, piezein means “to press” in Greek. Thus, piezoelectric means “pressure-electric,” describing the nature by which electrical voltage and current are related to displacement and mechanical stress on the rock (the relationship is two-way). There is, as always, an intensely cumbersome set of mathematical equations describing these relationships, which aren’t exactly solvable in closed form without simplification. This does not significantly limit the ability to design robust, high-quality crystal resonators and oscillators to a very detailed set of specifications, which is a testimony to the skill with which the industry has learned to understand and work with quartz.

Crystal cuts and frequency
The cut of the crystal refers to the physical way in which the rock is sliced to create the resonator. The AT-cut and SC-cut are the most recognizable. The IT-cut and FC-cut are from the same family as the SC-cut, that of the doubly rotated. This means it is cut along two of the three axe relative to that defined by the crystal structure. The AT-cut is singly rotated, and, with the similar BT-cut, has dominated crystal oscillator design and production for much of the history of their use. The doubly rotated families were developed, as might be expected, while searching for new and improved performance of crystal technology. They ultimately became quite mature. The first practical AT-cut crystal, about 7 years after the first cut of temperature compensated quartz was discovered, occurred in 1934. Developing the SC-cut occurred much later, not beginning until 1974.

The first and foremost specification of a crystal resonator or oscillator is its frequency. Obviously, this number is determined by the application. The design of digital timing networks and/or RF frequency plans usually presents engineers with multiple options regarding the number and function of the various crystal oscillators in a system, as well as their frequencies. We won’t be discussing it in this article, but crystal resonators also play important roles in communication systems when used in crystal filters. It is described here because it is most straightforward to envision a crystal oscillator’s operation by understanding its action as a filter.

The crystal filter is of great significance because of its ability to have extremely narrow bandwidth with good filter shape factor (sharpness of passband/stopband characteristic). At their frequencies of operation, crystal filters can generate narrow bandwidths, unobtainable with lumped element inductors (Ls) and capacitors (Cs). The quality factor (Q) is the parameter, which describes this performance. By definition, Q is the ratio of energy stored by oscillation cycle to energy lost per cycle. (Refer to the crystal resonator equivalent circuit shown in Figure 1 )

What separates the Q capability of crystals from electrical Ls and Cs are the equivalent values of those elements for the crystal. The crystal’s series L and C circuit values, with virtually ideal equivalent component characteristics, are impractical to obtain from actual Cs and especially Ls. Inductors, in particular, introduce losses that degrade circuit selectivity. Crystal resonators have very high Qs, a result of very little equivalent circuit loss (resistance) relative to the equivalent inductance. A very common commercial crystal filter, for commercial FM, has a center frequency of 10.7 MHz and a bandwidth of about 10 kHz. As another example, I used a crystal filter with a bandwidth of about 20 kHz at a center frequency of 80 MHz in a frequency synthesizer design. A bandpass filter made of lumped element components at this frequency would be hard-pressed to be reliably designed, with no tuning, and with a bandwidth a hundred times as wide (2 MHz).

Now, let’s discuss the crystal oscillator. Consider the resonator used in the feedback path of a high gain amplifier. Without getting into circuit details of how the feedback and resonator are connected, which gives the oscillator types their various names (e.g. Colpitts, Pierce, Butler), the filter allows a feedback signal of a very limited frequency range. By building the proper circuit around the amplifier to funnel feedback, providing impedance transformation, and tapping oscillator power, the resonator makes an ideal feedback element of a high stability oscillator. Again, depending on the circuit around it, a crystal oscillator design may be based on series or parallel resonance of the crystal.

For series resonance, the frequency is determined by C1 and L in the equivalent circuit of Figure 1. A parallel resonant circuit would, instead, use the frequency determined by the inductance of the crystal in parallel with C2 and an external load capacitor that shunts the crystal terminals. This load must be defined ahead of time for the manufacturer to fabricate a crystal for a parallel resonant design (around 33 pf is commonly used). Again, circuit behavior of series and parallel resonant circuits are different — the former acts as a bandpass circuit, and the latter acts as a bandstop. This affects the nature of their frequency selectivity and, thus, determines exactly how they are connected within the circuit.

Quality factor and oscillator noise
The oscillator’s noise characteristics, a short-term form of stability, and the ability to pull the oscillator frequency are related to its Q. In fact, closest-in phase noise components can vary as the reciprocal of Q ⁴ . Note that when surrounded with a circuit, such as to make an oscillator, this very high resonator Q is degraded. Generally, Q and pulling qualities work against one another — a high Q oscillator is hard to pull, while (low Q) wideband RF voltage-controlled oscillators VCOs are considerably noisier. In a crystal oscillator design, several things can affect the Q and resulting noise performance. Among these are the crystal overtone used, mounting stresses on the resonator, material impurities, interfering modes of crystal excitation, gasses within the packaged crystal, and drive level. It is important to recognize that Q is not the only important factor affecting short-term noise in a crystal oscillator.

Other important items affecting short-term noise include the external circuitry (the transistor 1/f spectrum), thermal noise (the transistors noise figure), vibration environment (not at all to be overlooked), stress relief events, thermal instabilities, and losses that modify loaded Q, such as piece part variations in temperature. The nature of both crystal implementation and oscillator operation itself is nonlinear, so it is difficult to precisely analyze or simulate the various impacts and inter-relationships among design variables. However, many years of designs, including the first bible of crystal oscillator design, have led to known topologies and good RF practices, yielding high-quality crystal oscillator designs. ³ Furthermore, PC-based simulation development, particularly using time-domain simulators like SPICE, has become quite practical and valuable.

Interfering modes
Now, here is a word about interfering modes. While it would be just peachy if crystals only responded at a single resonant frequency, the mechanical-to-electrical relationship allows other physical dimensions to have resonant frequencies as well. Some crystal designs purposely take advantage of responses at overtone frequencies (to be discussed later). Without proper care in fabrication (and sometimes despite proper care and fabrication), additional frequencies will be excitable, and/or unwanted activity dips can occur. This is the reason that good design approaches use some form of RF filter as preselection of oscillator feedback signals, which rejects unwanted modes since transistors are likely to have enough gain to oscillate at many of these frequencies.

Now, a further word about activity dips (it’s more than a description of your propensity to workout before age 25 versus after age 35). Activity dips describe anomalous behavior of a resonator due to short-term increases of series resistance. It was not in the list previously given, but it can also be a contributor to short-term instabilities. It wasn’t mentioned, because it is slightly mysterious and generally not considered an element in well-designed and very well-tested oscillators. Added resistance degrades Q, increases losses, and can kill overall circuit feedback gain. Possible effects include loss of oscillation (however briefly), slight frequency shifts, phase glitches, etc. You are most likely to hear about it from an “old-timer” (author not included) who was perhaps party to troublesome designs in less sophisticated crystal fab environments. Quality fab and extensive testing, including accelerated life runs, and temperature, are the best deterrents. Work has been done to completely understand the phenomenon, which occurs essentially when a frequency versus time curve of a desired mode and undesired mode cross. The situation is a strong function of drive level and load resistance.

Phase noise
Because a resonator will attenuate frequency components outside a very narrow bandwidth, the frequency of oscillation will shift very little, a quality referred to as oscillator stability. Stability, jitter, and phase noise describe essentially the same phenomenon, only with a different scale of time. Phase noise can be converted to frequency noise, and vice versa. It describes the short-term noise-like phase modulation typically measured in the frequency domain, which corrupts an otherwise ideal sinusoidal waveform. A single line represents a sinusoid in the frequency domain, while a noisy one has frequency components offset from the center “line.” This energy offset from the carrier frequency represents this nonideality. For various complicated reasons, the noise spectrum rolls off from the center frequency as a power such as 1/f ⁴ or 1/f ³ . This behavior is part of the so-called 1/f noise in literature. This noise energy can be represented in degrees root mean square (RMS). The frequency noise version would, instead, be in RMS Hz. In timing networks, RMS phase noise may be described as timing jitter in units of time, such as nanoseconds RMS, peak-to-peak, or unit elements (UE).

Stability can also be described by second-to-second behavior, a parameter typically evaluated by Allan variance. While this may seem confusing, overlapping, and unnecessary, two things must be kept in mind. First, multiple descriptions are necessary, because some functions and applications performed by crystals require knowledge of these various parameters to guarantee system performance. Secondly, crystals are spread across so many applications that their specifications must adapt to the lingo and mindset of each.

Thermal stability
The long-term, temperature-related stability part of the crystal’s specification is probably the version most shared among any application. Stability is given in parts-per-million (ppm), which is convenient for crystals because the movement in absolute frequency of resonators is proportional to the center frequency. The ppm terminology means that a 10-MHz crystal oscillator with a specified stability of +/-50 ppm over some temperature range can shift from 500 Hz below 10 MHz to 500 Hz above 10 MHz. Note the great accuracy available (50 ppm is actually an unspectacular specification) — 500 Hz out of 10,000,000 Hz.

Observe the curves in Figure 2 . One great advantage of an AT-cut crystal is that its angle can be varied to produce a desired frequency-versus-temperature characteristic. As such, a designer can choose the cut based on the thermal requirements of the application. SC-cut crystals have different curves that make them less suitable to operate over wide temperature ranges. Whereas AT-cuts have inflection points in their frequency versus temperature characteristic at around 26°C, an SC-cut has its inflection at about 100°C. There is a 25°C range about this temperature where the SC-cut is highly stable, with frequency shifts of only 1 ppm over that range. However, if the temperature becomes too cool, the frequency versus time curve of an SC-cut falls off dramatically, meaning the frequency will begin to shift rapidly. As such, SC-cuts are not well-suited to applications other than ovenized units and/or like oven-controlled crystal oscillators (OCXOs). It is apparent from the curves that if a narrow ambient temperature range is expected, very tight stability can be maintained for basic AT-cuts. Of course, temperature variation is not the only determinant of crystal stability. Crystal electrical drive, power supply effects, radiation, humidity, and vibration (a to-be-discussed situation) all contribute. Another major factor is time.

Aging and overtones
Unlike in people, aging effects on crystals are generally quite predictable. Known causes are pretty well pinned down to quartz imperfections. Contamination (package leak, handling) within the resonator housing can result in transfer of quartz mass. Since frequency is proportional to this, the frequency will shift. Also, to work this crystal, you have to mount it properly on electrodes to allow it to vibrate, another trick that results in stresses on the tiny mounting structures, the bonding material, and on the slice of rock. There are, in fact, mounts that use two points, three points, and even four points. External circuit effects manifest themselves as frequency drift, although they are unrelated to the resonator changing. Examples of this are drive level, impedance loading of resonator, and oven circuit changes.

Since typical resonator aging curves are known, specifications giving maximum aging characteristics can be confidently given. A common example would be 2 ppm/yr for the first year and 1 ppm thereafter. Pre-aging, including accelerated thermal cycling, is done in critical applications to guarantee aging limits, “exercising” the stresses prior to delivery.

As previously mentioned, for both better and worse, crystals have responses other than the fundamental mode. The “better” part of this paradox is the ability to use overtones as a way to establish higher frequency oscillators of crystal stability, without the need to continually cut more difficult (thin) quartz sizes. Fundamental frequency crystals become more burdensome beyond 30 MHz, and overtones become common. Fortunately, odd harmonic responses exist, the result of a mechanical mode that is more than a single wavelength between the electrodes. Overtones are typically thirds and fifths, although higher are possible. As overtones increase, there comes a point at which it is just more cost-effective to build an RF multiplier circuit that follows the crystal to boost the output frequency.

There are other good reasons to use overtones, besides the fact that it is the only way, for example, to achieve a 90-MHz crystal. Overtones have higher Q than their fundamental counterparts. In addition, they have better aging characteristics relative to same-frequency fundamental units. This is attributable to the sturdier crystal blank of the overtone, because its fundamental is a lower frequency and the resonator is therefore bigger. Because of this, high performance crystals (typically 5-MHz or 10-MHz precision references) often use overtone designs, although fundamental cuts could easily cover this frequency range. Interestingly, overtones are not harmonics (or that is what they would be called). Actual mathematical solutions would show the overtones to be Bessel function-related, and their results would be slightly lower in frequency than the harmonic.

More about cuts
First, let’s establish some distinguishing characteristics of the two primary crystal cuts, the AT and SC. They are summarized here. SC-cuts are an improvement on AT-cuts in the following ways:

• Better aging characteristics

• Faster warm-up speed

• Higher Q, better close-in phase noise

• Better orientation sensitivity (For example, less change in frequency when turned upside down.)

• Better g-sensitivity (lower noise sideband levels when vibrated).

The primary disadvantage of the SC-cut is the cost, because it is more difficult to obtain the doubly rotated cut. Also, the higher Q means less pullability, and makes SC-cuts basically unsuitable for voltage-controlled crystal oscillator (VCXOs) or even temperature-compensated crystal oscillator (TCXOs). This is, again, a reason why they find their way primarily into OCXOs.

Types of crystal oscillators
The basic crystal oscillator (XO) includes a simple packaged resonator in a circuit that has no means of reducing the frequency versus temperature characteristic. These units are of the AT-cut type, as SC-cuts do not operate in a well-behaved region of frequency versus temperature curves at room ambient. The simplest may have stabilities in the 1e-4 or 1e-5 range, suitable for computer timing. Free-running crystals that can maintain somewhere on the order of 50 ppm (5e-5) are widely used in commercial digital communications applications.

In TCXO designs, the output from a thermistor generates a correction voltage that is applied to a varactor (a diode, optimized for its depletion region to function effectively as a voltage-variable capacitance). This compensates for the frequency versus temperature characteristic. Stability performance is in the 1e-6 range, such as ±2 ppm over some reasonably wide temperature range. Applications include mobile radios, satellite systems, and spread-spectrum systems — actually, most any RF system looking for a relatively inexpensive stability upgrade. Quite recently, TCXO capabilities have dramatically improved in performance, size, and cost. This makes them more attractive in many new applications, including those that are cost-conscious.

OCXOs represent the best stability you can expect without moving up to a different, much more costly technology such as Rubidium and Cesium standards. Typical stability performance is in the 1e-8 range, the kind of performance necessary in applications varying from some types of sophisticated radar, to a reference frequency standard in a satcom system and global positioning system (GPS) navigation. These units package the crystal oscillator, and as much critical circuitry as necessary, within a single housing that is held at a constant temperature consistent with what is best for the crystal cut (typically SC). This arrangement makes dc power and size more of a concern, both of which are key design criteria in many system architectures.

The microcomputer-compensated crystal oscillator (MCXO) device is relatively new to the family. The MCXO uses digital techniques to observe the frequency drift, and compensates through D/A conversion to a tuning port in the circuit, similar to the way a TCXO corrects. Stability values in the 1e-7 range are obtainable, generally between TCXOs and OCXOs. If you have done oscillator design in the past, then you are likely to be aware that the mix of digital and RF has its dangers. Mainly, digital signals are very strong and rich in harmonics. Thus, careful design and test are necessary to ensure spectral purity of the RF output without discrete interferers from digital circuitry.

The VCXO is the high-stability equivalent of the commonly encountered VCO in RF design. In VCXOs, a pin connected to a varactor within the resonant circuit of the oscillator is brought out externally for frequency tuning. The equivalent circuit of a crystal places some restrictions on where a capacitor can be placed effectively without degrading its high performance. Recall it’s harder to pull high-Q oscillators. This is most easily recognized by noting that by trying to pull the frequency off center too far, the resonator attenuation becomes very high, thus eliminating oscillation. Properly placed tuning elements in VCXOs do not degrade the Q too much. The tuning element is placed in the circuit so as to ensure that the crystal resonator dominates resonator behavior.

VCXOs provide frequency pulling over ranges usually given in some hundreds of ppm on both sides of a center frequency. They allow narrowband phase-locked loops implementation with low-noise performance, and are well-suited to carrier or timing recovery subsystems in receiver synchronization topologies.

I once had the opportunity several years ago to have an engineering-type tour through a crystal fab and circuit design facility (Piezo Crystal Company, Carlisle, PA). Knowing oscillators well didn’t help much in the fab area, where I must’ve looked like a 6-year old watching his dad or mom putting his new bike together. The fab area was of interest, because this was for the no-spec-is-too-small satellite biz. As informative as having the important key references, this type of observation lends an entirely new and interesting physical perspective to the technology. ^{1, 3} Basically a crystal can be made for every stability need. Due to their incomparable cost/performance relationships, crystals have comfortably remained in use for many of the same critical functions they have always held, despite the introduction of many new technologies in communications.

Robert Howald is a staff engineer in the transmission network systems group at General Instrument in Hatboro, PA. He has a BSEE and an MSEE from Villanova University, and received his PhD from Drexel University. He can be reached at rhowald@gi.com.

Vendor List

Abracon Corp. 125 Columbia Aliso Viejo, CA 92656 714.448.7070 Ardin Frequency Control Inc. 150 Paularino Ave., Suite 166 Costa Mesa, CA 92626 714.437.9377 Bliley Electric Co. 2545 W. Grandview Blvd. P.O. Box 3428 Erie, PA 16508-0428 814.838.3571 C-Mac Quartz Crystals Inc. 4709 Creekstone Dr. Durham, NC 27703-8411 919.941.0430 Cardinal Components Inc. Wayne Interchange Plaza II 155 Route 46 West Wayne, New Jersey 07470 973.785.1333 Champion Technologies, Inc. 2553 North Edgington St. Franklin Park, IL 60131 847.451.1000 Colorado Crystal Corp. 2302 W. 8th St. Loveland, CO 80537 970.667.9248 Connor-Winfield Corp. 2111 Comprehensive Dr. Aurora, IL 60505 630.851.4722 CTS Frequency Controls 40 Reimann Ave. Sandwich, IL 60548 815.786.8411 Ecliptek Corp. 3545 Cadillac Ave. Costa Mesa, California 92626-1401 714.433.1200 ECS Inc. International 1105 South Ridgeview Olathe, KS 66062 613.782.7787 Epson America Inc. 20770 Madrona Ave. P.O. Box 3842 Torrance, CA 90509 310.787.6300 FEI Communications Inc. 55 Charles Lindbergh Blvd. Mitchel Field, NY 11553 516.794.4500 Fordahl 65 Northcrest Dr. Newnan, GA 770.253.2088 Fox Electronics Inc. 5570 Enterprise Pkwy Fort Meyers, FL 33905 941.693.0099 Frequency Management 15302 Bolsa Chica St. Huntington Beach, CA 92649 800.800.9825 Hybrids International Ltd. 707 N. Lindenwood Dr. Olathe, KS 66062 913.764.6400 International Crystal Manufacturing Co., Inc. 10 North Lee P.O. Box 26330 Oklahoma City, OK 73126-0330 800.725.1426 Isotemp Research Inc. P.O. Box 3389 Charlottesville, VA 22903 804.295.3101 Jan Crystals Co. 2341 Crystal Dr. P.O. Box 60017 Fort Meyers, FL 33906-6017 800.526.9825 KDS America 10901 Granada Ln. Overland Park, KS 66211 913.491.6825 McCoy Ovenaire 100 Watts St., P.O. Box B Mt. Holly Springs, PA 17065 717.486.3411 M-Tron Industries Inc. P.O. Box 630 100 Douglas Ave. Yankton, SD 57078 800.762.8800, ex. 176

MF Electronics Corp. 10 Commerce Dr. New Rochelle, NY 10801 914.576.6570 Micro Crystal, Div. of ETA 41.32.655.7213 Mini-Circuits P.O. Box 350166 Brooklyn, NY 11235-0003 718.934.4500 Monitor Products 502 Via Del Monte Oceanside, CA 92054 619.433.4510 Murata 2200 Lake Park Drive Smyrna, GA 30080 800.831.9172 NEL Frequency Controls Inc. 357 Beloit Street, Burlington, WI 53105-0457 414.763.3591 Oak Technology Inc. 139 Kifer Ct. Sunnyvale, CA 94089 408.737.0888 Oscillatek Inc. 620 North Lindenwood Dr. Olathe, KS 66062 913.829.1777 Piezo Crystal Company 100 K St. Carlisle, PA 17013 717.249.2151 Piezo Technology Inc. 2525 Shader Rd. Orlando, FL 32804 407.298.2000 Q-Tech Corp. 10150 W. Jefferson Blvd. Culver City, CA 90232 310.836.7900 Raltron Electronics 2315 NW 107th Ave. Miami, FL 33172 305.593.6033 Reeves-Hoffman 400 W. North St. Carlisle, PA 17013 717.243.5929 RXD Inc. 806 Custer Ave. Norfolk, VA 68701 402.379.0112 Saronix 151 Laura Ln. Palo Alto, CA 94303 415.855.6887 Siward International Inc. One Gatehall Dr., Plaza Level Parsippany, NJ 07054 973.898.1234 Stanford Research Systems 1290-D Reamwood Ave. Sunnyvale, CA 94089 408.744.9040 Tellurian Technologies Inc. 1801 Hicks Road, Suite B Rolling Meadows, IL 60008 847-934-4141 Toyocom USA Inc. 617 E. Golf Rd. Suite 112 Arlington Heights, IL 60005 800.869.6266 Trak Microwave Corp. 4726 Eisenhower Blvd. Tampa, FL 33634 813.884.1411, ex.208 Valpey-Fisher Corp. 75 South St. Hopkinton, MA 01748 508.435.6831, ex.235 Vectron Laboratories Inc. 166 Glover Ave. Norwalk, CT 06856 203.853.4433 Vectron Technologies Inc. 267 Lowell Rd. Hudson, NH 03051 603.577.6721 Verticom 2330 Circadian Way Santa Rosa 707.570.3315 Wenzel Associates Inc. 1005 La Posada Dr. Austin, TX USA 78752 512.450.1400