Republished from the February, 1998 issue of Wireless Design & Development

by James B. Northcutt, Engineer, Fox Electronics

Quartz crystals can be an excellent choice for the frequency-determining component in wireless communication systems. Designers appreciate the high Q value (quality factor), reasonable cost, and temperature performance of quartz crystals relative to other options, such as inductor-capacitor, ceramic, microstrip and surface acoustic wave resonators. When quartz crystal oscillators are used in wireless designs, multiplication and phase lock loop circuits are often used to extend their practical frequency range across the wireless spectrum.

When specifying crystals for use in oscillators, informed consideration of basic parameters early in the design process is important. These parameters become critical when developing voltage controlled crystal oscillators (VCXOs) and temperature compensated crystal oscillators (TCXOs), as such fundamental choices set the stage for these devices and affect the success of the resulting designs.

Making the Cut
Quartz is uniquely suited, in terms of mechanical, electrical and chemical properties, for the manufacture of frequency control devices. Quartz crystals are cut from a quartz bar, which is grown in an autoclave. The angle at which the saw blade cuts through the quartz determines many of the electrical properties of the crystal.

The most popular angle of cut for crystals used in wireless applications is the AT cut (see Figure 1). Crystals fabricated in this manner are available at relatively high frequencies, exhibit excellent frequency vs. temperature stability, and come at a moderate cost. Fundamental resonant frequencies from 1MHz to over 1 GHz are possible, but most AT-cut crystals are manufactured to have fundamental frequencies between 1.8 and 40MHz, due to price and other constraints. The resonant modes (overtones) of AT-cut crystals are at roughly odd multiples of the fundamental mode (see Figure 2). Crystals specified for these overtones typically fall in the 24 to 200MHz frequency range.

Important Specification Parameters
When specifying crystals for use in wireless designs, some parameters are of particular importance, including tolerance, stability, temperature range and load capacitance. These parameters require special consideration because they are essential to a sound design and can also impact the manufacturability and cost of the specified crystal.

Tolerance of a crystal refers to the maximum allowable frequency deviation from the target frequency at room temperature, expressed in parts per million (ppm). For example, a 10MHz crystal having a 10ppm frequency tolerance could have an actual resonant frequency response that is higher or lower than 10MHz by as much as 100 Hz (10ppm X 10MHz = 100 Hz). Tolerance default values range from 30 to 50ppm; values below 10ppm are available depending on frequency and holder, at an increased price.

Crystal stability is the allowable frequency error over the operating temperature range referenced to a baseline 25�C reading. The default values are 50ppm to 100ppm, although crystals having stabilities as low as 10ppm are available, depending again on the frequency and package desired.

For a given operating mode, the frequency of a crystal is inversely proportional to its thickness. Higher frequency crystals are thin and more sensitive to the kinds of shock and vibration typically encountered in portable and mobile wireless applications.

Several crystal holders are available to the wireless design engineer. The lowest cost holder with the greatest amount of design flexibility is the HC49U. This resistance welded package is a direct replacement for the older solder-sealed HC-18/U. The HC80U and the FD are also popular holder models.

In addition to the mechanical demands of wireless application environments, designers need to consider the thermal requirements. Most wireless applications require crystals that can operate over the industrial temperature range of -40�C to +85�C. Crystals can also be specified for use over the commercial temperature range (0�C to 70�C) and, with some products, over the military temperature range (-55�C to +105�C).

Load Capacitance
Load capacitance is one of the most overlooked parameters when specifying crystals. In the popular Pierce oscillator circuit, which has a capacitor to ground on either side of the crystal, the load capacitance is equal to the series combination of the two capacitors plus Cstray. (Cstray is the sum of capacitances that are contributed to the circuit by the layout, board material, and the input and output impedance of the active device.)

A good rule of thumb for Cstray is 5pF. If one of the capacitors is replaced with a varactor, the frequency can be "pulled" by applying a tuning voltage on the varactor. This configuration can be the basis for a simple VCXO. If the tuning voltage is derived from a thermistor network, the frequency can be adjusted to null out the effects of temperature. This configuration is an approach for a TCXO. A combination of both features is known as a TCVCXO.

A pullability specification for an HC49U crystal used in a fundamental mode VCXO might have the following form:

CL = 20 to 45pF, pullability = -100ppm max, CL = 20 to 10pF, pullability = +100ppm min.

Smaller crystals have about half the pullability of the HC49U. The pullability of overtone crystals is reduced by 1/n2, where n is the overtone mode (i.e. 1, 3, 5, etc.).

Crystal Modeling
Crystals are often modeled as series R-L-C networks (see Figure 3), which are known as the motional arms of the model. Generally, only the arm representing the frequency of operation is specified and often even this is left to the manufacturer's defaults. In the model, R is called equivalent series resistance (ESR). Motional capacitance, C, represents the elasticity of the quartz; and motional inductance, L, represents the vibrating mass of the crystal unit. The CO, or shunt capacitance, is capacitance formed by the metal electrodes deposited on either side of the quartz blank, plus the strays associated with the holder and leads. CO is generally specified as 7pF maximum.

If an electrode is especially large, it will cause a large motional capacitance in addition to causing a large CO. The larger the motional capacitance, the greater the pullability of the crystal. The converse is true as well. Small motional capacitance, especially on overtones, makes a crystal less sensitive to pulling effects. This can be useful in TCXO and VCXO designs. There are trade-offs, however, between maximizing the motional capacitance and adequately suppressing the spurious responses. A good design must balance these trade-offs in a way that best meets the needs of a particular application.

A common error in specifying crystals is to assume that the motional parameters and oscillator performance will remain the same when board designs are modified to use smaller crystal packages. Whenever a design goes through a "shrink," it is best to re-evaluate the impact on the oscillator design.

Additional Design Considerations
Controlling spurious responses -- unwanted responses that can cause problems such as temperature anomalies, VCXO linearity bumps, etc. -- often is a significant part of the design process. Typically, these unwanted responses should be 6dB down relative to the fundamental and 3dB down relative to the overtone responses. Alternatively, these unwanted responses can be specified in terms of a spur to main mode resistance ratio. For example, 6dB is equivalent to a spur resistance ratio of 2:1 (20 log10 Rspur/ESR). Development cycles for square and rectangular crystals typically take more iterations to achieve adequate spurious rejection.

The drive level is another important element to take into consideration when modeling VCXOs and TCXOs. This is the amount of power the crystal will have to dissipate in a given oscillator circuit. Overdriven crystals tend to age faster and have more and stronger temperature anomalies. The smaller the crystal, the more pronounced these problems become. Most crystal manufacturers recommend a maximum drive level of 100mW.

An undesirable characteristic, but one to which designers must attend, is the aging factor. The aging of a crystal refers to the amount of frequency drift per year at 25�C. Default aging specifications are in the 3 to 5ppm/year range. Specials can be produced at 1ppm/year depending on the frequency and holder. Generally, crystals age the most in their first year of operation.

Design to Test Standards
Environmental and reliability specifications, for the most part, should reference the test procedures and methods outlined in MIL-STD-883 and MIL-STD-202. Some of the procedures include tests for shock, vibration, solvent resistance, terminal strength, gross leaks, fine leaks, low-temperature exposure, high-temperature exposure, thermal cycling, solder heat resistance, and others.

Closing the Loop
This tutorial provides the basis for specifying crystals for VCXO and TCXO designs used in wireless applications. It is possible to over-specify a crystal or specify crystals that cannot be manufactured cost-effectively. Because this is the case, Fox Electronics' Engineering Department routinely offers advice on customer drawings and designs. For more information on-line see ;; and

James B. Northcutt is an Engineer with Fox Electronics, Fort Myers, Florida, a leading supplier of frequency control products.

Because it offers frequency and cost benefits, the AT cut crystal is preferred for use in wireless application
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The overtones of AT-cut crystals fall at roughly odd multiples of the fundamental mode. (Re-published by permission of Intel Corporation; Copyright 1983 Intel Corporation)
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A common modeling series for crystals is the R-L-C network, where R is equivalent series resistance (ESR); L is motional inductance, and C is motional capacitance.