"Strip" vs. Conventional Crystals: Why the Use of "Strips" Should Be Carefully Considered

By: Louis Bradshaw, Technical Support Engineer, Fox Electronics

Published in the November issue of Microwaves & RF

Introduction and History
The terms "strip resonator," "AT strip resonator," and "BT strip resonator" are commonly used to describe low profile, surface mount crystal units. The words "strip" and "resonator" imply that they are fundamentally different from conventional crystal units. However, there are no such differences; the term "resonator" could be used equally well to describe a conventional circular quartz plate crystal. A "resonator" is simply "an apparatus or system, as a piezoelectric crystal or a circuit, capable of being put into oscillation by oscillations in another system" (Webster's New World Dictionary, Third College Edition, 1986). The word "strip" does imply a rectangular shape, but since many surface mount crystal packages house a square resonator plate, in this discussion we will use the term "quadrangular," instead of "square" and "rectangular."

In 1880 the Currie brothers demonstrated the existence of piezoelectricity in experiments conducted using quadrangular plates cut from various types of crystals. While the reason for their use of quadrangular plates is not (to my knowledge) recorded, one assumes that it was a matter of simple expediency.

The discovery that piezoelectric resonators could control the frequency of an oscillator created a market for crystal units, at first composed primarily of amateur radio operators. As the benefits of crystal control became more widely appreciated, commercial radio stations converted their equipment, and the market expanded rapidly. In the first years of crystal unit manufacture, nearly all commercial units were fabricated using quadrangular plates, because of the relative ease of shaping such plates.

The use of quadrangular plates continued with the adoption of crystal control by the military, well into the middle of World War II. Many of the plates in both military and commercial use were large-one inch per side or larger. During the war years, the increase in demand for crystal units made quartz an increasingly valuable commodity; the need for more efficient utilization drove the development of alternate (smaller) plate designs. The use of quadrangular plates, nonetheless, continued into the early 1960s, particularly in "ham" radio applications.

The crystal industry has now seemingly come full circle: driven by the ever-expanding demand for smaller size packages in surface mount devices, quadrangular plates have returned to the market. Despite improvements in technology, quadrangular plates still present troublesome characteristics that challenge today's manufacturers as they challenged those of yesteryear. Most of today's demand is for the higher-frequency "AT-" and "BT-" cut crystals; thus we will limit our discussion to those, with emphasis on AT-cut crystals.

Orientation
Figure 1.0 represents the top view of a cultured (man-made) quartz stone. The Y-axis is the mechanical axis, extending from end to end as shown. Y-cut plates are cut from the stone in such a way that the thickness dimension is parallel to the Y-axis. The frequency of Y-cut plates is primarily determined by their thickness. However, Y-cut plates exhibit undesirable characteristics making them unsuitable for commercial use, so most plates used today are cut with a slightly rotated angle, resulting in plates with more desirable, reproducible attributes (most importantly in frequency stability vs. temperature). The two most common singly rotated Y-cuts are the AT- and BT- cuts, which as can be seen from the figure, are nearly opposite one another in orientation. This difference in orientation results in substantial differences in operating characteristics, as discussed below.

 

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Quadrangular Plates: "Spurious" Frequencies and "Coupled Modes"
Figure 2.0 illustrates the various vibration modes that can be induced in a quartz plate. AT and BT plates vibrate primarily in the thickness shear mode. However, it's important to understand that any quartz plate can be made to vibrate in one or more of the illustrated modes, and even in some combination of two or more. The "other" types of vibration may be induced electrically, mechanically, acoustically, thermally or by some combination of these factors; these induced responses are usually referred to as "coupled" or "unwanted" modes. As a further complication, any singly rotated thickness shear resonator will also vibrate in the face shear mode whenever the thickness shear mode is energized.

 

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The thickness shear frequency response of an AT plate can be described using a three-digit system: the first digit represents the number of half-waves through the thickness of the plate, the second represents the number of loops along the plate's X-axis and the third, the number of loops along the Z-axis. Overtones are always odd numbered multiples of the fundamental, so using this nomenclature, the modes 1,1,1; 3,1,1; 5,1,1; etc., represent the main mode, the third and the fifth harmonic overtones, respectively.

A resonator plate with straight sides and square edges is ideally shaped to reflect waves and facilitate the generation of standing waves. The generation of waves of undesired frequency can cause problems; in the case of thickness-shear plates, "spurious" frequency responses and "coupled modes" are of particular note.

For a quadrangular AT-cut plate, the equation for the approximate frequency is:

 

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where m, n, and p are integers, r is the density of quartz (2.65), T is the thickness, L the length, and W the width of the plate in centimeters; and C66, C11, and C55 are the elastic constants of the quartz in the X, Y, and Z directions, respectively.

In the above equation, if m = n = p = 1, the frequency so noted is the main mode frequency, or the lowest frequency at which the plate would vibrate in the thickness shear mode. In theory, such a plate at the given dimensions would be free of "spurious" responses. However, it is extraordinarily difficult to achieve this condition in using quadrangular plates; they typically display a range of frequencies, described as f 1,3,1 or f 1,3,3 or some other combination of integers. Thus the plate vibrates not only at the main mode, but at several "spurious" frequencies as well. Quadrangular plates tend to exhibit "spurious" frequencies of large amplitude, and their "spurious" frequencies tend to be close to the main mode, making these "spurious" frequencies particularly problematic. [Note: the use of the word "spurious" to describe frequencies other than the fundamental dates to the early years of crystal unit manufacture. When strong vibrations were observed at frequencies where it was thought they couldn't or shouldn't exist, the word "spurious" was employed for lack of a better term. It is now known that these frequencies are naturally occurring and predictable thickness shear frequency responses that are in no way "spurious." Nonetheless, the term is still in wide use and probably will continue to be so for some time; in this discussion, we will continue to enclose the term in quotes.]

The amplitude and separation (from the main mode) of "spurious" frequency responses can to some extent be controlled by careful selection of plate dimensions and/or by beveling the plate edges. However, in general, the use of a circular quartz plate with circular electrodes makes the separation and suppression of "spurious" responses much more straightforward. The use of a round blank eliminates one of the variables from the frequency equation; the approximate frequency is derived by:

 

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in which all terms except D (the diameter of the plate in centimeters) are as in equation 1. In addition, the use of round plates eliminates the straight sides of quadrangular plates, which tend to intensify the amplitude of "spurious" frequencies. Thus, even the use though of round plates doesn't eliminate "spurious" responses entirely, they are usually small in amplitude and not as troublesome.

It should be noted that both equations yield only approximate frequencies, in part because plates are not infinite. They do, however, make it possible to estimate the frequency of "spurious" responses and, more importantly, their separation from the main mode. Careful selection of the electrode diameter and the amount of metal used allow, to some extent, for the control and suppression of "spurious" responses.

In addition to "spurious" frequency responses, quadrangular plates are also likely to have other vibration modes energized at frequencies near or identical to the main or desired mode. The frequencies of these "coupled modes" are functions of the lateral plate dimensions; thus the dimensions of the plate to be used must be carefully selected to minimize or eliminate "coupled modes." Often changes of only a few kHz require significant changes in dimensions. During WWII, elaborate tables of "safe" dimensions vs. frequency were developed and remained in common use for years thereafter.

Temperature Dependence of Frequency and Motional Parameters
Up to this point, we have only considered the performance of quadrangular vs. circular plates at a specific temperature, +25� C. The crystal's elastic constants change with variation in temperature, resulting in new frequency responses. These affect not only the thickness shear response, but also any other energized vibration. Just as the thickness shear will energize at odd integer multiples of its fundamental frequency, so will the other vibration modes. Typically, the temperature-induced frequency shifts in the "other" modes are quite large, on the order of hundreds of parts per million per degree C. Thus, a coupled mode interfering with the main mode response may be the nth overtone of the face shear, or some other, response.

As noted above, coupled modes are easily induced in quadrangular plates. Although the amplitude of these responses is normally suppressed enough to avoid gross perturbations, the presence of any coupled mode will perturb the fundamental response, if only slightly. In addition, certain demands for frequency deviation over specific temperature ranges simply cannot be met using quadrangular plates. If the application demands purity of frequency or precise frequency deviation over a specific temperature range, the use of a quadrangular plate must be carefully evaluated.

Comparison of Motional Parameters
The operation of a quartz crystal is frequently explained using the familiar "Equivalent Circuit," illustrated in Figure 3.0.

 

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The crystal in question is assumed to be vibrating at a specific frequency and order of overtone and free of coupled modes. The capacitance labeled "C0" is a real capacitance, comprising the capacitance between the electrodes and the stray capacitance associated with the mounting structure; it is also known as the "shunt" or "static" capacitance, and represents the crystal in a non-operational, or static, state. The other components represent the crystal in an operational, or motional state: "L1," "C1," and "R1" identify the "motional inductance," the "motional capacitance," and the "motional resistance," respectively. The motional inductance represents the vibrating mass of the quartz plate while the motional capacitance represents the elasticity or stiffness of the plate. The motional resistance, often simply called the "resistance," represents the bulk losses due to friction within the vibrating plate and the losses that can occur through stress at the mounting points.

As represented by the Equivalent Circuit, the frequency of an operating crystal can be found by:

 

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where L1 is the motional inductance in mH, C1 is the motional capacitance in pF, and f is the frequency in MHz.

The motional inductance and the motional capacitance depend on one another-a change in the value of one results in a change in the value of the other, provided the frequency remains constant. Changes in either of the two nearly always result in a change in the resistance, though this is not a hard and fast rule.

When dealing with a plano-plano (flat) plate, the electroded area must be varied in order to vary the values of the motional capacitance and inductance. If the electroded area is increased, the static and motional capacitances both increase, the motional inductance decreases, and typically, the resistance decreases. An increase in the motional capacitance results in increased pullability and a less stable crystal. Conversely, if the electroded area is decreased, the static and motional capacitances both decrease, the motional inductance increases, and (usually) the resistance increases, if only slightly. An increase in motional inductance results in decreased pullability and thus a more stable crystal.

Conventional crystal units (such as those packaged in the HC-49/U holder) typically use a circular quartz resonator plate equipped with circular electrodes. The electrodes are applied to the surface of the quartz plate using metal deposition under vacuum. Proper placement is ensured through the use of masks that cover all of the plate except the area to be electroded. The masks are usually made of three parts: a center part with nests for the plate, and upper and lower parts that provide the apertures for the electrode. When making such masks, it is easy to change the aperture that determines the electrode's size; thus a wide variety of electrode sizes can be applied to a resonator plate of specific diameter. As noted above, the size of the electroded area determines the crystal's motional parameters, and it is thus possible to specify those parameters to fit the part to a specific application.

For example, for an application requiring a crystal with high pullability, it is simple to apply electrodes that result in such a resonator. Conversely, if pullability is to be avoided, electrodes that avoid this condition can be easily designed. If the electrode required by the application is as large as or even larger than the resonator plate, one can often use a somewhat larger plate in the specified holder.

While it is theoretically possible to apply the same design and manufacturing techniques to strip resonators, it is much less practical to do so. Quadrangular resonators are manufactured in extremely large quantities to meet the high demand; standardization is critical to efficient productivity. The quadrangular masks used in the deposition of quadrangular electrodes are difficult to fabricate, so it is unlikely that manufacturers will be willing to customize them to any great extent.

Moreover, the degree of customization is sharply limited by the limitations of quadrangular plates: those placed on the dimensions of the plate by the holder/package, and those necessitated by avoiding coupled modes. The limitations on the dimensions of the electrodes and electroded area, in turn, limit the ranges of values for the shunt and motional capacitances and the motional inductance, and ultimately impact the value for the resistance.

Depending on the application, these limitations may not be significant. In many cases, the values of motional parameters for quadrangular plates compare quite favorably with those for conventional circular crystal units. Table 1 compares the parameters at a frequency of 20.000MHz for a circular resonator housed in the familiar Fox Electronics HC49U holder and a "strip" resonator housed in the Fox Electronics HC49S.

 

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It must be remembered that both parts are mass produced and intended for the mass market in microprocessors; however, such parts are often employed in more demanding applications. Some significant differences exist; it is particularly interesting to note that the increased motional inductance observed in the HC49S ("strip" resonator) is more than enough to offset the increased resistance, and results in a higher "Q" value than that of the HC49U.

Comparison of "AT-cut" vs. "BT-cut" Resonators
Because the AT- and BT- cuts are made at different angles through the quartz stone, they differ in their operating characteristics. The most noticeable difference is that at a given frequency, a BT plate will be about 1.5 times the thickness of an AT plate. In the example above, to generate a crystal operating at 20.000MHz, an AT plate would be about 0.083mm thick, while a BT plate would be about 0.128mm thick. Thus a crystal with a higher fundamental mode frequency can be made using a BT-cut plate. If the plate thickness is arbitrarily limited, for example to 0.05mm, an AT-cut plate will oscillate at 33.200MHz while a BT-cut plate will oscillate at 51.200MHz.

The other significant operating difference is that the AT exhibits a cubic change in frequency vs. temperature change, while the BT exhibits a parabolic change in frequency vs. temperature change. Over a wide enough temperature range, the AT-cut plate will exhibit three points at which the change in frequency vs. change in temperature is zero, or nearly so; casino the BT will exhibit only one (usually room temperature). Thus, over the usual commercial temperature ranges, the AT is capable of holding much tighter frequency deviation than the BT.

Small differences in motional parameter values at a given frequency are also observed between the AT and BT; however, these are usually not operationally significant.

Conclusions
We have shown that potentially significant differences exist in the values of motional parameters between conventional circular crystal units and surface mount (i.e., "strip" resonator) devices. The severe limitations in design and manufacture of quadrangular plates, imposed by their tendency to support "spurious" frequency responses and coupled modes, make it extremely difficult for them to be customized for specific applications. These difficulties are particularly apparent when the plate must conform to stringent operating characteristics over wide temperature ranges.

This discussion should not be taken to discourage the use of quadrangular plates under any circumstances; their economy, based on mass production, make them an attractive alternative for many applications. It should be emphasized, however, that the simple replacement of a tried and true conventional resonator with a quadrangular resonator must be approached with extreme caution, even when both operate at the same frequency. The detailed evaluation typically brought to bear on the initial selection of a crystal unit should apply to any change in resonator configuration.