Timing is a critical part of almost every electronic application. Communication and data transfer generally requires a reference signal or source that enables system synchronization and signal generation. At the heart of most reference sources is the oscillator.
A specific type of oscillator is the VCXO, or voltage-controlled crystal oscillator. The VCXO introduces to the system a mechanism to adjust an oscillator output frequency as a function of an input control signal. The VCXO functions as part of a larger closed-loop system, serving as a frequency tracking mechanism from external sources. An error signal in the form of a control voltage is typically generated by the system as part of the demodulation process.
A problem can arise when the quartz crystal frequency is changed by the VCXO. Non-monotonic behavior in the control voltage characteristic causes the larger system to become unstable. This can lead to total system failure. System failure can occur when the physical crystal design parameters inadvertently create a situation where there is coupling between the electrical harmonic of the gain element and the mechanical third harmonic of the crystal.
This is insidious in nature since the third overtone parameters of a quartz crystal are not generally specified for a fundamental mode crystal design. It is important for engineers to understand the relationship between physical crystal design parameters and the resulting placement in frequency of the crystal’s mechanical third overtone.
The placement of the mechanical third overtone of the crystal will specifically determine if there will be an interaction with the electrical third harmonic of the gain element and subsequently a detrimental impact on the fundamental mode frequency response of the VCXO. With proper placement of the mechanical third overtone, developers can select a robust crystal design that avoids total system failure, resulting in a stable system and a viable end product.
For a general primer on VCXOs and their inherent pull curve response, as well as a discussion of the difference between the electrical third harmonic and the mechanical third overtone, see “VCXO Basics” at www.cypress.com/vxcobasics.
VCXO Design Considerations
Figure 1 shows two VCXO tracking curves operating across three zones consisting of "a", "b" and "c".
Figure 1: VCXO Transfer Function of Voltage vs. Normalized Output Frequency
Of the two curves presented, the red curve operates properly across all three zones and clearly represents an expected response. At first glance, the second curve appears to deviate only in zone"b". In reality, this curve shows inconsistency in all three zones. While "b" is considered to be where real system failure is prone to breakage, the surrounding zones are giving you a big clue leading around zone "b".
About half-way through the "a" zone, the frequency starts to deviate. Why is it that the frequency wants to deviate? What is causing the sharp transition in the "b" zone? To help understand our dilemma let us turn back to the basics of oscillation consisting of gain and phase.
First, too little gain or excessive phase shift results in loss of oscillation, which is not an issue in this case. Remaining possibilities include too much gain, and shift in phase. Can too much gain be detrimental? Yes, especially if there is enough energy present to overcome the natural insertion loss of mechanical overtones!
Subtle changes to the VCXO reactive load CSub>L end up changing the amount of power in the tank where some portions of the sweep may excite mechanical overtone operation. As of now, none of this explains why the fundamental shifts in frequency. In most scenarios, consider the effects of the impedance of the output driver. As mechanical overtone excitation occurs, the power absorbed by the network changes by unexpected amounts, sometimes radically different from that expected by a normal pull. Such change often results in additional phase change impacted by the impedance found in the output driver.
Again, in order to sustain oscillation, the frequency must change more than intended by the shunt capacitors alone. Zone "a" and "c" show weak overtone coupling while zone "b" is showing strong effects of mechanical third-overtone excitation. To clarify this principle, consider the following.
Figure 2 is really "A Tale of Two Overtones", and how they relate to one another.
Figure 2: Fundamental and third Overtone Operational Relationships
The electrical fundamental and third overtone are represented in green. Blue represents the crystal fundamental and mechanical third overtone response. The respective height is different so that we can better visualize what is going on. The width is representative of the pull (or swing) range.
Naturally, the fundamentals both exactly overlap, otherwise oscillation would ease (as shown by the boundary). Now, turn your attention to the effects of the third harmonic, the pull range between the fundamental and third electrical overtone is a 1:1 relationship, but the mechanical third does not behave in a 1:1 relationship! Remember that the ratio reduction is by a motional capacitive factor of 1/N2.
In other words, a crystal running in third overtone is stiffer (more stable) versus that of the fundamental. Another important point to consider is that the placement of the electrical third (f3ce) does not necessarily align to the crystal mechanical third center (f3cm). As discussed earlier, misalignment is due to multi-dimensional effects in the crystalline structure and electrode size.
Figures 3-5 illustrate a VCXO sweep showing overlap effects of the electrical and mechanical third overtones.
Figure 3: VCXO Low-side Pull with no Overlap
Figure 4: Electrical and Mechanical third Overlap
Figure 5: VCXO High-side Pull with no Overlap
Each illustration is mapped to the respective VCXO operating zone shown in Figure 1. During the normal course of operation through "a", (Figure 3) everything proceeds normal until f3 begins to close the gap on f3m, or in other words as Δf approaches 0, the VCXO frequency response begins to deviate from the expected ideal response.
As the VCXO enters zone "b", an unexpected sharp frequency transition occurs. That is, as f3) passes through the f3m zone, third-overtone coupling takes effect between the electrical and mechanical third. Continuing the VCXO pull transition into zone "c", f3 breaks away from f3m as the VCXO frequency response once again attempts to regain the expected response. In selection of the crystal intended for a VCXO application (and not just something you find on the shelf that meets the fundamental frequency) placement of the mechanical third is important and can be controlled to a certain degree.
Imagine what would happen if the mechanical third is shifted away from the electrical third as shown in Figure 6, or where no overlap between f3ce and f3cm exists.
Figure 6: Non-overlap, Mechanical third low-side Placement
Figure 7: Non-overlap, Mechanical third high-side Placement
Through proper positioning of f3e with respect to f3<>, the electrical third overtone will never overlap the mechanical third. Because no mechanical overtone coupling takes place, the result will be a smooth transition in the VCXO curve with no abrupt frequency transitions, or subtle pulling. In order to meet these operating conditions, two choices exist for the VCXO designer either one of which involves placement of f3m excitation range either below or above f3e.
Depending on placement, certain rules apply as to recommend minimum separation. This is important to combat process variation and temperature related effects. In cases where f3m is placed below f3e, a minimum separation (worst-case for VCXO maximum negative pull) is on the order of one times the VCXO total pull range stipulated as Δf3sepLO. On the flip side, if f3m is placed above f3e, then the minimum separation (worst-case for VCXO maximum positive pull) is on the order of two times the VCXO total pull range designated as Δf3sepHI.
General Crystal Specification Suggestions
The fundamental goal in specification and selection of a crystal for proper VCXO operation is in the ability to specify a pull range no greater than necessary in order to meet the needs of the pull range and to ensure that electrical and mechanical modes never overlap. The key is in specifying the minimum amount of motional capacitance C1 which meets the needs of a programmable CL to satisfy minimum and maximum system specific part-per-million pull range.
The crystal electrode size plays three pivotal roles. First, the size dictates the value of motional capacitance C1. Second the determination of C1 sets the position for the mechanical third with respect to the electrical third. Third, due to the reduced or increased area, the amount of network energy transfer through the piezoelectric structure is affected (remember the problem of too much power). A larger electrode size increases effective power to the crystal.
Use of the term “pullable crystal” is generally indicative of an intrinsic motional capacitance C1 that runs in the range of 25 to 30 fF; greater C1 leads to greater pullability, which also leads to a lower C0/C1 ratio. Such a range most typically leads to a crystal that exhibits an undesirable mechanical third that appears above the electrical third. In this case, as the maximum positive PPM offset is reached the gain present in the amplifier (-R) actually increases due to a smaller C1 value.
In such a situation, with a high amplifier gain present, small noise perturbations may be just enough for the network to allow the start of energy injection in the region of the mechanical third. In addition, since the electrode size is larger, more energy that is undesirable maybe transferred into the crystalline structure further eroding the possibility for a stable system.
On the other hand, reducing C1 to function around the range of 18 fF ±20% generally leads to a mechanical third that appears below the electrical third. The benefit of this design is to reduce network gain as the maximum negative PPM is reached due to a larger CL value. In addition, the smaller electrode size contributes to less energy absorption further helping to maintain a well-behaved system.
Design of a VCXO appears almost trivial until loss of lock occurs in the system. Casual observation of the VCXO would indicate a fully functional response. Only under careful observation over different operating parameters (including temperature) can the VCXO be ruled out as a possible troublemaker. This article should help the user understand core oscillator operating principles and the specifics on crystal operational modes. Through proper use of the concepts and principles discussed, better crystal specification and screening guides for stable VCXO operation may begin. The principles outlined in this paper provide the VCXO system designer greater insight as to the potential pitfalls of VCXO design seldom found in clocking literature.
About The Authors
David Green is Department Manager for Advanced Technology Business Development for the Consumer and Computation Division of Cypress Semiconductor Corp., Cypress Semiconductor Corp. and can be reached at firstname.lastname@example.org. Anthony M. Scalpi is an Applications Engineer Senior Staff in Cypress Semiconductor’s Consumer and Computation Division. He is a graduate of Manhattan College and can be reached at email@example.com.