Introduction
From the early days of navigational instruments to today's supercomputers, the challenge of timekeeping and synchronizing remote nodes occupies engineers. Timekeeping is a trivial task today, but as the universe of electronic applications expands, such synchronization remains a persistent challenge, whether the distance is thousands of miles or hundreds of microns. From simple garage door openers to elaborate celestial navigation systems, every electronic device requires synchronization. And the component which enables that is a frequency source which provides the primary timing signal to facilitate communication among ICs, PC boards, and eventually systems.

From the few $10,000/unit hydrogen maser oscillators whose accuracy is essential to radio astronomy, to ceramic resonators whose low cost is necessary for the proliferation of electronic devices, the universe of frequency sources is as broad as the applications that need them. However, as diverse and expansive the landscape is, it's reasonable to say that today's mainstream electronics utilize only three categories of frequency sources: ceramic resonators, CMOS resonators and quartz-based crystal resonators.

As mentioned, of the three product categories ceramic resonators represent the lowest cost point. They are used extensively as microcontroller clocks, where the timing accuracy requirements are more relaxed than most applications. Ceramic resonators are built on piezoelectric substrates with two electrodes on top and bottom of the substrate, causing it to vibrate periodically under an electrical field. The typical accuracy of a ceramic resonator ranges from +0.05% to +1.0%, with a temperature variation of greater than +5 ppm/°C (Reference 1).

CMOS resonators, which are open-loop solid-state circuit oscillators, are the most reliable of the three categories of frequency sources. They are built using well-studied semiconductor processes that have been characterized extensively through years of high volume manufacturing. Unlike most other types of frequency sources, CMOS resonators don't rely on a mechanically moving element to generate clock signals, but instead depend on self-sustaining circuit design and mobile electrons.

Of the three categories of frequency sources, however, the most popular are quartz-based crystal resonators. While far from an ideal solution, quartz crystals are the most acceptable option today, even as the industry continues to seek alternatives to overcome their limitations in size, frequency and scalability.

Quartz crystal resonators
Quartz crystal resonators have been used extensively for decades due to the remarkable frequency stability of quartz. These piezoelectric materials expand and stretch their lattice structure when subject to a surface charge. Commercial quartz oscillators take advantage of this property by applying an electrical field to generate a periodic movement in pre-defined axes (Figure 1).

(Click to enlarge)
Figure 1: Crystal equivalent circuit and resultant frequency

With a steady growth for decades, over 10 billion crystals and oscillators are produced worldwide each year now. While the make-up of electronic devices underwent significant transformation over that time--from tubes to transistors, and from analog to digital processing--dependence on quartz crystals as frequency generators remained virtually unchanged, due to refinements in the utilization of the material properties of quartz crystals (Reference 2).

"Fundamental mode" crystals, which operate up to around 100 MHz, can be manufactured in volume at acceptable costs. "Fundamental mode" refers to those used with an amplifier circuit tuned to sustain the oscillation at the crystal's fundamental harmonic as opposed to a 3rd, 5th or higher-order overtone harmonic (Reference 3). The accompanying amplifier circuit commonly resides in the ASIC, μC, or ASSP, and connects the crystal resonator to the internal clock-generation tree of the ASIC. While appropriate for early communication standards, this practical upper limit of quartz proves insufficient to meet the bandwidth demand for today's ubiquitous interface standards.

One method of increasing the maximum "fundamental mode" frequency obtained from a crystal wafer is grinding it to a thinner profile. Although this process increases manufacturing cost, reduces yield, and brings about reliability issues, it is nevertheless used to produce oscillators that can fit into small packages required by today's portable electronic devices. Unfortunately, grinding resonators to thinner profiles makes them more fragile physically. Additionally, a thinner profile increases the proportional impact of surface contamination and leads to higher frequency instability due to varying environmental conditions (Reference 4). A derivative crystal product addresses the need:

Quartz crystal oscillators
As mentioned, a solution to the frequency limitation of quartz is to force the resonator to oscillate at a higher-order harmonic than its natural center frequency. Third- and fifth-order crystals are common. As the names imply, these devices oscillate at the 3rd or 5th multiples of the fundamental harmonic (that is, the natural center frequency). They extend the frequency limit of crystals to greater than 100 MHz.

These devices usually contain multiple components in a package that includes the resonator and a programmable amplifier. The complementary amplifier circuit drives the output of the resonator in the harmonic of interest, while suppressing tones at other harmonics and at the fundamental mode. Although it's possible to design an overtone oscillation circuit on the board, external to the resonator, it's not recommended to overdrive a fundamental mode crystal manually.

One successful alternative to higher-order, and on average higher-priced, crystal oscillators emerged from the PC market in the early '90s. Then, as today, the many crystals needed to run the multiple sub-sections of the motherboard were consolidated into a single crystal resonator and a CMOS PLL IC. The function of the PLL was to multiply up the frequency and distribute it across the board, and hence eliminate the "fundamental mode" limitation of the crystal resonator.

A typical motherboard PLL IC today can distribute over 20 clocks in six different frequency domains ranging from 33 MHz for the PCI interface, to above 400 MHz for the CPU, and uses only a single 14.318 MHz crystal resonator as reference. Today there are also oscillators which combine a crystal resonator with a built-in PLL, and offer high-frequency and programmable outputs in a single package.

Although the crystal-plus-PLL approach addresses the frequency limitation problem effectively, it has only limited application due to performance, cost, and power efficiency concerns. For portable consumer applications, the excessive power consumption and the additional cost of the PLL IC is prohibitive. For storage and communication applications, where high-data-rate digital modulation schemes require accurate time bases, frequency multiplication with a PLL bears a penalty on phase noise and jitter, which are the two key figures of accuracy for clock signals.

Phase noise is the magnitude of energy in dB of a clock signal measured at an offset 'f' in Hz from the carrier. It's commonly measured in units of -dBc/Hz, and is useful for quantifying the spectral purity of the clock signal. While phase noise is a frequency-domain qualifier, period jitter is a time-domain qualifier. Period jitter is the difference between the measured clock period and the ideal clock period. It has been shown that period jitter is correlated to single sideband (SSB) phase noise by the following expression (Reference 5):

(Click to enlarge)

where ω₀ is the fundamental oscillation frequency, (N₀/P₀)_fm is the SSB phase noise at an offset of f_m from carrier, and h(f_m) sets the bandwidth of the system. It can be observed from the expression above that the trigonometric function reduces the close-to-carrier contributions of phase noise to the period jitter.

Conversely, as f_m increases away from the carrier, the trigonometric function increases, and the SSB phase noise contributes more significantly to period jitter. In RF systems, close-to-carrier phase noise is critical because it can lead to down-conversion issues. Just as critical in most consumer and communication applications is far-from carrier phase noise because of the impact of random period jitter in these designs.

The problem with PLL multiplication in the oscillator is that while the output of the PLL tracks the resonator phase noise within the loop bandwidth, it begins to track the phase noise of the PLL's internal VCO at frequencies higher than this bandwidth. Since commonly used ring oscillator VCOs have poor phase noise compared to crystals, frequency multiplication with PLLs may yield poor phase noise where it matters most, far from carrier frequency offsets.

Manufacturers build many different cuts of crystals today. ("Cuts" represent the angle-of-cut of the quartz crystal from a reference plane.) Different cuts of crystals have different modes of motion, and therefore varying degrees of temperature dependency, frequency limitations and manufacturability. A common one is "AT-Cut", which has a cubic curve temperature dependency which can be adjusted and compensated fairly easily for a variety of applications. AT-cut crystals are the most popular in the industry.

A similar but more expensive cut, called "SC-cut" crystals, are worth mentioning because they offer good temperature stability and are preferred over AT-cut crystals in high-accuracy designs. On resonators of similar geometry, SC-cut crystals have better close-in phase noise than AT-cut crystals (References 6 and 7) when operating in fundamental mode.

While clock signals for datacom links have always required excellent phase noise, the increased bandwidth requirements of high-speed serial communication interfaces have expanded the need for low phase noise, along with low period and phase jitter. For improved bit error rate (BER), crystals are preferred due to their good stability and low phase noise, down to -140 dBc/Hz or less, at 1 MHz offset.

Note that the noise spectrum of the frequency source that falls within a certain bandwidth in the frequency-response plot of the receiver PLL ultimately affects the BER of the transmission. While the absolute boundaries of this region depend on the specific design, in most serial links it covers the spectrum where the magnitude response of the loop has considerable gain, and the phase response is non-zero.

VCXO--oscillators for broadcast applications
The need for using ever-higher frequencies is less pronounced in applications that are defined by long-time standards. Most of such applications require established infrastructure that is too costly to change and upgrade frequently. For instance, driven by video broadcast standards, TV and most graphics encode/decode applications use clock frequencies that are easily generated by mainstream crystal resonators. In such devices, one low phase-noise, 27-MHz crystal resonator can be sufficient to generate a multitude of reference clocks for different scan standards from standard to high definition.

A unique property of broadcast applications is the vast distance between the source and destination of the transmission. Since the encoding clock must be extracted from the incoming data-stream, precise synchronization with the source clock is required in video equipment to ensure playback without any frame distortions. The clock domain on a video system is comprised of a pixel clock, a horizontal sync pulse, a vertical sync pulse, a frame/field reference pulse and color burst frequency. In almost all systems, these clock signals are extracted from the incoming signal with the help of a local oscillator.

Since quartz-based crystals depend on the load capacitors across their terminals to determine the oscillation frequency, a type of oscillator called VCXO (voltage controlled crystal oscillator) (Figure 2), which allows for tuning its center frequency by adjusting the effective load, is commonly used in broadcast applications.

(Click to enlarge)
Figure 2: VCXO block diagram

As discussed, crystal oscillators are a combination of the crystal resonator, an amplifier circuit, and load capacitors. The addition of a variable load element to this oscillator circuit allows for shifting the frequency of resonance by adjusting the effective crystal load. The frequency can then be adjusted by applying an external control signal to the variable load element. In the case of a VCXO, the phase shift element is typically a varactor diode and the control signal is a voltage. Given the previous model for crystal, the frequency of a VCXO can be expressed as follows:

(Click to enlarge)

In video applications, a frequency-lock loop changes the control voltage of the local VCXO until synchronization with the received signal is achieved. While the control voltage offsets the center frequency of the crystal, it doesn't affect its accuracy over temperature or supply voltage variations. The VCXO is only as accurate as the quartz crystal resonator it contains. Therefore, the system needs to be designed with appropriate margins.

While optimal for most applications, non-linearity of the varactor response is a problem with VCXOs in some designs, and a new generation of digitally "pullable" VCXOs (DXCO) addresses this problem. They utilize a precision ADC and a digital control loop to compensate for any non-linearities in the tuning slope.

Higher-accuracy requirements
In addition to the loading capacitors that are connected to its external pins, quartz crystals, whether used in a VCXO, or by themselves or in combination with a PLL, change their resonant frequency due to environmental conditions such as temperature, voltage, and vibration, as well as other factors. The amount of variation is specified relative to the frequency of operation in parts-per-million (ppm). A typical consumer-grade, quartz-based, crystal resonator may have approximately 25-100 ppm initial frequency error. The error occurs in the plating process of the quartz wafer due to surface variations in the deposited film thickness. The thickness of the film changes the vibrating mass of the resonator, and thus the resultant center frequency.

As mentioned, crystals are sensitive to variations in temperature. Manufacturers may cut the crystal in an angle that minimizes the temperature variation at nominal room temperatures, but increases significantly at temperature extremes (Figure 3). A mainstream crystal could have total temperature-induced frequency variation of 50-150 ppm over 0-70°C commercial temperature range.

(Click to enlarge)
Figure 3: Typical temperature dependency of a common crystal

Other factors that affect the frequency stability are supply voltage dependency and aging variation. As such, the total frequency deviation from the ideal operating point could vary from 100 to 350 ppm for common crystals (see below). Most commercially available fundamental crystals, higher-order oscillators, and VCXO/DCXOs fall into this accuracy range.

(Click to enlarge)

The budget for frequency error in radio-frequency (RF) systems is significantly less than those in lower-frequency systems, and the frequency variations of most low-cost crystals exceed this budget due to their temperature dependency. A type of crystal oscillator called TCXO (temperature-compensated crystal oscillator) is designed to minimize temperature dependency. TCXOs combine the crystal oscillator circuit with a temperature sensor and a variable reactance element. The output voltage of the temperature sensor is applied to a varactor (or an ADC) and dynamically changes the reactance that the crystal resonator sees.

The circuit can be tuned to compensate for the intrinsic temperature drift of the resonator across the desired range (Figure 4). TCXOs can provide up to 20x improvement over uncompensated oscillators (Reference 6). The primary drawback of mainstream TCXOs is their high price. While they were initially available at high average selling price (ASP) of over $3, the significant size of the wireless market (in particular cell phones) has pushed the prices down to less than $1 in volume.

(Click to enlarge)
Figure 4: TCXOs compensate for the intrinsic temperature variation of crystal resonators

Part 2 of this article concludes with a look at general problems associated with quartz crystals, new approaches, and important trends. Read Part 2 by clicking here.

References
1. J.R. Lichter, "Crystals and Oscillators", JL9113, Rev.B.
2. J.R.Vig, "Introduction to Quartz Frequency Standards", IEEE UFFC tutorial.
3. "Introduction to Fundamental Crystal Oscillators", tutorial, http://hem.passagen.se/communication/txo.html
4. YK Yong, "Resonator Surface Contamination-A cause of Frequency Fluctuations?", IEEE-UFFC, July, 1989.
5. M. McCorquodale "Study and Simulation of CMOS LC Oscillator Phase Noise and Jitter", ISCAS, 2003.
6. J.R. Vig, "Quartz crystal resonators and oscillators-A tutorial", Feb 2005.
7. Ramon M. Cerda, "Impact of ultralow phase noise oscillators on system performance."

About the author

Tunc Cenger, director of product marketing at Mobius Microsystems, has held project lead, marketing and business management positions at Cypress Semiconductor, and most recently at Maxim where he was business manager for audio products. He holds a BSEE in microelectronics from Istanbul Technical University. Mobius Microsystems, based in Sunnyvale, CA, is a fabless start-up developing all-CMOS oscillators.