Quartz Crystal Resonators and Oscillators For Frequency Control and Timing Applications - A Tutorial (Part 1)

Quartz   Crystal   Resonators   and Oscillators

For Frequency Control and Timing Applications - A Tutorial

                      November 2008

Electronics Applications of Quartz Crystals

Navigation

Precise time is essential to precise navigation. Historically, navigation has been a principal motivator in man's search for better clocks. Even in ancient times, one

could measure latitude by observing the stars' positions. However, to determine

longitude, the problem became one of timing. Since the earth makes one revolution in 24 hours, one can determine longitude form the time difference between local time (which was determined from the sun's position) and the time at the Greenwich

meridian (which was determined by a clock):

Longitude in degrees = (360 degrees/24 hours) x t in hours.

In 1714, the British government offered a reward of 20,000 pounds to the first

person to produce a clock that allowed the determination of a ship's longitude to 30 nautical miles at the end of a six week voyage (i.e., a clock accuracy of three

seconds per day). The Englishman John Harrison won the competition in 1735 for his chronometer invention.

Today's electronic navigation systems still require ever greater accuracies. As

electromagnetic waves travel 300 meters per microsecond, e.g., if a vessel's timing was in error by one millisecond, a navigational error of 300 kilometers would result. In the Global Positioning System (GPS), atomic clocks in the satellites and quartz oscillators in the receivers provide nanosecond-level accuracies. The resulting

(worldwide) navigational accuracies are about ten meters (see chapter 8 for further details about GPS).

Navigation

Precise time is essential to precise navigation. Historically, navigation has been a principal motivator in man's search for better clocks. Even in ancient times, one

could measure latitude by observing the stars' positions. However, to determine

longitude, the problem became one of timing. Since the earth makes one revolution in 24 hours, one can determine longitude form the time difference between local time (which was determined from the sun's position) and the time at the Greenwich

meridian (which was determined by a clock):

Longitude in degrees = (360 d

Commercial Two-way Radio

Historically, as the number of users of commercial two-way radios

have grown, channel spacings have been narrowed, and higher-

frequency spectra have had to be allocated to accommodate the

demand.  Narrower channel spacings and higher operating frequencies   necessitate tighter frequency tolerances for both the transmitters and the receivers.  In 1940, when only a few thousand commercial broadcast

transmitters were in use, a 500 ppm tolerance was adequate.  Today, the oscillators in the many millions of cellular telephones (which operate at    frequency bands above 800 MHz) must maintain a frequency tolerance    of 2.5 ppm and better.  The 896-901 MHz and 935-940 MHz mobile radio bands require frequency tolerances of 0.1 ppm at the base station and     1.5 ppm at the mobile station.

The need to accommodate more users will continue to require higher and higher frequency accuracies.  For example, a NASA concept for a  personal satellite communication system would use walkie-talkie-like

hand-held terminals, a 30 GHz uplink, a 20 GHz downlink, and a 10 kHz channel spacing.  The terminals' frequency accuracy requirement is a     few parts in 10 8.

Digital Processing of Analog Signals

Digital Network Synchronization

•   Synchronization plays a critical role in digital telecommunication systems.    It ensures that information transfer is performed with minimal buffer overflow or underflow events, i.e., with an acceptable level of "slips."  Slips cause

problems, e.g., missing lines in FAX transmission, clicks in voice transmission, loss of  encryption key in secure voice transmission, and data retransmission.

•  In AT&T's network, for example, timing is distributed down a hierarchy of   nodes. A timing source-receiver relationship is established between pairs of    nodes containing clocks.  The clocks are of four types, in four "stratum levels."

Phase Noise in PLL and PSK Systems

The phase noise of oscillators can lead to erroneous detection of  phase transitions, i.e., to bit errors, when phase shift keyed (PSK) digital modulation is used.  In digital communications, for example, where       8- phase PSK is used, the maximum phase tolerance is ±22.5o, of which

±7.5o is the typical allowable carrier noise contribution.  Due to the

statistical nature of phase deviations, if the RMS phase deviation is 1.5o, for example, the probability of exceeding the ±7.5o phase deviation is

6 X 10-7 , which can result in a bit error rate that is significant in some applications.

Shock and vibration can produce large phase deviations even in  "low noise" oscillators.  Moreover, when the frequency of an oscillator is multiplied by N, the phase deviations are also multiplied by N.  For

example, a phase deviation of 10-3  radian at 10 MHz becomes 1 radian at 10 GHz.  Such large phase excursions can be catastrophic to the

performance of systems, e.g., of those which rely on phase locked loops (PLL) or phase shift keying (PSK).  Low noise, acceleration insensitive    oscillators are essential in such applications.

Crystal Oscillator

Oscillation

• At the frequency of oscillation, the closed loop phase shift = 2nπ .

• When initially energized, the only signal in the circuit is

noise. That component of noise, the frequency of which    satisfies the phase condition for oscillation, is propagated around the loop with increasing amplitude.  The rate of

increase depends on the excess; i.e., small-signal, loop gain and on the BW of the crystal in the network.

• The amplitude continues to increase until the amplifier gain is reduced either by nonlinearities of the active elements     ("self limiting") or by some automatic level control.

• At steady state, the closed-loop gain = 1.

Oscillation and Stability

• If a phase perturbation Δφ occurs, the frequency must shift Δf to maintain the 2nπ  phase condition, where Δf/f=-Δφ/2QL for a series-resonance oscillator,    and QL is loaded Q of the crystal in the network.  The "phase slope," dφ/df

is proportional to QL   in the vicinity of the series resonance frequency (also see "Equivalent Circuit" and "Frequency vs. Reactance" in Chapt. 3).

•  Most oscillators operate at "parallel resonance," where the reactance vs.  frequency slope, dX/df, i.e., the "stiffness," is inversely proportional to C1, the motional capacitance of the crystal unit.

• For maximum frequency stability with respect to phase (or reactance)

perturbations in the oscillator loop, the phase slope (or reactance slope) must be maximum, i.e., C1 should be minimum and QL should be maximum.  A

quartz crystal unit's high Q and high stiffness makes it the primary frequency (and frequency stability) determining element in oscillators.

Tunability and Stability

Making an oscillator tunable over a wide frequency range degrades its stability because making an oscillator susceptible to intentional tuning also  makes it susceptible to factors that result in unintentional tuning.  The

wider the tuning range, the more difficult it is to maintain a high stability. For example, if an OCXO is designed to have a short term stability of

1 x 10-12  for some averaging time and a tunability of 1 x 10-7 , then the

crystal's load reactance must be stable to 1 x 10-5   for that averaging time. Achieving such stability is difficult because the load reactance is affected   by stray capacitances and inductances, by the stability of the varactor's

capacitance vs. voltage characteristic, and by the stability of the voltage on the varactor.  Moreover, the 1 x 10-5   load reactance stability must be maintained not only under benign conditions, but also under changing

environmental conditions (temperature, vibration, radiation, etc.).

Whereas a high stability, ovenized 10 MHz voltage controlled

oscillator may have a frequency adjustment range of  5 x 10-7 and an

aging rate of  2 x 10-8   per year, a wide tuning range 10 MHz VCXO may have a tuning range of 50 ppm and an aging rate of 2 ppm per year.

Oscillator Acronyms

Most Commonly Used:

• XO…………..Crystal Oscillator

• VCXO………Voltage Controlled Crystal Oscillator

•  OCXO………Oven Controlled Crystal Oscillator

• TCXO………Temperature Compensated Crystal Oscillator

Others:

•  TCVCXO..…Temperature Compensated/Voltage Controlled Crystal Oscillator

•  OCVCXO.….Oven Controlled/Voltage Controlled Crystal Oscillator

•  MCXO………Microcomputer Compensated Crystal Oscillator

•  RbXO……….Rubidium-Crystal Oscillator

Crystal Oscillator Categories

The three categories, based on the method of dealing with the crystal unit's frequency vs. temperature (f vs. T) characteristic, are:

• XO, crystal oscillator, does not contain means for reducing the crystal's f vs. T characteristic (also called PXO-packaged crystal oscillator).

• TCXO, temperature compensated crystal oscillator, in which, e.g., the

output signal from a temperature sensor (e.g., a thermistor) is used to

generate a correction voltage that is applied to a variable reactance (e.g., a varactor) in the crystal network.  The reactance variations compensate for   the crystal's f vs. T characteristic.  Analog TCXO's can provide about a 20X improvement over the crystal's f vs. T variation.

•  OCXO, oven controlled crystal oscillator, in which the crystal and other    temperature sensitive components are in a stable oven which is adjusted to the temperature where the crystal's f vs. T has zero slope. OCXO's can

provide a >1000X improvement over the crystal's f vs. T variation.

Crystal Oscillator Categories

Hierarchy of Oscillators

*   Sizes range from <1cm3 for clock oscillators to > 30 liters for Cs standards Costs range from <$1 for clock oscillators to > $50,000 for Cs standards.

**  Including environmental effects (e.g., -40oC to +75oC) and one year of aging.

Oscillator Circuit Types

Of the numerous oscillator circuit types, three of the more common ones, the Pierce, the Colpitts and the Clapp, consist of the same circuit except that the rf ground points are at different locations.  The   Butler and modified Butler are also similar to each other; in each, the emitter current is the crystal

current. The gate oscillator is a Pierce-type that uses a logic gate plus a resistor in place of the transistor in the Pierce oscillator.  (Some gate oscillators use more than one gate).

OCXO Block Diagram