e01b032.PDF

GENERAL INTEREST

Crystals

and Oscillators

when stability counts…

By Owen Bishop

A survey of these essential electronic systems, how they work, and how

they are used. Practical component values are given for each oscillator.

used in various applications. In addi-

tion, there are ceramic materials

such as the PZT ceramics, consisting

of solid solutions of lead, zirconium

and titanium. Another piezo-electric

group comprises polymers such as

polyvinyl chloride and difluorpoly-

ethylene. For these, the piezo-elec-

tric property depends on their pro-

cessing. A thin plastic foil is warmed

and exposed to a strong electric

field, then cooled to room tempera-

ture. This causes polarisation of the

material, which then has piezo-elec-

tric properties.

to C is very much higher that we

could obtain by using real compo-

nents, giving the crystal a very high

Q (quality factor). A crystal may

have Q of up to 100,000. Compare

this with Q of only a few hundred for

a typical LC network.

Crystals can be driven in series

resonance or in parallel resonance .

At the series resonance frequency,

the crystal acts as a capacitor and

inductance in series. The impedance

across the crystal is at a minimum

(equal to R only). At the parallel res-

onance frequency, which is slightly

higher, the crystal acts as an induc-

tor and capacitor in parallel. Its

impedance rises to a maximum at

this frequency. Crystals are usually

cut so as to operate best in one or

other of these modes. Additionally,

they may be cut to operate in funda-

mental mode or harmonic (overtone)

mode. The overtones are the odd

harmonics of the fundamental so

that, for example a crystal cut to

oscillate at 100 kHz will also oscillate

at 300 kHz, 500 kHz, 700 kHz and

higher harmonics.

One of the limitations of crystals

is that a crystal cut to have a high-

frequency fundamental may be very

thin and therefore easily subject to

mechanical damage. The upper limit

for fundamental mode crystals is

about 70 Hz. Crystals for frequencies

in the hundreds of megahertz ranges

C o

010083 - 12

Figure. 1. The electronic equivalent of a quartz

crystal.

The stability of the better RC oscillators is

about 0.1%, while LC oscillators are stable up

to 0.01%. If we require greater stability, the

choice falls on a crystal oscillator. Certain

crystalline substances, of which quartz is a

prime example, have the property that they

produce an electric ﬁeld when they are sub-

jected to stress and, conversely, become

physically distorted when they are subjected

to an electric field. This is known as the

piezo-electric effect. Consequently, it is pos-

sible to cut a crystal so that it will physically

vibrate at a given frequency when it is sub-

ject to an alternating electric ﬁeld. Instead of

the electro-magnetic resonance of the LC net-

work, we have the electro-mechanical reso-

nance of the piezo-electric crystal. The differ-

ence is that crystals can easily be machined to

high precision, with natural frequencies as

close as 10 parts per million. (ppm)

Although quartz is the most often used

material, other substances such as lithium-

niobate, lithium-tantalate, bismuth-germa-

nium oxide, and aluminium-phosphate are

Electronic equivalent

From the electronic viewpoint an

RLC circuit ( Figure 1 ) may model the

behaviour of the crystal. The induc-

tor L corresponds to the mass of the

quartz slab. The capacitor C models

the stiffness of the slab. The resistor

R represents losses of energy occur-

ring when the crystal is flexed or

flexes. The second capacitor, C o , is

the capacitance between the elec-

trodes plated on either side of the

slab. Typically, L is a very high

inductance while C is very low. For

example, in a crystal cut to oscillate

at 200 kHz, L is 27 H, C is only

0.024 pF, R is 2 kΩ and C 0 is 9 pF. Val-

ues such as these are used when

modelling the action of a crystal in

computer simulations. The ratio of L

Elektor Electronics

11/2001

GENERAL INTEREST

are cut to have a relatively low fun-

damental but are operated in har-

monic mode. A maximum frequency

of about 500 MHz is obtainable by

this means.

Thermal stability is important in

some applications of oscillators. The

temperature coefficient depends on

the way the crystal is cut. For exam-

ple, the popular AT-cut gives a crys-

tal with a coefficient of ±0.002% over

the range

ance at the resonant frequency and

therefore producing an output signal

of maximum amplitude.

The Pierce oscillator ( Figure 2 ) is

an instance of the use of series reso-

nance. Feedback is routed through

the crystal and is a maximum when

the crystal is resonating in series

mode, with minimum impedance.

Note that this oscillator has no need

for a tuned circuit, relying only on

the crystal to determine its oscillat-

ing frequency.

Crystal oscillators are not only the

most precise but also among the

fastest of the oscillators in common

use. Modern digital circuits require

fast clocks to drive them, clocks with

frequencies measured in tens or hun-

dreds of megahertz. The circuit for

using a crystal to provide feedback

from the output of a CMOS inverter

gate is too well known to need

repeating here.

Some of the fastest oscillators

make use of surface acoustic wave

(SAW) devices. These are small

strips of piezo-electric material with

an array of electrodes plated on

them at both ends ( Figure 3 ). At one

end (the input end) an electric field

between the electrodes causes the

surface of the strip to become dis-

torted. This creates a wave that

passes along the surface of the strip.

It is an acoustic wave and travels

through the strip at the speed with

which sound travels in that material

(about 3000 m/s). A fraction of a sec-

ond later, when the wave reaches

the other (output) end of the strip,

the electric ﬁeld associated with the

wave produces a pd between the

electrodes there. SAWs are used as

bandpass filters, for the spacing

between the electrodes at each end

determines which frequency will be

most strongly fed into the SAW and

recovered at the other end. The time

taken for the wave front to pass

along the strip gives the filter the

+12V

2mH6

Feedback

Output

200kHz

10n

C. This

compares with several percent for

most capacitors. For greater stability

the crystal may be enclosed in an

‘oven’. The crystal is cut so as to

have a minimum temperature coeffi-

cient at a particular temperature

higher than room temperature. The

oven is then maintained at this tem-

perature. There are the disadvan-

tages of providing power for the

oven, the large volume of the oven,

and the time it takes to warm up.

Against this, there is the improved

thermal stability, in the region of

−

C to +105

Tuned

Element

2N3819

Amplifier

010083 - 11

Figure. 2. Pierce crystal oscillator.

parts per ten million.

With the increasing use of high-

frequency communications channels,

and high clock speeds in digital

equipment, greater use is being made

of resonators in place of crystals.

These are small discs of PZT ceram-

ics or similar piezo-electric materials

that are capable of operating at fre-

quencies in the Gigahertz range.

Input

Output

Piezo-electric

strip

010083 - 13

Figure. 3. A surface acoustic wave (SAW)

device.

Crystal oscillators

Crystals are used to replace or to

partly replace the resonant circuit in

all the oscillators that normally rely

on an LC circuit. For example, the

crystal-controlled version of the Col-

pitts oscillator has a crystal and a

capacitor in place of the inductor L1.

With a crystal fitted instead of the

inductor, the frequency is more pre-

cisely fixed. In such a circuit, the

crystal is being operated in parallel

resonance, having maximum imped-

properties of a delay line. As a component of

an oscillator, a SAW delay line is used in the

same way at the RC network of a phase shift

filter. The time taken to introduce a phase

shift of 180° is extremely short and so the fre-

quency of such oscillators is extremely high.

Typically, they range up to about 2 GHz.

Oscillators employing dielectric resonators in

the feedback loop exceed even this ﬁgure. At

this point we are well into the microwave

ranges, with their specialised features, and

will bring this discussion to a close.

(010083-1)

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www.elektor-electronics.co.uk

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