1996 Oct 02 8
Philips Components
Quartz crystals General Introduction
Level of drive
The power dissipated in a quartz
crystal is termed ‘level of drive’ and is
usually expressed in mW. In the level
of drive range 10−12 to 10−4W the
drive level dependency of the crystal
characteristics is almost negligible.
For drive levels greater than
approximately 0.1 mW, the crystal
characteristics tend to change. For
this reason the crystal characteristics
are specified at drive levels of
0.05 mW to 0.5 mW depending on the
crystal type.
Low drive levels
When a quartz crystal oscillator is
switched on, there will initially be
some noise in the circuit. The noise
power, which depends on the circuit
design and on the components used,
will be in the region of 10−16 W. From
this level, the oscillatory power builds
up in the quartz crystal, passing
through a power range of
approximately 12 decades to its
maximum value. At the extremely low
power levels that occur during build
up of oscillation, the resonance
resistance (Rr) may increase slightly.
The quartz crystal oscillator should,
therefore, have sufficient loop gain to
avoid start-up problems. Typically, a
negative resistance of three times the
specified Rr(max) value is sufficient.
High drive levels
For applications requiring high
stability, a drive level between 5 µW
and 100 µW should be used. Drive
levels exceeding 0.5 µW should be
avoided, and excessively high drive
levels (exceeding 5 mW) may
seriously affect the quartz crystal's
behaviour (see Fig. 9).
Frequency/temperature
characteristics
The frequency drift as a function of
temperature can be represented by a
graph showing the temperature
coefficient (TC) curve or drift
characteristic. In the case of AT cuts,
the relation of drift and temperature is
approximated by a cubic curve; the
drift characteristic of most other cuts
is parabolic.
Figure 7 shows a number of
frequency-temperature curves
obtained from AT-cut crystals with
various angles of cut (α from −4' to
+16' increasing angle of cut). The
curves are symmetrical with respect
to approximately +27 °C.
A temperature range which is fairly
symmetrical with respect to 27 °C
(e.g. 0 to 60 °C) will, therefore, result
in the smallest frequency drift in that
range. A small frequency drift over a
wide temperature range, e.g. −40 to
+80 °C, will result in a fairly steep
temperature coefficient at room
temperature.
Advantages of all-glass holders
Quartz crystals with all-glass holders
show the following advantages over
those with metal holders:
1. A lower ageing rate.
2. A lower series resistance, which
also means a higher Q-factor,
due to the fact that glass holders
are evacuated giving less
mechanical damping.
3. Better performance under
adverse climatic conditions.
4. Smaller adjusting tolerances.
Ageing
A gradual change in resonance
frequency with time is called (an
effect of) ageing. Only where very
good long-term stability is required
should ageing be of consequence.
It should be borne in mind that (with a
view to ageing only):
1. Quartz crystals with an all-glass
holder have a lower ageing rate
than metal sealed crystals.
2. Low frequency crystals are
preferred to high frequency
crystals.
3. Overtone crystals are preferred to
fundamental crystals for the same
frequency.
Crystal behaviour in an oscillator
In the vicinity of resonance, the
impedance of a quartz crystal can be
represented by a circle (see Fig.8).
The circle is shifted downwards with
respect to the resistance axis over:
(9)
When a load capacitance is
connected in series with the quartz
crystal the shift is X0 + XL, where
(10)
The difference between
anti-resonance frequency and
resonance frequency
(11)
is assumed to be 100%.
It can be seen that the difference
between the two frequencies,
determined by the phase angle ϕ,
disappears at fw = 50%. The phase
angle in the oscillator should be kept
sufficiently small to avoid quartz
crystal operation in the uncertain area
above 50% (frequency switching).
X01
2πfrC0
------------------
=
XL1
2πfLCL
-------------------
=
fafr
–C1
2C0
---------- fr
×CL
C0CL
+
--------------------
×≈