Page 243 - Complete Wireless Design

Oscillator Design

242 Chapter Four

C is a capacitance value that can be measured across a crystal at rest, and
0
does not vary with frequency of operation nor with the number of its overtone,
but only by the crystal’s distance between its electrodes and the electrode’s
area. This value will normally be between 2 to 8 pF. The lower the value, the
better for oscillator operation.
Various crystal specifications can greatly affect an oscillator’s performance.
The frequency accuracy of a crystal, while at room temperature in an oscillator
test circuit, can vary from ±5 to ±100 ppm. The lower this value, the more accu-
rate the oscillator’s output frequency will be at 25°C, and the more costly the
crystal. Frequency stability over some chosen temperature range is another
specification, important to maintaining frequency accuracy under varying
ambient and internal temperatures.
Aging affects the crystal’s frequency accuracy over time, and can change this
accuracy by as much as 6 ppm during a 12-month period—or as little as 0.75
ppm, depending on the type of package, crystal quality, crystal stresses, tem-
perature, and frequency. However, the aging of a crystal will mostly occur
within its first year; after which the rate will slow down to perhaps one-fifth
its first year’s value. For instance, a crystal might age 2 ppm over the first
year and only 4 ppm over the next 10-year period.

4.3.2 Types of crystal oscillators
Since there are so many different circuit designs available, we will focus on only
the most common crystal oscillators, such as the Hartley crystal oscillator of Fig.
4.23, the Colpitts crystal oscillator of Fig. 4.24, and the Pierce crystal oscillator
of Fig. 4.25. As we can see, the crystals for the first two oscillators are placed in
series in the transistor’s feedback path, and, as a crystal has a very high Q (in
excess of 75,000) and will thus have a very narrow bandwidth (BW f /Q), only
r
the tight band of frequencies within the crystal’s natural resonance will actual-
ly pass onto the phase-shifting circuits, and will thus be in-phase at the oscilla-
tor’s input. In fact, feedback that is off frequency by even the smallest amount
will be rigorously attenuated, decreasing the level of the transistor’s feedback,
forcing the oscillator to return to its desired frequency. The phase-shifting net-
work for the Hartley and Colpitts oscillators is the LC tank components, while
the Pierce crystal oscillator employs a slightly different method of operation.
In the Pierce oscillator, a series resonant crystal has been substituted for the
inductor of the Colpitts. Since at series resonance a crystal will display only a
small, pure resistance to the oscillator’s feedback from its output to its input,
but will exhibit either a capacitive or an inductive element if not within this
small window of series resonance, this will allow the 180 degree phase shift
required for positive, oscillatory feedback. However, this point is usually shifted
slightly higher in frequency than as marked on the series resonant crystal by
about 50 ppm. In other words, the Pierce will oscillate by a very small amount
higher in frequency than may be expected by the crystal’s marked frequency
(more on this below). This action forces the Pierce oscillator to stay accurately
on frequency in low-power, medium-frequency applications.

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