Page 250 - Complete Wireless Design

Oscillator Design

Oscillator Design 249

with f being a frequency that is approximately midway between the desired
mid
harmonic that we wish to output and the next lowest odd harmonic (of the fun-
damental) that is below this desired output harmonic.
Example: A frequency of 133 MHz is required. Design the Pierce overtone
oscillator to function at 133 MHz with a 19-MHz crystal. In other words, the
crystal will operate at its seventh overtone of 133 MHz, but has a fundamen-
tal resonant frequency of only 19 MHz. Choose L and C so that f (in this
1 1 mid
case 114 MHz) is resonant or:
1
114 MHz

2 10 nH 195 pF

Now tune L for the maximum power at the desired overtone. The C , L tank
1 1 1
will resonate at somewhere in the vicinity of 114 MHz, but the oscillator will
output 133 MHz, or the seventh harmonic of 19 MHz.

4.3.4 Crystal oscillator issues
The different crystal oscillator circuit configurations employed in circuit
design are required because of the various impedance levels found at different
frequencies of oscillator operation. Since a crystal’s internal series resistance
can be as low as 20 ohms at 25 MHz, all the way up to 0.25 megohms at 500
Hz, special circuit designs are required to efficiently match and drive the crys-
tal at these resistance values. The Pierce circuits above will be almost ideal for
the majority of crystal oscillator needs in most wireless systems.
Any oscillator crystal in RF circuits should be calibrated to 5 or 6 decimal
places in order to supply an accurate frequency for most LO applications. A
crystal with less accuracy, especially at high frequencies, can result in an oscil-
lator that can become unstable as a result of the huge frequency adjustments
that must be made.
Oscillator start-up time is directly correlated to the Q of the oscillator’s res-
onator, so the higher the Q the longer the start-up time. Crystal oscillators,
with their ultrahigh Q, have prolonged start-up times up to, and sometimes
surpassing, 100 mS. Start-up time will also be affected by the bias network of
the oscillator’s active device, since the bias network must reach its steady-
state value before reliable oscillations will occur. Thus the RC time constant of
the bias network can substantially slow down the onset of oscillations.
Obviously all passive and active components must be rated above the oscil-
lator’s frequency of operation, as well as the oscillator’s voltage, current, or
power. The inductors and capacitors must not have any series or parallel res-
onances that will interfere with oscillations, and the active element must have
a gain that is more than sufficient to sustain oscillations at the frequency of
operation.
Board layout is another critical aspect to proper oscillator operation (see
Sec. 10.3, “Wireless board design”).

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