At frequencies up to the order of 120-150 MHz, it is possible to use a quartz crystal as resonator and thus achieve simultaneously a high Q and good frequency stability and accuracy. At still higher frequencies the phase noise performance of a simple oscillator will be degraded both due to the higher value of f0 and simultaneously the lower Q of a suitable resonant circuit which can no longer be a quartz crystal. A further penalty is that the frequency accuracy and stability will be degraded. Thus it is apparent that a considerable improvement in performance might be achieved by using a crystal oscillator followed by a frequency multiplier to give the required output frequency. This would appear to be a beneficial tradeoff even if the multiplication process produced a phase noise degradation proportional to the square of the multiplication ratio. This degradation would be exactly offset by the f0 2 term in the numerator of the RHS of equation (6.1), leaving the improvement in Q as a bonus, to say nothing of the improved frequency stability. A further bonus is often available in that the noise figure of the transistor oscillator may be considerably better if the oscillator is operated at a sub-multiple of the required output frequency.