Frequency Multiplication Effects on Oscillator Instability

The effects which frequency multiplication produces on the power spectral density of an oscillator is examined as a function of the multiplication ratio and the power spectral density of the phase noise process. In addition, the power spectral density (PSD) of the multiplied-up oscillation is interconnected with the frequency standard L(f). It is explicitly demonstrated how errors are introduced when one attempts to define the rms fractional frequency deviation Δf(τ)/f0 and the Allan variance σ2y(τ) using the measurement of L(f). Finally, the genesis of spectral spreading of the PSD due to frequency multiplication is demonstrated in such a way that this interesting and important phenomena can be grasped by the practicing engineer.