Experimental results and their interpretation

Abstract

The methods detailed in Chapter 2 give the mean frequency f ₀ = ω₀/2π of an oscillator and the spectral densities of phase and relative frequency fluctuations, S _φ (F) and S _y (F), which we will refer to as low-frequency spectra for short. The relation between these densities is

$${{S}_{y}}(F) = \frac{{4{{\pi }^{2}}{{F}^{2}}}}{{\omega _{0}^{2}}}{{S}_{\Phi }}(F)$$

(3.1)

where y = (1/2π)/(φ/f ₀), the oscillator signal is given by

$$ \upsilon = V_0 \sin [\omega _0 t + \Phi (t)] $$

(3.2)

and amplitude fluctuations are assumed to be negligible. Figure 3.1 shows a few examples of the results obtained. The frequency axis has a logarithmic scale and the ordinates are plotted in dB/Hz since the spectral densities are normalised to the total power of the oscillator signal. The frequency spectrum is usually well described by a five-parameter model of the form

$${{S}_{y}}(F) = \frac{{{{h}_{{ - 2}}}}}{{{{F}^{2}}}} + \frac{{{{h}_{{ - 1}}}}}{F} + {{h}_{0}} + {{h}_{1}}F + {{h}_{2}}{{F}^{2}} + \ldots$$

(3.3)