11.7: Local Oscillator

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In an oscillator noise close to the oscillation center frequency is called flicker noise or \(1/f\) noise and in offsets below a few tens of megahertzis much larger than thermal noise and so a big concern in microwave systems. The noise manifests itself as random fluctuations of amplitude and phase of the carrier. The amplitude fluctuations are quenched by saturation in the oscillator and so are not of concern. Thus the close-in noise of concern is just phase noise. The phase noise of an oscillator with a low \(Q\) feedback loop is shown in Figure \(\PageIndex{1}\)(a) and in Figure \(\PageIndex{1}\)(b) for a high \(Q\) loop. The physical origin of the straight line phase regions is nt understood.

Phase noise is expressed as the ratio of the phase noise power in a \(1\text{ Hz}\) bandwidth of a single sideband (SSB) to the total signal power. This is measured at a frequency \(f_{m}\) offset from the carrier and denoted \(\mathcal{L}(f_{m})\) with the units of \(\text{dBc/Hz}\) (i.e., decibels relative to the carrier power per hertz). The phase noise that is important in RF and microwave oscillators (having relatively low \(Q\)) is usually dominated by a \(1/f_{m}^{2}\) shape. Then the phase noise

Figure \(\PageIndex{1}\): Log-log plot of oscillator noise spectra: (a) closed-loop noise with low-\(Q\) loop; and (b) closed-loop noise with high-\(Q\) loop.

at \(1\text{ MHz}\) (a common frequency for comparing the phase noise performance of different oscillators) is related to the phase noise measured at \(f_{m}\) by

\[\label{eq:1}\mathcal{L}(1\text{MHz})=\mathcal{L}(f_{m})-10\log\left(\frac{1\text{ MHz}}{f_{m}}\right)^{2} \]