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MPhil thesis of Lo Chi Wa - Department of Electronic & Computer ...

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spirals <strong>of</strong> similar sizes is around 2-2.5 which will dominate the overall quality factor <strong>of</strong>the whole LC tanks and limit the phase noise performance <strong>of</strong> the oscillator.Phase noise performanceThe phase noise <strong>of</strong> a LC oscillator can be calculated by the equation,L(∆ω)=⎛ ω o ⎞kTRs(1 + A)⎜ ⎟⎝ ∆ω⎠2V22where Rs is the equivalent series resistance <strong>of</strong> the LC tank, V is the oscillationamplitude and A is the excess noise factor <strong>of</strong> the oscillator. The phase noise depends onthe power <strong>of</strong> the carrier (V 2 /2), the noise power <strong>of</strong> the lossy resistance (kTRs), and thenoise power <strong>of</strong> the compensation (kTRsA).To determine the phase noise, the power <strong>of</strong> the carrier, the noise power <strong>of</strong> the lossyresistance, and the noise power <strong>of</strong> the compensation. The noise power due to the lossyresistance in the LC tanks depends on the resistance in the inductor and the varactorwhich is process-dependent. The carrier power (or the amplitude <strong>of</strong> oscillation) and thecompensation can be calculated based on the criterion for oscillation. The simplestcriterion for oscillation is:“<strong>Lo</strong>op gain is larger than one when 360 o phase shift.”In a most simple LC oscillator, as shown in Fig. 26, the criterion can be explained asfollow:39

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