Note that time domain stability measures sometimes depend onfhandflwhich should be given to obtain numerical results. In this paper,fh = 5kHz andfl = 0.01Hz are assumed.The phase useful handbook noise in time domain can then be represented by��osc(t)=Kx(t)?h(t),(5)where K is a constant,(t)denotes the phase noise sequence in time domain and denotes the convolution operator.3.2. Model of Phase-Locked Loop (PLL) Phase NoiseFigure 2 shows a fairly general PLL arrangement with a phase detector (PD), a low-pass loop filterHL(s), a voltage controlled oscillator (VCO) in the forward path and a mixer, an intermediate frequency (IF) filterHM(s), and a divider (��N). Additionally, a divider (��Q) and a multiplier (��N) are also placed.

Since all the noises generated or added in individual PLL blocks are small compared with the useful signals, the small signal theory makes it possible to use the Laplace transform to find the output noise of the considered PLL system or, more exactly, the, respectively, power spectral densities.Figure 2Model of a general PLL with additive noise.According to Figure 2, we can get that +Nmu(s)?Nmi(s)]?H(s)+Nosc[1?H(s)],(6)where??+(NDQ(s)?Ndn(s)+VPDn(s)+VFn(s)Kd)NFM(s)???=[Nin(s)(M+NQ1FM(s))?[31]NPLL(s) the effective loop transfer functionH(s)isH(s)=K0KdF(s)s+K0KdF(s),(7)withF(s)=1+s��2s��1.(8)The��1and��2are the loop low-pass filter parameters. The details can be found in [32]. Note that all the other variables are illustrated in Figure 2. Since most of the noise components are random and uncorrelated, the power spectral density of ?|H(jf)|2+S��,osc(f)|1?H(jf)|2.

(9)We??��N2+S��,mu(f)+S��,mi(f)}???+[S��,DQ(f)+S��,dn(f)+S��,PDn(f)+S��,Fn(f)Kd2]???={S��,in(f)(M+NQ)2?the PLL output phase noise isS��,PLL(f) see that the first term in the brace of (9) is inevitable since it is merely a multiplied reference oscillator noise. The second term includes the divider noise, phase detector noise, and loop filter noise, all multiplied by the division ratio N. Finally, with the third term, the multiplier and mixer noises are added; generally, they are small compared with the second term [33]. Hence, all the additive Dacomitinib noises, due to the phase detector, loop frequency divider, loop amplifiers, and loop filters are required to quantify prior to predicting the synchronization accuracy.3.2.1. Phase Detector and Mixer There are both theoretical and experimental lines of evidences that additive noise due to the mixers is quite small and of the order of the loading circuit noise. Experimental results show that the best phase detector is a double-balanced mixer [28].