2.(11)3.2.2. Frequency Divider Theoretically, the division process reduces the input PSD in proportion to the square of the division factorN2. However, investigation of the divider output phase noise performed by Kroupa [35] reveals that the output phase noise isS��,dn(f)��S��,dn,in(f)N2+10?10��1+10?27��1f02f+10?16��1+10?22��1f0.(12)3.2.3. Frequency Multiplier The phase noise PSD at the output selleck chemicals Tofacitinib of a frequency multiplier is equal to its input multiplied by the square of multiplication factor plus an additive term, that is,S��,mu(f)��S��,mu,in(f)?N2+10?13��2f+10?16��1.(13)3.2.4. Amplifier The output phase noise in the low-frequency operational amplifier implemented with GaAs/GaA1As heterojunction bipolar transistors is [36]S��,amp,IF(f)��10?13f.

(14)For radio frequency (RF) amplifier noise, generally, only a narrow bandwidth around the carrier is considered; one-half of the thermal white noise contributes to the amplitude noise modulation and the other half to the phase noise modulation. Hence, a theory limit of the phase noise at the RF amplifier output is [36]S��,amp,RF(f)��4kTRVrms2,(15)wherekandTare Boltzmann’s constant and temperature in Kelvin, respectively.3.2.5. VCO The VCO phase noise improves as it goes to farther offsets from the carrier. Although there could be more regions with different slopes to the phase noise, a reasonable model for this is to divide this noise into three regions. A fairly general VCO phase noise equation is [37]S��,vco(f)��f02?10?11.6f3?QL2+f02?10?15.6f2?QL2+10?11f?QL2+10?15,(16)whereQLis the loaded quality factor of the oscillator.

3.2.6. Loop Filter As one of the most important parts in the PLL synthesizer, loop filter has various topologies. For distributed radar systems, passive filters are generally recommended, because they have the advantages of lower cost and no active devices to add noise. Moreover, to reduce spur levels, a fourth-order filter is used in this paper, because fourth order and higher-order filters become more practical when the spurs to be filtered are at least 20 times the loop bandwidth [32]. As all resistors create thermal noise, there are two major sources of noise, namely, some types of capacitors and resistors. Typically, the contribution from this resistor noise within the loop bandwidth is negligible. In the case of a resistor, this noise voltage is the thermal noise generated by the resistor. We then haveRnoise(R)=4TkR,(17)where the units are??V/Hz. Since phase noise Cilengitide is normalized to a 1Hz bandwidth, one can disregard the denominator and consider the units to be in Volts.3.3. Model of Receiver Noise The receiver noise, consisting of thermal noise and the noise collected by the antenna, will introduce both amplitude and phase fluctuation to the synchronization signal.