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Content  Analog Dialogue 335 (© 1999 Analog Devices)1 PhaseLocked Loopsfor HighFrequencyReceivers andTransmitters–Part 2 by Mike Curtin and Paul O’Brien The first part of this series of articles introduced the basic concepts of phaselocked loops (PLLs). The PLL architecture and principle of operation was described and accompanied by an example of where a PLL might be used in a communication system. In this second part, we will focus on a detailed examination of two critical specifications associated with PLLs: phase noise and reference spurs. What causes them and how can they be minimized? The discussion will include measurement techniques and the effect of these errors on system performance. We will also consider output leakage current, with an example showing its significance in open loop modulation schemes. Noise in Oscillator Systems In any oscillator design, frequency stability is of critical importance. We are interested in both longterm and shortterm stability. Long term frequency stability is concerned with how the output signal varies over a long period of time (hours, days or months). It is usually specified as the ratio, ∆f/f for a given period of time, expressed as a percentage or in dB. Shortterm stability, on the other hand, is concerned with variations that occur over a period of seconds or less. These variations can be random or periodic. A spectrum analyzer can be used to examine the shortterm stability of a signal. Figure 1 shows a typical spectrum, with random and discrete frequency components causing a broad skirt and spurious peaks. Frequency AmplitudeRandom Noise Fluctuation Discrete Spurious Signal f0 Figure 1.Shortterm stability in oscillators. The discrete spurious components could be caused by known clock frequencies in the signal source, power line interference, and mixer products. The broadening caused by random noise fluctuation is due to phase noise. It can be the result of thermal noise, shot noise and/or flicker noise in active and passive devices. Phase Noise in VoltageControlled Oscillators Before we look at phase noise in a PLL system, it is worth considering the phase noise in a voltagecontrolled oscillator (VCO). An ideal VCO would have no phase noise. Its output as seen on a spectrum analyzer would be a single spectral line. In practice, of course, this is not the case. There will be jitter on the output, and a spectrum analyzer would show phase noise. To help understand phase noise, consider a phasor representation, such as that shown in Figure 2. wo wm Dq rms VN rms VSPK Figure 2.Phasor representation of phase noise. A signal of angular velocity ωO and peak amplitude VSPK is shown. Superimposed on this is an error signal of angular velocity ωm. ∆θrms represents the rms value of the phase fluctuations and is expressed in rms degrees. In many radio systems, an overall integrated phase error specification must be met. This overall phase error is made up of the PLL phase error, the modulator phase error and the phase error due to base band components. In GSM, for example, the total allowed is 5 degrees rms. Leeson’s Equation Leeson (see Reference 6) developed an equation to describe the different noise components in a VCO. LFkT AQ f f PM L O m ≈æ èç ö ø÷ é ë êêê ù û úúú 101 82 2 log(1) where: LPM is singlesideband phase noise density (dBc/Hz) F is the device noise factor at operating power level A (linear) k is Boltzmann’s constant, 1.38 × 10–23 J/K T is temperature (K) A is oscillator output power (W) QL is loaded Q (dimensionless) fO is the oscillator carrier frequency fm is the frequency offset from the carrier 
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