ECEN 5014, Spring 2013 Special Topics: Active Microwave Circuits and MMICs Zoya Popovic, University o Colorado, Boulder LECTURE 13 PHASE NOISE L13.1. INTRODUCTION The requency stability o an oscillator is deined by two parameters: long-terms and short-term stability, as illustrated in Figure L13.1. The irst reers to slow changes in average or nominal requency, while the second reers to instantaneous (a ew seconds or less) requency variations. The border-line between long and short term depends on the application. For example, in a communications applications, long-term would most likely be several periods o the data or the inverse o the tracking loop bandwidth, typically the border line is a raction o a second. On the other hand, in a clock, several day, or even month irregularities might be relevant. 0 days, months, years t seconds t Figure L13.1. Illustration o long-term and short-term stability. Long-term requency instability is usually reerred to as drit, and the ratio / is usually linear or exponential with time. Short-term drit are changes in requency which cannot be described as oset, but are observed as random and/or periodic luctuations about a mean, Figure L13.2. Deterministic requency variations are discrete signals which appear in the spectrum, commonly called spurious signals (or spurs), and are related to things like power line requency, vibration requency, mixer products, etc. Short-term random luctuations is called phase noise. The sources o phase noise are what we studied last time in class: thermal, shot, and licker noise in both active and passive devices. Phase noise is oten the limiting actor in an application. As an example, consider a highperormance superheterodyne receiver with two signals at the input, Figure L13.3. The two signals need to be down-converted to an intermediate requency (IF) where ilters can separate them or detection. There should not be a problem in separating the larger o the two signals. However, since the phase noise o the local oscillator (LO) is translated directly to the mixing products, it may mask the smaller signal. This simpliied example illustrates how the phase noise o the LO determines the receiver s dynamic range and selectivity. It also determines the minimal IF that can be received. 1
Res BW 10Hz span 500Hz center 10GHz random short-term luctuations (phase noise) deterministic short-term luctuations (spurious) Figure L13.2. Illustration o deterministic (spurious) short-term requency luctuations and random short-term luctuations (phase noise) as they would be observed on an ideal spectrum analyzer. Intererence Wanted signal Receiver LO Down-converted wanted signal spectrum Down-converted intererence signal spectrum Receiver IF bandwidth Figure L13.3. Spectrum o local oscillator (LO) and wanted RF signal in a superheterodyne receiver. Another application where phase noise determines system perormance is radar. For example, Doppler radar determine the velocity o a target by measuring Doppler shits in the requency o the return echo, which are at a much lower requency than the microwave carrier, illustrated in Figure L13.4. The return signal has a rich content in which the desired Doppler shit is buried. For example, in the case o an airborne radar [Stimpson, IEEE Press], there is large signal due to the echo rom the ground, reerred to as clutter. The ratio o main-beam clutter to desired target signal may be as high as 80dB, making it a challenge to separate the desired signal rom the clutter. The problem is worse when the received spectrum has requency instabilities caused 2
by phase noise o either the transmitter power ampliier or the receiver local oscillator. Thereore, speciications or phase noise o radar ront ends are extremely stringent. Transmitter v Moving target clutter D ± D Stationary object Transmitter signal Clutter Down-converted clutter noise ± D Doppler signal D Figure L13.4. Illustration o the eect o carrier phase noise on sensitivity o Doppler radar. L13.2. QUANTIFYING PHASE NOISE Phase noise is described with a power level in a 1Hz bandwidth at some requency oset rom the carrier, in dbc/hz at x Hz away rom carrier, where x can be rom 100Hz to 10MHz, depending on the application. Figure L13.5 illustrates approximately the dierent requirements, and consequently oscillators or these dierent applications will be quite dierent. For example, Figure L13.6 shows a spectrum rom a Gunn-diode (low-cost) oscillator and a synthesized source at 10GHz as measured by a high-quality spectrum analyzer (receiver). The question we try to answer now is how to quantiy this dierence. In the time domain, an ideal carrier is expressed as vt () Vcos2 t, where V is the amplitude and the nominal requency. A realistic carrier signal can be written with AM and phase noise as vt ( ) [ Vnt ( )]cos[2 t ( t)]. In the requency domain, the ideal signal is a delta unction, while the real signal spreads both below and above the nominal requency. 3
Single-sideband phase noise to carrier ratio (NCR) Mobile FM Doppler radar Data communications QPSK 10 0 10 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 Oset rom carrier Figure L13.5. Illustration o oset-rom-carrier requency at which phase noise becomes important in dierent applications. Synthesizer Gunn diode Center: 10GHz Span: 20kHz Res BW: 100Hz Noise loor Figure L3.6. Comparing the phase noise o a 10-GHz Gunn diode and a requency synthesizer with a direct measurement on a spectrum analyzer. Phase noise is oten categorized as absolute (total) or two-port (additive, or residual) noise. The latter reers to noise added by devices such as ampliiers, dividers, multipliers and delay lines. This is noise contributed by a device regardless o the phase noise o the oscillator that supplies the signal. For example, in an ampliier, the input noise is thermal noise, and the ampliier adds noise (described by noise igure, as we shall see in the next lecture). The phase noise o the output signal will depend on the level o thermal noise and the noise igure. In addition to thermal (white) noise which is independent in requency, active devices exhibit licker noise below a certain cuto requency, and or oset requencies below this cuto, the noise increases, Figure L13.7. A rule o thumb is that or most components licker noise is at around 120dBc/Hz at 1Hz oset. In an oscillator, the white and licker noise cause even 4
greater slopes o the spectral power density as a unction o requency. To understand this, consider a simple eedback model o an oscillator ollowed by a buer ampliier, Figure L13.8. A resonator with some Q actor is added to the ampliier output, and then the output o the resonator is connected back to the ampliier input with phase that ensures positive eedback. 0 1 Consider the white and licker noise (with slopes and ) o the ampliier to be represented with a phase modulator in ront o an ideal ampliier. When the phase in the eedback loop changes, the oscillator requency shits: 0. 2Q Spectral energy random walk --4 licker FM --3 --2 --1 --1 c white FM licker white active device alone Frequency oset rom carrier (Hz) Figure L13.7. Typical phase noise distribution as a unction o oset requency rom carrier. (NIST has a number o detailed technical notes, should you be interested.) oscillator Buer amp 1, 0 1, 0 becomes 3, -2 Figure L13.8. Simple eedback oscillator model with buer ampliier. Since 0 and Q are constant, phase modulation is converted directly to requency modulation. 2 This results in a white FM noise with a slope o 3 and a licker FM noise with a slope. The buer ampliier (present in most oscillators) adds its own white and licker noise, and the 5
resulting noise power spectral density as a unction o requency oset rom carrier is as shown in Figure L13.7. Due to its random nature, the phase deviation is represented by a spectral density distribution plot. Four quantities are used to quantiy the spectral density: (1) S ( ), the power spectral density o phase luctuations, is the most basic measure, described in Figure L13.9. (2) L ( ), the single-sideband phase noise is the most commonly used expression or phase noise. It relates the energy in a single phase modulation sideband to the total signal power. (3) S ( ), power spectral density o requency luctuations is used to quantiy the eects o phase noise on FM systems. It is equal to S () ^2. (4) Sy ( ) spectral density o ractional requency luctuations is used to relate phase noise at one carrier requency to phase noise at any other carrier requency. L ( ) is an indirect measure o noise energy and can be easily related to the RF power spectrum as measured by a spectrum analyzer. We can relate L ( ) to S ( ) using simple phase modulation theory. This is illustrated in Figure L13.10. V K out in 2 rms ( ) S ( ) BW S ( ) rad Hz 2 Oset rom carrier (Hz) Figure L13.9. Description o S ( ), the power spectral density o phase modulation. In a phase modulated signal spectrum, the sideband amplitudes are Bessel-unction coeicients o an argument that contains the modulation index. L ( ) reers to the power density in one modulation sideband. There will be only one sideband or small modulation indices. With this (relatively strong assumption), L ( ) =1/2 S ( ). 6
J 1 (β) J 2 (β) 0 - m 0 0 + m m Figure L13.10. Phase modulated signal spectrum. 50 dbc/hz 0 S ( ) 2-30 -150-10dB/decade ( ) valid 1 10 100 1k 10k 100k 1k, oset rom carrier (Hz) Figure L13.11. Region o validity or L ( ) =1/2 S ( ). When is this assumption valid? Figure L13.11 shows this approximately. The measured S ( ) is valid, but the approximation L ( ) =1/2 S ( ) is not valid below a certain oset (otherwise, the noise power would blow up to ininity). The typical limit or the small-signal criterion is a line drawn with a slope o 10dB/decade that passes through a 1Hz oset at 30dBc/Hz. A time domain term used or quantiying requency stability is called the Allan variance, ( ). It is the standard deviation o ractional requency luctuations ( / ). There is a relatively complicated relationship between ( ) and S ( ). An example o typical values is as ollows: 11 or S (1kHz) =-157dBc/Hz, the Allan variance is (1ms) 3.9 10 or a carrier requency o 10MHz. An important eect in millimeter-wave circuits is increase in phase noise due to requency multiplication (we will mention multipliers later in the class). For small signals and a good multiplier design, the increase in phase noise is 6dB or a doubler. Thereore, one needs to be careul with multipliers or LOs that require good phase noise. 7
The most common methods o measuring phase noise are 1. direct measurement, using a spectrum analyzer. This is an easy measurement to perorm, but is good or relatively poor oscillators 2. phase detector method 3. phase discriminator method. Bellow is copied the relevant portion o a very good Hewlett Packard Application Note on phase noise measurements: 8
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