Bruno Duarte 27/06/2019 Application Engineer 1 • Phase Noise Basics • What is Phase Noise? • Review: AM, PM & Phase Noise • Theory & Mathematics of Phase Noise • Noise Sources that Contribute to Phase Noise • Phase Noise Applications • Radar • Digital Communications • Phase Noise Measurements • Phase Detector Techniques • Reference Source/PLL Measurement Method • Frequency Discriminator Measurement Method • Cross-correlation • Conclusion 2 FREQUENCY INSTABILITY Long-term frequency instability f • Slow change in average or nominal center frequency time Phase noise is generally considered (days, months, years) the short-term phase/frequency instability of an oscillator or other RF/µW component Short-term frequency instability f • Instantaneous frequency fo variations around a nominal center frequency time (seconds) 3 Two categories of PM signals: Random Signals: • Noise which modulates the carrier • Produces continuous spectral density plot similar to broadband noise • Measured power is proportional to the bandwidth used Deterministic: • Discrete signals due to repetitive, constant rate events • Spurs related to power line frequency, AC magnetic fields, mechanical vibration, etc. • Measured power constant independent of bandwidth 4 IDEAL VERSUS REAL - WORLD SIGNALS Ideal sinusoidal signal Real sinusoidal signal V(t) = Aosin(2πƒot) V(t) = [Ao+E(t)]sin[2πƒot+ 흓(t)] where where Ao = nominal amplitude E(t) = random amplitude fluctuations ƒo = nominal frequency 흓(t) = random phase fluctuations V(t) V(t) E(t) t t ƒo ƒ 흓(t) ƒo Time Frequency Time Frequency 5 POWER SPECTRAL DENSITY OF NOISE SIDEBANDS • Phase fluctuation of an oscillator produced by different random noise sources is phase noise P0 • Just phase modulation with noise as the message signal SSB • Mostly concerned with frequency domain where phase noise is simply noise sidebands or skirt around “ideal” delta function from sinusoidal oscillator • Because PM is symmetrical in magnitude around center frequency, can measure a single noise sideband (SSB) f0 6 HOW TO DEFINE PHASE NOISE MEASUREMENTS Three elements: P • Upper sideband only, offset frequency (fm) from carrier 0 frequency (f0) • Power spectral density, in 1 Hz BW SSB (퓛(풇)) • PSD relative to carrier power in dBc 1 Hz BW dBc/Hz @ offset frequency fm from specified carrier frequency f0 f0 fm (offset freq.) 7 PHASE NOISE & JITTER • In the time domain, rms phase deviation is called jitter • Frequently, people concerned about jitter deal with clock ∆풕 = 풋풊풕풕풆풓 signals, and thus are more concerned about measuring square wave type signals as opposed to the sinusoids we’ve been dealing with • To relate rms phase deviation to jitter, we can use the following mathematical relation: 푻풑풆풓풊풐풅 흓푹푴푺 흓푹푴푺 풋풊풕풕풆풓(풔풆풄풐풏풅풔) = [푻풑풆풓풊풐풅(풔풆풄풐풏풅풔)] = ퟐ흅 ퟐ흅풇풄 Percentage of total angular period Carrier signal period affected by rms phase noise (time) –same as ퟏ/풇풄 8 PHASE NOISE ON A SPECTRUM ANALYZER • As we saw before, single sideband phase noise 퓛 풇 is a relative power measurement –we measure the power density of the noise sideband relative to the power of the carrier: 퓛 풇 푷 (푾/푯풛) ퟏ 풓풂풅ퟐ 풓풂풅ퟐ 푺푺푩 = 흓ퟐ = 퓛 풇 푷 (푾) ퟐ 풓풎풔 푯풛 푯풛 풄 Pcarrier (dBm) • These ratios (relative power measurements) are suited quite well to spectrum analyzers –which measure signals Pnoise (dBm/Hz) using a log-transformed power scale Ps (dBm) • Context matters because 퓛 풇 is used for both linear units and log-transformed phase noise (in dBc/Hz) Pn (dBm/Hz) • The log scale (dB) allows us to replace the division of the carrier with subtraction and gives us units of dBc/Hz 1 kHz measurement bandwidth using noise density marker 퓛 풇 = Pnoise (dBm/Hz) - Pcarrier (dBm) = -121.28 dBc/Hz (generally normalized to 1 Hz) 9 MATHEMATICAL DERIVATION OF NARROWBAND PM • Phase noise (퓛(풇)) is a phase phenomenon • Simply PM of carrier signal with noise message signal • Deriving narrowband PM mathematically shows extreme similarities between AM & PM 흓 풕 = 푡푚푒 푣푎푟푦푛푔 푟푎푛푑표푚 푛표푠푒 푠푔푛푎푙 푤푡ℎ 푟푎푛푑표푚푙푦 푣푎푟푦푛푔 푓푟푒푞푢푒푛푐푦 & 푎푚푝푙푡푢푑푒 풄풐풔 흎풄풕 = 푑푒푎푙 푐푎푟푟푒푟 푠푛표푑푎푙 푠푔푛푎푙 푓푟표푚 표푠푐푎푙푙푎푡표푟 풄풐풔(흎풄풕 + 흓 풕 ) = 푟푒푎푙 푠푔푛푎푙 푤푡ℎ 푝ℎ푎푠푒 푛표푠푒 표푛 푡 Recall: 풄풐풔 휶 + 휷 = 풄풐풔 휶)풄풐풔(휷 − 풔풊풏 휶)풔풊풏(휷 where: 휶 = 흎풄풕 풂풏풅 휷 = 흓 풕 ퟏ Small-angle approximations: 흓 풕 < 풓풂풅 퐚퐧퐝 퐟퐫퐨퐦 퐭퐡퐢퐬 풄풐풔 흓 풕 ≈ ퟏ 풂풏풅 풔풊풏 흓 풕 ≈ 흓 풕 ퟓ Result: Noise that modulates phase of carrier 풄풐풔(흎풄풕 + 흓 풕 ) = 풄풐풔 흎풄풕 − 흓 풕 풔풊풏 흎풄풕 becomes amplitude modulation of carrier 10 AM VS. NARROWBAND PM ON SPECTRUM ANALYZER • SSB noise contains both AM & PM components • Compare double sideband (DSB) AM with narrowband PM signal where both have 흓 풕 as sinusoidal message/modulating signal: DSB AM: Narrowband PM: ퟏ + 흓 풕 풄풐풔(흎풄풕) = 풄풐풔 흎풄풕 + 흓 풕 풄풐풔(흎풄풕) 풄풐풔(흎풄풕 + 흓 풕 ) = 풄풐풔 흎풄풕 − 흓 풕 풔풊풏 흎풄풕 Difference is just a phase shift *DSB AM signal with 0.8% modulation index, AM Rate=10 kHz *Narrowband PM signal with ∆흓풑풌= ퟎ. ퟐ 풓풂풅 index, PM Rate=10 kHz • Because legacy spectrum analyzer shows magnitude spectrum, AM & narrowband PM look identical. Thus, need to remove AM component to accurately measure only the phase noise component of total noise 11 THERMAL NOISE (JOHNSON - NYQUIST NOISE) –174 dBm/Hz Thermal noise is “white” (i.e., same magnitude power spectral Displayed average noise level (DANL) of signal analyzer is density at all frequencies, or –174 dBm/Hz) thermal noise plus analyzer’s own internal noise k = Boltzmann's constant T = temperature (K) B = bandwidth (Hz) Np = Noise Power Density = kT 푑퐵(푊푎푡푡푠) 푑퐵푚 For T = 290 K ➔ 푁 = −204 = −174 푝 퐻푧 퐻푧 12 1/F “MODULATION” NOISE & THERMAL NOISE • Beyond thermal noise floor (approx. constant spectral density), another contributor to total phase noise is inversely proportional to frequency (∝1/f) • Exhibited by virtually all electronic devices –10 dB/decade • In devices operating at RF or µW frequencies, 1/f noise is modulation on carrier emerging from or passing through device • Wouldn’t exist in absence of device electronics (unlike thermal noise) • On Bode plot, has easy-to-use property of decreasing by 10 dB/decade • 1/f noise meets thermal noise floor (i.e., broadband noise) at 1/f crossing frequency • Beyond that point, thermal noise dominates & obscures 1/f still present Broadband noise * Note: Broadband/thermal noise floor is not “modulation noise” by itself, until it is decomposed into equivalent AM & PM on a carrier 13 AL L P O W E R - LAW NOISE PROCESSES IN AN OSCILLATOR Theoretical noise processes Real noise processes in VCO 퓛 풇 (퐝퐁) Frequency Offset from Carrier (Hz) * Dr. Sam Palermo, Texas A&M 14 Better PN → lower skirt Better chance to find Doppler reflection signals Highest performance radar transceiver designs demand best phase noise to find moving targets, fast or slow Slower V target Faster 15 QPSK EXAMPLE I I I RF LO Q Q 90o Q Ideal QPSK constellation Degraded signal with phase noise QPSK constellation 16 64QAM EXAMPLE I Symbols far from I origin on I/Q constellation are spread more for Q given amount of phase noise on LO Q 17 SIGNAL SOURCE AS LO FOR WIDEBAND SINGLE CARRIER QPSK PSG is LO MXG is LO EXG is LO EVM = ~1.8% EVM = ~2.1% EVM = ~2.1% Test configuration Baseband IF Upconverter Oscilloscope M8190A E8267D PSG Infiniium 5 GHz 60 GHz WARNING: Exit 89600 VSA Software Test signal before changing instrument setup QPSK LO PSG/MXG/EXG 10 GHz x6 18 OFDM EXAMPLE Power Power • LTE uses OFDM with many subcarriers, each spaced at 15 kHz • Lower (i.e., better) phase noise of receiver or transmitter LO improves Frequency Frequency each subcarrier’s resolution & OFDM subcarriers Downconverted OFDM thus EVM performance subcarriers with LO phase Power noise added • Unlike case with wideband single- carrier modulation, OFDM requires extremely good close-in phase Phase noise noise performance Frequency LO with phase noise 19 Direct-spectrum method Carrier-removal method (phase detector in quadrature) • By sampling the carrier, direct-spectrum method • Increased sensitivity obtained by nulling carrier & then immediately yields amplitude & phase information amplifying & measuring phase noise of resulting • Employed in signal analyzers & some phase noise systems baseband signal with high-gain, low noise figure amplifiers • Far less sensitive than carrier-removal method because carrier limits ceiling of system components • Both frequency discriminator and PLL/reference • ADC full scale, receiver preamp compression level, etc. source methods discussed next use carrier removal via phase detectors in quadrature 0 Hz 20 PHASE NOISE APP ON X - SERIES ANALYZERS Pros: • Easy to configure & use • Quick phase noise check • Log plot • Spot frequency (PN change vs. time) DUT • RMS PN, RMS jitter, residual FM • X-Series phase noise application automates PN measurements Cons: • Uses less-sensitive direct-spectrum method • Limited by internal PN floor of SA • Caution: With older spectrum analyzers, AM noise cannot be separated from PM noise • In today’s modern signal analyzers, AM component is removed N9068C X-Series Phase Noise Application 21 • Frequency-discriminator & reference source/PLL methods both use phase detector as heart of system for absolute measurements • Phase detector also enables residual phase noise • Phase detector takes two input signals & compares phase • Output of phase detector is DC voltage proportional to delta phase of input signals (∆흓) • Constant of proportionality, K, has units of volts per radian (V/rad) & must be measured • Phase detectors also tend to suppress AM noise ∆흓 풕풐 푽풐풍풕풂품풆 푪풐풏풗풆풓풕풆풓 (풑풉풂풔풆 풅풆풕풆풄풕풐풓) 22 THE MATHEMATICS Product-to-sum identity: LPF • Double-balanced mixers produce 푥 푡 = 퐴푠푛[휔0푡 + 흓푥 푡 ] sinusoids at sum & difference 1 1 × 퐴퐵푐표푠[흓푥 푡 − 흓푦 푡 ] − 퐴퐵푐표푠[2휔0 + 흓푥 푡 + 흓푦 푡 ] frequencies of two input signals, 2 2 푦 푡 = 퐵푠푛[휔0푡 + 흓푦 푡 ] 푥 푡 & y 푡 • If both signals are at same frequency 휔0 & 90° offset, yields 0 Hz (DC) & high-frequency (2휔0) sum term that is removed using low-pass filtering (LPF) 1 푉 ∝ 퐴퐵푐표푠[흓 푡 − 흓 푡 ] 표푢푡 2 푥 푦 • After LPF, resulting DC term varies in amplitude as cosine function of ∆흓 of the two signals ∆흓 • This is a delta-phase to voltage converter or phase detector ∆흓 풕풐 푽풐풍풕풂품풆 푪풐풏풗풆풓풕풆풓 ("푷풉풂풔풆 푫풆풕풆풄풕풐풓") 23 IMPORTANCE OF QUADRATURE • Phase detector’s cosine output voltage, cos ∆흓 , is nonlinear Phase detector output voltage vs.