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 = 푡𝑖푚푒 푣푎푟푦𝑖푛푔 푟푎푛푑표푚 푛표𝑖푠푒 푠𝑖푔푛푎푙 푤𝑖푡ℎ 푟푎푛푑표푚푙푦 푣푎푟푦𝑖푛푔 푓푟푒푞푢푒푛푐푦 & 푎푚푝푙𝑖푡푢푑푒 풄풐풔 흎풄풕 = 𝑖푑푒푎푙 푐푎푟푟𝑖푒푟 푠𝑖푛표𝑖푑푎푙 푠𝑖푔푛푎푙 푓푟표푚 표푠푐𝑖푎푙푙푎푡표푟 풄풐풔(흎풄풕 + 흓 풕 ) = 푟푒푎푙 푠𝑖푔푛푎푙 푤𝑖푡ℎ 푝ℎ푎푠푒 푛표𝑖푠푒 표푛 𝑖푡

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 = 퐴푠𝑖푛[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 = 퐵푠𝑖푛[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. delta phase • Want to linearize to create linearly proportional relationship between ∆흓 & output voltage Slope is K • If DUT & reference signal inputs to phase detector are offset ± 90°, output is zero volts & derivative of cosine function is maximized (i.e., maximum sensitivity) • As ∆흓 increases or decreases about 90°, output voltage changes approximately linearly with ∆흓 and having slope or 180° ퟗퟎ° derivative K (also known as proportionality constant in V/rad) • Quadrature also allows high AM suppression ( up to 30 dB) so are measuring only PM • After characterizing K, get output voltage that varies linearly with delta phase: 푽 = 푲∆흓 • This is a phase detector! 푷풊풆풄풆-풘풊풔풆 푳풊풏풆풂풓 푹풆품풊풐풏 풂풃풐풖풕 풒풖풂풅풓풂풕풖풓풆 (∆흓 = ퟗퟎ°) where 푽 = 푲∆흓

24 • Absolute phase noise measurement is direct characterization of DUT (e.g., an oscillator) performance, inclusive of reference source • A one-port measurement • Reference-source/PLL method is phase- detector technique that uses a phase- locked loop (PLL) system to set & keep DUT & reference sources in quadrature • Keeps phase detector in linear region • Limited by noise floor of system itself if have an ideal reference source with zero phase noise

25 • An absolute (one-port) measurement that also uses a phase detector • Signal from DUT is split into two paths • Signal in one path is delayed relative to the other • Delay line converts frequency fluctuations into phase fluctuations • Delay line (or phase shifter) is adjusted so that inputs to mixer are in quadrature • Phase detector converts phase fluctuations into voltage fluctuations that are analyzed using the baseband analyzer • Less sensitive than PLL/reference-source method for close-to-carrier measurements

26 • Uses two phase detectors & two references to further improve phase noise floor (i.e., sensitivity) • Two channels are uncorrelated so remove noise from references & system components through computational process (time vs. performance tradeoff) • DUT signal is common to both channels so is perfectly correlated in both channels & kept as measurement result • Available in Keysight E5052B SSA and N5511A Phase Noise Test System (PNTS)

27 TIME VERSUS PERFORMANCE IMPROVEMENT

internal system noise N1 measured noise Nmeas

Signal source channel 1 under test (SUT) DSP splitter cross-correlation source noise (correlation# = M)

NS.U.T. channel 2

internal system noise N2

assuming N and N are uncorrelated Nmeas = NS.U .T . + (N1 + N2 ) / M 1 2

M (number of correlations) 10 100 1,000 10,000

Noise reduction on (N1+N2) –5 dB –10 dB –15 dB –20 dB

28 CROSS - CORRELATION SYSTEM W/ BUILT- IN REFERENCES

• Keysight E5052B incorporates two-channel cross- correlation measurement system to reduce measurement noise • Can configure as: • Two-channel phase noise (phase detector) reference/PLL system • Two-channel heterodyne digital-discriminator system • Provides excellent phase noise measurement performance for many classes of sources & oscillators • Well suited to free-running oscillators

29 RESIDUAL MEASUREMENTS USING A PHASE DETECTOR

• Can think of as completely different class of measurement vs. absolute phase noise measurements • Is “additive” or residual noise added to electronic signal • Often performed on two-port device (e.g., amplifier, mixer, multiplier, divider) • Phase noise of stimulus doesn’t affect performance of residual measurement • Stimulus perfectly correlated at both ports of phase detector & will cancel in quadrature (∆흓 = ퟗퟎ° so 푽 = 푲∆흓 = 0V) • Leaves only additional phase noise added to signal by DUT

30 31 NOISE SIDEBANDS MAY NOT BE ENTIRELY PHASE

32 NOISE SIDEBANDS MAY NOT BE ENTIRELY PHASE

33 NOISE SIDEBANDS MAY NOT BE ENTIRELY PHASE

34 Phase Noise is superimposed on every spectral component

V (specifically, every PRF line)

PRF ƒc

PRF /2

• Max phase noise measurement offset is PRF/2 • PRF lines dominate the phase noise plot > PRF • AM detector for AM measurements see all the Power 35 PRF /2

36 GOLD STANDARD PHASE DETECTOR - BASED SYSTEM

• Can configure E5500 system as: • Reference-source/PLL system • Frequency-discriminator system • Solution for absolute & residual phase noise measurements • Solution for pulsed phase noise measurements • System is complex, but offers most measurement flexibility & best overall system performance • Can use any frequency-tunable reference sources for best possible absolute phase noise measurements

37 INDUSTRY LEADING REPLACEMENT FOR E5500 PHASE NOISE TEST SYSTEM

“See Farther Down in Phase Noise” • Best-in-Class Absolute and Residual Measurements • Measure down to kT thermal phase noise floor: - 177dBm/Hz • Extremely fast and flexible for the most demanding measurements • Phase detector method for best dynamic range (by canceling the carrier) • Multi-Segment cross-correlation in FPGA Hardware PNTS

• Ability to add external splitters, attenuators, amplifiers, f Det RF In RF and other test setup independently to each channel FFT LO accessories and suppress any additive noise from these REF DUT LO In CH 1 ∫ Cross devices via the cross-correlation process Correlate Vtune Out

• Completely code compatible with the E5500A f Det RF RF In FFT LO • “Future Proof” with PXIe REF CH 2 LO In ∫ Coming… Vtune Out …JuneKeysight 2019 38 Confidential 39 1

160MHz

40 MORE ACCURATE ANALYSIS - RUNS FASTER - FULLY UPGRADABLE

• Models from 13 GHz to 110 GHz of real-time bandwidth • 2 or 4 channels per scope - ALL with FULL rated bandwidth • Best in class sample rates: • 13 – 33 GHz 3.5 mm models: 128 GSa/s per channel • 25 – 110 GHz 1 mm & 1.85 mm models: 256 GSa/s per channel • 200 Mpts/ch standard – Upgradable to 2 Gpts per channel • High-Definition 10-bit Analog-to-Digital Converter (ADC)

Fully upgradable modular design • Best signal integrity and vertical resolution • Hardware based acceleration ASICs • Optional self calibration module – enables you to perform a factory quality frame calibration at your location

41 42 WHY MEASURE PHASE NOISE WITH A SCOPE?

• As clocking requirements get tighter, phase noise measurements supplement traditional jitter measurements

• mmWave applications require the ability to measure low phase noise at high frequencies

• Ability to measure phase noise on a variety of signals (square waves differential, probed signals, with SSC…)

43 44 • Becker, Randy, and Antonio Castro. “Generating and Analyzing MmWave Signals for Imaging Radar and Wideband Communications.” Keysight AD Symposium 2015. Worldwide , Worldwide . • Gheen, Kay. “Phase Noise Measurement Methods and Techniques.” Agilent/Keysight AD Symposium 2012. Worldwide & Webcast, Worldwide & Webcast. • Hati, Archita, et al. “Calibration Uncertainty for the NIST PM/AM Noise Standards.” U.S. National Institute of Standards & Technology, U.S. Department of Commerce , 23 Mar. 2018, www.nist.gov/publications/calibration-uncertainty-nist-pmam-noise-standards. • Hewlett Packard/Keysight. Application Note 150-1: Spectrum Analysis Amplitude & Frequency Modulation. Application Note 150-1: Spectrum Analysis Amplitude & Frequency Modulation, Hewlett Packard, 1989. • Hewlett Packard/Keysight Technologies. Phase Noise Characterization of Microwave Oscillators: Frequency Discriminator Method. Phase Noise Characterization of Microwave Oscillators: Frequency Discriminator Method, Hewlett Packard, 1985. • Hewlett Packard/Keysight Technologies. Phase Noise Characterization of Microwave Oscillators: Phase Detector Method. Phase Noise Characterization of Microwave Oscillators: Phase Detector Method, Hewlett Packard, 1984. • “IEEE 1139-1999: IEEE Standard Definitions of Physical Quantities for Fundamental Frequency and Time Metrology— Random Instabilities.” IEEE Xplore, Institute of Electrical and Electronics Engineers, 26 Mar. 1999, ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=807679A. • Kanemitsu, Rich. “Phase Noise Measurement Basics -An Overview .” Keysight Customer Training. 2018, USA, USA. • Keysight Technologies . Phase Noise Measurement Solutions. Phase Noise Measurement Solutions, Keysight, 2018, literature.cdn.keysight.com/litweb/pdf/5990- 5729EN.pdf?id=1896487. • Leeson, David B. “Oscillator Phase Noise: A 50-Year Review.” IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control, vol. 63, no. 8, 2016, pp. 1208–1225., doi:10.1109/tuffc.2016.2562663. • Nelson, Bob. “Demystify Integrated-Phase-Deviation Results In Phase-Noise Measurements.” Microwaves & RF, 2 Oct. 2012, www.mwrf.com/test-amp-measurement- analyzers/demystify-integrated-phase-deviation-results-phase-noise-measurements. • Palermo, Sam. “ECEN 620: Network Theory: Broadband Circuit Design.” Sam Palermo - ECEN 620, Texas A&M University , ece.tamu.edu/~spalermo/ecen620.html. • Prodanov, Vladamir. “Lecture 25: Introduction to Phase Noise.” EE412: Advanced Analog Circuits. 2013, San Luis Obispo, California Polytechnic State University . • Trump, Bruce. “1/f Noise-the Flickering Candle.” EDN, Electrical Design News (EDN) Network, www.edn.com/electronics-blogs/the-signal/4408242/1-f-Noise-the-flickering- candle-.

45 Bruno Duarte [email protected] (11) 98353-0059

46