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2011 NCSL International Workshop and Symposium Establishing Traceability for Quantities Derived from Multiple Traceable Quantities Alberto Campillo, Jian Liu Agilent Technologies

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2011 NCSL International Workshop and Symposium Sharing of learning experience Target audience: Engineers new to metrology and traceability Learning objectives: Concept of SI, base quantity, derived quantity and traceability. General approach of establishing traceability. Concept, measurement techniques and traceability of phase noise.

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2011 NCSL International Workshop and Symposium Agenda Derived quantity and traceability: concept Establishing traceability: general approach Phase noise: example Definition and expressions Direct spectrum method Phase detector method Summary

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2011 NCSL International Workshop and Symposium Agenda Derived quantity and traceability: concept Establishing traceability: general approach Phase noise: example Definition and expressions Direct spectrum method Phase detector method Summary

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2011 NCSL International Workshop and Symposium Introduction Traced to the same quantity STD weight: 50 g ± 0.1 g UUT weight: 50 g ± 1 g Derived from several different quantities v = d / t I = V / R phase noise = f(x 1,x 2,…)

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2011 NCSL International Workshop and Symposium Derived quantity concept International System of Units (SI)* * Base quantity Base unit NameSymbol NameSymbol lengthl, x, r… meterm massm kilogramkg time, durationt seconds electric currentI, i ampereA thermodynamic temperatureT kelvinK amount of substancen molemol luminous intensityIvIv candelacd Derived quantity Derived unit NameSymbol NameSymbol speedvmeter per secondm/s voltageUVoltV (m 2 kg s 3 A 1 ) phase noise decibel relative to carrier per Hertz dBc/Hz (s) …… ……

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2011 NCSL International Workshop and Symposium Derived quantity concept SI base quantities = speedvoltage phase noise NOT EXACTLY SO! / top of traceability chain current voltage (Josephson) resistance (Quantum Hall) Any quantities can be derived traceable voltage traceable resistance

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2011 NCSL International Workshop and Symposium Derived quantity concept * JCGM 200:2008, International vocabulary of metrology - Basic and general concepts and associated terms (VIM) International Vocabulary of Metrology (VIM)*

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2011 NCSL International Workshop and Symposium Traceability concept * JCGM 200:2008, International vocabulary of metrology - Basic and general concepts and associated terms (VIM) International Vocabulary of Metrology (VIM)*

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2011 NCSL International Workshop and Symposium Agenda Derived quantity and traceability: concept Establishing traceability: general approach Phase noise: example Definition and expressions Direct spectrum method Phase detector method Summary

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2011 NCSL International Workshop and Symposium Establishing traceability: general approach Required content: Measurand Measurement method Measurement equation(s) Uncertainty equation(s) MU contributors Final MU Supporting evidences Physical principle: most essential!

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2011 NCSL International Workshop and Symposium Agenda Derived quantity and traceability: concept Establishing traceability: general approach Phase noise: example Definition and expressions Direct spectrum method Phase detector method Summary

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2011 NCSL International Workshop and Symposium Definition and expressions Phase noise: short-term frequency stability in frequency domain Expression 1: Single sideband power 1 Hz bandwidth frequency f offset from the carrier referenced to the carrier frequency power. f

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2011 NCSL International Workshop and Symposium Definition and expressions Expression 2: Spectral density of phase fluctuations Phase variance per 1 Hz BW In dB when referenced to 1 rad/sqrt(Hz) When total phase fluctuation in the modulation sideband << 1 radian (small angle criterion):

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2011 NCSL International Workshop and Symposium Direct spectrum method 8563A SPECTRUM ANALYZER 9 kHz GHz UUT Spectrum Analyzer

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2011 NCSL International Workshop and Symposium Direct spectrum method Major MU contributors: Bandwidth normalization (shape of IF filter & amplifier) Amplitude accuracy High offset frequency Mismatch Phase noise traced to Frequency RF power Attenuation Reflection coefficient

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2011 NCSL International Workshop and Symposium Phase detector method

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2011 NCSL International Workshop and Symposium Phase detector method Major MU contributors: Phase detector K factor Baseband analyzer accuracy Test set frequency response PLL suppression correction High offset frequency mismatch Phase noise traced to Frequency RF power AC Voltage Attenuation Reflection coefficient Noise

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2011 NCSL International Workshop and Symposium Summary Derived quantity & traceability: concept Derived quantity in SI and on traceability chain are not the same Measurement uncertainty determines the validity of traceability Establishing traceability: general approach Details from measurement method to final MU should be documented. Pay special attention to the physical principle. Phase noise: example Different measurement methods and ranges may give different traceability.

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2011 NCSL International Workshop and Symposium THANK YOU! Questions & comments?

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2011 NCSL International Workshop and Symposium BACKUP SLIDES

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2011 NCSL International Workshop and Symposium Phase Noise Overview

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2011 NCSL International Workshop and Symposium Direct Spectrum Method Overall sensitivity limited by SA internal LO 8563A SPECTRUM ANALYZER 9 kHz GHz UUT Spectrum Analyzer

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2011 NCSL International Workshop and Symposium Phase Detector Method PROS AM noise suppression Low overall noise floor Wide offset frequency range Wide carrier frequency range CONS Requires an extra reference source (and downconverter) with much lower phase noise (15 dB less than the UUT) High drift rate UUT requires high peak-tune-range (PTR) reference source Close-in measurements require additional correction

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2011 NCSL International Workshop and Symposium Phase Noise traced to Noise Figure 1

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2011 NCSL International Workshop and Symposium Phase Noise traced to Noise Figure 2

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