2011 NCSL International Workshop and Symposium

Establishing Traceability for Quantities Derived from

Multiple Traceable Quantities

Alberto Campillo, Jian LiuAgilent Technologies

alberto_campillo@agilent.comjian_liu@agilent.com

2011 NCSL International Workshop and SymposiumSharing 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.

2011 NCSL International Workshop and SymposiumAgenda

• Derived quantity and traceability: concept

• Establishing traceability: general approach

• Phase noise: example

• Definition and expressions

• Direct spectrum method

• Phase detector method

• Summary

2011 NCSL International Workshop and SymposiumAgenda

• Derived quantity and traceability: concept

• Establishing traceability: general approach

• Phase noise: example

• Definition and expressions

• Direct spectrum method

• Phase detector method

• Summary

2011 NCSL International Workshop and SymposiumIntroduction

• 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(x1,x2,…)

2011 NCSL International Workshop and SymposiumDerived quantity concept

International System of Units (SI)*

* http://www.bipm.org/en/si/si_brochure/

Base quantity     Base unit  Name Symbol   Name Symbollength l, x, r…   meter mmass m   kilogram kgtime, duration t   second selectric current I, i   ampere Athermodynamic temperature T   kelvin Kamount of substance n   mole molluminous intensity Iv   candela cd

Derived quantity     Derived unit  

Name Symbol   Name Symbol

speed v meter per second m/svoltage U Volt V (m2 kg s−3 A−1)phase noise decibel relative to carrier per Hertz dBc/Hz (s)… …   … …

( )fL

2011 NCSL International Workshop and SymposiumDerived quantity concept

SI base quantities =

speed voltage

phase noise

NOT EXACTLY SO!

/ top of traceability chain

current

voltage(Josephson)

resistance(Quantum Hall)

Any quantities can be derived

traceablevoltage

traceableresistance

2011 NCSL International Workshop and SymposiumDerived quantity concept

* JCGM 200:2008, International vocabulary of metrology - Basic and general concepts and associated terms (VIM)

International Vocabulary of Metrology (VIM)*

2011 NCSL International Workshop and SymposiumTraceability concept

* JCGM 200:2008, International vocabulary of metrology - Basic and general concepts and associated terms (VIM)

International Vocabulary of Metrology (VIM)*

2011 NCSL International Workshop and SymposiumAgenda

• Derived quantity and traceability: concept

• Establishing traceability: general approach

• Phase noise: example

• Definition and expressions

• Direct spectrum method

• Phase detector method

• Summary

2011 NCSL International Workshop and SymposiumEstablishing traceability:

general approach

Required content:

• Measurand

• Measurement method

• Measurement equation(s)

• Uncertainty equation(s)

• MU contributors

• Final MU

• Supporting evidences

Physical principle: most essential!

2011 NCSL International Workshop and SymposiumAgenda

• Derived quantity and traceability: concept

• Establishing traceability: general approach

• Phase noise: example

• Definition and expressions

• Direct spectrum method

• Phase detector method

• Summary

2011 NCSL International Workshop and SymposiumDefinition 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.

Noise Power in 1 Hz BW( ) 10log

Total Signal Powerf

L ( )[dBc/Hz] [dBm/Hz] [dBm]n sf P P L

f

2011 NCSL International Workshop and SymposiumDefinition and expressions

Expression 2:

•Spectral density of phase fluctuations

•Phase variance per 1 Hz BW

•In dB when referenced to 1 rad/sqrt(Hz)

2 2rms

rms

rad( )

BW used to measure Hz

fS f

When total phase fluctuation in the modulation sideband << 1 radian (small angle criterion): 1

( ) ( )2

f S fL

2011 NCSL International Workshop and SymposiumDirect spectrum method

8563A SPECTRUM ANALYZER 9 kHz - 26.5 GHz

UUT

Spectrum Analyzer

( )[dBc/Hz] [dBm/Hz] [dBm]n sf P P L

2011 NCSL International Workshop and SymposiumDirect spectrum method

Major MU contributors:

•Bandwidth normalization (shape of IF filter & amplifier)

•Amplitude accuracy

•High offset frequency Mismatch

( )[dBc/Hz] [dBm/Hz] [dBm]n sf P P L

2011 NCSL International Workshop and SymposiumPhase detector method

2rms

rms

( )BW used to measure

fS f

2011 NCSL International Workshop and SymposiumPhase detector method

Major MU contributors:

•Phase detector K factor

•Baseband analyzer accuracy

•Test set frequency response

•PLL suppression correction

•High offset frequency mismatch 2

rms

rms

( )BW used to measure

fS f

2011 NCSL International Workshop and SymposiumSummary

• 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.

2011 NCSL International Workshop and Symposium

THANK YOU!

Questions & comments?

2011 NCSL International Workshop and Symposium

BACKUP SLIDES

2011 NCSL International Workshop and SymposiumPhase Noise Overview

2011 NCSL International Workshop and SymposiumDirect Spectrum Method

Overall sensitivity limited by SA internal LO

8563A SPECTRUM ANALYZER 9 kHz - 26.5 GHz

UUT

Spectrum Analyzer

2011 NCSL International Workshop and SymposiumPhase 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

2011 NCSL International Workshop and SymposiumPhase Noise traced to Noise Figure 1

http://www.hparchive.com/seminar_notes/HP_PN_seminar.pdf

2011 NCSL International Workshop and SymposiumPhase Noise traced to Noise Figure 2

http://www.hparchive.com/seminar_notes/HP_PN_seminar.pdf