Establishing Traceability for Quantities Derived from Multiple Traceable Quantities

1. Establishing Traceability for Quantities Derived from Multiple Traceable Quantities Alberto Campillo, Jian Liu Agilent Technologies alberto_campillo@agilent.com jian_liu@agilent.com

2. 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.

3. Agenda • Derived quantity and traceability: concept • Establishing traceability: general approach • Phase noise: example • Definition and expressions • Direct spectrum method • Phase detector method • Summary

4. Agenda • Derived quantity and traceability: concept • Establishing traceability: general approach • Phase noise: example • Definition and expressions • Direct spectrum method • Phase detector method • Summary

5. 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(x1,x2,…)

6. Derived quantity concept * http://www.bipm.org/en/si/si_brochure/ International System of Units (SI)*

7. Derived quantity concept / top of traceability chain voltage (Josephson) resistance (Quantum Hall) traceable voltage traceable resistance NOT EXACTLY SO! speed voltage current phase noise Any quantities can be derived SI base quantities =

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

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

10. Agenda • Derived quantity and traceability: concept • Establishing traceability: general approach • Phase noise: example • Definition and expressions • Direct spectrum method • Phase detector method • Summary

11. 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!

12. Agenda • Derived quantity and traceability: concept • Establishing traceability: general approach • Phase noise: example • Definition and expressions • Direct spectrum method • Phase detector method • Summary

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

14. 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):

15. 8563A SPECTRUM ANALYZER 9 kHz - 26.5 GHz Direct spectrum method Spectrum Analyzer UUT

16. Direct spectrum method Phase noise traced to Frequency RF power Attenuation Reflection coefficient • Major MU contributors: • Bandwidth normalization (shape of IF filter & amplifier) • Amplitude accuracy • High offset frequency Mismatch

17. Phase detector method

18. 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

19. 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.

20. THANK YOU!Questions & comments?

21. Backup slides

22. Phase Noise Overview

23. 8563A SPECTRUM ANALYZER 9 kHz - 26.5 GHz Direct Spectrum Method Spectrum Analyzer UUT Overall sensitivity limited by SA internal LO

24. 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

25. Phase Noise traced to Noise Figure 1 http://www.hparchive.com/seminar_notes/HP_PN_seminar.pdf

26. Phase Noise traced to Noise Figure 2 http://www.hparchive.com/seminar_notes/HP_PN_seminar.pdf