Reverberation Chamber Calibration Procedures · 2019-10-28 · SKA/15/08/07/REV0 August 07, 2015 orewFord This document has been written as a practical Reverberation Chamber (RC)

❚❡❝❤♥✐❝❛❧ ●✉✐❞❡

❘❡✈❡r❜❡r❛t✐♦♥ ❈❤❛♠❜❡r

❈❛❧✐❜r❛t✐♦♥ Pr♦❝❡❞✉r❡s

❲♦r❦ ❞♦♥❡ ❢♦r✿ ❙q✉❛r❡ ❑✐❧♦♠❡tr❡ ❆rr❛② ❙♦✉t❤ ❆❢r✐❝❛

❆✳ ❘✳ ❇♦t❤❛✱ ❏✳ ❆✳ ❆♥❞r✐❛♠❜❡❧♦s♦♥ ❛♥❞ ❆✳ ❏✳ ❖tt♦

❉♦❝✉♠❡♥t ◆✉♠❜❡r✿ ❙❑❆✴✶✺✴✵✽✴✵✼

❘❡✈✐s✐♦♥ ◆✉♠❜❡r✿ ❘❊❱✵

❉♦❝✉♠❡♥t ❉❛t❡✿ ✼ ❆✉❣✉st ✷✵✶✺

❚❤✐s ❞♦❝✉♠❡♥t ❝♦♥t❛✐♥s ♣r♦♣r✐❡t❛r② ✐♥❢♦r♠❛t✐♦♥ ❛♥❞ ♠❛② ♥♦t ❜❡ ❞✐s❝❧♦s❡❞ ✇✐t❤♦✉t t❤❡✇r✐tt❡♥ ❝♦♥s❡♥t ♦❢ ▼❊❙❆ ❙♦❧✉t✐♦♥s ✭Pt②✮ ▲t❞✳ ♦r t❤❡ ❝❧✐❡♥t ❢♦r ✇❤♦♠ ✐t ✐s ✐♥t❡♥❞❡❞✳

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❉♦❝✉♠❡♥t ❆♣♣r♦✈❛❧

◆❛♠❡ ❆✣❧✐❛t✐♦♥ ❉❡s✐❣♥❛t✐♦♥ ❙✐❣♥❛t✉r❡

❙✉❜♠✐tt❡❞ ❆✳ ❏✳ ❖tt♦ ▼❊❙❆ ❙♦❧✉t✐♦♥s ▼❛♥❛❣✐♥❣ ❉✐r❡❝t♦r

P✳ ❙✳ ✈❛♥ ❞❡r ▼❡r✇❡ ▼❊❙❆ ❙♦❧✉t✐♦♥s ▼❛♥❛❣✐♥❣ ❉✐r❡❝t♦r

❍✳ ❈✳ ❘❡❛❞❡r ▼❊❙❆ ❙♦❧✉t✐♦♥s ❈♦♥s✉❧t✐♥❣ ❉✐r❡❝t♦r

❆❝❝❡♣t❡❞ ▼r✳ ❈❛r❡❧ ✈❛♥ ❞❡r ▼❡r✇❡ ❙❑❆✲❙❆ ❘❋■ ▼❛♥❛❣❡r

▼r✳ ▲ött❡r ❑♦❝❦ ❙❑❆✲❙❆ ❘❋■ ❊♥❣✐♥❡❡r

❉♦❝✉♠❡♥t ❍✐st♦r②

❘❡✈✐s✐♦♥ ❉❛t❡ ♦❢ ■ss✉❡ ❈♦♠♠❡♥ts

❉❘❆❋❚ ✷✽ ❏✉❧② ✷✵✶✺ ❚❡❝❤♥✐❝❛❧ ●✉✐❞❡ ❙❑❆✴✶✺✴✵✽✴✵✼

❘❊❱✵ ✼ ❆✉❣✉st ✷✵✶✺ ❚❡❝❤♥✐❝❛❧ ●✉✐❞❡

❈♦♠♣❛♥② ❉❡t❛✐❧s

◆❛♠❡ ▼❊❙❆ ❙♦❧✉t✐♦♥s ✭Pt②✮ ▲t❞✳

P❤②s✐❝❛❧✴P♦st❛❧ ❆❞❞r❡ss ❆❛♥✲❞❡✲✇❛❣❡♥ ❈❡♥tr❡

❆❛♥✲❞❡✲✇❛❣❡♥ ❘♦❛❞

❙t❡❧❧❡♥❜♦s❝❤

✼✻✵✵

❚❡❧✳ ✵✽✷ ✽✹✺ ✽✻✸✵

❲❡❜s✐t❡ ❤tt♣✿✴✴✇✇✇✳♠❡s❛s♦❧✉t✐♦♥s✳❝♦✳③❛✴

P❛❣❡ ✶ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋♦r❡✇♦r❞

❚❤✐s ❞♦❝✉♠❡♥t ❤❛s ❜❡❡♥ ✇r✐tt❡♥ ❛s ❛ ♣r❛❝t✐❝❛❧ ❘❡✈❡r❜❡r❛t✐♦♥ ❈❤❛♠❜❡r ✭❘❈✮ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡ ❣✉✐❞❡✳ ❆s s✉❝❤✱✐t ✐s ♣r❡s❡♥t❡❞ ✐♥ ❛ st❡♣✇✐s❡ ❢♦r♠❛t ✇✐t❤ ❧✐♠✐t❡❞ t❤❡♦r❡t✐❝❛❧ ❡①♣❧❛♥❛t✐♦♥✳ ❚❤❡ t❡①t s❤♦✉❧❞ ❜❡ r❡❛❞❛❜❧❡ ✇❤✐❧st ❛ ✉s❡r✐s ✉♥❞❡rt❛❦✐♥❣ ❛ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡✳

❚❤❡ ❜✐❜❧✐♦❣r❛♣❤② ❝♦♥t❛✐♥s s❡✈❡r❛❧ r❡❢❡r❡♥❝❡s ❢♦r ❛ ♠♦r❡ ✐♥✲❞❡♣t❤ st✉❞②✱ ✐♥❝❧✉❞✐♥❣ t❤❡ ❢✉♥❞❛♠❡♥t❛❧ ■❊❈ ✻✶✵✵✵✲✹✲✷✶ st❛♥❞❛r❞ ❢♦r ❘❈s✳

❚❤❡ ❢♦❝✉s ❤❡r❡ ✐s ♦♥ t❤❡ ♣r❛❝t✐❝❛❧ ❛s♣❡❝ts ♦❢ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ♠❡t❤♦❞♦❧♦❣② t❤❛t ♠✉st ❜❡ ❝♦♥s✐❞❡r❡❞ t♦ ❡♥s✉r❡ ✐♥t❡❣r✐t②✐♥ ❝❛❧✐❜r❛t❡❞ ♠❡❛s✉r❡♠❡♥t r❡s✉❧ts✳

P❛❣❡ ✷ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❈♦♥t❡♥ts

❋♦r❡✇♦r❞ ✷

❈♦♥t❡♥ts ✸

◆♦♠❡♥❝❧❛t✉r❡ ✹

▲✐st ♦❢ ❋✐❣✉r❡s ✺

▲✐st ♦❢ ❋✐❣✉r❡s ✺

❆❝❦♥♦✇❧❡❞❣❡♠❡♥ts ✻

✶ ■♥tr♦❞✉❝t✐♦♥ ✼✶✳✶ ❆ss❡ss✐♥❣ ◆❡❡❞ ❢♦r ❈❛❧✐❜r❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼

✷ ❊q✉✐♣♠❡♥t ❛♥❞ Pr❡♣❛r❛t✐♦♥ ✾✷✳✶ ❊q✉✐♣♠❡♥t ▲✐st ❛♥❞ ❘❡❝♦♠♠❡♥❞❛t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✷✳✷ ❲♦r❦s♣❛❝❡ ❈♦♥s✐❞❡r❛t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷✳✸ ❍❛r❞✇❛r❡ Pr❡♣❛r❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶

✷✳✸✳✶ ❈♦♥♥❡❝t♦r ❈❛r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷✳✸✳✷ ❈❛❜❧❡ ❘❡❝♦♠♠❡♥❞❛t✐♦♥s ❛♥❞ ❈❛r❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✸✷✳✸✳✸ ❆♥t❡♥♥❛ P♦s✐t✐♦♥s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✺

✷✳✹ ❱◆❆ ❙❡t✉♣ ❛♥❞ ❈❛❧✐❜r❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✽✷✳✺ ❱◆❆ ❈❛❧✐❜r❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✾✷✳✻ Pr❡✲▼❡❛s✉r❡♠❡♥t ❚❡sts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶

✷✳✻✳✶ ❱◆❆ ❈❛❧✐❜r❛t✐♦♥ ❈❤❡❝❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✶✷✳✻✳✷ ❈❛❜❧❡ ❙❤✐❡❧❞✐♥❣ ❚❡st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✸✷✳✻✳✸ ❆♥t❡♥♥❛ ❚❡st ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺

✸ ❘❈ ❈❛❧✐❜r❛t✐♦♥ ✷✻✸✳✶ ❈❛❧✐❜r❛t✐♦♥ ▼❡❛s✉r❡♠❡♥ts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✻✸✳✷ ❉❛t❛ Pr♦❝❡ss✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✽

✹ ❈❛❧✐❜r❛t✐♦♥ ❱❛❧✐❞❛t✐♦♥ ▼❡❛s✉r❡♠❡♥ts ✸✷✹✳✶ ❈♦♥t✐♥✉♦✉s✲❲❛✈❡ t❡sts ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷

❘❡❢❡r❡♥❝❡s ✸✹

❆ ▼❆❚▲❆❇ s❝r✐♣ts✿ ✸✺❆✳✶ ❆♥t❡♥♥❛ ❈❤❡❝❦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✺❆✳✷ ❉❛t❛ ❆❝q✉✐s✐t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✽❆✳✸ ❉❛t❛ Pr♦❝❡ss✐♥❣ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✶❆✳✹ ❈❛❧✐❜r❛t✐♦♥ ❱❛❧✐❞❛t✐♦♥ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹

P❛❣❡ ✸ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

◆♦♠❡♥❝❧❛t✉r❡

❆❈❋ ❆♥t❡♥♥❛ ❈❛❧✐❜r❛t✐♦♥ ❋❛❝t♦r

❆❱❋ ❆♥t❡♥♥❛ ❱❛❧✐❞❛t✐♦♥ ❋❛❝t♦r

❈❈❋ ❈❤❛♠❜❡r ❈❛❧✐❜r❛t✐♦♥ ❋❛❝t♦r

❈▲❋ ❈❤❛♠❜❡r ▲♦❛❞✐♥❣ ❋❛❝t♦r

❉❯❚ ❉❡✈✐❝❡ ❯♥❞❡r ❚❡st

❊✲✜❡❧❞ ❊❧❡❝tr✐❝ ❋✐❡❧❞

❊❘❙ ❊♠✐ss✐♦♥s ❘❡❢❡r❡♥❝❡ ❙♦✉r❝❡

❋❉ ❋r❡q✉❡♥❝② ❉♦♠❛✐♥

●❍③ ●✐❣❛❤❡rt③

●▲P❉❆ ●✐❞❡♦♥✲▲P❉❆

❍❋ ❍✐❣❤ ❋r❡q✉❡♥❝②

■▲ ■♥s❡rt✐♦♥ ▲♦ss

▲P❉❆ ▲♦❣ P❡r✐♦❞✐❝ ❉✐♣♦❧❡ ❆rr❛②

▲❯❋ ▲♦✇❡st ❯s❛❜❧❡ ❋r❡q✉❡♥❝②

▼❍③ ▼❡❣❛❤❡rt③

◆P▲ ◆❛t✐♦♥❛❧ P❤②s✐❝❛❧ ▲❛❜♦r❛t♦r②

❖❆❚❙ ❖♣❡♥ ❆r❡❛ ❚❡st ❙✐t❡

❘❈ ❘❡✈❡r❜❡r❛t✐♦♥ ❈❤❛♠❜❡r

❙❆ ❙♣❡❝tr✉♠ ❆♥❛❧②③❡r

❙❑❆ ❙q✉❛r❡ ❑✐❧♦♠❡tr❡ ❆rr❛②

❙❑❆✲❙❆ ❙q✉❛r❡ ❑✐❧♦♠❡tr❡ ❆rr❛② ❙♦✉t❤ ❆❢r✐❝❛

❙❖▲❚ ❙❤♦rt✲❖♣❡♥✲▲♦❛❞✲❚❤r♦✉❣❤

❚❉ ❚✐♠❡ ❉♦♠❛✐♥

❚❘▲ ❚❤r♦✉❣❤✲❘❡✢❡❝t✲▲✐♥❡

❱◆❆ ❱❡❝t♦r ◆❡t✇♦r❦ ❆♥❛❧②③❡r

P❛❣❡ ✹ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

▲✐st ♦❢ ❋✐❣✉r❡s

✶ ❙❝❤❡♠❛t✐❝ ♦❢ ❘❈ ❝❛❧✐❜r❛t✐♦♥ ♠❡❛s✉r❡♠❡♥ts✳ ◆♦t❡ t❤❡ ❞❡✜♥✐t✐♦♥ ♦❢ t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳ ❆❧s♦✱●▲P❉❆✶ r❡♣r❡s❡♥ts t❤❡ st❛t✐❝ ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥ ✇✐t❤ ❆✶✲❆✹ ❛♥❞ ❇✶✲❇✹ r❡♣r❡s❡♥t✐♥❣ ❞✐s♣❧❛❝❡❞✲❛♥t❡♥♥❛ ✭●▲P❉❆✷✮ ♣♦s✐t✐♦♥s ❛t t❤❡ ❝♦r♥❡rs ♦❢ t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽

✷ ❈♦♥♥❡❝t♦r ❝❧❡❛♥✐♥❣ ✇✐t❤ ❧✐♥t✲❢r❡❡ ❝❧♦t❤ ❛♥❞ ■s♦♣r♦♣②❧ ❆❧❝♦❤♦❧✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✸ ❚♦rq✉✐♥❣ ❝❛❜❧❡ ❝♦♥♥❡❝t♦r ❛t ●▲P❉❆✳ ◆♦t❡ ❧❡❢t✲❤❛♥❞ s✉♣♣♦rt ✇✐t❤ ✜♥❣❡rs ❛♥❞ s♣❛♥♥❡r✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✷✹ ▲❛②♦✉t ✇✐t❤ ❝❛❜❧❡ ❝❧❡❛r ♦❢ ✇❛❧❦✐♥❣ ❛r❡❛s ❛♥❞ s✉♣♣♦rt❡❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✺ ❈❛❜❧❡ s✉♣♣♦rt❡❞ ❜② ❛♥t❡♥♥❛ ♠♦✉♥t t♦ ❧✐♠✐t str❡ss ❛t ❝♦♥♥❡❝t♦rs✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✹✻ ❆♥t❡♥♥❛ ❛❧✐❣♥❡❞ t♦ ❝♦r♥❡r ♦❢ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳ ◆♦t❡ t❛♣❡ ♠❛r❦❡r ❢♦r ✈♦❧✉♠❡ ❝♦r♥❡r ❛t ▲❯❋✳ ✳ ✳ ✳ ✳ ✳ ✶✻✼ ❙♠❛❧❧ ♠❡t❛❧❧✐❝ ❜r❛❝❦❡ts ❝♦♠❜✐♥❡❞ ✇✐t❤ r♦♣❡ ❢♦r ❆✶✲❆✹ ❛♥t❡♥♥❛ ♠♦✉♥ts✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✻✽ ❙❝❤❡♠❛t✐❝ s❤♦✇✐♥❣ ❘❈✲❝❛❧✐❜r❛t✐♦♥ ❛♥t❡♥♥❛ ♣❧❛❝❡♠❡♥t✳ ❆✶✲❆✹ r❡❢❡r t♦ ♣♦s✐t✐♦♥s ✐♥ t❤❡ ✉♣♣❡r ❝♦r♥❡rs

❛♥❞ ❇✶✲❇✹ t❤❡ ❧♦✇❡r ❝♦r♥❡rs ♦❢ t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✱ r❡s♣❡❝t✐✈❡❧②✳ ◆♦t❡ t❤❡ ❞✐✛❡r❡♥❝❡ ✐♥ ❛♥t❡♥♥❛♣♦❧❛r✐s❛t✐♦♥s ❢♦r ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥s ✐♥ ❝❧♦s❡ ♣r♦①✐♠✐t②✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✼

✾ ❙❝❤❡♠❛t✐❝ ♦❢ ❱◆❆ ❝❛❧✐❜r❛t✐♦♥ ❧❛②♦✉t✳ ◆♦t❡ t❤❛t ❱◆❆ P♦rts ✶ ❛♥❞ ✷ ❝♦♥♥❡❝t t♦ t❤❡ st❛t✐❝ ❛♥❞❞✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛ ❝❛❜❧❡s✱ r❡s♣❡❝t✐✈❡❧②✱ ♠❛✐♥t❛✐♥✐♥❣ t❤❡ ❝♦♥✈❡♥t✐♦♥✳ ❆❧s♦✱ t❤❡ ❛✉t♦♠❛t✐❝ ❝❛❧✐❜r❛t✐♦♥✉♥✐t✬s ❝♦♥tr♦❧ ❝❛❜❧❡ ✐s ♣❛ss❡❞ ✈✐❛ ❛♥ ♦♣❡♥ ❘❈ ✐♥t❡r❢❛❝❡ ✭t♦♣ r✐❣❤t✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✵

✶✵ ❱◆❆ s❝r❡❡♥ s❤♦✇✐♥❣ r♦✉❣❤❧② ✲✸✵ ❞❇ S11 ❛♥❞ S22 r❡s✉❧ts✱ ✐♥❞✐❝❛t✐♥❣ ♠❛t❝❤✐♥❣ ❛t ❜♦t❤ ♣♦rts✳ ◆♦t❡tr❛❝❡s st♦r❡❞ t♦ ♠❡♠♦r② ✇✐t❤ ❝✉rr❡♥t ♠❡❛s✉r❡♠❡♥ts ♦✈❡r❧❛✐❞✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✷

✶✶ ❈❛❜❧❡✲✐♥t❡❣r✐t② t❡st ✇✐t❤ ❞✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛ ❝❛❜❧❡ r❛✐s❡❞ ✐♥t♦ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✹✶✷ P❧♦t ❣❡♥❡r❛t❡❞ ❜② ❆♥t❡♥♥❛❴❈❤❡❝❦✳♠ s❝r✐♣t✳ ◆♦t❡ t❤❡ ❝❧♦s❡ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ r❡❢❡r❡♥❝❡ ❛♥❞

❘❈✲♠❡❛s✉r❡❞ ♣❧♦ts✱ ✐♥❞✐❝❛t✐♥❣ ❡①♣❡❝t❡❞ ❛♥t❡♥♥❛ ♣❡r❢♦r♠❛♥❝❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✺✶✸ ●P■❇ ❛❞❛♣t❡r ❛❧❧♦❝❛t❡❞ ❛s ◆♦✳ ✵✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼✶✹ ❈❛❧❴♣r♦❝❡ss✐♥❣✳♠ ❣❡♥❡r❛t❡❞ ✜❡❧❞ ✉♥✐❢♦r♠✐t② ♣❧♦t✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾✶✺ ❋✐❡❧❞ ✉♥✐❢♦r♠✐t② ♣❧♦t s❤♦✇✐♥❣ ♣♦♦r r❡s✉❧ts ❢♦r ♣♦s✐t✐♦♥ ❆✹ ✭❞❛t❛✹✮✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✾✶✻ ❈❛❧❴♣r♦❝❡ss✐♥❣✳♠ ❣❡♥❡r❛t❡❞ ❝❛❧✐❜r❛t✐♦♥ ✈❛❧✐❞❛t✐♦♥ ♣❧♦t✳ ◆♦t❡ t❤❛t t❤❡ ♠❡❛s✉r❡❞ ❊✲✜❡❧❞ ✈❛r✐❛♥❝❡

✐s ✇❡❧❧ ❜❡❧♦✇ t❤❡ st❛♥❞❛r❞ ❛❝r♦ss t❤❡ ❝❤❛♠❜❡r ✇♦r❦✐♥❣ r❛♥❣❡✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵✶✼ ❈❛❧❴♣r♦❝❡ss✐♥❣✳♠ ❣❡♥❡r❛t❡❞ ❘❈✲❧♦ss ♣❧♦ts✳ ◆♦t❡ t❤❡ ❞✐✛❡r❡♥❝❡ ♦❢ ❛♣♣r♦①✐♠❛t❡❧② ✼ ❞❇ ❜❡t✇❡❡♥

t❤❡ ❝✉r✈❡s✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✵✶✽ ❙❝❤❡♠❛t✐❝ ♦❢ t❤❡ ❝❛❧✐❜r❛t✐♦♥✲✈❛❧✐❞❛t✐♦♥ t❡st s❡t✉♣✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✷✶✾ ❈❛❧✐❜r❛t✐♦♥ ✈❛❧✐❞❛t✐♦♥ r❡s✉❧ts ♣❧♦tt❡❞ ❜② ✈❛❧✐❞❛t✐♦♥✳♠✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✸

P❛❣❡ ✺ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❆❝❦♥♦✇❧❡❞❣❡♠❡♥ts

▼❊❙❆ ❙♦❧✉t✐♦♥s ✇♦✉❧❞ ❧✐❦❡ t♦ ❛❝❦♥♦✇❧❡❞❣❡✿

❼ ❉r ❏♦❡❧② ❆✳ ❆♥❞r✐❛♠❜❡❧♦s♦♥ ❢♦r s❤❛r✐♥❣ ❤✐s ❡①♣❡rt✐s❡ ♦♥ t❤❡ t♦♣✐❝ ♦❢ r❡✈❡r❜❡r❛t✐♦♥ ❝❤❛♠❜❡rs✱ ❝♦♥tr✐❜✉t✐♥❣ t♦t❤✐s ❞♦❝✉♠❡♥t ❛♥❞ t♦ ❛ ❜❡s♣♦❦❡ tr❛✐♥✐♥❣ ❡①❡r❝✐s❡ ❛t t❤❡ ❙❑❆✲❙❆✱ P✐♥❡❧❛♥❞s✳ ❚❤❡ ❝♦♥tr♦❧ ❛♥❞ ❞❛t❛ ♣r♦❝❡ss✐♥❣s❝r✐♣ts ♣r❡s❡♥t❡❞ ✐♥ t❤❡ t❡①t ✇❡r❡ ❛❧s♦ ❞❡✈❡❧♦♣❡❞ ❜② ❉r ❆♥❞r✐❛♠❜❡❧♦s♦♥✳

P❛❣❡ ✻ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✶ ■♥tr♦❞✉❝t✐♦♥

❆ ❘❡✈❡r❜❡r❛t✐♦♥ ❈❤❛♠❜❡r ✭❘❈✮ ✐s ✐s ❛ ❢❛❝✐❧✐t② ❢♦r ❝♦♥❞✉❝t✐♥❣ ❡❧❡❝tr♦♠❛❣♥❡t✐❝ ✭❊▼✮ ❡♠✐ss✐♦♥ ❛♥❞ s✉s❝❡♣t✐❜✐❧✐t②t❡sts ✐♥ ❛ ❝♦♥tr♦❧❧❛❜❧❡ ❡♥✈✐r♦♥♠❡♥t✳ ❚❤✐s ❞♦❝✉♠❡♥t ✇✐❧❧ ❢♦❝✉s ♦♥ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ♦❢ t❤❡ ❘❈ ❢♦r ❊▼ ❡♠✐ss✐♦♥s ✭❊▼■✮t❡st✐♥❣✳ ❈❛r❡ ♠✉st ❜❡ t❛❦❡♥ t♦ r❡t❛✐♥ t❤❡ s❤✐❡❧❞✐♥❣ ✐♥t❡❣r✐t② ♦❢ t❤❡ ❝❤❛♠❜❡r t♦ ❡①❝❧✉❞❡ ❡①t❡r♥❛❧ ❘❛❞✐♦ ❋r❡q✉❡♥❝②■♥t❡r❢❡r❡♥❝❡ ✭❘❋■✮✳ ❆tt❡♥t✐♦♥ s❤♦✉❧❞ t❤✉s ❜❡ ❣✐✈❡♥ t♦ ❛♥② ❝❛❜❧❡ ✐♥t❡r❢❛❝❡s ❛t t❤❡ ❘❈ ✇❛❧❧s✳❆♥ ❘❈ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡ ❝♦♠♣r✐s❡s ❡❧❡♠❡♥ts ♦❢ ♣r❡♣❛r❛t✐♦♥✱ ♠❡❛s✉r❡♠❡♥t ❛♥❞ ❞❛t❛ ♣r♦❝❡ss✐♥❣✳ ❚❤❡s❡ ❡❧❡♠❡♥ts❛r❡ ♣r❡s❡♥t❡❞ ✐♥ ❛ st❡♣✇✐s❡ ❢❛s❤✐♦♥ t♦ ❡♥❝♦✉r❛❣❡ ❛ ❝❤❛♠❜❡r ♦♣❡r❛t♦r t♦ ❛❞♦♣t ❛ s②st❡♠❛t✐❝ ❛♣♣r♦❛❝❤ ❛♥❞ t♦ ♠❛❦❡t❤✐s t❡①t ❛ ❤❡❧♣❢✉❧ r❡❢❡r❡♥❝❡ ✇❤✐❧❡ ♣❡r❢♦r♠✐♥❣ ❛ ❝❛❧✐❜r❛t✐♦♥✳ ❯❧t✐♠❛t❡❧②✱ ❛ ❝❤❛✐♥ ♦❢ ♠❡❛s✉r❡♠❡♥ts ✐s ♦♥❧② ❛s ❣♦♦❞ ❛s✐ts ✇❡❛❦❡st ❧✐♥❦✳ ❚❤❡ s❡q✉❡♥❝❡ ♦❢ t❤❡ ❣✉✐❞❡✬s s❡❝t✐♦♥s ❛❧s♦ r❡♣r❡s❡♥t t❤❡ ♦r❞❡r ♦❢ t❤❡ t❛s❦s✳

❆❧t❤♦✉❣❤ t❤❡ ♠❛t❡r✐❛❧ ❢♦❝✉s❡s ♦♥ ❘❈s✱ ✐t ✐s ♥ t❤❛t ♠✉❝❤ ♦❢ ✐t ❤❛s ♣r❛❝t✐❝❛❧ ✈❛❧✉❡ ❢♦r ❊▼ ♠❡tr♦❧♦❣② ✐♥ ❣❡♥❡r❛❧✳

■t ✐s ❛ss✉♠❡❞ t❤❛t r❡❛❞❡rs ♦❢ t❤✐s ❣✉✐❞❡ ❛r❡ ❢❛♠✐❧✐❛r ✇✐t❤ ❛❧❧ t❤❡ ❜❛s✐❝ ❘❈ ❞❡✜♥✐t✐♦♥s ❛♥❞ t❤❡♦♣❡r❛t✐♦♥ ♦❢ t❤❡ ❝❤❛♠❜❡r✱ ❛s ✇❡❧❧ ❛s t❤❡ ❡q✉✐♣♠❡♥t ✉s❡❞ ❞✉r✐♥❣ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡ss ❬✷❪✳

❚❤❡ ❣✉✐❞❡ ❢♦❝✉s❡s ♦♥ t❤❡ ❙❑❆✲❙❆ ❘❈ ✐♥ P✐♥❡❧❛♥❞s✱ ❈❛♣❡ ❚♦✇♥✱ ❛♥❞ t❤❡ ❛ss♦❝✐❛t❡❞ ❡q✉✐♣♠❡♥t✳ ❚❤✐s r❡❝t❛♥✲❣✉❧❛r ❝❤❛♠❜❡r ❤❛s ❜❡❡♥ s❤♦✇♥ t♦ ❤❛✈❡ ❛ ✈✐❛❜❧❡ r❛♥❣❡ ♦❢ ✶✽✵ ▼❍③ t♦ ✻ ●❍③✱ ✉s✐♥❣ ●▲P❉❆ ❛♥t❡♥♥❛s ❬✸❪✳ ◆♦t❡ t❤❛t■❊❈ ■❊❈ ✻✶✵✵✵✲✹✲✷✶ s❡r✈❡s ❛s t❤❡ ❢♦✉♥❞❛t✐♦♥ ❢♦r t❤✐s t❡①t ❛♥❞ s❡✈❡r❛❧ ♦❢ t❤❡ ❜✐❜❧✐♦❣r❛♣❤② ❡♥tr✐❡s ❬✶❪✳

❋✐❣✳ ✶ r❡♣r❡s❡♥ts ❛♥ ❘❈✲❝❛❧✐❜r❛t✐♦♥ ❧❛②♦✉t✱ ✐❧❧✉str❛t✐♥❣ t❤❡ ✇♦r❦✐♥❣✲✈♦❧✉♠❡ ❜♦✉♥❞❛r✐❡s✱ ❛♥t❡♥♥❛ ❝❛❧✐❜r❛t✐♦♥ ♣♦✲s✐t✐♦♥s✱ ❱◆❆ ♣❧❛❝❡♠❡♥t✱ ✐♥t❡r❢❛❝❡ ♣♦rts✱ t✇♦ ●▲P❉❆ ❛♥t❡♥♥❛s ❛♥❞ st✐rr❡r✳ ◆♦t❡ t❤❛t t❤❡ st✐rr❡r ❛❧s♦ ❧✐♠✐ts t❤❡✇♦r❦✐♥❣ ✈♦❧✉♠❡✳ ●▲P❉❆✶ ❛♥❞ ●▲P❉❆✷ ❛r❡ r❡❢❡rr❡❞ t♦ ❛s t❤❡ st❛t✐❝ ❛♥t❡♥♥❛ ❛♥❞ ❞✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛r❡s♣❡❝t✐✈❡❧②✱ t❤r♦✉❣❤♦✉t t❤❡ t❡①t✳

✶✳✶ ❆ss❡ss✐♥❣ ◆❡❡❞ ❢♦r ❈❛❧✐❜r❛t✐♦♥

❆ r❡❝❛❧✐❜r❛t✐♦♥ ♦❢ t❤❡ ❘❈ ✐s r❡q✉✐r❡❞ ✇❤❡♥❡✈❡r ♥♦t❛❜❧❡ ❝❤❛♥❣❡s ❛r❡ ♠❛❞❡ t♦ t❤❡ ❝♦♥✜❣✉r❛t✐♦♥✿

❼ ❉❯❚ ♦❢ ❝♦♥s✐❞❡r❛❜❧❡ s✐③❡❚❤❡ ✐♥tr♦❞✉❝t✐♦♥ ♦❢ ❛ ❉❡✈✐❝❡ ❯♥❞❡r ❚❡st ✭❉❯❚✮ ❧♦❛❞s t❤❡ ❝❤❛♠❜❡r✱ ❞❡♣❡♥❞✐♥❣ ♦♥ ✐ts ♠❛t❡r✐❛❧s ❛♥❞ s✉r❢❛❝❡❛r❡❛ r❡❧❛t✐✈❡ t♦ t❤❛t ♦❢ t❤❡ ❘❈✳

❼ ❘❡♣❛✐rs t♦ ❘❈❘❡♣❛✐rs ♠❛② ❝♦♠♣r♦♠✐s❡ s❤✐❡❧❞✐♥❣ ♦r ✐♥✢✉❡♥❝❡ ❝❤❛♠❜❡r ❧♦ss✳

❼ ❆❧t❡r❛t✐♦♥s t♦ ❘❈●❡♥❡r❛❧ ❝❤❛♥❣❡s✱ ♣❛rt✐❝✉❧❛r❧② t♦ t❤❡ ✐♥t❡r✐♦r✳ ■♥❝❧✉❞❡s ✐♥tr♦❞✉❝t✐♦♥ ♦❢ ❛♥② ♠❛t❡r✐❛❧s✱ r❡✢❡❝t✐✈❡ ♦r ❛❜s♦r❜✐♥❣✳

❚❤❡r❡ ✐s ♥♦ ❝❧❡❛r r✉❧❡✲♦❢✲t❤✉♠❜ ❛♥❞ ❝❤❛♠❜❡r r❡❝❛❧✐❜r❛t✐♦♥✳ ❆ ❝❛❧✐❜r❛t✐♦♥ ❝♦✉❧❞ ❜❡ ❝♦♥❞✉❝t❡❞ ♦♥ ❛♥ ❛♥♥✉❛❧ ♦r❜✐❡♥♥✐❛❧ ❜❛s✐s✳ ❈♦♠♣❛r✐s♦♥s t♦ ♣r❡✈✐♦✉s ❝❛❧✐❜r❛t✐♦♥s s❤♦✉❧❞ ❛❧✇❛②s ❜❡ ♠❛❞❡ ❛♥❞ ❛♥② s✐❣♥✐✜❝❛♥t ✈❛r✐❛t✐♦♥s s❤♦✉❧❞❜❡ ✐♥✈❡st✐❣❛t❡❞✳

❚❤❡ r❛t✐♦ ♦❢ t❤❡ ❈❤❛♠❜❡r ❈❛❧✐❜r❛t✐♦♥ ❋❛❝t♦r ✭❈❈❋✮ ✭❧♦❛❞❡❞ ❘❈✮ t♦ t❤❡ ❆♥t❡♥♥❛ ❱❛❧✐❞❛t✐♦♥ ❋❛❝t♦r ✭❆❱❋✮ ✭✉♥✲❧♦❛❞❡❞✮ ✐s t❤❡ ❈❤❛♠❜❡r ▲♦❛❞✐♥❣ ❋❛❝t♦r ✭❈▲❋✮ ❬✷❪✳ ❚❤❡ ❈▲❋ ✐♥❞✐❝❛t❡s t❤❡ ❡rr♦r t❤❛t ✇✐❧❧ ❜❡ ♠❛❞❡ ✐❢ t❤❡ ✉♥❧♦❛❞❡❞❝❛❧✐❜r❛t✐♦♥ ❢❛❝t♦rs ❛r❡ ✉s❡❞ ❢♦r ❧♦❛❞❡❞ ♠❡❛s✉r❡♠❡♥ts✳ ❚♦ ❛❝❤✐❡✈❡ t❤❡ ❜❡st ❛❝❝✉r❛❝②✱ ❢♦❧❧♦✇ t❤❡ ❝❛❧✐❜r❛t✐♦♥ r♦✉t✐♥❡❛♥❞ ✉s❡ t❤❡ r❡❧❡✈❛♥t ❝♦rr❡❝t✐♦♥ ❢❛❝t♦rs✳

P❛❣❡ ✼ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✶✿ ❙❝❤❡♠❛t✐❝ ♦❢ ❘❈ ❝❛❧✐❜r❛t✐♦♥ ♠❡❛s✉r❡♠❡♥ts✳ ◆♦t❡ t❤❡ ❞❡✜♥✐t✐♦♥ ♦❢ t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳ ❆❧s♦✱ ●▲P❉❆✶r❡♣r❡s❡♥ts t❤❡ st❛t✐❝ ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥ ✇✐t❤ ❆✶✲❆✹ ❛♥❞ ❇✶✲❇✹ r❡♣r❡s❡♥t✐♥❣ ❞✐s♣❧❛❝❡❞✲❛♥t❡♥♥❛ ✭●▲P❉❆✷✮ ♣♦s✐t✐♦♥s❛t t❤❡ ❝♦r♥❡rs ♦❢ t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳

P❛❣❡ ✽ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷ ❊q✉✐♣♠❡♥t ❛♥❞ Pr❡♣❛r❛t✐♦♥

❚❤❡ ♣r❡✲♠❡❛s✉r❡♠❡♥t ❢♦❝✉s ✐s ♦♥ ❡q✉✐♣♠❡♥t ❛♥❞ t❤❡ ♣r❡♣❛r❛t✐♦♥ ♥❡❝❡ss❛r② t♦ ❡♥s✉r❡ ❛♥ ❛❝❝✉r❛t❡ ❘❈ ❝❛❧✐❜r❛t✐♦♥✳❆❧t❤♦✉❣❤ s❡✈❡r❛❧ ♣r❡✲♠❡❛s✉r❡♠❡♥t t❡sts ❛r❡ s✉❣❣❡st❡❞✱ ✐t ✐s ❛ss✉♠❡❞ t❤❛t ❛❧❧ ✐♥str✉♠❡♥ts ❛♥❞ t♦♦❧s ❛r❡ ✐♥ ❣♦♦❞❝♦♥❞✐t✐♦♥✳ ❚❤❡ ♣r❡♣❛r❛t✐♦♥ s❤♦✉❧❞ ❜❡ ❝♦♠♣❧❡t❡❞ ♣r✐♦r t♦ ♣❡r❢♦r♠✐♥❣ ❛♥② ♠❡❛s✉r❡♠❡♥ts✳

✷✳✶ ❊q✉✐♣♠❡♥t ▲✐st ❛♥❞ ❘❡❝♦♠♠❡♥❞❛t✐♦♥s

❚❤❡ ❡ss❡♥t✐❛❧ ✐♥str✉♠❡♥ts ❛♥❞ t♦♦❧s ❛r❡ ✐❞❡♥t✐✜❡❞ ✐♥ t❤❡ ❧✐st❡❞ ❜❡❧♦✇✳

❘❈ ❈❛❧✐❜r❛t✐♦♥ ❊q✉✐♣♠❡♥t ▲✐st✿❚❤❡ ♥♦t❡s ❛r❡ ❜r✐❡❢ ❞❡s❝r✐♣t✐♦♥s ♦❢ ❞❡s✐r❡❞ s♣❡❝✐✜❝❛t✐♦♥s✳

❼ ❱❡❝t♦r ◆❡t✇♦r❦ ❆♥❛❧②s❡r ✭❱◆❆✮❖✈❡r❧❛♣ ❘❈ ✇♦r❦✐♥❣ ❢r❡q✉❡♥❝② r❛♥❣❡✱ s✉♣♣♦rt ❡①t❡r♥❛❧ ❝♦♥tr♦❧✱ ❤✐❣❤ ❞❛t❛✲♣♦✐♥ts✱ ❤✐❣❤ ❞②♥❛♠✐❝ r❛♥❣❡✱ s❤♦rts✇❡❡♣ t✐♠❡✳

❼ ❱◆❆ ❈❛❧✐❜r❛t✐♦♥ ❑✐t■❢ ❛✉t♦♠❛t❡❞ ❝❛❧❦✐t✱ t❤✐s ♠✉st s✉♣♣♦rt ❤✐❣❤ ✐♥♣✉t ♣♦✇❡r ✭❞②♥❛♠✐❝ r❛♥❣❡✮ ❛♥❞ ❡♥❛❜❧❡ ❝❛❧✐❜r❛t✐♦♥ ❛✇❛② ❢r♦♠❱◆❆✳

❼ ❈♦♥tr♦❧❧✐♥❣ ❈♦♠♣✉t❡r❋❛❝✐❧✐t❛t❡s ❜♦t❤ st✐rr❡r ❛♥❞ ❱◆❆ ❝♦♥tr♦❧✱ ❞❛t❛ ♣r♦❝❡ss✐♥❣✱ ❞❛t❛✴r❡s✉❧ts ❞✐s♣❧❛②s✳

❼ ❈♦♥tr♦❧ ❈❛❜❧❡s❊✳❣✳ ❢♦r ❝♦♠♣✉t❡r✲t♦✲❱◆❆ ❝♦♥tr♦❧ ❛♥❞ ❱◆❆ t♦ ❛✉t♦♠❛t❡❞ ❝❛❧✐❜r❛t✐♦♥ ✉♥✐t❙✉♣♣♦rts ✐♥str✉♠❡♥t ❝♦♥tr♦❧✳ ❊♥s✉r❡ t❤✐s ❞♦❡s ♥♦t ❝❧✉tt❡r ✇♦r❦s♣❛❝❡ ❛♥❞ s❡♣❛r❛t❡ ❢r♦♠ ♠❡❛s✉r❡♠❡♥t ❘❋❝❛❜❧❡s✳

❼ ❘❋ ❈❛❜❧❡s✿ ❱◆❆ ♣♦rts t♦ ❊①t❡r♥❛❧ ❘❈ ✐♥t❡r❢❛❝❡❊①❝❡❧❧❡♥t s❤✐❡❧❞✐♥❣ ❛♥❞ ♣❤❛s❡ st❛❜✐❧✐t②✱ ✢❡①✐❜❧❡✱ ❞♦❡s ♥♦t ♦❜str✉❝t ❱◆❆ ✐♥t❡r❢❛❝❡✳

❼ ❘❋ ❈❛❜❧❡s✿ ■♥t❡r♥❛❧ ❘❈ ✐♥t❡r❢❛❝❡ t♦ ❆♥t❡♥♥❛s❊①❝❡❧❧❡♥t s❤✐❡❧❞✐♥❣ ❛♥❞ ♣❤❛s❡ st❛❜✐❧✐t②✳ ❋♦r ❞✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛✿ ❋❧❡①✐❜❧❡✱ s✉✣❝✐❡♥t r❡❛❝❤ ✐♥s✐❞❡ ❝❤❛♠❜❡r✳ ❋♦rst❛t✐❝ ❛♥t❡♥♥❛✿ ❙❡♠✐✲r✐❣✐❞ ❝❛❜❧❡✱ ♥♦♥✲♦❜str✉❝t✐✈❡ ❧❛②♦✉t✳

❼ ❆♥t❡♥♥❛s❖✈❡r❧❛♣ ❘❈ ✇♦r❦✐♥❣ ❢r❡q✉❡♥❝② r❛♥❣❡✱ ✇❡❧❧✲♠❛t❝❤❡❞✱ ❝❤❛r❛❝t❡r✐s❡❞ ✭●❛✐♥✱ ❡✣❝✐❡♥❝②✱ r❡✢❡❝t✐♦♥ ❝♦❡✣❝✐❡♥ts✮✱❡❛s✐❧② ♠♦✉♥t❡❞✱ s♠❛❧❧✳

❼ ❆♥t❡♥♥❛ ♠♦✉♥ts❊❧❡❝tr♦♠❛❣♥❡t✐❝❛❧❧② ♥❡✉tr❛❧✱ ❤❡✐❣❤t ❛❞❥✉st❛❜❧❡✱ ❡❛s② ❞❡♣❧♦②♠❡♥t✳

❼ ❙♣❛♥♥❡r s❡t✱ ✐♥❝❧✉❞✐♥❣ t♦rq✉❡ ✇r❡♥❝❤❡s❊①❛❝t s✐③❡s ❢♦r ❛❧❧ ❝♦♥♥❡❝t♦rs ✴ ✐♥t❡r❝♦♥♥❡❝t✐♦♥s✳ ❈♦rr❡❝t t♦rq✉❡ ❢♦r ✈❛r✐♦✉s ❝♦♥♥❡❝t♦r t②♣❡s✳

❼ ▼❛t❝❤❡❞ ❧♦❛❞s❖✈❡r❧❛♣ ♠❡❛s✉r❡♠❡♥t ❜❛♥❞✇✐❞t❤✱ ♠❛t❡ ✇✐t❤ ❛♥t❡♥♥❛✲❝❛❜❧❡ ❝♦♥♥❡❝t♦rs✳

❼ ❇❛rr❡❧s❖✈❡r❧❛♣ ♠❡❛s✉r❡♠❡♥t ❜❛♥❞✇✐❞t❤✱ ♠❛t❡ ✇✐t❤ ❛♥t❡♥♥❛✲❝❛❜❧❡ ❝♦♥♥❡❝t♦rs✳

❼ ▼❛r❦✐♥❣ t❛♣❡❊❛s✐❧② ❛♣♣❧✐❡❞ ✴ r❡♠♦✈❡❞✱ r❡❧✐❛❜❧❡ ❜♦♥❞✐♥❣✱ ♥♦♥✲♠❡t❛❧❧✐❝✳

P❛❣❡ ✾ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷✳✷ ❲♦r❦s♣❛❝❡ ❈♦♥s✐❞❡r❛t✐♦♥s

❆ ✇❡❧❧✲♦r❣❛♥✐s❡❞ ✇♦r❦s♣❛❝❡ ✇✐❧❧ ❛❧✇❛②s ❡♥❤❛♥❝❡ ❛ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡✳ ❖♥❡ s❤♦✉❧❞ ❛tt❡♠♣t ❛ t❤♦✉❣❤t❢✉❧ ❧❛②♦✉t♦❢ t❤❡ ❡q✉✐♣♠❡♥t ❛♥❞ ❝♦♥s✐❞❡r t❤❡ ❢✉♥❝t✐♦♥s ✈❛r✐♦✉s ❡❧❡♠❡♥ts ♣❡r❢♦r♠✳

❙✉❣❣❡st✐♦♥s ❢♦r ❲♦r❦s♣❛❝❡ ▲❛②♦✉t✿

❼ ❙❡♣❛r❛t❡ ❘❋ ❝❛❜❧❡s ❢r♦♠ ❞✐❣✐t❛❧ ✴ s✉♣♣❧② ❝❛❜❧❡s▲✐♠✐ts r✐s❦ ♦❢ ✐♥t❡r❢❡r❡♥❝❡✳

❼ ❚♦♦❧s ✈✐s✐❜❧❡ ❛♥❞ ❛❝❝❡ss✐❜❧❡

❼ ❈❧❡❛r ✇❛❧❦✇❛②s

P❛❣❡ ✶✵ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷✳✸ ❍❛r❞✇❛r❡ Pr❡♣❛r❛t✐♦♥

❘❋ ❤❛r❞✇❛r❡ ✐s ♦❢t❡♥ ✈❡r② ❡①♣❡♥s✐✈❡ ❛♥❞ ❢r❛❣✐❧❡✳ ▼♦r❡♦✈❡r✱ ❤✐❣❤✲q✉❛❧✐t② ❡q✉✐♣♠❡♥t ✇✐❧❧ ♦♥❧② ♣❡r❢♦r♠ t♦ s♣❡❝✐✜❝❛✲t✐♦♥ ✐❢ ✐t ✐s ✇❡❧❧ ♠❛✐♥t❛✐♥❡❞ ❛♥❞ ❣❡♥❡r❛❧❧② ❤❛♥❞❧❡❞ ✇✐t❤ ❝❛r❡✳

✷✳✸✳✶ ❈♦♥♥❡❝t♦r ❈❛r❡

❈♦♥♥❡❝t♦rs ❛r❡ ♦❢t❡♥ t❤❡ ♠♦st ❡①♣♦s❡❞ ♣❛rt ♦❢ ❛♥ ✐♥str✉♠❡♥t✱ ❝❛❜❧❡ ♦r ❛♥t❡♥♥❛✳ ❚❤❡r❡❢♦r❡✱ t❤❡s❡ ✐♥t❡r❢❛❝❡s ❛r❡ ✈✉❧✲♥❡r❛❜❧❡ ❛♥❞ ❝❛♥ ❜❡ ❛ ❝❛✉s❡ ♦❢ ♠❡❛s✉r❡♠❡♥t ✐ss✉❡s✳ ■❞❡❛❧❧②✱ ❝♦♥♥❡❝t♦rs s❤♦✉❧❞ ❜❡ ❝❧❡❛♥❡❞ ♣r✐♦r t♦ ❛♥② ♠❡❛s✉r❡♠❡♥t✱❜✉t t❤✐s ✐s ❛ r❡q✉✐r❡♠❡♥t ❢♦r ❛ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡❞✉r❡✳

❈♦♥♥❡❝t♦r ❈❛r❡ ❛♥❞ ❚❡st✐♥❣

❼ ❘❡♣❧❛❝❡ ❝♦♥♥❡❝t♦r ❞✉st ❝❛♣s❆❧✇❛②s ❝♦✈❡r ❝♦♥♥❡❝t♦rs ✇❤❡♥ ♥♦t ✐♥ ✉s❡✳ ❚❤✐s ♣r♦t❡❝ts ❛♥❞ ❦❡❡♣s ✐♥t❡r❢❛❝❡s ❝❧❡❛♥✳

❼ ❱✐s✉❛❧❧② ✐♥s♣❡❝t ❝♦♥♥❡❝t♦r ✐♥t❡r❢❛❝❡s❉❛♠❛❣❡ ♠❛② ❜❡ ❛♣♣❛r❡♥t ❛♥❞ ❛ ♠✐❝r♦s❝♦♣❡ ✴ ♠❛❣♥✐❢②✐♥❣ ❧❡♥s ❝❛♥ ❜❡ ✉s❡❞ ❢♦r ❢✉rt❤❡r ✐♥s♣❡❝t✐♦♥✳❉♦ ♥♦t ✉s❡ ❡q✉✐♣♠❡♥t ✇✐t❤ s✉s♣❡❝t ❝♦♥♥❡❝t♦rs✳

❼ ❘❡♠♦✈❡ ❣r✐♠❡✱ ❞✐rt ❛♥❞ ♠❡t❛❧❧✐❝ s❤❛✈✐♥❣s❯s❡ ❡❛r❜✉❞s ❛♥❞ ❧✐♥t✲❢r❡❡ ❝❧♦t❤ ❛❧♦♥❣ ✇✐t❤ ❝♦♠♣r❡ss❡❞ ❛✐r ✭❋✐❣✳ ✷✮✳

❼ ▼❡t❛❧❧✐❝ ♣❛rts ❝❧❡❛♥❡❞ ✇✐t❤ ■s♦♣r♦♣②❧ ❆❧❝♦❤♦❧❈❧♦t❤ ❝❛♥ ❜❡ ❞❛❜❜❡❞ ✐♥ ❛❧❝♦❤♦❧ ❢♦r ❛♣♣❧✐❝❛t✐♦♥ t♦ ❣r✐♠❡✳

❼ ❈❧❡❛♥ ❛❧❧ ❝♦♥♥❡❝t♦rs❋♦r ❜♦t❤ t❤❡ q✉✐❝❦ t❡sts ❛♥❞ ❘❈ ❝❛❧✐❜r❛t✐♦♥✳ ❚❤✐s ✐♥❝❧✉❞❡s ❛♥t❡♥♥❛s✱ ❝❛❜❧❡s✱ r❡❝❡✐✈❡rs✱ ✐♥t❡r❝♦♥♥❡❝t✐♦♥s✱ ❡t❝✳

❼ ❯s❡ ❡①❛❝t s✐③❡ s♣❛♥♥❡rs❘❋ ❝♦♥♥❡❝t♦rs ♦❢t❡♥ r❡q✉✐r❡ ✐♠♣❡r✐❛❧✲s✐③❡❞ t♦♦❧s ❛♥❞ ❝❛♥ ❜❡ ❞❛♠❛❣❡❞ ✐❢ ✐♥❝♦rr❡❝t ✴ ♠❡tr✐❝ t♦♦❧s ❛r❡ ✉s❡❞✳

❼ ❯s❡ ❝♦rr❡❝t✱ ❝❛❧✐❜r❛t❡❞ t♦rq✉❡ ✇r❡♥❝❤❡s❉✐✛❡r❡♥t t②♣❡s ♦❢ ❝♦♥♥❡❝t♦rs ❛♥❞ ♠❛t❡r✐❛❧s ❤❛✈❡ ❞✐st✐♥❝t t♦rq✉❡ r❛t✐♥❣s✳❊✳❣✳ ◆✲t②♣❡ ✭✶✷✲✶✺ ✐♥✲❧❜s✮ ❛♥❞ ❙▼❆ ✭st❛✐♥❧❡ss st❡❡❧✮ ✭✼✲✶✵ ✐♥✲❧❜s✮✳

❼ ❙✉♣♣♦rt ❝❛❜❧❡ ✴ ❝♦♠♣♦♥❡♥t ✇❤❡♥ t♦rq✉✐♥❣ ❝♦♥♥❡❝t♦r✳❯s❡ ②♦✉r ❢r❡❡ ❤❛♥❞ ✴ ✜♥❣❡rs t♦ ❛❧✐❣♥ ❛♥❞ st❡❛❞② t❤❡ ❝♦♥♥❡❝t✐♦♥ ✭❋✐❣✳ ✸✮✳

❚❤❡ ❢♦❧❧♦✇✐♥❣ t❡sts ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝❤❡❝❦ ❝♦♥♥❡❝t♦rs✿

❼ ❈❤❡❝❦ ❝♦♥♥❡❝t♦r ♣❡r❢♦r♠❛♥❝❡❯s❡ ❝❛❧✐❜r❛t❡❞ ❱◆❆ ♠❡❛s✉r❡♠❡♥ts ✭❋r❡q✉❡♥❝② ❉♦♠❛✐♥✮ t♦ ❝♦♠♣❛r❡ t♦ ❦♥♦✇♥ r❡s♣♦♥s❡s✳

❼ ❚✐♠❡✲❞♦♠❛✐♥ ❱◆❆ ♠❡❛s✉r❡♠❡♥ts■❞❡♥t✐❢② r❡✢❡❝t✐♦♥s ❢r♦♠ ❝♦♥♥❡❝t♦r ❞❛♠❛❣❡ ❜❛s❡❞ ♦♥ ♣r♦♣❛❣❛t✐♦♥ t✐♠❡s✳

P❛❣❡ ✶✶ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✷✿ ❈♦♥♥❡❝t♦r ❝❧❡❛♥✐♥❣ ✇✐t❤ ❧✐♥t✲❢r❡❡ ❝❧♦t❤ ❛♥❞ ■s♦✲♣r♦♣②❧ ❆❧❝♦❤♦❧✳

❋✐❣✉r❡ ✸✿ ❚♦rq✉✐♥❣ ❝❛❜❧❡ ❝♦♥♥❡❝t♦r ❛t ●▲P❉❆✳ ◆♦t❡ ❧❡❢t✲❤❛♥❞ s✉♣♣♦rt ✇✐t❤ ✜♥❣❡rs ❛♥❞ s♣❛♥♥❡r✳

P❛❣❡ ✶✷ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷✳✸✳✷ ❈❛❜❧❡ ❘❡❝♦♠♠❡♥❞❛t✐♦♥s ❛♥❞ ❈❛r❡

■♥ ❘❈ ❝♦♥✜❣✉r❛t✐♦♥s ✐♥ ♣❛rt✐❝✉❧❛r✱ ❝❛❜❧❡s ❛r❡ ♦❢t❡♥ ❧♦♥❣ ❛♥❞ ✐♥ ✈✉❧♥❡r❛❜❧❡ ♣♦s✐t✐♦♥s✳ ■t ✐s ✐♠♣♦rt❛♥t t♦ ❜❡ ♠✐♥❞❢✉❧♦❢ ❝❛❜❧❡s ♦♥ t❤❡ ❣r♦✉♥❞ ♦r ♥❡❛r ♠❡❝❤❛♥✐s♠s ❧✐❦❡ ❞♦♦rs✳ ❙✐♥❝❡ ❝❛❜❧❡ s❤✐❡❧❞✐♥❣ ✐s ✈✐t❛❧ t♦ ❣♦♦❞ ❘❈ ♠❡❛s✉r❡♠❡♥ts✱ ❛❞❛♠❛❣❡❞ ❝❛❜❧❡ ✐s ❧✐❦❡❧② t♦ ❝❛✉s❡ ♠❡❛s✉r❡♠❡♥t ❡rr♦rs✳

❋♦r t❤❡ st❛t✐❝✲❛♥t❡♥♥❛ ♣♦s✐t✐♦♥✱ ❛ ❧❡♥❣t❤ ♦❢ s❡♠✐✲r✐❣✐❞ ❝❛❜❧❡ ✐s r❡❝♦♠♠❡♥❞❡❞ ✇✐t❤ ❛ ♣r♦t❡❝t❡❞ ❧❛②♦✉t ❝❧♦s❡ t♦t❤❡ ✐♥♥❡r s✉r❢❛❝❡✳ ❚❤❡ ❞✐s♣❧❛❝❡❞✲❛♥t❡♥♥❛ ♣♦s✐t✐♦♥s r❡q✉✐r❡ ❛ ❣♦♦❞✱ ✢❡①✐❜❧❡ ❝❛❜❧❡ ❧♦♥❣ ❡♥♦✉❣❤ t♦ ❝♦♠❢♦rt❛❜❧② r❡❛❝❤t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✬s ❡❞❣❡s✳

❈❛❜❧❡ ❈❛r❡ ❛♥❞ ❚❡st✐♥❣ ●✉✐❞❡❧✐♥❡s

❼ ❈❛❜❧❡ ❧❛②♦✉t t♦ ♠✐♥✐♠✐③❡ r✐s❦❚❤❡ ❧❛②♦✉t s❤♦✉❧❞ ♠✐♥✐♠✐③❡ r✐s❦ ♦❢ ❞❛♠❛❣❡ t♦ ❝❛❜❧❡s✱ ✐❢ ♣♦ss✐❜❧❡ ✭❋✐❣✳ ✹✮✳

❼ ❙✉♣♣♦rt ❝❛❜❧❡s❈❛❜❧❡s s❤♦✉❧❞ ♥♦t ❤❛♥❣ ♦r ❜❡❛r ✇❡✐❣❤t✱ ♣❛rt✐❝✉❧❛r❧② ❛t ❝♦♥♥❡❝t♦rs✳ ❆♥t❡♥♥❛ ♠♦✉♥ts ❝❛♥ ❜❡ ✉s❡❞ ❢♦r s✉♣♣♦rt✭❋✐❣✳ ✺✮✳

❼ ❙❛❢❡❧② st♦r❡ ❝❛❜❧❡s❘♦❧❧ ❝❛❜❧❡ ✐♥t♦ ❧♦♦♣ ✇✐t❤♦✉t t✇✐st✐♥❣ ♦r ❡①❝❡ss✐✈❡ ❜❡♥❞✐♥❣✱ r❡♣❧❛❝❡ ❞✉st ❝❛♣s ❛♥❞ st♦r❡ ✐♥ ❞❡s✐❣♥❛t❡❞ ❝♦♥t❛✐♥❡r✳

❚❤❡ ❢♦❧❧♦✇✐♥❣ t❡sts ❝❛♥ ❜❡ ✉s❡❞ t♦ ❝❤❡❝❦ ❝♦♥♥❡❝t♦rs✿

❼ ❈❤❡❝❦ ❝❛❜❧❡ ♣❡r❢♦r♠❛♥❝❡❯s❡ ❝❛❧✐❜r❛t❡❞ ❱◆❆ ♠❡❛s✉r❡♠❡♥ts ✭❋r❡q✉❡♥❝② ❉♦♠❛✐♥✮ t♦ ❝♦♠♣❛r❡ t♦ ❦♥♦✇♥ r❡s♣♦♥s❡s✳

❼ ❚✐♠❡✲❞♦♠❛✐♥ ❱◆❆ ♠❡❛s✉r❡♠❡♥ts■❞❡♥t✐❢② r❡✢❡❝t✐♦♥s ❢r♦♠ ❞❛♠❛❣❡❞ ❝♦♥♥❡❝t♦rs ♦r ❝❛❜❧❡ ❞✐s❝♦♥t✐♥✉✐t✐❡s ❜❛s❡❞ ♦♥ ♣r♦♣❛❣❛t✐♦♥ t✐♠❡s✳

P❛❣❡ ✶✸ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✹✿ ▲❛②♦✉t ✇✐t❤ ❝❛❜❧❡ ❝❧❡❛r ♦❢ ✇❛❧❦✐♥❣ ❛r❡❛s ❛♥❞s✉♣♣♦rt❡❞✳

❋✐❣✉r❡ ✺✿ ❈❛❜❧❡ s✉♣♣♦rt❡❞ ❜② ❛♥t❡♥♥❛ ♠♦✉♥t t♦ ❧✐♠✐tstr❡ss ❛t ❝♦♥♥❡❝t♦rs✳

P❛❣❡ ✶✹ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷✳✸✳✸ ❆♥t❡♥♥❛ P♦s✐t✐♦♥s

❚❤❡ ❝❛❧✐❜r❛t✐♦♥ st❛♥❞❛r❞ ♣r❡s❝r✐❜❡s t❤❛t ✽ s❡ts ♦❢ ♠❡❛s✉r❡♠❡♥ts ❜❡ t❛❦❡♥ ✇✐t❤ t❤❡ ❞✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛ ♠♦✉♥t❡❞ ❛t❞✐st✐♥❝t ♣♦s✐t✐♦♥s ❛t t❤❡ ❡❞❣❡s ♦❢ t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳ ❚❤❡ t❡r♠ ❞✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛ ♠❛❦❡s r❡❢❡r❡♥❝❡ t♦ ✐t ❜❡✐♥❣♠♦✈❡❞ t♦ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ♣♦s✐t✐♦♥s ✭❆✶✲✹ ❛♥❞ ❇✶✲✹✮✱ ✇❤✐❧❡ t❤❡ st❛t✐❝ ❛♥t❡♥♥❛ r❡♠❛✐♥s ✐♥ t❤❡ ✐♥t❡♥❞❡❞ r❡❝❡✐✈✐♥❣♣♦s✐t✐♦♥✳ ■❢ t❤❡ st❛t✐❝ ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥ ✐s ♥♦t❛❜❧② ❝❤❛♥❣❡❞✱ ❛ r❡❝❛❧✐❜r❛t✐♦♥ s❤♦✉❧❞ ✐❞❡❛❧❧② ❜❡ ♣❡r❢♦r♠❡❞✳

❆♥t❡♥♥❛ ♣❧❛❝❡♠❡♥t

❼ ▼❛r❦ ✇♦r❦✐♥❣ ✈♦❧✉♠❡ ❜♦✉♥❞❛r✐❡s❚❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡ ✐s q✉❛rt❡r✲✇❛✈❡❧❡♥❣t❤s ❛✇❛② ❢r♦♠ ♠❡t❛❧❧✐❝ str✉❝t✉r❡s✱ ✐♥❝❧✉❞✐♥❣ ❉❯❚s ❛♥❞ st✐rr❡rs✳❚②♣✐❝❛❧❧② ❞❡✜♥❡❞ ❛t t❤❡ ▲♦✇❡st ❯s❛❜❧❡ ❋r❡q✉❡♥❝② ✭▲❯❋✮ ✭✹✷ ❝♠ ❅ ✶✽✵ ▼❍③✮✳❚❤❡ st❛♥❞❛r❞ r❡❝♦♠♠❡♥❞s ❛ ♠✐♥✐♠✉♠ s❡♣❛r❛t✐♦♥ ♦❢ ✼✳✺ ❝♠ ❛❜♦✈❡ ✶ ●❍③ ❬❬✶❪❪✳

❼ ❙❡t✉♣ ❛♥t❡♥♥❛ ♠♦✉♥ts❘♦✉❣❤❧② ♠❛t❝❤ ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥s t♦ t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡ ❝♦r♥❡rs ✭❋✐❣✳ ✻✮✳ ◆♦t❡ t❤❛t s♦♠❡ ❛♥t❡♥♥❛s str✉❝t✉r❡s✭▲P❉❆✮ ❤❛✈❡ ❞✐s♣❡rs❡❞ ❡❧❡♠❡♥ts✳ ❊♥s✉r❡ t❤❛t ❧♦✇ ❢r❡q✉❡♥❝② ❡❧❡♠❡♥ts ❛r❡ ✇✐t❤✐♥ t❤❡ ✈♦❧✉♠❡ ♠❛r❣✐♥s✳

❼ ❯s❡ ❊▼✲♥❡✉tr❛❧ ✴ s♠❛❧❧ ♠❡t❛❧❧✐❝ ♠♦✉♥ts■❢ ♠❡t❛❧❧✐❝ ♠♦✉♥ts ❛r❡ ✉s❡❞✱ t❤❡s❡ ♠✉st r❡♠❛✐♥ ✐♥ t❤❡ ❝❤❛♠❜❡r ♣♦st ❝❛❧✐❜r❛t✐♦♥✳ ❘♦♣❡ ❛♥❞ ❝❧❛♠♣s ✉s❡❞ ✐♥❋✐❣✳ ✼✳

❼ ❆✈♦✐❞ ❞✐r❡❝t✲❝♦✉♣❧✐♥❣❈❛♥ ♦❝❝✉r ❢♦r ❛♥t❡♥♥❛s ✇✐t❤ s✐♠✐❧❛r ♣♦❧❛r✐s❛t✐♦♥s ✐♥ ❝❧♦s❡ ♣r♦①✐♠✐t②✳

❼ Pr♦✈✐❞❡ ❝❛❜❧❡ s✉♣♣♦rt✳❚❛♣❡ ♠✐❣❤t ❜❡ ✉s❡❢✉❧✳

❼ ❱❡r✐❢② ❛♥t❡♥♥❛ ✇✐t❤✐♥ ✇♦r❦✐♥❣ ✈♦❧✉♠❡❈❤❡❝❦ t❤❛t ♠❡t❛❧❧✐❝ ♣❛rts ♦❢ t❤❡ ❛♥t❡♥♥❛ ❛r❡ ❛t ❧❡❛st ❛ q✉❛rt❡r✲✇❛✈❡❧❡♥❣t❤ ❛✇❛② ❢r♦♠ ❝❤❛♠❜❡r ❛t r❡❧❡✈❛♥t❢r❡q✉❡♥❝② ♦❢ ♣❛rt✐❝✉❧❛r ❡❧❡♠❡♥t✳

P❛❣❡ ✶✺ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✻✿ ❆♥t❡♥♥❛ ❛❧✐❣♥❡❞ t♦ ❝♦r♥❡r ♦❢ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳◆♦t❡ t❛♣❡ ♠❛r❦❡r ❢♦r ✈♦❧✉♠❡ ❝♦r♥❡r ❛t ▲❯❋✳

❋✐❣✉r❡ ✼✿ ❙♠❛❧❧ ♠❡t❛❧❧✐❝ ❜r❛❝❦❡ts ❝♦♠❜✐♥❡❞ ✇✐t❤ r♦♣❡ ❢♦r❆✶✲❆✹ ❛♥t❡♥♥❛ ♠♦✉♥ts✳

P❛❣❡ ✶✻ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✽✿ ❙❝❤❡♠❛t✐❝ s❤♦✇✐♥❣ ❘❈✲❝❛❧✐❜r❛t✐♦♥ ❛♥t❡♥♥❛ ♣❧❛❝❡♠❡♥t✳ ❆✶✲❆✹ r❡❢❡r t♦ ♣♦s✐t✐♦♥s ✐♥ t❤❡ ✉♣♣❡r ❝♦r♥❡rs❛♥❞ ❇✶✲❇✹ t❤❡ ❧♦✇❡r ❝♦r♥❡rs ♦❢ t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✱ r❡s♣❡❝t✐✈❡❧②✳ ◆♦t❡ t❤❡ ❞✐✛❡r❡♥❝❡ ✐♥ ❛♥t❡♥♥❛ ♣♦❧❛r✐s❛t✐♦♥s ❢♦r❛♥t❡♥♥❛ ♣♦s✐t✐♦♥s ✐♥ ❝❧♦s❡ ♣r♦①✐♠✐t②✳

P❛❣❡ ✶✼ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷✳✹ ❱◆❆ ❙❡t✉♣ ❛♥❞ ❈❛❧✐❜r❛t✐♦♥

❚❤❡ s❡❧❡❝t✐♦♥ ♦❢ ❱◆❆✲s❡t✉♣ ♣❛r❛♠❡t❡rs ❛♥❞ t❤❡ ❛❝❝♦♠♣❛♥②✐♥❣ ❝❛❧✐❜r❛t✐♦♥ ♣r♦❝❡ss ✐s ❞❡s❝r✐❜❡❞ ❜❡❧♦✇✳ ❚❤❡ ❱◆❆s❡t✉♣ ✐s t②♣✐❝❛❧❧② ❞♦♥❡ ♦♥ t❤❡ ✐♥str✉♠❡♥t✬s ✐♥t❡r❢❛❝❡ ♣❛♥❡❧✱ ♥♦t ✈✐❛ t❤❡ ❝♦♥tr♦❧❧✐♥❣ ❝♦♠♣✉t❡r✳

❱◆❆ ❙❡t✉♣

❼ ▼❡❛s✉r❡♠❡♥t ❋r❡q✉❡♥❝② ❘❛♥❣❡ ✲ ♠❛t❝❤ ❡q✉✐♣♠❡♥t s♣❡❝✐✜❝❛t✐♦♥s ❛♥❞ ❛r❡❛s ♦❢ ✐♥t❡r❡st✳❚②♣✐❝❛❧❧② ✼✵ ▼❍③ ✲ ✻ ●❍③ ❢♦r ❙❑❆✲❙❆ P✐♥❡❧❛♥❞s✬ ❘❈ ✭✶✽✵ ▼❍③ ✲ ✽ ●❍③✮ ✉s✐♥❣ ●▲P❉❆ ❛♥t❡♥♥❛s ✭✶✺✵▼❍③ ✲ ✻ ●❍③✮✳ ❊①t❡♥❞❡❞ ❧♦✇❡r r❛♥❣❡ t♦ ❝❤❛r❛❝t❡r✐s❡ ▲❯❋✳

❼ ❙♦✉r❝❡ P♦✇❡r ✲ ▼❛①✳ ❛❧❧♦✇❡❞▼✐❣❤t ♥♦t ❜❡ ❱◆❆ ♠❛①✳ ♦✉t♣✉t✱ ❡✳❣✳ ❘♦❤❞❡ ❛♥❞ ❙❝❤✇❛r③ ❩❱❇ ❛✉t♦♠❛t❡❞ ❝❛❧✐❜r❛t✐♦♥ ✉♥✐t ♠❛①✳ ✐♥♣✉t✿✷✸ ❞❇♠ ✱ ❱◆❆ ▼❛①✳ ✷✼ ❞❇♠✦

❼ ◆♦✳ ♦❢ P♦✐♥ts ✲ ❝❛❧✐❜r❛t✐♦♥ ❞❡♣❡♥❞❡♥t❙❡ts ❝❛❧✐❜r❛t✐♦♥ r❡s♦❧✉t✐♦♥✳ ❋♦r ✼✵ ▼❍③ ✲ ✻ ●❍③ r❛♥❣❡✿ ✶✮ ✺✾✸ ♣♦✐♥ts ❂ ✶✵ ▼❍③ ✱ s✉✣❝✐❡♥t ❢♦r ❝❛❧✐❜r❛t✐♦♥✱✷✮ ✻✵ ♣♦✐♥ts ❂ ✾✽✳✸✸ ▼❍③ ✱ ❢♦r r♦✉❣❤ ❝❤❡❝❦✳

❼ ❆✈❡r❛❣✐♥❣ ✲ ♦✛◆♦t s✉♣♣♦rt❡❞ ❜② ❝♦♥tr♦❧✳ ▼❛①✳ ♣♦✇❡r ❝♦♠♣❡♥s❛t❡s ❢♦r t❤✐s✳

P❛❣❡ ✶✽ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷✳✺ ❱◆❆ ❈❛❧✐❜r❛t✐♦♥

❚❤✐s ✇✐❧❧ ❝♦rr❡❝t t❤❡ ♠❡❛s✉r❡♠❡♥t ❢♦r s✐❣♥❛❧✲♣❛t❤ ❡✛❡❝ts ✉♣ t♦ r❡❢❡r❡♥❝❡ ♣❧❛♥❡s ✶ ❛♥❞ ✷✱ s✉❜s❡q✉❡♥t❧② r❡❢❡rr❡❞t♦ ❛s P♦rt ✶ ❛♥❞ P♦rt ✷✱ r❡s♣❡❝t✐✈❡❧②✳ ❚❤✐s ✐s s❤♦✇♥ ✐♥ ❋✐❣✳ ✾✳

❱◆❆ ❈❛❧✐❜r❛t✐♦♥

❼ ❆rr❛♥❣❡ ❝♦♥✈❡♥✐❡♥t ❝❛❧✐❜r❛t✐♦♥ ❧❛②♦✉t❋♦r ❛✉t♦♠❛t❡❞ ❝❛❧✐❜r❛t✐♦♥ ✉♥✐t✱ ♣❛ss ❝♦♥tr♦❧ ❝❛❜❧❡ ✈✐❛ ♠❡s❤❡❞ ❘❈✲✐♥t❡r❢❛❝❡ ♣♦rt✳

❼ ■❞❡♥t✐❢② ❝♦rr❡❝t ♣♦rts❉❡✜♥❡ ❛ ❝♦♥✈❡♥t✐♦♥✿ ❱◆❆ P♦rt ✶✮ ❙t❛t✐❝ ❆♥t❡♥♥❛ ✱ ❱◆❆ P♦rt ✷✮ ❉✐s♣❧❛❝❡❞ ❆♥t❡♥♥❛✳

❼ ❈♦♥♥❡❝t ❛♥❞ t♦rq✉❡ ❝❛❧✐❜r❛t✐♦♥ st❛♥❞❛r❞s✳

❼ ❋♦❧❧♦✇ ❈❛❧✐❜r❛t✐♦♥ ♣r♦♠♣ts❚②♣✐❝❛❧❧② ❱◆❆s ♣r♦✈✐❞❡ ❢❡❡❞❜❛❝❦ ✈✐❛ ✉s❡r ✐♥t❡r❢❛❝❡ ❢♦r ♥❡❝❡ss❛r② st❡♣s✳

❼ ❘❡♠♦✈❡ ❝❛❧✐❜r❛t✐♦♥ s❡t✉♣❘❡♠♦✈❡ ❝❛❧✐❜r❛t✐♦♥ ✉♥✐t✳■❢ ❛ ❝♦♥tr♦❧ ❝❛❜❧❡ ✇❛s ♣❛ss❡❞ t❤r♦✉❣❤ t❤❡ ❝❤❛♠❜❡r ✐♥t❡r❢❛❝❡✱ s❡❛❧ t❤✐s ♣♦rt ❜❡❢♦r❡ ❢✉rt❤❡r♠❡❛s✉r❡♠❡♥ts✦

P❛❣❡ ✶✾ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✾✿ ❙❝❤❡♠❛t✐❝ ♦❢ ❱◆❆ ❝❛❧✐❜r❛t✐♦♥ ❧❛②♦✉t✳ ◆♦t❡ t❤❛t ❱◆❆ P♦rts ✶ ❛♥❞ ✷ ❝♦♥♥❡❝t t♦ t❤❡ st❛t✐❝ ❛♥❞ ❞✐s♣❧❛❝❡❞❛♥t❡♥♥❛ ❝❛❜❧❡s✱ r❡s♣❡❝t✐✈❡❧②✱ ♠❛✐♥t❛✐♥✐♥❣ t❤❡ ❝♦♥✈❡♥t✐♦♥✳ ❆❧s♦✱ t❤❡ ❛✉t♦♠❛t✐❝ ❝❛❧✐❜r❛t✐♦♥ ✉♥✐t✬s ❝♦♥tr♦❧ ❝❛❜❧❡ ✐s♣❛ss❡❞ ✈✐❛ ❛♥ ♦♣❡♥ ❘❈ ✐♥t❡r❢❛❝❡ ✭t♦♣ r✐❣❤t✮✳

P❛❣❡ ✷✵ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷✳✻ Pr❡✲▼❡❛s✉r❡♠❡♥t ❚❡sts

❚❤❡ ♠❡❛s✉r❡♠❡♥t s❡t✉♣ ❝❛♥ ❜❡ ❝❤❡❝❦❡❞ ❢♦r s✐❣♥✐✜❝❛♥t ✐ss✉❡s ✇✐t❤ ❛ ❝❛❧✐❜r❛t❡❞ ❱◆❆✳ ❇② ♣❡r❢♦r♠✐♥❣ r❡❧❛t✐✈❡❧② q✉✐❝❦t❡sts✱ ❞✐✛❡r❡♥t ❝♦♠♣♦♥❡♥ts ♦❢ t❤❡ s❡t✉♣ ❝❛♥ ❜❡ ❝❤❡❝❦❡❞ ❜❡❢♦r❡ ❝♦♠❡♥❝✐♥❣ ✇✐t❤ t❤❡ ❧❡♥❣t❤② ❘❈ ❝❛❧✐❜r❛t✐♦♥ ♠❡❛s✉r❡✲♠❡♥ts✳ ■❢ ❛ ♣r♦❜❧❡♠ ✐s ✐❞❡♥t✐✜❡❞✱ t❤✐s ✇✐❧❧ ❛✈♦✐❞ ❛ ✇❛st❡❞ ❝❛❧✐❜r❛t✐♦♥ ❡✛♦rt✳

✷✳✻✳✶ ❱◆❆ ❈❛❧✐❜r❛t✐♦♥ ❈❤❡❝❦

❚❤❡ ❝❤❡❝❦ ✇✐❧❧ ❝♦♥✜r♠ t❤❛t t❤❡ ❱◆❆ ❝❛❧✐❜r❛t✐♦♥ ✐s r❡❧❛t✐✈❡❧② ❣♦♦❞ ❛♥❞ t❤❛t t❤❡ ❝❛❜❧❡s ❤❛✈❡ ❛❝❝❡♣t❛❜❧❡ ♣❡r❢♦r♠❛♥❝❡✱✐♥ ♣❛rt✐❝✉❧❛r ♣❤❛s❡ st❛❜✐❧✐t② ❛♥❞ ♠❡❝❤❛♥✐❝❛❧ ✐♥t❡❣r✐t②✳

❼ ❚❡r♠✐♥❛t❡ ❝❛❜❧❡s ❛t r❡❢❡r❡♥❝❡ ♣❧❛♥❡s ✶ & ✷ ✇✐t❤ ❦♥♦✇♥✱ ♠❛t❝❤❡❞ ❧♦❛❞s▼❛② r❡q✉✐r❡ ❛❞❞✐♥❣ ❜❛rr❡❧s t♦ ❝❛❜❧❡ ❝♦♥♥❡❝t♦rs✱ ✐❢ ❧♦❛❞s ✇✐t❤ ❝♦rr❡❝t s❡① ♦r t②♣❡ ❛r❡ ♥♦t ❛✈❛✐❧❛❜❧❡✳

❼ ❖❜s❡r✈❡ r❡✢❡❝t✐♦♥ ❝♦❡✣❝✐❡♥ts❉✐s♣❧❛② S11 ❛♥❞ S22 ♠❛❣♥✐t✉❞❡ ♦♥ ❱◆❆ ✇✐t❤ ✜♥❡ s❝❛❧❡ ✭✵✳✺ ❞❇✴❞✐✈✮

❼ ❈♦♥✜r♠ ❛❝❝❡♣t❛❜❧❡ r❡s✉❧tSxx ▼❛❣♥✐t✉❞❡ ❜❡t✇❡❡♥ ✵ ❞❇ ❛♥❞ ✲✶ ❞❇ ❛❝r♦ss r❛♥❣❡✳

❼ ❘❡❝♦r❞ ♠❡❛s✉r❡♠❡♥t■❢ ♣♦ss✐❜❧❡✱ st♦r❡ ♠❡❛s✉r❡♠❡♥ts t♦ ❱◆❆ ♠❡♠♦r②✱ r❡❝❛❧❧ ❛♥❞ ❞✐s♣❧❛② ❛s r❡❢❡r❡♥❝❡✳

❼ ❈❤❛♥❣❡ ❝❛❜❧❡ ❧❛②♦✉t✳▼♦✈❡ ✢❡①✐❜❧❡ ❝❛❜❧❡s❀ ❞✐s♣❧❛❝❡❞✲❛♥t❡♥♥❛ ❝❛❜❧❡ t♦ ❢✉rt❤❡st ❝♦r♥❡r ♦❢ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳

❼ ❱❡r✐❢② ❱◆❆✲❝❛❧✐❜r❛t✐♦♥ st❛❜✐❧✐t②❈❤❡❝❦ t❤❛t r❡s✉❧ts ❞❡♣✐❝t st❛❜❧❡ ❛♥❞ ❧♦✇ r❡✢❡❝t✐♦♥s ❛❝r♦ss r❛♥❣❡✱ ✐♥❞❡♣❡♥❞❡♥t ♦❢ ❝❛❜❧❡ ❧❛②♦✉t ✭❋✐❣✳ ✶✵✮✳

P❛❣❡ ✷✶ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✶✵✿ ❱◆❆ s❝r❡❡♥ s❤♦✇✐♥❣ r♦✉❣❤❧② ✲✸✵ ❞❇ S11 ❛♥❞ S22 r❡s✉❧ts✱ ✐♥❞✐❝❛t✐♥❣ ♠❛t❝❤✐♥❣ ❛t ❜♦t❤ ♣♦rts✳ ◆♦t❡ tr❛❝❡sst♦r❡❞ t♦ ♠❡♠♦r② ✇✐t❤ ❝✉rr❡♥t ♠❡❛s✉r❡♠❡♥ts ♦✈❡r❧❛✐❞✳

P❛❣❡ ✷✷ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷✳✻✳✷ ❈❛❜❧❡ ❙❤✐❡❧❞✐♥❣ ❚❡st

❚♦ ❝❤❡❝❦ t❤❡ ❝❛❜❧❡ s❤✐❡❧❞✐♥❣ ✐♥t❡❣r✐t②✱ t✇♦ ♠❡❛s✉r❡♠❡♥t s❡ts ❛r❡ ♣❡r❢♦r♠❡❞ ✇✐t❤ ♦♥❡ ❝❛❜❧❡ t❡r♠✐♥❛t❡❞ ✐♥ ❛ ♠❛t❝❤❡❞❧♦❛❞ ❛♥❞ t❤❡ ♦t❤❡r r❛❞✐❛t✐♥❣ ❢r♦♠ ❛♥ ❛♥t❡♥♥❛✳ ❚❤❡ ❧♦❛❞✲t❡r♠✐♥❛t❡❞ ❝❛❜❧❡ ✇✐❧❧ ❜❡ ✐❧❧✉♠✐♥❛t❡❞✱ ✐♥❞✉❝✐♥❣ ❝✉rr❡♥ts ♦♥✐ts s✉r❢❛❝❡✳ ❚❤✉s✱ ❜r❡❛❦s ✐♥ ✐ts s❤✐❡❧❞✐♥❣ ✇✐❧❧ ❧❡❛❦ ✐♥t♦ t❤❡ ❝❛❜❧❡ ✐♥t❡r✐♦r ❛♥❞ ✇✐❧❧ ❜❡ ❞❡t❡❝t❡❞ ❜② t❤❡ ❱◆❆✳

❼ ❚❡r♠✐♥❛t❡ st❛t✐❝ ❝❛❜❧❡ ✐♥ ♠❛t❝❤❡❞ ❧♦❛❞

❼ ❘❛✐s❡ st❛t✐❝ ❝❛❜❧❡ ✐♥t♦ ✇♦r❦✐♥❣ ✈♦❧✉♠❡❚❤✐s ❛❧❧♦✇s ❝❛❜❧❡ t♦ ❜❡ ✐❧❧✉♠✐♥❛t❡❞✳

❼ ❈♦♥♥❡❝t ❞✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛❆♥② ♠♦✉♥t✐♥❣ ♣♦s✐t✐♦♥ ✐s ❛❧❧♦✇❡❞✳

❼ ❈❧♦s❡ ❘❈ ❞♦♦r✳

❼ ❉✐s♣❧❛② S21 ❛♥❞ S12 tr❛❝❡s

❼ ■♥s♣❡❝t ♣❛r❛♠❡t❡r ♠❛❣♥✐t✉❞❡s❙❤♦✉❧❞ ❜❡ ±✲✾✵ ❞❇♠ ❛❝r♦ss t❤❡ r❛♥❣❡ ❢♦r ❣♦♦❞ ❝❛❜❧❡s❊ss❡♥t✐❛❧❧②✱ t❤❡ ✐s♦❧❛t✐♦♥ ♦❢ t❤❡ ❝♦♥✜❣✉r❛t✐♦♥ ✐s t❡st❡❞ ❛♥❞ s❤♦✉❧❞ ❜❡ r♦✉❣❤❧② ✶✵ ❞❇ ❧♦✇❡r t❤❛♥ ❛♥② S21 ❛♥❞S12 ♠❡❛s✉r❡❞ ❞✉r✐♥❣ ❝❛❧✐❜r❛t✐♦♥ ✭❙❡❝✳ ✸✳✷✮✳■❢ t❤❡ ✐s♦❧❛t✐♦♥ ✐s ♥♦t ❡♥♦✉❣❤✱ t❤❡ ♥♦✐s❡ ✢♦♦r ✇✐❧❧ ✐♥✢✉❡♥❝❡ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ❞✉❡ t♦ ❛ ❧❛❝❦ ♦❢ ❞②♥❛♠✐❝ r❛♥❣❡✳

❼ ❈②❝❧❡ ❛♥t❡♥♥❛ r♦❧❡s ❛♥❞ r❡♣❡❛t❲✐t❤ ♠❛t❝❤❡❞ ❧♦❛❞ ♦♥ ❞✐s♣❧❛❝❡❞ ❝❛❜❧❡✱ r❛✐s❡❞ ✐♥t♦ ✇♦r❦✐♥❣ ✈♦❧✉♠❡ ❛♥❞ ❛♥t❡♥♥❛ ✐♥ st❛t✐❝ ♣♦s✐t✐♦♥ ✭❋✐❣✳ ✶✶✮✳

P❛❣❡ ✷✸ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✶✶✿ ❈❛❜❧❡✲✐♥t❡❣r✐t② t❡st ✇✐t❤ ❞✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛ ❝❛❜❧❡ r❛✐s❡❞ ✐♥t♦ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✳

P❛❣❡ ✷✹ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✷✳✻✳✸ ❆♥t❡♥♥❛ ❚❡st

❚❤❡ ✜♥❛❧ t❡st ✐s ❛♥ ❛♥t❡♥♥❛ ✐♥t❡❣r✐t② ❝❤❡❝❦ ✱ ❝♦♠♣❛r✐♥❣ t❤❡ ❦♥♦✇♥ ❛♥t❡♥♥❛ r❡✢❡❝t✐♦♥ ❝♦❡✣❝✐❡♥ts t♦ t❤❡ ❝♦rr❡s♣♦♥❞✐♥❣Sxx ♣❛r❛♠❡t❡rs ❛✈❡r❛❣❡❞ ❢♦r ❛❧❧ st✐rr❡r ♣♦s✐t✐♦♥s✳

❼ ❈♦♥♥❡❝t ♠♦✉♥t❡❞ ❛♥t❡♥♥❛s✳❉✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛ t②♣✐❝❛❧❧② ❛t ❆✶✱ ❛❧s♦ t❤❡ ✜rst ❝❛❧✐❜r❛t✐♦♥ ♠❡❛s✉r❡♠❡♥t✳

❼ ❈❧♦s❡ ❝❤❛♠❜❡r ❞♦♦r✳

❼ ❘✉♥ ❆♥t❡♥♥❛❴❈❤❡❝❦✳♠ s❝r✐♣t✳❆♣♣❡♥❞✐① ❆✳✶✳

❼ ❈❤❡❝❦ ❛♥t❡♥♥❛❡ r❡✢❡❝t✐♦♥ ❝♦❡✣❝✐❡♥ts❙❝r✐♣t ❞✐s♣❧❛②s ♦✈❡r❧❛② ♦❢ r❡✢❡❝t✐♦♥ ❝♦❡✣❝✐❡♥ts ❢♦r ❢✉❧❧ st✐rr❡r r♦t❛t✐♦♥ ❛♥❞ r❡❢❡r❡♥❝❡ ♠❡❛s✉r❡♠❡♥ts ✭❋✐❣✳ ✶✷✮✳❚❤❡ ❘❈ r❡s✉❧ts s❤♦✉❧❞ r❡♠❛✐♥ st❛❜❧❡ ❛♥❞ s✐♠✐❧❛r t♦ t❤❡ r❡❢❡r❡♥❝❡ ❝✉r✈❡s✳ ■❢ ❞❡✈✐❛t✐♦♥ ♦❢ ♠♦r❡ t❤❛♥ ✸ ❞❇ ✐ss❡❡♥ ♦r t❤❡ ✐♥✲❘❈ Sxx ✐s ❛❜♦✈❡ ✲✸ ❞❇✱ ❢✉rt❤❡r ✐♥s♣❡❝t✐♦♥ ♦❢ t❤❡ ❛♥t❡♥♥❛ ✐s r❡q✉✐r❡❞✳

❋✐❣✉r❡ ✶✷✿ P❧♦t ❣❡♥❡r❛t❡❞ ❜② ❆♥t❡♥♥❛❴❈❤❡❝❦✳♠ s❝r✐♣t✳ ◆♦t❡ t❤❡ ❝❧♦s❡ ❝♦rr❡❧❛t✐♦♥ ❜❡t✇❡❡♥ t❤❡ r❡❢❡r❡♥❝❡ ❛♥❞❘❈✲♠❡❛s✉r❡❞ ♣❧♦ts✱ ✐♥❞✐❝❛t✐♥❣ ❡①♣❡❝t❡❞ ❛♥t❡♥♥❛ ♣❡r❢♦r♠❛♥❝❡✳

P❛❣❡ ✷✺ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✸ ❘❈ ❈❛❧✐❜r❛t✐♦♥

❚❤❡ ❘❈ ❈❛❧✐❜r❛t✐♦♥ ❝❛♥ st❛rt ♦♥❝❡ t❤❡ ❡q✉✐♣♠❡♥t ❧❛②♦✉t ❤❛s ❜❡❡♥ ❝♦♠♣❧❡t❡❞ ❛♥❞ t❤❡ ✐♥t❡❣r✐t② ♦❢ t❤❡ s❡t✉♣ ❝❤❡❝❦❡❞✳❚✇♦ ❝♦♥tr♦❧ s❝r✐♣ts ❛r❡ ✉s❡❞✿ ✶✮ ❙❑❆❴❈❛❧❴❉❛t❛❴❆❈◗✳♠ ❛♥❞ ✷✮ ❘✉♥ ❈❛❧❴♣r♦❝❡ss✐♥❣✳♠ ✱ ♣❡r❢♦r♠✐♥❣ ❞❛t❛❛❝q✉✐s✐t✐♦♥ ❛♥❞ ♣r♦❝❡ss✐♥❣✱ r❡s♣❡❝t✐✈❡❧②✳ ❚❤❡ s❝r✐♣ts ✭❆♣♣❡♥❞✐① ❆✮ ❛✉t♦♠❛t❡ st✐rr❡r ❝♦♥tr♦❧✱ ❞❛t❛ ❛q✉✐s✐t✐♦♥ ❛♥❞♣r♦❝❡ss✐♥❣✳ ❚❤❡ ♦♣❡r❛t♦r ✐s r❡q✉✐r❡❞ t♦ r✉♥ t❤❡ ❝♦❞❡✱ ❢♦❧❧♦✇ ♣r♦♠♣ts✱ ♣r♦✈✐❞❡ ❞❛t❛ ❧♦❝❛t✐♦♥s ❛♥❞ ❛❞❥✉st ❛♥t❡♥♥❛♣♦s✐t✐♦♥s✳

✸✳✶ ❈❛❧✐❜r❛t✐♦♥ ▼❡❛s✉r❡♠❡♥ts

❚❤❡ ❙❑❆❴❈❛❧❴❉❛t❛❴❆❈◗✳♠ ✭❆♣♣❡♥❞✐① ❆✳✸✮ s❝r✐♣t ✐s r✉♥ ✐♥ ▼❆❚▲❆❇ ❛♥❞ ❝②❝❧❡s t❤r♦✉❣❤ ❛ ♠❡❛s✉r❡♠❡♥tr♦✉t✐♥❡ ❢♦r ❛❧❧ ✽ ❞✐s♣❧❛❝❡❞✲❛♥t❡♥♥❛ ♣♦s✐t✐♦♥s✳ ❆ ❞✐r❡❝t♦r② s❤♦✉❧❞ ❜❡ ❝r❡❛t❡❞ s♣❡❝✐✜❝❛❧❧② ❢♦r ❘❈ ❝❛❧✐❜r❛t✐♦♥✱ ♦♥ ❛st♦r❛❣❡ ✈♦❧✉♠❡ ✇✐t❤ ❛♠♣❧❡ ❢r❡❡ s♣❛❝❡✳ ❚❤❡ ❝♦❞❡ ✇✐❧❧ ❝♦rr❡❝t❧② ❧❛❜❡❧ t❤❡ ❞❛t❛ ❢♦r t❤❡ ♣♦st✲♣r♦❝❡ss✐♥❣ s❝r✐♣t✱ ✇r✐t✐♥❣❛ ✜❧❡ ❢♦r ❡❛❝❤ st✐rr❡r st❡♣ ✐♥t♦ s❡❧❢✲❣❡♥❡r❛t❡❞ ❞✐r❡❝t♦r✐❡s ❛ss♦❝✐❛t❡❞ ✇✐t❤ t❤❡ ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥ ✭P♦✐t✐♦♥ ❳ ✮✳ ❙t✐rr❡r❝♦♥tr♦❧ ✐s ❛❧s♦ ❡♠❜❡❞❞❡❞ ✐♥ t❤✐s ❝♦♥tr♦❧✳

❼ ❋♦❧❧♦✇ ♦r❞❡r ♦❢ ❞✐s♣❧❛❝❡♠❡♥t✲❛♥t❡♥♥❛ ♣♦s✐t✐♦♥s❋♦❧❧♦✇ ❋✐❣✳ ✶ ❞❡✜♥✐t✐♦♥s✿ ✭❆✶✲✹ ✫ ❇✶✲✹✮✳■ss✉❡s ❝❛♥ ❜❡ r❡tr❛❝❡❞ ✐❢ t❤❡ ♦r❞❡r ✐s ❦♥♦✇♥✱ ✇❤✐❝❤ ♠❛② r❡q✉✐r❡❞ ❛ s✐♥❣❧❡ r❡♣❡❛t❡❞ ✐♥st❡❛❞ ♦❢ ✽✦

❼ ▼♦✉♥t ❞✐s♣❧❛❝❡❞ ❛♥t❡♥♥❛ ❛t ♣♦s✐t✐♦♥ ✭❆✶✮❊♥s✉r❡ t❤❛t ❧♦✇✲❢r❡q✉❡♥❝② ❡❧❡♠❡♥ts ♦❢ ❛♥t❡♥♥❛ ❛r❡ ✇✐t❤✐♥ ✇♦r❦✐♥❣ ✈♦❧✉♠❡ ✭▲❯❋✮ ❛♥❞ ❝❛❜❧❡ ✐s s✉♣♣♦rt❡❞✳

❼ ❈❤❡❝❦ ❛❧❧ ♠♦✈✐♥❣ ❝♦♥♥❡❝t♦rs❆♥t❡♥♥❛ ✴ ❈❛❜❧❡ ♠♦✈❡♠❡♥t ❝❛♥ ❧♦♦s❡♥ ❝♦♥♥❡❝t✐♦♥s✳

❼ ❈❧♦s❡ ❘❈ ❞♦♦r

❼ ❘✉♥ ❙❑❆❴❈❛❧❴❉❛t❛❴❆❈◗✳♠

❼ ❊♥t❡r ◆♦✳ ♦❢ ❙t✐rr❡r P♦s✐t✐♦♥s❚②♣✐❝❛❧❧② ✼✷

❼ ❊♥t❡r ❞❛t❛ ❞✐r❡❝t♦r② ♥❛♠❡❚②♣✐❝❛❧❧② ❈❛❧✐❜r❛t✐♦♥❴❨❨❴▼▼❴❉❉✱ ♣♦ss✐❜❧② ❛❞❞✐♥❣ ❞❡s❝r✐♣t✐✈❡ ♥♦t❡s✳

❼ ❲❛✐t ▼❆❚▲❆❇ ❝♦♠♠❛♥❞✲❧✐♥❡ ♣r♦♠♣t❆♥t❡♥♥❛ ♣♦s✐t✐♦♥ ★ ❋✐♥✐s❤❡❞▼♦✈❡ ❛♥t❡♥♥❛ t♦ ♥❡①t P♦s✐t✐♦♥✦✦✦✦ ❉❖◆✬❚ ❋❖❘●❊❚ ❚❖ ❘❯◆ ❚❍❊ ❙❚■❘❘❊❘ ✦✦✦✦

❼ ❈❤❛♥❣❡ t♦ ♥❡①t ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥ ✭❆✷✮

❼ ❈❤❡❝❦ ❛❧❧ ♠♦✈✐♥❣ ❝♦♥♥❡❝t♦rs

❼ ❈❧♦s❡ ❘❈ ❞♦♦r

❼ ❙❡❧❡❝t ▼❆❚▲❆❇ ✇✐♥❞♦✇ ❛s ❛❝t✐✈❡❈❧✐❝❦ ♦♥ t❤❡ ✉♣♣❡r ✇✐♥❞♦✇ ♣❛♥❡✳

P❛❣❡ ✷✻ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❼ ❊♥t❡r ❛♥② ❦❡②

❼ ❘❡♣❡❛t ❧❛st ✻ st❡♣s ❢♦r ✻ r❡♠❛✐♥✐♥❣ ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥s❆✸ ❃ ❆✹ ❃ ❇✶ ❃ ❇✷ ❃ ❇✸ ❃ ❇✹

❼ ❆❧❧ ❞❛t❛ st♦r❡❞ ✐♥ ♦r❞❡r❡❞ ❢❛s❤✐♦♥ ❛♥❞ r❡❛❞② ❢♦r ♣♦st✲♣r♦❝❡ss✐♥❣

■❢ ✐ss✉❡s ✴ ❡rr♦rs ❛r❡ ❡♥❝♦✉♥t❡r❡❞ ❞✉r✐♥❣ ▼❆❚▲❆❇ s❝r✐♣t ❡①❡❝✉t✐♦♥✱ t❤❡s❡ ♣❛r❛♠❡t❡rs ♠❛② r❡q✉✐r❡ ❛❞❥✉st♠❡♥t✿

❼ ❈❤❡❝❦ ●P■❇✲❜♦❛r❞ ❛❞❞r❡ss❆ ❞✐st✐♥❝t ♥✉♠❜❡r ✐s ❛ss✐❣♥❡❞ t♦ ●P■❇ ❜♦❛r❞ ✉s❡❞ ✇✐t❤ ❛ ♣❛rt✐❝✉❧❛r ❝♦♠♣✉t❡r ❢♦r t❤❡ ✜rst t✐♠❡✳▼❛r❦ ●P■❇ ❜♦❛r❞s t♦ ❡❛s✐❧② r❡❝❛❧❧ t❤❡ ♥✉♠❜❡r✐♥❣ ❛ss✐❣♥❡❞ t♦ ✐t ❜② t❤❡ ❝♦♥tr♦❧❧✐♥❣ ❝♦♠♣✉t❡r ✭❋✐❣✳ ✶✸✮✳❙❝r✐♣t ❧✐♥❡✿ ❣ ❂ ❣♣✐❜✭✬◆■✬✱✵✱✷✵✮❀ ✇❤❡r❡ ❱◆❆ ❛❞❞r❡ss ❂ ✷✵ ❛♥❞ ●P■❇✲❜♦❛r❞ ◆♦✳ ❂ ✵

❼ ❙♣❡❝✐❢② ✈❛❧✐❞ st♦r❛❣❡ ❞✐r❡❝t♦r② ♥❛♠❡✳❙♦♠❡ ❝❤❛r❛❝t❡rs ♠❛② ❜❡ ✐♥✈❛❧✐❞ ❢♦r ❞✐r❡❝t♦r② ♥❛♠❡✳

❋✐❣✉r❡ ✶✸✿ ●P■❇ ❛❞❛♣t❡r ❛❧❧♦❝❛t❡❞ ❛s ◆♦✳ ✵✳

P❛❣❡ ✷✼ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✸✳✷ ❉❛t❛ Pr♦❝❡ss✐♥❣

❚❤❡ ❞❛t❛ ❛❝q✉✐s✐t✐♦♥ s❝r✐♣t st♦r❡s ❛❧❧ ❝❛❧✐❜r❛t✐♦♥ ❞❛t❛ ✐♥ t❤❡ ❝♦rr❡❝t ♦r❞❡r ❢♦r t❤❡ ♣r♦❝❡ss✐♥❣ s❝r✐♣t✳

❼ ❘✉♥ ❈❛❧❴♣r♦❝❡ss✐♥❣✳♠

❼ ❊♥t❡r ❞❛t❛ ❞✐r❡❝t♦r② ♥❛♠❡■❢ r✉♥ ❢r♦♠ t❤❡ ❞✐r❡❝t♦r② ❝♦♥t❛✐♥✐♥❣ t❤❡ ♠❛✐♥ ❝❛❧✐❜r❛t✐♦♥✲♠❡❛s✉r❡♠❡♥t ❞❛t❛✱ ♦♥❧② t❤❡ ♠❛✐♥✲❞✐r❡❝t♦r② ♥❛♠❡ ✐sr❡q✉✐r❡❞✳

❼ ❆❧❧♦✇ ✶✵ ✲ ✹✵ ♠✐♥ ❢♦r ♣r♦❝❡ss✐♥❣✳❉❡♣❡♥❞s ♦♥ ❞❛t❛ s✐③❡ ❛♥❞ ❝♦♠♣✉t✐♥❣ ♣♦✇❡r✳

❊①❛♠✐♥✐♥❣ ❘❡s✉❧ts✿

❼ ❋✐❡❧❞ ✉♥✐❢♦r♠✐t②P❧♦t s❤♦✇s ♦✈❡r❧❛✐♥ ✉♥✐❢♦r♠✐t② ❢♦r ❛❧❧ ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥s ✭❋✐❣✳ ✶✹✮✳❆ ❜❛❞ ♠❡❛s✉r❡♠❡♥t ✐s ❝❤❛r❛❝t❡r✐s❡❞ ❜② ❛ ♥♦♥ ✉♥✐❢♦r♠ ❊✲✜❡❧❞ ✈❛r✐❛t✐♦♥✳ ❙❡❡ ❋✐❣✳ ✶✺✳

❼ ❊✲✜❡❧❞ ❙t❛♥❞❛r❞ ❉❡✈✐❛t✐♦♥▼✉st ❜❡ ✇✐t❤✐♥ st❛♥❞❛r❞✬s ❧✐♠✐ts✳ ■♥❞✐❝❛t❡s ❘❈ s❡t✉♣ ♦♣❡r❛t✐♥❣ r❛♥❣❡✳ ❊①❛♠♣❧❡ ✐♥ ❋✐❣✳ ✶✻

❼ ■▲ ❛♥❞ ❆❱❋■▲ ❛♥❞ ❆❱❋ r❡♣r❡s❡♥t ✐♥❝r❡❛s✐♥❣ ❧♦ss ✇✐t❤ ❢r❡q✉❡♥❝② ♦✈❡r ♦❜s❡r✈❡❞ ♦♣❡r❛t✐♥❣ r❛♥❣❡✳❆❱❋ ± ✼ ❞❇ ♠♦r❡ ❧♦ss t❤❛♥ ■▲✱ ❛s s❤♦✇♥ ✐♥ ❋✐❣✳ ✶✼✳

❼ ❋♦r s❛t✐s❢❛❝t♦r② r❡s✉❧ts✱ ❝♦♥t✐♥✉❡ ✇✐t❤ ❝❛❧✐❜r❛t✐♦♥ ✈❛❧✐❞❛t✐♦♥✳

P❛❣❡ ✷✽ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✶✹✿ ❈❛❧❴♣r♦❝❡ss✐♥❣✳♠ ❣❡♥❡r❛t❡❞ ✜❡❧❞ ✉♥✐❢♦r♠✐t② ♣❧♦t✳

❋✐❣✉r❡ ✶✺✿ ❋✐❡❧❞ ✉♥✐❢♦r♠✐t② ♣❧♦t s❤♦✇✐♥❣ ♣♦♦r r❡s✉❧ts ❢♦r ♣♦s✐t✐♦♥ ❆✹ ✭❞❛t❛✹✮✳

P❛❣❡ ✷✾ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✶✻✿ ❈❛❧❴♣r♦❝❡ss✐♥❣✳♠ ❣❡♥❡r❛t❡❞ ❝❛❧✐❜r❛t✐♦♥ ✈❛❧✐❞❛t✐♦♥ ♣❧♦t✳ ◆♦t❡ t❤❛t t❤❡ ♠❡❛s✉r❡❞ ❊✲✜❡❧❞ ✈❛r✐❛♥❝❡ ✐s✇❡❧❧ ❜❡❧♦✇ t❤❡ st❛♥❞❛r❞ ❛❝r♦ss t❤❡ ❝❤❛♠❜❡r ✇♦r❦✐♥❣ r❛♥❣❡✳

❋✐❣✉r❡ ✶✼✿ ❈❛❧❴♣r♦❝❡ss✐♥❣✳♠ ❣❡♥❡r❛t❡❞ ❘❈✲❧♦ss ♣❧♦ts✳ ◆♦t❡ t❤❡ ❞✐✛❡r❡♥❝❡ ♦❢ ❛♣♣r♦①✐♠❛t❡❧② ✼ ❞❇ ❜❡t✇❡❡♥ t❤❡❝✉r✈❡s✳

P❛❣❡ ✸✵ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

P♦♦r ♦r ✉♥❡①♣❡❝t❡❞ r❡s✉❧ts✿

❼ P♦♦r ✜❡❧❞ ✉♥✐❢♦r♠✐t②■❞❡♥t✐❢② ✇❤✐❝❤ ❛♥t❡♥♥❛ ♣♦s✐t✐♦♥✴s ❣✐✈❡ ♣♦♦r r❡s✉❧ts ❛♥❞ r❡♣❡❛t t❤❡s❡ ♠❡❛s✉r❡♠❡♥ts ✭❋✐❣✳ ✶✺✮✳❚❛❦❡ ❝❛r❡ t♦ ❧❛❜❡❧ t❤❡ ♥❡✇ ✜❧❡s ❝♦rr❡❝t❧② ❛♥❞ ♣❧❛❝✐♥❣ ✐t ✐♥ t❤❡ r✐❣❤t ❞✐r❡❝t♦r② ❢♦r t❤❡ ♣r♦❝❡ss✐♥❣ s❝r✐♣t✳

❼ ❊✲✜❡❧❞ st❛♥❞❛r❞ ❞❡✈✐❛t✐♦♥ ❡①❝❡❡❞s ❧✐♠✐ts■❢ t❤❡ ❧✐♠✐ts ❛r❡ ❡①❝❡❡❞❡❞ ✇✐t❤✐♥ t❤❡ ❡①♣❡❝t❡❞ ❢r❡q✉❡♥❝② r❛♥❣❡✱ t❤❡ ❝❛❧✐❜r❛t✐♦♥ ✐s ♥♦t ✈❛❧✐❞✳■♥❝r❡❛s✐♥❣ t❤❡ ♥✉♠❜❡r ♦❢ st✐rr❡r ♣♦s✐t✐♦♥s ✇✐❧❧ ✐♠♣r♦✈❡ r❡s✉❧ts ♠❛r❣✐♥❛❧❧②✳

❼ ■▲ ✴ ❆❱❋ ♥♦t ❝♦♥t✐♥✉♦✉s❧② ❞❡❝r❡❛s✐♥❣■❢ ■▲ ✴ ❆❱❋ ❞♦❡s ♥♦t s❤♦✇ ✐♥❝r❡❛s✐♥❣ ❧♦ss ✇✐t❤ ❢r❡q✉❡♥❝② ❛❝r♦ss t❤❡ ❡①♣❡❝t❡❞ r❛♥❣❡✱ t❤❡ ❞②♥❛♠✐❝ r❛♥❣❡ ♠❛②♥♦t ❜❡ s✉✣❝✐❡♥t✳▼♦r❡ ❡✣❝✐❡♥t ❛♥t❡♥♥❛s ❝♦✉❧❞ ❜❡ ✉s❡❞✳❋✐♥❞ ♠❡❛♥s ♦❢ ✐♥❥❡❝t✐♥❣ ❤✐❣❤ ♣♦✇❡r ❧❡✈❡❧s✳▲❛r❣❡r ❛✈❡r❛❣✐♥❣✱ ✐✳❡✳ ✐♥❝r❡❛s❡ st✐rr❡r ♣♦s✐t✐♦♥s✳

❼ ❯♥❡①♣❧❛✐♥❡❞ r❡s✉❧ts❯s❡ ❣✉✐❞❡ ❛♥❞ s②st❡♠❛t✐❝❛❧❧② ❝❤❡❝❦ ❢♦r ❡rr♦rs✳

P❛❣❡ ✸✶ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

✹ ❈❛❧✐❜r❛t✐♦♥ ❱❛❧✐❞❛t✐♦♥ ▼❡❛s✉r❡♠❡♥ts

❆ s❡t ♦❢ ♠❡❛s✉r❡♠❡♥ts ✐s r❡❝♦♠♠❡♥❞❡❞ t♦ t❡st t❤❡ ❝❛❧✐❜r❛t✐♦♥ ❛❝❝✉r❛❝②✳ ❯s✐♥❣ ❛ tr✉st❡❞ ❈♦♥t✐♥✉♦✉s✲❲❛✈❡ ✭❈❲✮s♦✉r❝❡✱ ❦♥♦✇♥ ♣♦✇❡r ❧❡✈❡❧s ❛r❡ ✐♥❥❡❝t❡❞ ✐♥t♦ t❤❡ ❝❛❜❧❡ ❝♦♥✜❣✉r❛t✐♦♥ ❛♥❞ r❡❝♦r❞❡❞ ♦♥ ❛ ❝❛❧✐❜r❛t❡❞ r❡❝❡✐✈❡r✳ ❚❤✐s♣r♦✈✐❞❡s ❡①♣❡❝t❡❞ ❦♥♦✇♥ ♣♦✇❡r ❧❡✈❡❧s t❤❛t ✐♥❝❧✉❞❡ ❧♦ss❡s ♦❢ t❤❡ ❝❛❜❧❡s ❛♥❞ ✐♥t❡r❢❛❝❡s✳ ❚❤❡ ❈❲ t♦♥❡s ❛r❡ t❤❡♥✐♥❥❡❝t❡❞ ✐♥t♦ t❤❡ ❘❈ ❢r♦♠ ❛♥ ❛♥t❡♥♥❛ ✭●▲P❉❆✮ ✇✐t❤✐♥ t❤❡ ✇♦r❦✐♥❣ ✈♦❧✉♠❡✱ r❡♣r❡s❡♥t✐♥❣ ❛ ❉❯❚✱ ❛♥❞ t❤❡ ❛✈❡r❛❣❡♣♦✇❡r ❧❡✈❡❧s r❡❝♦r❞❡❞✳ ❆ ♣r♦❝❡ss✐♥❣ s❝r✐♣t✱ ✈❛❧✐❞❛t✐♦♥✳♠ ✭❆♣♣❡♥❞✐① ❆✳✹✮✱ ❛✉t♦♠❛t❡s t❤❡ ♣r♦❝❡❞✉r❡ ❛♥❞ ♣❧♦ts t❤❡r❡s✉❧ts r❡❧❛t✐✈❡ t♦ t❤❡ ❡①♣❡❝t❡❞ ❧❡✈❡❧s✳ ❋✐❣✳ ✶✽ ❞❡♣✐❝ts t❤❡ ♠❡❛s✉r❡♠❡♥t s❡t✉♣✳

❋✐❣✉r❡ ✶✽✿ ❙❝❤❡♠❛t✐❝ ♦❢ t❤❡ ❝❛❧✐❜r❛t✐♦♥✲✈❛❧✐❞❛t✐♦♥ t❡st s❡t✉♣✳

✹✳✶ ❈♦♥t✐♥✉♦✉s✲❲❛✈❡ t❡sts

❼ ❙❡t✉♣ ❈❲ s♦✉r❝❡❙❡t ♣♦✇❡r ❤✐❣❤ ❡♥♦✉❣❤ ❢♦r ❣♦♦❞ ❙✐❣♥❛❧ t♦ ◆♦✐s❡ ❘❛t✐♦ ✭❙◆❘✮✳❆ ❈❲ s✇❡❡♣ ♦r s✐♥❣❧❡✲❢r❡q✉♥❝② ♣♦✐♥ts ❝❛♥ ❜❡ ❡✈❛❧✉❛t❡❞✳

❋♦r ❈❲ s✇❡❡♣s✿

❊♥s✉r❡ t❤❛t ❛ ❢✉❧❧ s✇❡❡♣ ✐s ♣❡r❢♦r♠❡❞ ❛t ❡❛❝❤ st✐rr❡r ♣♦s✐t✐♦♥✳❯s❡ ❛ ❞✇❡❧❧ t✐♠❡ ❧♦♥❣ ❡♥♦✉❣❤ ❢♦r ❈❲ r❡s♣♦♥s❡✿ ❃ ✶✵ ✉s

❼ ❘❡❝♦r❞ ❢r❡q✉❡♥❝✐❡s ❛♥❞ ♣❡❛❦ ♣♦✇❡r ❧❡✈❡❧s❊♥t❡r ✐♥t♦ ❛ s♣r❡❛❞s❤❡❡t ✴ ❛♥ ❛rr❛② ❢♦r♠❛t✳

❼ ❊♥t❡r ❢r❡q✉❡♥❝✐❡s ❛♥❞ ♣♦✇❡r ❧❡✈❡❧s ✐♥t♦ ▼❆❚▲❆❇❈r❡❛t❡ ♠❛tr✐① ✐♥ ✈❛r✐❛❜❧❡ s♣❛❝❡✳

❼ ❘✉♥ ✈❛❧✐❞❛t✐♦♥✳♠

❼ ❈❤❡❝❦ r❡s✉❧ts❘❡s✉❧ts s❤♦✉❧❞ ❜❡ ✇✐t❤✐♥ ❡①♣❡❝t❡❞ ❛❝❝✉r❛❝② ✭❋✐❣✳ ✶✾✮✳

P❛❣❡ ✸✷ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❋✐❣✉r❡ ✶✾✿ ❈❛❧✐❜r❛t✐♦♥ ✈❛❧✐❞❛t✐♦♥ r❡s✉❧ts ♣❧♦tt❡❞ ❜② ✈❛❧✐❞❛t✐♦♥✳♠✳

P❛❣❡ ✸✸ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

▼❊❙❆ ❙♦❧✉t✐♦♥s❉rs ❆✳ ❏✳ ❖tt♦ ❛♥❞ P✳ ❙✳ ✈❛♥ ❞❡r ▼❡r✇❡❏✉❧② ✷✵✶✺

❘❡❢❡r❡♥❝❡s

❬✶❪ ■❊❈ ✻✶✵✵✵✲✹✲✷✶✱ ❊❧❡❝tr♦♠❛❣♥❡t✐❝ ❈♦♠♣❛t✐❜✐❧✐t② ✭❊▼❈✮ P❛rt ✹✲✷✶✿ ❚❡st✐♥❣ ❛♥❞ ▼❡❛s✉r❡♠❡♥t ❚❡❝❤♥✐q✉❡s ✲ ❘❡✲✈❡r❜❡r❛t✐♦♥ ❈❤❛♠❜❡r ❚❡st ▼❡t❤♦❞s✱ ❖❝t♦❜❡r ✷✵✵✾✱ ❉r❛❢t✳

❬✷❪ ❆✳ ❏✳ ❖tt♦ ❛♥❞ P✳ ❙✳ ✈❛♥ ❞❡r ▼❡r✇❡✱ ❙❑❆✲❙❆ ❘❡✈❡r❜❡r❛t✐♦♥ ❈❤❛♠❜❡r ❝❤❛r❛❝t❡r✐s❛t✐♦♥✱ ❚❡❝❤♥✐❝❛❧ ❘❡♣♦rt✱ ▼❊❙❆❙♦❧✉t✐♦♥s✱ ❙♦✉t❤ ❆❢r✐❝❛✱ ❏❛♥✉❛r② ✷✵✶✹✳

❬✸❪ ❆✳ ❘✳ ❇♦t❤❛✱ ❏✳ ❆✳ ❆♥❞r✐❛♠❜❡❧♦s♦♥✱ ❙❑❆✲❙❆ ❘❡✈❡r❜❡r❛t✐♦♥ ❈❤❛♠❜❡r ❈❛❧✐❜r❛t✐♦♥✱ ❚❡❝❤♥✐❝❛❧ ❘❡♣♦rt✱ ▼❊❙❆❙♦❧✉t✐♦♥s✱ ❙♦✉t❤ ❆❢r✐❝❛✱ ❏✉❧② ✷✵✶✺✳

❬✹❪ ❏✳ ❆✳ ❆♥❞r✐❛♠❜❡❧♦s♦♥✱ ❲✐❞❡❜❛♥❞ ❈♦❛①✐❛❧ ❚r❛♥s❢❡r ■♠♣❡❞❛♥❝❡ ❢♦r ❑❛r♦♦ ❆rr❛② ❚❡❧❡s❝♦♣❡✱ ▼❛st❡rs ❚❤❡s✐s✱ ❯♥✐✲✈❡rs✐t② ♦❢ ❙t❡❧❧❡♥❜♦s❝❤✱ ❲❡st❡r♥ ❈❛♣❡✱ ❙♦✉t❤ ❆❢r✐❝❛✱ ❉❡❝❡♠❜❡r ✷✵✶✶✳

P❛❣❡ ✸✹ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❆♣♣❡♥❞✐❝❡s

❆ ▼❆❚▲❆❇ s❝r✐♣ts✿

❆✳✶ ❆♥t❡♥♥❛ ❈❤❡❝❦

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

%

% ANTENNA S11 VERIFICATION

%

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% Clear everything before statrting the measurement

clear all;

clc;

close all;

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% GPIB Connection Initialisation

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

g = gpib('NI',0,20); % create the connection. 20 is the VNA address. 0 is the GPIB board address

g.inputBufferSize=1000000; % input buffer

g.outputBufferSize=1000000; % output buffer

g.EOIMode='on'; % input data

g.EOSMode='none'; % output data

Channel = 1;

Trace = 1;

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% READ S11 and S22

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Stirrer_Pos = 72; % Number of stirrer position per revolution

Time_Interval = 2.95; % Delay between each S11 reading for a 3s stirrer dwell time

for k = 1:Stirrer_Pos

tic;

fopen(g); % starts the communication with the network analyzer.

fprintf(g,'calc%d:par:sel "Trc%d"',[Channel,Trace]); % default trace (Trace = 1)

fprintf (g,'sens%d:freq:star?',Channel); % default start frequency (300Khz)

Start = str2num(fscanf(g));

fprintf (g,'sens%d:freq:stop?',Channel); % default stop frequency (8Ghz)

Stop = str2num(fscanf(g));

fprintf (g,'sens%d:swe:poin?',Channel); % default number of points (200)\

Point = str2num(fscanf(g));

F = linspace(Start,Stop,Point); % Define Frequency range

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% Get S−Parameter per stirrer position

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% Read S11 data Real Part

fprintf(g,'calc%d:par:sel "Trc1"',Channel);

fprintf(g,'calc%d:par:meas "Trc%d","s11"',[Channel,Trace]);

fprintf(g,'calc%d:form %s;*wai',[Trace,'real']);

fprintf(g,'CALC%d:DATA? FDAT',Channel);

S11_Re =str2num(fscanf(g));


fprintf(g,'calc%d:form %s;*wai',[Trace,'imag']);

P❛❣❡ ✸✺ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺


S11_Im =str2num(fscanf(g));

S11(k,:) = S11_Re+1i*S11_Im;







%fprintf(g,'calc%d:par:meas "Trc%d","s22"',[x,w]);




S22(k,:) = S22_Re+1i.*S22_Im;

% Load previous Averaged antenna S11

OldS11 = csvread('GLPDAs_Reference\\s11_Ref_SKA_GLPDA.csv');

F_S11_Old = OldS11(:,1);

S11_Old = OldS11(:,2);

figure(1);

grid on;

hold all;

plot(F*1e−9, 20*log10(abs(S11(k,:))));

plot(F*1e−9, 20*log10(abs(S22(k,:))));

legend('Current GLPDA S_{11}','Current GLPDA S_{11}');

xlabel('Frequency in GHz');

ylabel('Reflections in dB');

title('GLPDAs Reflection');

% Close GPIB Connection

fclose(g);

toc

pause(Time_Interval);

end

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% PLOT S11 and S22 FOR COMPARISON WITH REFERENCE S11

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

figure(2);

grid on;

hold all;

plot(F*1e−9, 20*log10(mean(abs(S11))));

plot(F_S11_Old.*1e−3, 20*log10(S11_Old));

legend('Current GLPDA S_{11}','GLPDA S_{11} Reference');


ylabel('S_{11} in dB');

title('S_{11}');

figure(3);

grid on;

hold all;

plot(F*1e−9, 20*log10(mean(abs(S22))));

plot(F_S11_Old.*1e−3, 20*log10(S11_Old));

legend('Current GLPDA S_{22}','GLPDA S_{22} Reference');


ylabel('S_{22} in dB');

title('S_{22}');

clc;

P❛❣❡ ✸✻ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

fprintf('!!!! FINISHED !!!!\n');

P❛❣❡ ✸✼ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❆✳✷ ❉❛t❛ ❆❝q✉✐s✐t✐♦♥

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

%

% SKA CHAMBER CALIBRATION SCRIPT

%

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% Interface: GPIB (Address: 0)

% Receiver: R&S ZVB−8 (Address: 20)

% Probe: Two GLPDAs

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

clear all;

clc;

close all;

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% GPIB Connection Initialisation

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

g = gpib('NI',0,20); % create the connection. 20 is the ZVB−8 address

g.inputBufferSize=1000000; % input buffer

g.outputBufferSize=1000000; % output buffer

g.EOIMode='on';

g.EOSMode='none';

Channel = 1;

Trace = 1;

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% RC and Measurement Parameters

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% Define: − Directory for data storage

% − Number of Stirrer Position

%

% Read: − Measurement Frequency range

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

Main_Folder = 'Calibration' % Name of the directory where the data will be stored

Stirrer_Pos = input('Enter the number of stirrer position per revolution: '); % Number of stirrer position per revolution

Antenna_Pos = 8;

Time_Interval = 3.8; % Time interval necessary for VNA and stirrer synchronisation (in second)

for m = 1:Antenna_Pos

for k = 0:Stirrer_Pos−1

tic;

fopen(g); % starts the communication with the network analyzer.

fprintf(g,'calc%d:par:sel "Trc%d"',[Channel,Trace]); % default trace (Trace = 1)

fprintf (g,'sens%d:freq:star?',Channel); % default start frequency (300Khz)

Start = str2num(fscanf(g));

fprintf (g,'sens%d:freq:stop?',Channel); % default stop frequency (8Ghz)

Stop = str2num(fscanf(g));

fprintf (g,'sens%d:swe:poin?',Channel); % default number of points (200)\

Point = str2num(fscanf(g));

F = linspace(Start,Stop,Point); % Define Frequency range

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% Get S−Parameter per stirrer position

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−







P❛❣❡ ✸✽ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺





S11 = S11_Re+1i*S11_Im;

% Read S22









S22 = S22_Re+1i.*S22_Im;

% Read S21


fprintf(g,'calc%d:par:meas "Trc%d","s21"',[Trace,Trace]);







S21 = S21_Re+1i*S21_Im;

% Read S12









S12 = S12_Re+1i.*S12_Im;

% Close GPIB connection

fclose(g);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% Save data to CSV file

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% The code check if Directory exists. If it does not exist the code will

% create a new directory. A new directory is created for each

% stirrer position.

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% Save data to file

Dirname = strcat(Main_Folder,'\\Position',num2str(m));

if exist(Dirname, 'dir')

;

else

mkdir(Dirname);

end

% Save current file in a csv format

filename = strcat(Dirname,'\\Pos_',num2str(k),'.csv');

P❛❣❡ ✸✾ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

data = [F' S11' S21' S12' S22'];

csvwrite(filename,data);

fprintf('Data for Position %d saved\n',k);

toc;

pause(Time_Interval);

figure(1);

plot(F,20.*log10(abs(S11)));

grid on;

hold all;

plot(F,20*log10(abs(S22)));

figure(2);


grid on;

hold all;


end

clc;

fprintf('Antenna position %d Finished\n',m);

fprintf('Move antenna to next Position \n');

fprintf('!!!! DON''T FORGET TO RUN THE STIRRER !!!!\n');

input('Press any key to continue');

clc;

end

P❛❣❡ ✹✵ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

❆✳✸ ❉❛t❛ Pr♦❝❡ss✐♥❣

%==========================================================================

%

% SKA CHAMBER CALIBRATION

%

%==========================================================================

% Calibration data processing

% by: Joely Andriambeloson

% Date: 7/27/2015

%==========================================================================

clc; % Clear Matlab Command window

clear all; % Clear Matlab workspace

close all; % Close all figures

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% MEASUREMENT PARAMETER

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% Specify the directory where the calibration CSV files are stored

% also insert the number of stirrer position that was used

Path = input('Main folder containg the CSV files for all stirrer position? (example: GLPDA3_GLPDA4): ','s');

Stirrer_Pos = input('Number of stirrer positions? : ');

% Specify the VNA output power (in dBm) that was used for the chamber calibration in

% dBm here.

P_VNA = 23; % Change this value if a different input power was used.

% LPDA efficiency definition

D_LPDA1 = 0.75;

D_LPDA2 = 0.75;

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% COMBINE S−PARAMETER FOR ALL POSITIONS IN ONE MATRIX

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

disp('−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−');

disp('| Extracting S−parameter for each antenna position |');

disp('−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−');

for n = 1:8

Dirname = strcat(Path,'\\Position',num2str(n));

% Extracted Pulse file parameters

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

file = dir(Dirname);

k = 1;

VarName = ['Pos',num2str(n)];

VarName = genvarname(VarName);

for m=1:length(file)

[pathstr, name, ext] = fileparts(file(m).name);

if strcmp('.csv', ext) == 1

filename{k} = file(m).name;

S = csvread(strcat(Dirname,'\\',filename{k}));

if k <= Stirrer_Pos − 1

Data.(VarName).S11(:,k) = S(:,2);




end

k=k+1;

end

P❛❣❡ ✹✶ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

end

S11_Avg(:,n) = mean(abs(Data.(VarName).S11)');

S22_Avg(:,n) = mean(abs(Data.(VarName).S22)');

S11_Max_Tmp(:,n) = max(abs(Data.(VarName).S11)');

S22_Max_Tmp(:,n) = max(abs(Data.(VarName).S22)');

disp(['Position ' num2str(n) ' finished']);

end

S11_Mean = mean(S11_Avg');

S22_Mean = mean(S22_Avg');

S11_Max = mean(S11_Max_Tmp');

S22_Max = mean(S22_Max_Tmp');

F = S(:,1).*1e−9;

lambda = 3e8./F;

% Parameter for E−field calculation

neta = 120*pi;

N = 8;

Factor = 15/16*sqrt(pi/3)*(gamma(3*N)*sqrt(3*N)/gamma(3*N+1/2));

P_In = 10.^(P_VNA/10);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% PORT MISMATCHES CORRECTION

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

disp('');

disp('−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−');

disp('| Correcting data from port mismatches |');

disp('−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−');

for n = 1:8

VarName = ['Pos',num2str(n)];

VarName = genvarname(VarName);

Data.(VarName).S21_Corr = abs(Data.(VarName).S21).^2./((1 − abs(Data.(VarName).S11).^2).*(1 − abs(Data.(VarName).S22).^2));

AVF(n,:) = mean(Data.(VarName).S21_Corr')./(D_LPDA1.*D_LPDA2);

IL(n,:) = max(Data.(VarName).S21_Corr')./(D_LPDA1.*D_LPDA2);

Data.(VarName).P = (max(Data.(VarName).S21_Corr').*P_In)./D_LPDA2;

E(:,n) = sqrt(8*pi*neta*Data.(VarName).P'./(lambda.^2))*1e6*Factor;

disp(['Position ' num2str(n) ' finished']);

end

% Power Variation in the working volume

%======================================

AVF_Mean = mean(AVF);

IL_Mean = mean(IL);

% Standard deviation of E−field in dB

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

E_Mean = mean(E');

std_E = std(E');

std_E_dB = 20*log10((std_E + E_Mean)./E_Mean);

IEC_limit = [4 3 3];

F_IEC = [0.1 0.4 8];

IEC_limit = interp1(F_IEC,IEC_limit,F);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% EXPORT AVF and IL

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

data = [F*1e3 AVF_Mean'];

csvwrite('RC_Parameter\\AVF.csv',data);

data = [F*1e3 IL_Mean'];

csvwrite('RC_Parameter\\IL.csv',data);

P❛❣❡ ✹✷ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

data = [F*1e3 S11_Mean'];

csvwrite('RC_Parameter\\S11_Avg.csv',data);

data = [F*1e3 S22_Mean'];

csvwrite('RC_Parameter\\S22_Avg.csv',data);

data = [F*1e3 S11_Max'];

csvwrite('RC_Parameter\\S11_Max.csv',data);

data = [F*1e3 S22_Max'];

csvwrite('RC_Parameter\\S22_Max.csv',data);

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

% PLOT RESULTS

%−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

disp('Display results');

% Reflections coefficients

figure(1);

plot(F,20*log10(S11_Avg));

grid on;

hold all;

plot(F,20*log10(S11_Mean),'r','linewidth',2);

title('Reflection coefficients for Port1 − RED curve is the average');

xlabel('Frequency in GHz')

ylabel('Reflection coefficients in dB')

figure(2);

plot(F,20*log10(S22_Avg));

grid on;

hold all;

plot(F,20*log10(S22_Mean),'r','linewidth',2);

title('Reflection coefficients for Port2 − RED curve is the average');

ylabel('Reflection coefficients in dB')

% E−field variation in the working volume

figure;

for n = 1:8

dE = 20*log10(E(:,n)) − 20*log10(E_Mean');

plot(F,dE);

grid on;

hold all;

ylim([−10 10]);


ylabel('Variation in dB');

title('E−field variation in the working volume');


ylabel('E−field Variation in dB')

end

% Chamber attenuations (AVF and IL)

figure;

plot(F,10*log10(AVF_Mean));

grid on;

hold on;

plot(F,10*log10(IL_Mean),'r');


ylabel('Attenuation in dB')

title('Max and Avg Chamber Attenuations')

% E−field Standard deviation for field uniformity checking

P❛❣❡ ✹✸ ♦❢ ✹✹

❙❑❆✴✶✺✴✵✽✴✵✼✴❘❊❱✵ ❆✉❣✉st ✵✼✱ ✷✵✶✺

figure

plot(F,IEC_limit)

hold on

grid on

plot(F,std_E_dB,'*−g')

plot(F,smooth(std_E_dB,5),'y','linewidth',2);

plot(F,smooth(std_E_dB,10),'b')

plot(F,smooth(std_E_dB,15),'r')


ylabel('Standard deviation in dB')

title('E−field Standard Deviation');

legend('IEC−Limit','E−field Standard Deviation','smoothed standard Deviation: window of 5 points','smoothed standard

❆✳✹ ❈❛❧✐❜r❛t✐♦♥ ❱❛❧✐❞❛t✐♦♥

P❛❣❡ ✹✹ ♦❢ ✹✹

Documents

Reverberation Chamber Calibration Procedures · 2019-10-28 · SKA/15/08/07/REV0 August 07, 2015 orewFord This document has been written as a practical Reverberation Chamber (RC)