HAL Id: tel-01495449https://tel.archives-ouvertes.fr/tel-01495449

Submitted on 25 Mar 2017

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Design and characterization of a MEMS-based rotationsensor for seismic exploration

Maxime Projetti

To cite this version:Maxime Projetti. Design and characterization of a MEMS-based rotation sensor for seismic explo-ration. Other. Ecole Centrale Paris, 2014. English. NNT : 2014ECAP0030. tel-01495449

❯❯

P

♣rs♥t ②

❳ P

t♦ ♦t♥ t r

❯ P

t

s♥ ♥ rtr③t♦♥ ♦ s ♦tt♦♥ ♥s♦r ♦r

s♠ ①♣♦rt♦♥

♦t♦r tss ♥ ♦♥ r ♥ r♦♥t ♦ t r② ♦♠♣♦s ♦

❯❨ Pr♦ssr ♦ ♥tr Prs ♣rs♦r

❯❯ Pr♦ssr r

P ❯ Pr♦ssr ♦ ♥tr Prs Prs♥t

❯ Pr♦ssr ❯P r

❱❯❲ sr ♥♥r ♠rr ♣rs♦r

♦rt♦r é♥q s ♦s trtrs t tér① t

♦ ♥tr Prs

r♥ ❱♦ s ❱♥s

ât♥②r② ①

P

s ♣ s ♥t♥t♦♥② t ♥

♠r♠♥ts

t♥s t♦t ♦r à r♠rr ♠♦♥ rtr tès ♥s r② ♣♦r

♠♦r ♠♥t ♥♦ré à ♠ ♥r ♥s tt ♥tr t♦t ♥ ♠ ss♥t

♥ r♥ rté ♥s ♠♦♥ tr

r♠r s♥èr♠♥t s ♠♠rs r② P♣♣ r ♣rés♥t

r② ♥s q s r♣♣♦rtrs érô♠ r t r ♦r♦♥ q ♦♥t

♣t♥ t ♦♦♥té r ♠♦♥ ♠♥srt

t♥s é♠♥t à r♠rr éq♣ ♣r♦t ♥rt s♥s♦rs

♠rr s♥s q tt rr ♥rt ♣s ♣ ♦r ♦r Ps ♣rt

èr♠♥t ♣rés♥t t♦t ♠ rtt à r ❱♥♥r ♦

♥r♥t tès q ♠ t ♥tèr♠♥t ♦♥♥ ♠ré ♠ ♦♥♥ss♥

s♦♠♠r ♠♦♥ s s ♦♥ss t ♥♦s ♥♦♠rss sss♦♥s ♠♦♥t

é♥♦r♠é♠♥t ♥strt t ♦♥t ♦♥tré à rér ♥ ♠t tr é ♣♥♥t

s tr♦s ♥♥és r♠r é♠♥t ♦s ♦♦♥ t ♥s Ps♦♥

♠rr ❲str♥ ♦ q ♠♦♥t t é♥ér r ①♣ér♥ t r

s♦r rs♣t♠♥t sr s ♥str♠♥ts ♠sr ♥ ①♣♦rt♦♥ ss♠q t

♥ étr♦♥q Ps r♠r s♦♥ r ♣♦r tr r♠rq

♦♠♣ ♦rs s♦♥ st ♥ éts t ♣♦r s♦♥ ♥s ♣ré♣rt♦♥

♠s ♠srs ①♣ér♠♥ts

s r♠r♠♥ts ♦♥t é♠♥t à t♦ts s ♣rs♦♥♥s é♣rt♠♥t

♣♦r r ♦rs ♠s sts ♥ s ♥ s srt♦t

r♠r réér rt② ♣♦r s♦♥ tr sr rt♦♥ ♠s é♥t♦♥s

q ♦é ♥ rô és ♥s résst tt rr

♠r♠♥ts

♥st s♦t r♠rr ♠s ♦ès t ♠s ♥tr

♠rr q ♠♦♥t ôt♦②é q♦t♥ ♣♥♥t ♥térté ♠ tès ♦

t♠♠♥t ♣ë ♦r ♦♠s ♦t ♦r♥ ssr♠r♥

♥ r r♠♥ é♠ ♦t s ♦qr② ♥

t t♦s s trs ♣rés♥t ss ♠ rtt à Ptr ♥ ♠♥r

♥tr ♣♦r s♦♥ s♦t♥ t♥t ♣♥♥t ♠ tès q ♦rs ♠s ♦rts

♣♦r ♥térr r♦♣ ♠rr à ss

♥♥ ♥ r♥ ♠r à ♠ ♠ t ♠s ♠s ♣♦r r s♦t♥ ♥r♦②

s♥s q ♥ sr ♣s rré s sr♥♠♥t à ♦t tt ♥tr

♥tr♦t♦♥

qst♦♥ s②st♠ t♦ t sr s r♥ ♥

ss♠ t qst♦♥

♦♥t①t ♥ ♣r♥♣s ♦ ss♠ ①♣♦rt♦♥

qst♦♥ ♦ ♣♦♥t rr ♠sr♠♥ts ♥ ss♠ ①♣♦rt♦♥

♦tt♦♥ s♥s♦rs t♦ t ♦r♥t ♥♦s ♥ ♥ ss♠

♥♦♦② r ♦ r♦tt♦♥ s♥s♥ s②st♠s s ♥ ss♠♦♦②

②st♠s s♥ ♣♥♠

P s②st♠

♦rs♦♥ ♥

♣t ②r♦s♦♣s

♥ sr ②r♦s♦♣

r♣t ②r♦s♦♣s

tr♦♠ s♥s♦rs

♥rt s♥s♦rs

r♥st♦♥ ♦♣♦♥s

❱rt♥ ②r♦s♦♣s

♥r r♦♠trs

♠♠r② t

♣tr s♠♠r② ♥ ♦♥s♦♥s

❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠

♥ r♦tt♦♥ s♥s♦r

♥ qt♦♥s ♦ t r♦tt♦♥ s♥s♦r

♦t♦♥ qt♦♥

♥ ♥♦s

tr♦stt tt♦rs

tr♣t♦r ♦♥rt♦♥

♣t♥ t♦♥ ♥ ♦♥rt♦♥ s♥stt②

tr♦stt ♠♦♠♥t t♦♥

♥♥ ♦ t tr ♣t♦r ♦♥rt♦♥ ♦♥

t ♣r♦♦ ♠ss ♠♥ ♦r

♣♦s♥ ♣t♦r ♦♥rt♦♥

♣t♥ t♦♥ ♥ ♦♥rt♦♥ s♥stt②

tr♦stt ♠♦♠♥t t♦♥

♥♥ ♦ t ♣♦s♥ ♣t♦r ♦♥rt♦♥

♦♥ t ♣r♦♦ ♠ss ♠♥ ♦r

r♥t ♣t s♥s♥

r♦♥t♥ tt♦♥ s♥ r ♠♣r

♦♥ ♦ ♠♣r ♥♦s

t ♦r ♦♥tr♦ ♦♦♣

Σ∆ ♠♦t♦♥

♠♣♠♥tt♦♥ ♦ t t t t r♦tt♦♥ s♥s♦r

tstr♠ ♦♥rs♦♥ ♦r ♥r③

♦♥ ♦ ♥♦s ♥ t ♦s♦♦♣ ♠♦

♣tr s♠♠r② ♥ ♦♥s♦♥s

♦s♦♦♣ s♥ ♦r♠ ♦ s♥♣t ♣t♦rs

♦s♦♦♣ s♥ ♦r♠ ♦ ♣r♣t ♣t♦rs

s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♥ ♦♥str♥ts

♥ st② ♦ t r♦tt♦♥

tt ♠♦

♦tt♦♥ ♥ t ①② ♣♥

♥♥ ♦ r t♦♥s

❩①s tr♥st♦♥

♦tt♦♥ ♥ t ②③ ♣♥

rst ♠♦ rq♥s

♠♣♥ ♥②ss

♠♣♥ ♠♥s♠s ♦r t s♥♦♠ ♦♥rt♦♥ ♦

t r♦tt♦♥ s♥s♦r

q③♠ ♠♦

♠ ♠♣♥ ♠♦

♦t ♠♣♥ ♦♥t ♦ t s♥♦♠ ♦♥

rt♦♥

♠♣♥ ♠♥s♠s ♦r t ♣♦s♥ ♦♥rt♦♥ ♦

t r♦tt♦♥ s♥s♦r

♠♠r② ♦♥ t ♠♣♥ ♥②ss

♥t♦♥ ♦ t ♣rssr ♥ ♦r ♦ ♠♥

♥♦s

t② t♦r t♦♥

♥ ♥♦s t♦♥

tr ♠♦ ♦ r♦tt♦♥ s♥s♦r s♥s

♥♦♠ ♣t♦rs

♣♦s♥ ♣t♦rs

♠t♦♥ ♦ t ♥♦♠♥ ♣t♥

♥♥ ♦ ♥♦♥♥rts ♦♥ t rs♣♦♥s

♦♥♥r ♠♦ ♦ t r♦tt♦♥ s♥s♦r

Prt♦♥ ♦ t ♦♠♥♥t ♥♦♥♥r ♠♥s♠ ♦ t r♦

tt♦♥ s♥s♦r ♦♥rt♦♥s

♣t♠③t♦♥ ♦ r♦tt♦♥ s♥s♦r s♥s

♥♦♠ s♥s

Pr s♥♣t ♣t♦rs

②r ♣t♦rs

♣♦s♥ s♥s

♦s♦♦♣ s♠t♦♥ ♦ t ♦♣t♠♠ s♥s ♥t

sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦

t♦t②♣s

Pr♦ss♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♣t♥ s ❱♦t ❱ rtr③t♦♥

♣♥♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

t♣ ♦r t ♦♣♥♦♦♣ rtr③t♦♥

s♦♥♥ rq♥② ♥ t② t♦r ♠sr♠♥t

♦♥♥r ♦r ♥ ♦♣♥♦♦♣ ♠♦

♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

tr♦stt s♣r♥ rtr③t♦♥

①♣r♠♥t st♣ ♦r ♣r♦r♠♥ rtr③t♦♥

①♣r♠♥t ♣r♦r♠♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♦♠♣rs♦♥ t ♦tr r♦tt♦♥ s♥s♦rs

♦♣ r♦♠trs ♦r ♥r ♠sr♠♥ts

tr♦♠ s♥s♦r ♥t

♠♠r② t

♦♥s♦♥ ♦♥ ①♣r♠♥ts

♦♥s♦♥s ♥ ♣rs♣ts

♠♠r② ♦ t ♦r

♦♦♥

♣♣♥①

t♠t ♥♦t♦♥s ♦r rq♥② ♦♠♥ ♥②ss

♦♠tr ♣r♠tr s

♠♣♥ ♥②ss ♦ t s♥♦♠ s♥

♠♣♥ ♥②ss ♦ t ♣♦s♥ s♥

Pr♠trs ♦ s♥

Pr♠trs ♦ s♥

Pr♠trs ♦ s♥

r♥s

strt és♠é

st ♦ rs

t ♥ ss♠ ♣r♥♣ t r♥ ss♠ ♣r♥♣

tr♥t t♥q t♦ t sr s s♥ r♦tt♦♥ s♥s♦rs

♦♠♣rs♦♥ t♥ sr s ♥ ss♠ rt♦♥s t

sr ♣r♦ rtr③ ② s♦rt ♣♣r♥t ♥t

t t r sr t t②♣ ss♠ rt♦♥ r♦♠ ♣ s

sr rtr③ ② r ♣♣r♥t ♥t

♥t ♦ s♥ r♦tt♦♥ s♥s♦rs ♦r s♣rsr s♣t s♠♣♥

t ♦♥♥t♦♥ s♥s♦r ♥♦s ♦r ②qst s♠♣♥ t ♥♦s

s♥ ♦♥♥t♦♥ ♥ r♦tt♦♥ s♥s♦rs s ♦♥ P♣♦s s♠♣♥

Ptr ♦ t P s②st♠

♦rs♦♥ ♦st♦r ♣r♥♣ t strt♦♥ ♦ t s②st♠ t

s♠t r♠ ♦ t ♦♣ts

♥ sr ②r♦s♦♣ ♦r ♦tt♦♥ s♠♦♦② s♥s♦r

♥t ♦tt♦♥ s♥s♦r

♦t♣♦♥ ♣r♥♣

♦t♣♦♥ ♦♥rt♦♥s

strt♦♥ ♦ ♦r♦s ♦r r♦♠ ❬❪

②str♦♥ ♦♥♥r qrt③ rt s♥s♦r ♠♦

r♦♣♦t♦r♣s ♦ t ♥r r♦♠tr r♦♠ r♦

tr♦♥s t ♥tr ♦ t t t

♥trt♦♥ ♦ ♦♥ rt r♦♠tr ❩ t t♦ r♦tt♦♥ s♥

s♦rs ❳ ♥ ❨ ♥ ♦♥ rr ♥♦

❲♦r♥ ♣r♥♣ ♦ t ♥r r♦♠tr

♥♥ ♦ Q t ♥ ω0 rt ♦♥ t rq♥② rs♣♦♥s ♦ t

♥r r♦♠tr

♠♦ t♦ r t ♠♥ ♥♦s

♠t ♦ s♥ ♣t♦r

①

st ♦ rs

♠t ♦ ♥♦r♠ ♣t♦r

P♦st♦♥ ♠♣r ♣r♥♣

t♣t ♦t ♦ t r♦♥t♥ rt ♦r s♥♣t ♣t♦rs

t♣t ♦t ♦ t r♦♥t♥ rt ♦r ♣♦s♥ ♣t♦rs

q♥t ♠♣r ♥♦s ♠♦

Pr♥♣ ♦ Σ∆ ♠♦t♦♥

♦s s♣tr♠ ♦ r♥t r♦♠ ♥ ♦rs♠♣ q♥t③r t♦

t♦rr Σ∆♠♦t♦r

trtr ♦ t ♥rt s♥s♦r

♥♦ s♥ ♥ ts tstr♠ ♦♥rs♦♥

♠t ♦ t s♥s♦r ♦♦♣ t s♥♣t ♣t♦rs

♠t ♦ t s♥s♦r ♦♦♣ t ♣r♣t ♣t♦rs

r②st♦r♣ ①s ♦ rs s ♦r t r♦tt♦♥ s♥s♦r

♣r♦ss

s♥ t s♥♦♠ ♣t♦rs

s♥ t ♣♦s♥ ♣t♦rs

♠♦ ♦ ♥ s♦t ♠ t ts ♦♥r② ♦♥t♦♥s ♦r t

r♦tt♦♥ ♥ ①② ♣♥

r t♦♥ s s♠ t♦♥ ss♠♣t♦♥

♠♦ ♦ ♥ s♦t ♠ t ts ♦♥r② ♦♥t♦♥s ♦r t

tr♥st♦♥ ♦t ③①s

♠♦ ♦ ♥ s♦t ♠ t ts ♦♥r② ♦♥t♦♥s ♦r t

r♦tt♦♥ ♥ ②③ ♣♥

♠♦ ♦r t t♦♥ ♦ rst ♠♦ rq♥s

♠♣♥ ♠♥s♠s ♥ s♥♣t r♦tt♦♥ s♥s♦r t s♦

♠tr t t♦♣

♦ ♦ sq③♠ ♠♣r

♠♠t♦♥ ♦ ♠♣♥ t♦♥s ♦r ♦♠

♦ ♦ s♠ ♠♣r

s♠ ♠♣♥ ♦♥t ♦ t r♦tt♦♥ s♥s♦r

♠♣♥ ♠♥s♠s ♥ ♣♦s♥ r♦tt♦♥ s♥s♦r

t♦r ♦♠♣rs♦♥ ♦r t t♦ s♥s st

♥ ♥♦s ♦♠♣rs♦♥ ♦r t t♦ s♥s st

tr ♠♦ ♦r s♥♦♠ ♣t♦rs

tr ♠♦ ♦r ♣♦s♥ ♣t♦rs

♠t♦♥ ♦ t tr♦stt ♥r② ♦r ♦♠ strtr

①

st ♦ rs

strt♦♥ ♦ t rs♦♥♥ ♣ st t♦ ♥♦♥♥r ♠♥s♠s

♥tr♦ tr♦ t ♦♥t γ t γ > 0 t γ < 0

r♥ ♥ r rs r ♦t♥ ♦r s♠ ♠♠ ♥

str♦♥ rt♦♥ ♠♣t A rs♣t②

♦ t r♦tt♦♥ s♥s♦r s♥st ♠♥t t ♥♦r rs

♥ t s♥st ♠♥t s③ r ① ② t ♣r♦ss

♥②ss ♦ ♣r s♥ ♦♠s

♥②ss ♦ ②r s♥ ♦♠s

♥②ss ♦ ♣♦s♥ ♣t♦rs

♠t P ♦ t tr s♥s st ♦♣ s♥

s♥ ♦tt♦♠ s♥

r♦tt♦♥ s♥s♦r ♣r♦ss

s♥ ♣r s♥ ♦♠s

s♥ ②r ♦♠s

s♥ ♣♦s♥ tr♦s

rt♥ ♦ tr♦s

strt♦♥ ♦ ❱ rtr③t♦♥ ♦♥ s♥ s

♦♠♣rs♦♥ t♥ ❱ ♠sr♠♥ts ♥ s♠t♦♥s ♦♣ t

s♥ ♦♣ rt s♥ ♦tt♦♠ s♥

strt♦♥ ♦ t ♦♣♥♦♦♣ rtr③t♦♥

Ptr ♦ t ♠ ♠r s ♦r ♦♣♥♦♦♣ rtr③t♦♥

sr♠♥ts ♦ ♥♦♥♥r tr♥sr ♥t♦♥s ♦♣ t s♥

♦♣ rt s♥ ♦tt♦♠ s♥

②♣ P rs♣♦♥s ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♥♥ ♦ t ♦t ♦♥ t P rs♣♦♥s ♦♣ s♥

s♥ ♦tt♦♠ s♥

t♣ s ♦r t ♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥

s♦r t t r♦tt♦♥ t t t tr♦♥ ♦r t t

♠♥t

①♣r♠♥t s♥ ♦r ♣r♦r♠♥ t♦♥

♥♦s ♥st② ♦ t tr s♥s

♣t♠③ P rs♣♦♥ss t ♦t VDC st t V ♦♣

s♥ s♥ ♦tt♦♠ s♥

tr♦♥ ♦r t t♦ r♦♠trs ♦♥ ♦t ss ♦

r♦tt♦♥ s♥s♦r

①

st ♦ rs

♥②ss ♦ ♦♣ r♦♠trs ♦r ♥r ♠sr

♠♥ts t P ♣♦t t ♥♦s ♥st② ♣♦t

Prs♥tt♦♥ ♦ t ♥t

♦♠♣rs♦♥ ♦ t ♥♦s ♥st② ♦ t ♥t t t ♦♥s ♦♥

♦r t r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s t ♦ ♣♦t t

❩♦♦♠ ♦♥ ♥♦s ♥st② ♦ mrad/s2/√Hz

①

st ♦ s

♠♠r② ♦ t t♥♦♦② r

t ♣r♠trs ♥ q♥t ♥♦s s♦rs ♦r r♦tt♦♥

s♥s♦r t s♥♣t ♣t♦rs

t ♣r♠trs ♥ q♥t ♥♦s s♦rs ♦r r♦tt♦♥

s♥s♦r t ♣r♣t ♣t♦rs

♥ s♣t♦♥s

Pr♠trs s ♥ t rt♦♥ ♦ t st♥ss ♦♥ts

♠r ♥②ss rsts

♣♣r♦①♠t♦♥s ♦r Qpr2 ♥ s♠ ♠♣♥

♦♠tr ♣r♠trs rtr③♥ t tr ♣r♦♣rts ♦

t s♥♦♠ s♥

♦♠tr ♣r♠trs rtr③♥ t tr ♣r♦♣rts ♦

t ♣♦s♥ s♥

❱s ♦ t ♦♠tr ♣r♠trs s ♦r t♦♥s

♦♠♣rt t ♦ t ♥♦♠♥ ♣t♥ t t

♥ t ♥②t ♦r♠s

sr ♣r♠trs ♦r ♦♣rt♦♥s t t tr♦♥s

Pr♦r♠♥ ♦ ♣r s♥ ♦♠s

Pr♦r♠♥ ♦ ②r s♥ ♦♠s

Pr♦r♠♥ ♦ ♣♦s♥ ♣t♦rs

♦♠♥ ♣t♥ ♥ ♣rst ♣t♥ ♠sr♠♥ts

♦♠♣rs♦♥ ♦ ♠sr tr♦♠♥ rs♦♥♥ rq♥②

♥ qt② t♦r ♦r t tr s♥s ♦♥sr

♦♠♣rs♦♥ t♥ ♠sr ♥ s♠t s ♦ t tr♦

stt s♣r♥

sr ♣r♦r♠♥s ♦ t tr s♥s st

①

st ♦ s

rs♦t♦♥ ♦ t tr s♥s st

rs♦t♦♥ ♦ ♦tr r♦tt♦♥ s♥s♥ s②st♠s

①

♣tr

♥tr♦t♦♥

♥ ss♠ ①♣♦rt♦♥ ♠♦st ♦ t s♥ qr ② ♣♦♥trr ♦♣♦♥s

s ♦♠♥t ② sr s ♦r r♦♥ r♦s s t② ♣r♦♣t ♥ t ♥r

sr r♦♥ r♦s ♦ ♥♦t ♦♥t♥ ♥② ♥♦r♠t♦♥ ♦♥ ♣r trts s

s♦rt s♣♥ t♥ rrs s rqr s♦ tt ts ♥♦s ♦♠♣♦♥♥t ♥

rt② rtr③ ♥ r♠♦ ② t tr♥ ♦r ♦♥sr♥

t ♦st ♦ ss♠ ①♣♦rt♦♥ ♥trs ♥ qst♦♥ t♥qs s♥ r

♣♦♥t rrs ♥ rr s♣♥ t♦ ♦♣ t♥q s r②

♥tr♦ ♥ ts ssrtt♦♥ rqr♥ rt ♠sr♠♥ts ♦ r♦♥ r♦t

t♦♥s t t r sr t ♠♥♠♠ ♦st t ♥ ♣♦r ♦♥s♠♣t♦♥

r♦r t ♠ ♦ ts ssrtt♦♥ s t s♥ ♥ t rtr③t♦♥ ♦

♠r♦tr♦♠♥ ♥r r♦♠tr tt ♥trs t ♥

♦♣t♠③ ♦♥tr♦ tr♦♥s t♦ ♠♣♠♥t ♦♠♣t rs♦t♦♥ ♥ s♥

stt② r♦tt♦♥ s♥s♥ ♠r♦s②st♠s ♥ ♥r r♦♠tr s s♥s♦r s

t♦ ♠sr rt♦♥ ♦ r♦tt♦♥ ♥ ♥♦♥ ②r♦s♦♣s ♠sr

♦t② ♦ r♦tt♦♥

♥ tr♠s ♦ ♠rt ♠♥s ♥r r♦♠trs r s ♣r♠r

② t♦ ♦♠♣♥st ♦r ♥r s♦s ♥ rt♦♥s ♥ rsr ss♠

s s s r r② s♠r t♦ ♥r r♦♠trs t t② ♦ ♥♦t

♠t t s♠ sss s♥ ♦♣♠♥ts ♥ ♣r♦♣♦s s♦ r ♦r

♣r♦r♠♥ ♣♣t♦♥s strt② ♦ ts ssrtt♦♥ s t♥ t♦ ♦♥trt t♦

t ♦♣♠♥t ♦ ♣r♦r♠♥ ♥r r♦♠tr ② rs♥

♦♥tr♦ tr♦♥s ♦♣ ♦r ♥r r♦♠trs ♣♦② ♥ ss♠

①♣♦rt♦♥ s rst t ♦r s ♦s ♦♥ ♥rst♥♥ t ♦r ♦

♠r♦strtr s♥st t♦ ♥r rt♦♥s ♥ ♦ t ♥trts t t

♥ tr♦♥s ♥ ♦rr t♦ ♥ t st strtr ♦r t s♥st ♠♥t

♣tr ♥tr♦t♦♥

r♥t s♥s♥ ♣r♥♣s r st tr♦♦t t ssrtt♦♥ ♥ t ♣r♦

t♦t②♣♥ ♦ t st s♥s ♦s t rtr③t♦♥ ♥ tr♠s ♦ rs♦t♦♥ ♥

s♥stt② t♦ ♦♥ ♦♥ t ♣♦sst② t♦ ♠sr sr s r♥ ss♠

①♣♦rt♦♥

tss s strtr s ♦♦s

♣tr s t t ♦♥t①t ♦ t st② t ♣rtr ♦s ♦♥ t

♥ t♦ s r♦tt♦♥ s♥s♦rs ♥ ss♠ ①♣♦rt♦♥ stt ♦ t rt ♦♥ t♥♦♦

s s t♦ ♠sr r♦tt♦♥s s t♥ ♣rs♥t ♦ rss ss♠ ①♣♦rt♦♥

rqr♠♥ts t ♥ r♦tt♦♥ s♥s♦r ♠st ♦♠♣t rt② ♥①♣♥s

t rs♦t♦♥ ♥ s♥stt② ♣t s♦t♦♥s r ♣r♦♠s

♥ ♥ts t♦ ♠t ts rqr♠♥ts

♣tr ♣r♦s t ♦r♥ ♣r♥♣ ♦ ♣r♦r♠♥ ♣t ♥

r r♦♠tr ♦ s♥s♥ ♣r♥♣s r ♣rs♥t t♦ s♥ rs

♦♥ s♥ tr ♣t♦rs ♥ t ♦tr s♥ ♣♦s♥ ♣t♦rs rst t

♠♦t♦♥ qt♦♥ ♥ t st② ♦ tr♦stt ♦rs ♦r t t♦ s♥s♥ ♣r♥♣s

r st ♥ s t s♥s♥ ♥ ♦♥tr♦ tr♦♥s ♦ t s♥s♦r s r②

st r rs ♦♥ ♣t s♥s♥ ♥ t ♦♥tr♦ r ♣r♦♣♦s

t♦ ♥rst♥ t r♥t ♠♥ts ♦ t s♥s♦r ♦♦♣ ♥trt♦♥s t♥

t t♦ s♥s♥ ♣r♥♣s ♥ t tr♦♥s r t♥ st t♦ ② ♥rst♥

t ♦r ♦ t

♣tr s t t s♥ ♦r ♦♠♣① t♦♣♦♦s ♥s♣r ② t

ss ♣rs♥t ♥ ♣tr s♥ s t♦ ♠t t♥ s♣

t♦♥s ♠♣♦s ② t tr♦♥s ♦r ♣r♦♣r ♣♥ ♥ rtr③t♦♥ ♥

♦♣t♠③t♦♥ st♣ s ♣r♦r♠ t♦ ♣r♦ ♣r♦t♦t②♣s t t st ♣r♦r♠♥s

♥ t st s♠t♦♥s r ♠ t♦ ♦rs t s♥s♦r rs♣♦♥s ♥ ts ♦♥tr♦

tr♦♥s ♥ ♥tr♠t ♦♥s♦♥ ♦♥ t st t♦♣♦♦s s ♥② ♥

♣tr ssss t rtr③t♦♥ ♥ t ①♣r♠♥t ♠sr♠♥ts

♦ t s♥s♦r s♥s st ♥ ♣tr ♦♠♣rs♦♥s t ♠♦s ♥ ♥

♣tr r ♣r♦♣♦s ♥ t ♣r♦r♠♥s r t♥ t ♥ ♥②③

♦♠♣rt ♥②ss t ♦tr t♥♦♦s r s♦ ♣r♦r♠

t t ♥ t ♦♥s♦♥ ♦♥ t st② ♦ s♥ ♥r r♦♠

trs ♦r ss♠ ①♣♦rt♦♥ s ♥ ♥ t♦♥ r♥t s r sst t♦

♠♣r♦ t ♣r♦t♦t②♣ ♣r♦r♠♥s tt ♥ r ♥ t s♦♣ ♦ ts

P

♣tr

qst♦♥ s②st♠ t♦ t

sr s r♥ ♥ ss♠

t qst♦♥

♦♥t①t ♥ ♣r♥♣s ♦ ss♠ ①♣♦rt♦♥

qst♦♥ ♦ ♣♦♥t rr ♠sr♠♥ts ♥ ss♠

①♣♦rt♦♥

♦tt♦♥ s♥s♦rs t♦ t ♦r♥t ♥♦s ♥ ♥

ss♠

♥♦♦② r ♦ r♦tt♦♥ s♥s♥ s②st♠s s

♥ ss♠♦♦②

♣tr s♠♠r② ♥ ♦♥s♦♥s

s ♣tr ♣rs♥ts t ♦♥t①t ♦ t st② ② ♥tr♦♥ t t② ♠t

② ♦♣②ssts t♦ t sr s r♥ ss♠ sr②s ♥ ♥♥♦t

s♦t♦♥ s♥ r♦tt♦♥ s♥s♦rs s ♣r♦♣♦s ♦♦ ② t♥♦♦② r ♦t

r♦tt♦♥ s♥s♥ t♥qs ♥ ss♠♦♦② t t ♥ ♦♠♣rs♦♥ t♥ t

r♥t t♥♦♦s s ♦♥ t♦ st ♦♥♣t st t♦ ♠t t s♣t♦♥s

♦ ss♠ ①♣♦rt♦♥

♣tr qst♦♥ s②st♠ t♦ t sr s r♥ ♥ ss♠ t qst♦♥

♦♥t①t ♥ ♣r♥♣s ♦ ss♠ ①♣♦rt♦♥

r t ♥ ss♠ ♣r♥♣ t r♥ ss♠ ♣r♥♣

①♣♦rt♦♥ ss♠♦♦② s t st② ♦ t ssr ② t s ♦ rt②

♥rt ss♠ s s st② ♣r♦s t tt ♥ ♦rrt t

♦tr ♦♣②s s♣ts ♥ ♥♦r♠t♦♥ ♦♥ r♦ ♣r♦♣rts ♥ ♠♥r

rs♦rs ♦t♦♥s ♦ ②r♦r♦♥s tr t s s♣♥ s ♥♦♠♣ss

♥ str♦♥ ss♠♦♦② s♠ s ♦r rtqs r ♥rt ♥ t

rs ♦♣♥ s s tr tr♦ ♦♥ st♥s ♥ ♥ r♦r t

ss♠♦r♣s ♥ ♥♦r♠t♦♥ ♦t t ♥tr ♦ r♦s ♠t ② t rtq

①♣♦rt♦♥ ss♠♦♦② s qt s♠r ①♣t tt ss♠ s♦rs r ♦♥tr♦

♥ t st♥ t♥ s♦rs ♥ rrs r rt② s♦rt

♠sr t r♥ ss♠ ①♣♦rt♦♥ s t trt♠ ♥ ♦r

s t♦ tr r♦♠ t s♦r t♦ srs ♦ s♥s♦rs s② rr♥ ♦♥

strt ♥ rt t♦r t s♦r r♦♠ t trt♠ t s ♣♦ss t♦

r♦♥strt t ♣t ♦ t ss♠ s r r t♦ t②♣s ♦ ss♠ sr②s

♥ ♥ ♠r♥ sr② ♥s ♣rtr ♣♣rts t♦ ♥rt ♥ t♦ r♦r

ss♠ s ♦r ♥st♥ s♣③ s♦rs r s t♦ ♥rt ♦st s

♥t♦ t r♦♥ s s rt♦rs ♦r ①♣♦s ♦♥ ♥ ♥ ♦♠♣rss r t s

s s r t♥ rt t t ♦♥r② t♥ t r♥t ♦♦

②rs ♥ t ssr ♥ r♦r ② rr②s ♦ ② s♥st s♥s♦rs ♦t

♦♥ t sr ♦♣♦♥s ♦r ♥ ♥ ②r♦♣♦♥s ♦r ♠r♥ r

qst♦♥ ♦ ♣♦♥t rr ♠sr♠♥ts ♥ ss♠ ①♣♦rt♦♥

qst♦♥ ♦ ♣♦♥t rr ♠sr♠♥ts ♥

ss♠ ①♣♦rt♦♥

♦t♦♥ ♦ ♣r♦r♠♥ ♦♠♣t♥ st ♦♦s ♦♦rs

♥s t♦ s♦ ♠♦r ♥ ♠♦r ♦♠♣① ♣r♦♠s ♥ ♣r♦s ♥ ②s ♦r

ss♠ t qst♦♥ ♦r ♥st♥ t ♥s ♥ rr r♥ ♥ ♦♠

♣tr st♦r ♦♥trt t♦ t qst♦♥ ♦ ♥s rr② ♦ s♥♣♦♥t

rrs ♥ ♦rr t♦ ♣rsr s ♠ s♥ s ♣♦ss ♦♠♣r t♦ r♦♣s ♦

♦♣♦♥s ❬❪ ♦r r♦rs ② s♥ ♣♦♥trr r ② ♦♠♥t ②

♥♦s ♦ t♦ r♦r s♥ ts ♥♦s s t♦ tr r♥ t

♣r♦ss♥ ♠♦r ♦♠♣♦♥♥t ♦ ♥♦s tt ♦♣②ssts t♦ t s

t ♦r♥t ♥♦s ♦r sr s

♦r ♥ t ♠♦st ♦ t s♦r ♥r② s ♦♥rt ♥t♦ sr s

② s ❬❪ r ♦♠♠♦♥② ♥♠ s r♦♥r♦s s t②

♣r♦♣t ♥ t ♥r ssr t② ♦ ♥♦t ♦♥t♥ ♥♦r♠t♦♥ ♦ ♣r tr

ts ♥ t♦ tr str♦♥ ♥r② t② ♦♠♥t ss♠ r♦rs ♦sr♥

rt♦♥s r♦♠ t ♣ ssr ② s t♥q t♦ s♣♣rss ♦r

♥t ♥♦s s t s ♦ tr♥ t♥qs ♥ t ♥♠rrq♥② κ

♦♠♥ ❬❪ ♦r ♦r ♦♦ tt♥t♦♥ ♦ ♦r♥t ♥♦s t ♣♦♥t rr

s♣♥ ♦r t s♣t rs♦t♦♥ ♠st rs t st ♦♥ t♦ t ②qst

st♥ ♥ssr② t♦ ♣ r♦♥r♦s ♥s ♦r ♥st♥ r♦♥r♦

♥ts ♥ ss t♥ ♠ rst♥ ♥ s♣♥ ♦ ♠ t♥ rrs

s s♦rt s♣♥ ♥ ss♠ sr②s ♠♥s t♥s ♦ t♦s♥ ♦ ♥♥s

s ♥ ♠♣t ♦♥ t t♠ ♣r♦tt② t♦ ♣r♣r t st♣ ♥ ♦♥ t ♣♦r

♦♥s♠♣t♦♥ ♦♥sr♥ ♦sts ss♦t t ♠♥♣♦r ♥ ♦sts ♥

qst♦♥ t♥qs t♦ ♦♣ t♦ ♣ t ♣r ♦r ss♠ sr②

♦♠♣tt ♥ t ② t♦ t ①♣♦rt♦♥ ♦ ♥ ♥ ♦♠♣① rsr♦rs

♦tt♦♥ s♥s♦rs t♦ t ♦r♥t ♥♦s

♥ ♥ ss♠

♥♦tr t♥q ♣rs♥t ♥ ❬❪ ♥tr♦s r♦tt♦♥ s♥s♦rs ♥ ♥ ss♠

t♦ ♠sr t r♥t ♦ t rt ♠sr ② ♦♥♥t♦♥ ♦

♣♦♥s ♥ r♦tt♦♥ s t r ♦ t ♥ ts s rt t♦ t

rts ♦ t s♣♠♥t t rs♣t t♦ s♣ ♦♦r♥ts

♣tr qst♦♥ s②st♠ t♦ t sr s r♥ ♥ ss♠ t qst♦♥

r tr♥t t♥q t♦ t sr s s♥ r♦tt♦♥ s♥s♦rs

①♣r♠♥t ss ♦♣ ♦♣♦♥s ♦♥ ♦t ss ♦ ♣r r♦tt♦♥ s♥s♦r ♥

strt♦♥ ♦ ts st♣ s ♣rs♥t ♥ r ❲t r♥t ss♠ s♦rs

t r♥t ♦ t rt s t r♦♠ t ♦♣♦♥s qst♦♥

♥ t♥ ♦♠♣r t♦ ♠sr♠♥ts r♦♠ t r♦tt♦♥ s♥s♦r ♦♦ tt♥ s

♦sr ♥ t♦ t ♦♥s♦♥ tt t t r sr r♦tt♦♥s ♦t ♦r

③♦♥t ①s r ♣r♦♣♦rt♦♥ t♦ t r♥t ♦ t rt ♦♠♣♦♥♥t

s♦ s♦♥ ♥ r s rst s ♦ ♠♥ ♥trst s♥ r♦tt♦♥ s♥s♦rs ♥

♠sr t r♥t ♦ ♥② s♥ qr ② ♦♣♦♥s r♥ ss♠ sr②

♦r t ss♠ qr r♥ ♦♣rt♦♥s ② s♥s♦r ♥♦s

r♥t ♦♠♣♦♥♥ts ♣♥♥ ♦♥ t t②♣ ♦ ss♠ s rr♥ r♦♠ t

ssr qst♦♥ s r s ♦♠♣♦♥♥t s ② t♦

♠sr ② r♦tt♦♥ s♥s♦r

t s ♣♦ss t♦ s♦rt ss♠ s ♣♥♥ ♦♥ tr ♣♣r♥t ♥ts

t t r sr r ♣♣r♥t ♥t s ♥t♦♥ ♦ t ♥

♥t ♥ θ ♦ ss♠ ♦r ♥st♥ sr s r♦♥ r♦s ♥

♥ ss♠ sr②s ♥ ♣♣r♥t ♥t ♦s t♦ tr tr ♥t

s♥ t② r ♣r♦♣t♥ t r ♠r♥t ♥ ♥ t ♦♥trr② ss♠

rt♦♥s s♠ ♠r♥t ♥ ♥ r ♣♣r♥t ♥ts

t♦ tr str♦♥r ♥r② ♥ tr s♠ ♣♣r♥t ♥t t t r

sr sr s r ♠♣ts ♥ ♠sr♥ tr s♣t r

♥ts s♥ r♦tt♦♥ s♥s♦rs ♦♠s ♣♦ss rs t s♠s ♠♦r ♦♠♣① t♦

♠sr t s♣t r♥t ♦ ss♠ rt♦♥s s ♦♥sq♥ r♦

tt♦♥ s♥s♦rs r st t♦ ♠sr t s♣t r♥ts ♦ ♥♦s ♦♠♣♦♥♥ts

t t r sr s rst s ♥trst♥ s♥ t ♦ ♣♦ss t♦ ♠sr

♦tt♦♥ s♥s♦rs t♦ t ♦r♥t ♥♦s ♥ ♥ ss♠

r ♦♠♣rs♦♥ t♥ sr s ♥ ss♠ rt♦♥s t sr ♣r♦ rtr③ ② s♦rt ♣♣r♥t ♥t t t r srt t②♣ ss♠ rt♦♥ r♦♠ ♣ ssr rtr③ ② r♣♣r♥t ♥t

t t s♠ ♥♦ ♣♦st♦♥ t t r sr t rt ♦♠♣♦♥♥t

♥ t r♥ts ♦ ♦♣rt♦♥ ♥♦ss r♥ ss♠ sr②

s ♣♦sst② ♥ ♠♦② str♦♥② t s♠♣♥ t♥q s ♥ ss♠

①♣♦rt♦♥ s♥ t ♦ ♣♦ss t♦ ♠♦ r♦♠ st♥r ②qst s♠♣♥

rqr♥ t♦ ♠sr♠♥ts ♦r t s♦rtst ♥t ♦ s♥ t♦ ♥ ♠

♣r♦ s♠♣♥ t♥q t P♣♦s s♠♣♥ ❬❪ P♣♦s s♠♣♥ rqrs

♦♦t ♠sr♠♥ts ♦ t rt ♥ ts r♥t t ② ♦r

t s♦rtst s♥ ♥t r s rst t s ♣♦ss t♦ ♥tr♣♦t

♥♦s ♦♠♣♦♥♥ts t♥ s♥s♦r ♥♦s ♦♥ s♣rsr s♣t s♠♣♥

r ♥t ♦ s♥ r♦tt♦♥ s♥s♦rs ♦r s♣rsr s♣t s♠♣♥ t♦♥♥t♦♥ s♥s♦r ♥♦s ♦r ②qst s♠♣♥ t ♥♦s s♥ ♦♥♥t♦♥♥ r♦tt♦♥ s♥s♦rs s ♦♥ P♣♦s s♠♣♥

♣tr qst♦♥ s②st♠ t♦ t sr s r♥ ♥ ss♠ t qst♦♥

♥♦♦② r ♦ r♦tt♦♥ s♥s♥ s②st♠s

s ♥ ss♠♦♦②

s♣t♦♥s ♦r r♦tt♦♥ s♥s♥ s②st♠s ♦♣r ♥ ss♠ ①♣♦rt♦♥

r ♦♥♥t ♦r t ♥ s tt ♦♣②ssts ♥ s t

♣♦♦rr rs♦t♦♥ t♥ ♦r r♦tt♦♥ ss♠♦♦② ② ♦rrs ♦ ♠♥t

♣② t ♦♦t ♥ qr ♦ t rs♦t♦♥ ♠st ss

t♥ mrad.s−2 ♦r µrad.s−1 ♦r ③ ♥ ♥ t♦♥ t rq♥②

♥ ♦ ♥trst ♥ r♦tt♦♥ ss♠♦♦② s ♦ ③ rs t ♦r♥

♥t rss ♥ ts ssrtt♦♥ s t♥ ③ ♥ ③ trs

t ♠①♠♠ s③ ♦ t s♥s♦r s ♠× ♠× ♠ ♥ t ♣♦r ♦♥s♠♣t♦♥

♠st ♦ ♠❲

♥♥ ♦♥♣t t♦ ♠sr r♦♥ ♥r rt♦♥s r♥ ss♠ sr

②s strts ② r♥ t s♥s♦rs s ♥ str♦♥ ss♠♦♦② ♥ t♦ tr

rs♦t♦♥s r r ttr t♥ ♥ ♦r ♥r ss♠ t ♦s t♦ ①trt

t♥ s♦t♦♥s tt ♥ s♣ ♦r ♦r ♣♣t♦♥ s ♦♥sq♥ ts

st♦♥ s r ♦ r♥t s②st♠s s t♦ ♠sr r♦♥ r♦tt♦♥s

♥ ♠s s②st♠s s♥ ♣♥♠ ♦♣t ②r♦s♦♣s tr♦♠

s♥s♦rs ♥ ♥rt s♥s♦rs ♥ ♠② s t t rs♣t t♦

r♥t rqr♠♥ts ♦st ♦♠♣①t② ♣♦r ♦♥s♠♣t♦♥ s③ ♥ rs♦t♦♥

s♠♠r② t ♥ ♦♥ t t ♥ ♦ ts st♦♥

②st♠s s♥ ♣♥♠

rst rtq tt♦r ♠ t ♣♥♠ s t ss♠♦s♦♣ r♦♠

t ♥s ss♠♦♦st ♥ ♥ ♥ ♣r♥♣ s ♥rst♦♦

ts t s ♥♦t sr♣rs t♦ ♥ s♦♣stt ♥str♠♥ts s♥ ts t②♣ ♦ t

♥♦♦②

P s②st♠

s ♠sr♥ t♥q ♦♥ssts ♥ ♦ ♥t♣r P♥♠ s♠♦♠

trs P stt t ♦♠♠♦♥ rt ①s tr♥st♦♥ ♠t♦ s

tr♦♠♥t t ♠♥t ♠♦♥ ♥s ♦ s s②st♠ s ♥ tst

♦r str♦♥ ♠♦t♦♥ ss♠ ♠①♠ t♦rt rs♦t♦♥ ♦ t ①

♣rss ♥ ♥r ♦t② s 10 nrad.s−1 ❬❪ r strts P

♦♥sr♥ tt ts s②st♠ s s ♥ r♦tt♦♥ ss♠♦♦② ts rs♦t♦♥ s

♥♦♦② r ♦ r♦tt♦♥ s♥s♥ s②st♠s s ♥ ss♠♦♦②

♦r rqr♠♥ts ♦r t ♣♣r♥t ♦♠♣①t② ♦ ts s②st♠ ♠s t

♥t ♦r r s ♣♦②♠♥t ♥ ss♠ ♣r♦s♣t♥

r Ptr ♦ t P s②st♠

♦rs♦♥ ♥

t♦rs♦♥ ♥ ♦r ♥r ss♠ ♥ ♥♥r♥ ♣♣t♦♥s s ♣r♦♣♦s

♥ ❬❪ ♥str♠♥t ♦♥ssts ♥ t♦rs♦♥ ♥ ♥ ♥tr rq♥②

s♥♥t② s♠r t♥ t r♦tt♦♥ ss♠ ♠♦t♦♥ t♦ r♦r ♥r

♣♦st♦♥ s qr t rr ♥trs ② ♠♥s ♦ rs♦t♦♥ ♦♣t r

♦ r ②♥♠ r♥ ♣r♥♣ ♥ ♦sr ♥ r ♣t s

s t♦ ss♣♥ t ♥ ♦ ♠rr♦r ♥ ①t♥s♦♥ r♠s ♣t ♦s t

♠♠ ♦ ♥t ♥s ♥ ♣t ♦s t t s♦r ♥ t P♦st♦♥

♥s♥ tt♦r P ♥♦s ♦♦r s st♠t t 3 µrad.s−1 ③

♥ ♠ ♦♠♠♥ts ♥ ♠ s P s②st♠ ♦t t st② t♦ s

ts ♥ ss♠ ①♣♦rt♦♥

r ♦rs♦♥ ♦st♦r ♣r♥♣ t strt♦♥ ♦ t s②st♠ ts♠t r♠ ♦ t ♦♣ts

♣tr qst♦♥ s②st♠ t♦ t sr s r♥ ♥ ss♠ t qst♦♥

♣t ②r♦s♦♣s

♣t ♥trr♦♠tr② s ss♠ ♥ ♠♣♦rt♥t r♦ ♥ ♣r♦r♠♥

♣♣t♦♥s ♥ s♣② ♦r str♦♥ r♦tt♦♥ ss♠♦♦②

♥ sr ②r♦s♦♣

♥ sr ②r♦s♦♣ ♥ t ♦r♥ s♥ ♦♥t♥s r♥s♣

t② t ♠① s t rt♥ t ♠s ♥rt ② sr t

♠srs t ♥ t rq♥② ♦ t♦ ♦♥tr♣r♦♣t♥ ♠s s t

rq♥② δf s rt② ♣r♦♣♦rt♦♥ t♦ t r♦tt♦♥ rt Ω r♦♥ t ♥♦r♠

t♦r t♦ t sr ♠ ♣♥ n ♥ ♥ ② ♥ qt♦♥

δf =4A

λPn ·Ω

r Ω s t r♦tt♦♥ ♦t② ♥♥ t rt r♦tt♦♥ rt ♥ ♦

r♦♥ r♦tt♦♥ P s t ♣r♠tr ♦ t r♥ A s t r ♥ λ s t

sr ♥t t s strt♦rr r♦♠ t qt♦♥ tt t s

♥♦t s♥st t♦ tr♥st♦♥ ♠♦t♦♥ t s♥st t♦ ♦r♠t♦♥s s♥ A P r

♥♥ ② t♠ ♦r ss♠♦♦ ♣♣t♦♥ t s t♦r4A

λL♠st

♠ ♠ rr t♥ ♦♠♠r r♥ srs s♥ rt s♥stt② ♥

rs♦t♦♥ r ♥

♥ s ♥ t ♥trr♦♠tr ♥ t s♥stt② rss r♦♠

t ♣♥♥② ♦ t sr rq♥② r♦♠ t t② ♥t t ♠♣♦rt♥t r

qr♠♥t ♦r ts s t ♠♥ stt② ♥ ♦rr t♦ ♦♣rt ♥ t

♠♦♥♦♠♦ s♥ r♠ rt♦♥s ♦ t t② ♥t ♠st ♥♦t ① ♦♥

♥t sts r② ♦♥str♥ts ♦r t rt② ♦ t sr ♠

♣r♠tr s ♣rssr ♥ t♠♣rtr tt♦♥s t t t② ♥t t

♥r♦♥♠♥t ♦♥t♦♥s t t ♦t♦♥ ♦ t ♠st ♣t t♥ tt

♠ts t♠♣rtr rt♦♥s ss t♥ 0.5C ♥ ♣rssr ♥ ss t♥

hPa

rr r♣♦rts ♥ ❬❪ t s♥ ♥ rst rsts r♦♠ t s♥s♦r r

s ♥ s♣② t ♦r sts ♥ r♦tt♦♥ ss♠♦♦②

s♥s♦r s ♦♣rt t t Pñ♦♥ t s♠♦♦ srt♦r② ♥ ♦tr♥

♦r♥ ♥str♠♥t s ♥t ♦♥ s ♦ m ♣r♦s t♦t r

♦ m2 s♥s♦r rs♦t♦♥ s st♠t t 0.3 nrad.s−1 ③ ♥

♥r st ♦♣rt♥ ♦♥t♦♥s

♥♦♦② r ♦ r♦tt♦♥ s♥s♥ s②st♠s s ♥ ss♠♦♦②

s ♦♠♣① s②st♠ s ♥♦t② r② ①♣♥s ♥ ♣♦r ♦♥

s♠♥ ♥ s♣t ♦ ♥ ①tr♠ rs♦t♦♥ ts s②st♠ s ♥♦t st ♦r ss♠

①♣♦rt♦♥

r ♥ sr ②r♦s♦♣ ♦r ♦tt♦♥ s♠♦♦② s♥s♦r

r♣t ②r♦s♦♣s

rqrs s♦♣stt ts ♥ ♦♠♣t ♦♣rt♦♥s s

♥♦t ♦♠♣t t rs ♥t♦rs ♦r ♠♦ ♦srt♦♥ ♥ ♦♠♣rs♦♥

r ♦♣t ②r♦s♦♣ s s♠ ♥ r♦st ♣r♥♣ s qt s♠♣

♥rr♦s♣tr t t ♠ s ♥rt ② s♦r ♥ ♣ss ♦♥ t♦ ♥

q ♥t♥st② ♠ s♣ttr rst♥t t♦ t ♠s r r♦♥

♠♦♥♦♠♦ r ♦ ♥ ♦♣♣♦st rt♦♥s tr ♣ss♥ tr♦ t r

♦t ♠s r s♣r♠♣♦s ♥ ② t s♠ ♠ s♣ttr ♥ str ♦♥t♦

♣♦t♦tt♦r t ♥tr s t ♦♠♣t rst ♠ trs t s♠

st♥ ♥ tr s ♥♦ ♣s r♥ t♥ t♠ ♦r t s

r♦tt♥ r♦♥ t ♥♦r♠ t♦r ♦ t r ♦ t t♦ ♠s ♦ ♥♦t tr

t s♠ st♥ ♥ s♠ ♣s st s ♦sr s t s♥ trs

t t s♣ ♦ t t ♦t♥ ♣s st r♠♥s r② s♠ r♦r

♠♦t♦♥ t♥q ♣s ♦♣rt♦♥ ♥π

2♣s st♥ ♦r ♦♥ s♥s ♦

♣r♦♣t♦♥ r s t♦ ♠①♠③ t s♥stt② ♦ t ♥str♠♥t rtr♠♦r

t ♦♣rts ♥ ♦s ♦♦♣ ♦♥rt♦♥ t♦ ♥sr ②♥♠ r♥

♦sr ♣s r♥ s ♥ ② t ♦♦♥ ①♣rss♦♥

δψ =8πA

λcn ·Ω

r c s t s♣ ♦ t s♥ rtrsts ♦ ②r♦s♦♣ ♦r

r♦tt♦♥ ss♠♦♦② r sr ♥ ❬❪ ♥ s♠♠r③ ♦

♣tr qst♦♥ s②st♠ t♦ t sr s r♥ ♥ ss♠ t qst♦♥

♥ ♠♦ r m ♦♥ ♥ m ♠tr s♥s♦r ♦♦♣

♦♣t ♣♦r s♦r

♣t ♦ss ♦ dB

❯♥r ts ♦♥t♦♥s t st♠t s♥stt② ♦ t s②st♠ s nrad.s−1

♦r t ♥t ③ ③ s♣t s♠r s③ s♠ ♦♠♠♥ts ♥

♠ s ♦r s ♦♥ ♣♦r ♦♥s♠♣t♦♥ ♥ ♦st ♦r t s ♦ ts t♥♦♦②

♥ ss♠ ①♣♦rt♦♥

tr♦♠ s♥s♦rs

tr♦♠ tr♥sr r♦♠ ♥t sr ♥ ❬❪ ♥ s

s s♥st ♠♥t ♦r r♦tt♦♥ s♥s♦rs r s tr♥sr r♣s

t ss♠ ♠ss ♦ ♠♥ ♣♥♠ ② q tr♦②t ♠♦t♦♥

♦ ts q ♥rts ♥ tr ♦t♣t s♥ s ♥t♦♥ ♦ t r♦♥

♠♦t♦♥ r r♦tt♦♥ ss♠♦♠tr t r② ♦♦ rs♦t♦♥ ♦ µrad.s−1

♦r t ♥t ♦ ③ ③ ♥ 110 dB ②♥♠ r♥ r

♦♠♠r② ♥ t♦♥ t s ♦♥ tt t s r② s♥st t♦

t♠♣rtr rt♦♥s

s♥s♦r ♠♥s♦♥s r ♠× ♠× ♠ ♦r t ♦ ♥

♣♦r ♦♥s♠♣t♦♥ ♦ ♠❲ ♣♣r♦①♠t② ♥ t♦♥ t ♦st ♦ ts s♥s♦r

s r② ♣r♦t ❯ s♣t ts rs♦t♦♥ t s ♥♦t st ♦r

ss♠ ①♣♦rt♦♥

r ♥t ♦tt♦♥ s♥s♦r

♥♦♦② r ♦ r♦tt♦♥ s♥s♥ s②st♠s s ♥ ss♠♦♦②

♥rt s♥s♦rs

♥rt s♥s♦rs r ② s ♥ ss♠ ①♣♦rt♦♥ t t ♥tr♦t♦♥ ♦

♦♣♦♥s ♥ ♠♦r t② r♦♠trs s ♣♦♥t rrs ❱r②

s♥stt② s t rs♦♥ ♦sts r♦r ♦♥ ♥ t♥ ♦ rs♥

ts ♥str♠♥ts t♦ ♠sr ♥r rt♦♥s tr s♥s♦rs r

s s rt♦r② ②r♦s♦♣s ♠t ♥ ♠♣♦rt♥t sss ♥ t ♥rt ♥

t♦♥ ♥str② ♦r ♥r r♦♠trs s ♦r rt♦♥ ♠♦♥t♦r♥

r♥st♦♥ ♦♣♦♥s

♦♥ r♦♦à ♥ à ♣r♦♣♦s r♦tt♦♥ s♥s♦r s②st♠

♦t♣♦♥ s s ♦♥ r♥t ♠♦t♦♥ ♠sr♠♥ts ♦ ♣r s♥s♦rs

♦♣♦♥s ❬❪ r♦tt♦♥ ♦♠♣♦♥♥t ♦ r♦♥ ♠♦t♦♥s s ♦t♥ ②

t♥ t s♣ rt ♦ t ③♦t② ♦t ① ♥ ②①s ♦r♥

t♦ t r t r ♦♠♣♦♥♥ts ①♣rss t t r sr r

Ωx =∂uz∂y

Ωy = −∂uz∂x

r ♦t♣♦♥ ♣r♥♣

♦ r tr r tr r♥t ♣r♦t♦t②♣s s♦♥ ♥ r ♦r ♦rt♦r②

♣r♦t♦t②♣s sr ♣r♦r♠♥ ♦♣♦♥s r s t♦rt rs♦t♦♥

♦ nrad.s−1 ♥ t rq♥② ♥ ③ ③ ♥ ♦r

t ♠tr ♦ t r s r t ♦♣♦♥s r ♠♦♥t s ♠ s

♥♦t ♦♠♣♥t t ♦r s♣t♦♥s

♣tr qst♦♥ s②st♠ t♦ t sr s r♥ ♥ ss♠ t qst♦♥

♦r③♦♥t ♦♣♦♥s ♥ ♣rs ♦r③♦♥t ♦♣♦♥s ♥ ♣rs

♦r③♦♥t ♦♣♦♥s ♥ ♣rs rt ♦♣♦♥

r ♦t♣♦♥ ♦♥rt♦♥s

s trs ♦ t ♦t♣♦♥ r s ♦ ② s♥st ♦♣♦♥s

♦♥♥t t♦ ♦♠♠♦♥ r♦rr t ♦♣♦♥s r ♠♦♥t ♥ ♠tr ♣rs

t♦ r r♠ ♦♣ t t r♦♥ t st♥ s♣rt♥ t ♦♣♦♥s

♥ ♥ ♣r s ♠ s♠r t♥ t ♥t ♦ t s♥ t♦ ♠sr

♥ r♦tt♦♥s r ♠sr tr♦ t rts ♦ t s♣♠♥t

t rs♣t t♦ s♣ ♦♦r♥ts s♦♠ sss ♥ ssss rst t

rsts r ①tr♠② s♥st t♦ rr♦rs s ② r♥s ♥ ♥str♠♥t r

s♣♦♥ss ♥ ♠♣ts tr r♦♠ ♥str♠♥t ♥♦s ♦r st ts ♦♥ t

st♠t♦♥ ♦ t ♦r③♦♥t ♦♠♣♦♥♥ts ♦ r♦tt♦♥s ♣♥s ♦♥ ss♠♣t♦♥s ♦♥

ssr ♣r♦♣rts

♥♦♦② r ♦ r♦tt♦♥ s♥s♥ s②st♠s s ♥ ss♠♦♦②

r strt♦♥ ♦ ♦r♦s ♦r r♦♠ ❬❪

❱rt♥ ②r♦s♦♣s

❱rt♥ ②r♦s♦♣s r s ♦♥ ♦r♦s t ♥♠♥t ♣r♥♣ s

s♠♣ ♣r♦♦ ♠ss s ①t ♦♥ ♥ ①s t rq♥② ω1 r ♠♦

♥ t s②st♠ ♥r♦s r♦tt♦♥ rt Ω s♠ s♣♠♥ts ♥ ♦sr

♥ ♣r♣♥r rt♦♥ ♥ rt♦♥ t♦ t r♥ ♠♦ t♦ ♦r♦s t

t rq♥② ω2 s♥s ♠♦ ♠♣t ♦ ♦r♦s ♦r s ♣r♦♣♦rt♦♥

t♦ t r♦tt♦♥ rt Ω tr♦ t ①♣rss♦♥

FCoriolis = −2m~Ω ∧ ~Vdrive

❲r m s t ♣r♦♦ ♠ss t ♥ ~Vdrive s t ♣r♦♦ ♠ss ♦t② ♦♥ t

r♥ ①s ♥ strt♦♥ ♦ ♦r♦s t s s♦♥ ♥ t r rt③

t♥♥ ♦r ②r♦s♦♣s ②str♦♥ ♦♥♥r ②r♦♣ ♠♦ ♣rs♥t ♥

r r tst t♦ ♠sr t r♦tt♦♥ ♦♠♣♦♥♥ts ♦ str♦♥ r♦♥

♠♦t♦♥s ❬❪ ❬❪ s♥s♦r rs♦t♦♥ s mrad.s−1 ③ ♥ ♦r

t ♦ r♠s ♥ ♣♦r ♦♥s♠♣t♦♥ ♦ ♠❲

r ②str♦♥ ♦♥♥r qrt③ rt s♥s♦r ♠♦

♣tr qst♦♥ s②st♠ t♦ t sr s r♥ ♥ ss♠ t qst♦♥

♥r r♦♠trs

♥r r♦♠trs r s t♦ ♠sr ♥r s♦s ♦r rt♦♥s

s s r s♥ t ③r♦ ♣♥♦st② ♥ ♦tr ♦rs t ♥tr ♦

rt② s ♦t t t ♥tr♦ ♦ t s♣♣♦rt♥ s♣r♥s ♥ t♦♥ t②

♦♠♣t② ♥♦r ♥r rt♦♥ ♥ ♠sr ♦♥② r♦tt♦♥ rt♦♥

♥r rt♦♥ t ss♦t ♥r ♦t② ♥ s♣♠♥t r

r② ♠♣♦rt♥t ♠sr♠♥ts t♦ ♠ ♥ t ♥②ss ♦ strtr

♦r ♥ ♥ ♦r t ♣r♦ss ♦ ♣♦♥t♥ ♠r ♣t♦r♠s ♥ sts ♥ sr

♠♦♥ts ♣ ♥ r♦tr♦♥s ♠♥trrs ♦ ♥r r♦♠

trs s ♣t s♥s♦rs ♥ st♦♠ ♣♣t♦♥ ♣ ♥trt r

ts s s ♦♥ t ♦♠♣♠♥tr② t ① ♠♦♥t♦r

t♥♦♦② ♥ ♥ ♥ ♥ r t ♥r r♦♠tr ♦♣ ②

r♦tr♦♥s rs♦t♦♥ ♦ rad.s−2 ♦r t rq♥②

♥ ③ ③ s ♦r ♣♦r ♦♥s♠♣t♦♥ ♦ ♠❲ ❬❪ r

tr♠♦r t ♠♥s♦♥s ♦ ts s♥s♦r r ♣♣r♦①♠t② ♠♠× ♠♠× ♠♠

♠ t ♥t ♦r ss♠ ①♣♦rt♦♥ ①♣t ♦r rs♦t♦♥

r r♦♣♦t♦r♣s ♦ t ♥r r♦♠tr r♦♠ r♦tr♦♥s t ♥tr ♦ t t t

s t♥♦♦② s sr ♥ts s♠♣t② s♠ s③ ♥ ♦ ♦st

♦r♦r t s r② s♠r t♦ ♥r r♦♠trs ♥ tr♠s ♦ rt♦♥ ♥

r♦t ♦r t ♠♥ s♦rt♦♠♥ s t ♦ rs♦t♦♥ ♦♠♣r t♦ ♦tr

s stt ♦♥ ts st♦♥ s♣t ts t♥♦♦② s ♥♦t ♥ ♦♣r

t t♦ ts ♠①♠♠ ♣♦t♥t ♦♠♣r t♦ r♦♠trs ♦r rt♥

②r♦s♦♣s

♥♦♦② r ♦ r♦tt♦♥ s♥s♥ s②st♠s s ♥ ss♠♦♦②

♠♠r② t

♣tr qst♦♥ s②st♠ t♦ t sr s r♥ ♥ ss♠ t qst♦♥

♥♦♦②t②♣

♦st

s♦t♦♥

③

P♦r

P♥♠s②st♠s

Ps②st♠

❬❪

♦rs♦♥

♥❬❪

>300❯

>300❯

10nra

d.s

−1③♥

3µra

d.s

−1③♥

♣t②r♦s♦♣s

❬❪

❬ ❪

>1000

❯

>1000

❯

0.3nra

d.s

−1③♥

nra

d.s

−1③♥

tr♦♠s♥s♦rs

♥t❬❪

≈5000

❯

µra

d.s

−1③♥

♥rts♥s♦rs

♦t♣♦♥

❬❪

❱rt♥

②r♦s♦♣s

❬❪

♥r

r♦♠trs❬❪

>200❯

≈100❯

≈10

❯

nra

d.s

−1

③♥

mra

d.s

−1③♥

ra

d.s

−2

③♥

♣t♦♥s♦rss♠①♣♦rt♦♥

<

❯

mra

d.s

−2

µra

d.s

−1

③♥

cm

3<

mW

♠♠r②♦

tt♥♦

♦②

r

♣tr s♠♠r② ♥ ♦♥s♦♥s

♣tr s♠♠r② ♥ ♦♥s♦♥s

♥ ss♠ ①♣♦rt♦♥ ♠♦st ♦ t s♥ qr ② ♣♦♥trr ♦♣♦♥s

s ♦♠♥t ② sr s ♦r r♦♥ r♦s s t② ♣r♦♣t ♥ t ♥r

sr r♦♥ r♦s ♦ ♥♦t ♦♥t♥ ♥② ♥♦r♠t♦♥ ♦♥ ♣r trts s

s♦rt s♣♥ t♥ rrs s rqr s♦ tt ts ♥♦s ♦♠♣♦♥♥t ♥

rt② rtr③ ♥ r♠♦ ② t tr♥ ♦r ♦♥sr♥

t ♦st ♦ ss♠ ①♣♦rt♦♥ ♥trs ♥ qst♦♥ t♥qs s♥ r

♣♦♥t rrs ♥ rr s♣♥ t♦ ♦♣ t♥q s

♥ ♣r♦♣♦s t t ♥s rt ♠sr♠♥ts ♦ r♦♥ r♦tt♦♥s t t

r sr t ♠♥♠♠ ♦sts

♦tt♦♥s ♥ ♠sr ② r♦ r♥ ♦ s♥s♦rs t ♥♦♥ ♦ t s♦

t♦♥s ♦♣ s♦ r s ② ♦♠♣♥t t ss♠ ①♣♦rt♦♥ rqr♠♥ts

♥ r♥t ♥str♠♥ts ♥ ♦♣ ♥ ♦rr t♦ ♠sr r♦♥ r♦

tt♦♥s ♥ rtq ss♠♦♦② rtss ss♠ t r ♠sr s♥

tr s♦♣stt ♥ ts ①♣♥s r♥ sr t♥♦♦② ♦r ♠rs♦♠ ss

♠ rr② t♥qs ♥♥ s♦♠ rstrt ss♠♣t♦♥s ♦t t

♥ ♥ ss♠ qst♦♥ r t ss♠ s♦r ♥ rrs r rt②

♦s ♦♠♣r t♦ str♦♥ ss♠♦♦② t ♥ s t♦ ♦♣ ♦♣r s♥s♦rs t

♥♦ s♥stt② t♦ ♠sr t r♦♥r♦ ♦r③♦♥t r♥t t ①♣♥s

② ♦♣②ssts ♦♦ t t ♥str② t♦ ①t♥ t♥♦♦② ♠ts ♠t

r♥ ss♠ ①♣♦rt♦♥

♥ t ♠r♥ ♦ s♦♥ ♠r♦rt♦♥ t♥qs s ♥ ♥

♠rt ♣♦ssts ♦st rt♦♥ ♥ ♥♥ ♣r♦r♠♥s ♥ s♦♠ ♣♣

t♦♥s ♥ s♣② ♥ s♥s♥ r♦tt♦♥ ♠♦t♦♥s ♥ ♦♥ ♥ s

②r♦s♦♣s r ♦♣ ♦r ♦♥s♠r ♣♣t♦♥ s♠rt♣♦♥s t s♦

♦r rs♦t♦♥ ♣♣t♦♥s s s ♥rt ♥t♦♥ ♦♥tss tsts

r ♣r♦r♠ t♦ t t s ♦ ②r♦s♦♣s ♥ ♥ ss♠ sr②s t

rs♦t♦♥s ♠♦♥strt ② ts s r ♦s t♦ t s♣t♦♥s ♥

♥ t ♦tr ♥ ♥r r♦♠trs ♦♣ ♦r rt♦♥ ♠♦♥

t♦r♥ r♣rs♥t ♥ ♥trst♥ s♦t♦♥ s♥ t② ♠sr rt② t ♥r

rt♦♥s ♥ t s♠ ② s ♥r r♦♠trs ♠sr rt② t

rt r♥ ss♠ sr②s

♣tr qst♦♥ s②st♠ t♦ t sr s r♥ ♥ ss♠ t qst♦♥

❲ ♥② st t♦ ♣♦t♥t s♦t♦♥s rt♥ ②r♦s♦♣s ♥

♥r r♦♠trs t ♥ t r♠ ♦ t P tss t ♦s s t♦

♣t ♦♥ ♦♥② ♦♥ s♦t♦♥ ♦ s ♠ t♦ ♣t③ ♦♥ ♣r♦

❬❪ s t♦ ♦♥tr♦ ♥r r♦♠tr s t ♥r

r♦♠tr s ♦♣t s ♥r r♦♠trs ♥ ♥r r♦♠trs

r s ♦♥ t s♠ ♦♣rt♥ ♣r♥♣s ♥q ♦♥tr♦ tr♦♥s ♥ s

t♦ ♥tr r♥t s t♦ ♠sr tr♥st♦♥ ♥ ♥r rt♦♥s

♥ s♥ s♥s♦r ♥♦ r♥ ss♠ sr②s ♦♥sq♥t② ♦♥ ♥ ♠♥ t

♥trt♦♥ ♦ t♦ r♦tt♦♥ s♥s♦rs t ♦♥ ♥r r♦♠tr ♦r♥ t

t s♠ ♦♥tr♦ tr♦♥s s strt ♥ r ❬❪

r ♥trt♦♥ ♦ ♦♥ rt r♦♠tr ❩ t t♦ r♦tt♦♥ s♥s♦rs❳ ♥ ❨ ♥ ♦♥ rr ♥♦

♥ ts ssrtt♦♥ ♣r♦r♠♥ ♦♣rt♥ t r♥t ♣

t♥ r♦♠trs s rs t♦ ♥tr t ♥ ♥r r♦♠tr ♦r♥

♦♥ t s♠ ♣r♥♣ ♦ ♦♣t♠③ t ♦r ♦ ts r♦tt♦♥ s♥s♦r ♦♥ s t♦

♥rst♥ t ② trs ♦ r♦tt♥ ♣r♦♦ ♠ss t r♥t ♣t

r♦t ♥ t ♦♥tr♦ t♥qs ss♦t s s t ♠ ♦ t

♥①t ♣tr

♣tr

❲♦r♥ ♣r♥♣s ♦

♣r♦r♠♥ ♣t

♠r♦♠♥ r♦tt♦♥ s♥s♦r

♥ qt♦♥s ♦ t r♦tt♦♥ s♥s♦r

♦t♦♥ qt♦♥

♥ ♥♦s

tr♦stt tt♦rs

tr♣t♦r ♦♥rt♦♥

♣♦s♥ ♣t♦r ♦♥rt♦♥

r♥t ♣t s♥s♥

r♦♥t♥ tt♦♥ s♥ r ♠♣r

♦♥ ♦ ♠♣r ♥♦s

t ♦r ♦♥tr♦ ♦♦♣

Σ∆ ♠♦t♦♥

♠♣♠♥tt♦♥ ♦ t t t t r♦tt♦♥

s♥s♦r

♣tr s♠♠r② ♥ ♦♥s♦♥s

♦s♦♦♣ s♥ ♦r♠ ♦ s♥♣t ♣t♦rs

♦s♦♦♣ s♥ ♦r♠ ♦ ♣r♣t ♣t♦rs

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

s ♣r♦s ♣tr st ♥r r♦♠trs s r♦tt♦♥ s♥s

♥ s②st♠s ♦r ss♠ ①♣♦rt♦♥ ♦ ♦♣ ♥ ♦♣t♠③ t st

♣r♦r♠♥s ♣r♦r♠♥ ♦♣ ♦r r♦♠trs s♥

r♥t ♣t♥ ♠sr♠♥t s s ♦r♦r t ♦r

♦♥tr♦ ♦♦♣ s ♠♣♠♥t t♦ ♠♣r♦ t s②st♠ ②♥♠ ♦r ♦♠

♥t♦♥ ♦ r♥t ♣t♥ tt♦♥ ♥ t ♦♥tr♦ ♦♦♣ s ②

s ♦r ♣r♦r♠♥ ♣♣t♦♥s ❬❪ ❬❪ ♦t ♦ ts ♣tr s

t♦ s♥ rs t♦ ♦t♥ ♠r♦strtr s♥st t♦ ♥r rt♦♥s

♥ t♦ ♦♣rt t t ♣r♦ tr♦♥s

r♦♦t ts ♣tr t ♦s s ♣t ♦♥ s♥s♦r rs♦t♦♥ ♦r ♥♦s ♦♦r

s♥s♦r ♥♦s ♦♦r s t t♦t ♦♥trt♦♥ ♦ ♥♦s s♦rs tt ♠t t ♦r

rs♦t♦♥ s ♠♥ ♥ tr♦♥ ♥♦ss t♦ r② st

♥ ♦rr t♦ t♦r t ♣♣r♦♣rt ♥♦s strt♦♥ ♥ t rq♥② r♥ ♥

♦r ss♠ ♣♣t♦♥s ♣tr s ♥ ♦r st♦♥s

rst t ♠♥ qt♦♥s ♦ t r♦tt♦♥ s♥s♦r r ♥ ♠♦t♦♥

qt♦♥ ♦ t strtr s sts t♦ ♥rst♥ ♦ t r♦tt♦♥s ♦

♣r♦♦ ♠ss r rt t♦ t ♥r rt♦♥s ♦ ts s♣♣♦rt♥ r♠

♥ s♦♥ st♣ t rt♦♥ ♦ t ♠♥ ♥♦s s ♥

♦♥ t tr♦stt ♦r ♦ t s②st♠ s st t rs♣t t♦

t♦ s♥s♥ ♣r♥♣s ♦♥ t tr ♣t♦rs ♥ t ♦tr t

♣♦s♥ ♣t♦rs tr♦stt ♠♦♠♥ts r t ♥ tr

♥♥ ♦♥ t ♠♥ qr♠ ♦ t s②st♠ s ♥②③

r t r♦♥t♥ tt♦r ♦ t ♣r♦ s st ♦♥r

s♦♥ ♦ t ♠♥ ♥♦r♠t♦♥ ♦ ♥trst ♥t♦ ♥ tr ♦t s

①♣♥ t rrs t♦ t t♦ s♥s♥ ♣r♥♣s sss ♦r ♥

r ♦♥ tt♦♥ ♥♦s s ♣rs♥t ♦♦ ② ♥♦s ♠♦♥ ♦ t

r♦♥t♥ tt♦r

♦rt t t ♦r rttr ♦ t s sr

r r ♦♥ Σ∆♠♦t♦♥ s ♣r♦ ♦♦ ② ts ♠♣♠♥tt♦♥

t♦ ♦♥tr♦ t r♦tt♦♥ s♥s♦r ♥♦s ♠♦♥ st♣ ♦ t

♥rt♦r s s♦ ♥

s ♣tr s ♦♥ ② t♦ s♠♠r② ts tr♥ t s♥ rs

♦♣ ♥ ts ♣tr

♥ qt♦♥s ♦ t r♦tt♦♥ s♥s♦r

♥ qt♦♥s ♦ t r♦tt♦♥ s♥s♦r

s st♦♥ s t t ♠♥ qt♦♥s ♦ t r♦tt♦♥ s♥s♦r s

t t♦ ♥r rt♦♥s ♦ ts rr♥ r♠ ♠♥ s♥stt② ♦r

♥ s ♥ s s t ♠♥ ♥♦s r ss♠♣t♦♥s r ♦♥sr

♥② s♠ r♦tt♦♥s r♦♥ t rt ①s ♦ t s♥s♦rs r♠ ③①s

r ♦♥sr

♥rt ♦ ♥♥ s♣r♥s s s♣♣♦s ♥

♦t♦♥ qt♦♥

r ❲♦r♥ ♣r♥♣ ♦ t ♥r r♦♠tr

♦r♥ ♣r♥♣ ♦ ♥ ♥r r♦♠tr s s♦♥ ♥ t r

t♦ ♥ ♥r rt♦♥ ♦ t s♥s♦r r♠ φ s t ♥♦r♠t♦♥

t♦ ♠sr ♥ ♥rt ♠♦♠♥t ts ♦♥ t ♣r♦♦ ♠ss r♦tts ② ♥ ♥

r s♣♠♥t ψ ♣♣♦rt♥ ♠s t♥ s♣r♥s ♦ ♦♥st♥t Km r

♦r♠ ② ts ♥rt t s♦ t s ss♠ ♠♣♥ ♠♥s♠ t♥

♦♥ t s②st♠ t ♠♣♥ ♦♥t D ♣r♦♣♦rt♦♥ t♦ t rt ♦t②

ψ − φ qr♠ qt♦♥ s ♥ ②

Jzd2ψ

dt2+D

(dψ

dt− dφ

dt

)+Km (ψ − φ) = 0

r Jz t ♠♦♠♥t ♦ ♥rt ♦ t r♥ ② ♥tr♦♥ θ = ψ−φ t qt♦♥ ♦♠s

Jzd2θ

dt2+D

dθ

dt+Kmθ = −Jz

d2φ

dt2

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

t ♥ ♥♦t r♦♠ qt♦♥ tt t ①tr♥ ♥r rt♦♥ ts

♥ ♥rt ♠♦♠♥t ♦♥ t ♣r♦♦ ♠ss s ♦♥sq♥ ♠sr♥ t

q♥tt② θ ♥ s t♦ r♦r t ♥♦r♠t♦♥ ♦ ♥trstd2φ

dt2

qt♦♥ ♥ rrtt♥ ♥ ♥♦♥ ♦r♠ ② ♥tr♦♥ t ♥tr

rq♥② ω0 =√Km/Jz ♥ t qt② t♦r Q = Jzω0/D

ss♠♥ r♠♦♥ ①tt♦♥ ♦ t r♠d2φ

dt2= −Φejωt t ♣r♦♦ ♠ss

rs♣♦♥s s r♠♦♥ ♥ ♥ s♦ s ♦♦s

Θ

Φ=

1

ω02

− ω2

ω02+ j

ω

ω0

1

Q+ 1

r Θ ♥ Φ r t ♠♣ts ♦ t ♣r♦♦ ♠ss r♦tt♦♥ ♥ t ♠♣t ♦

t r♠ ♥r rt♦♥ rs♣t② ♠♥ ♥ ♥ ♦t♥

② t♥ t ♠♥t ♦ qt♦♥

Gmech =1√

(ω02 − ω2)2 +

(ωω0

Q

)2

❲♥ ♦♣rt t rq♥s r ♦ r♦♠ t ♥tr rq♥② ♥

ω ≪ ω0 t qt♦♥ ♦♠s

Gmech =JzKm

=1

ω02

② ♦sr♥ t qt♦♥ t s ♦♦s tt t ♥tr rq♥② ♠st

s ♦ s ♣♦ss t♦ ♦t♥ ♠♥ s♥stt② ♥ ♦tr ♦rs s♦t

s♣r♥ ♥ rt ♥rt r ♠♣♦rt♥t t♦ ♠①♠③ t ♦♥rs♦♥ ♦ r♠ ♥r

rt♦♥s ♥t♦ ♣r♦♦ ♠ss ♥r s♣♠♥ts s t ♥ ♦sr

♥ t r

s♦ ♥ t r ♦♥ ♥ ♥♦t t t ♦ t t♦r ♦♥ t r

q♥② rs♣♦♥s ♦ t ♥r r♦♠tr t♦r s rt t♦ ♠♣♥

ts ♣♣ ♦♥ t ♣r♦♦ ♠ss rr t ♦ t sr♣r t rs

♦♥♥ ♣ ♦♣rt ♥ ♦♣♥♦♦♣ ♠♦ t t♦r ♠st t t rt

♠♣♥ t♦ ♠①♠③ t ♥t ♥ t s♥stt② ♦ t s②st♠ ❬❪

♦r ♠♣♥ ts r rt t♦ ♠♥ ♥♦s sss

tr ♥ s ♦ t♦r r ♥ t♦ ♦t♥ ♦r ♥♦s s s ②

♥ qt♦♥s ♦ t r♦tt♦♥ s♥s♦r

rs♦t♦♥ s♥s♦rs r ♦♣rt ♥ ♦s♦♦♣ ♠♦ ♦s t♦ ♦r ♥

♥r♠♣ ♦♥t♦♥s t r② s ♦ t♦r

r ♥♥ ♦ Q t ♥ ω0 rt ♦♥ t rq♥② rs♣♦♥s ♦ t♥r r♦♠tr

♥ ♥♦s

♥ t ♥tr♦t♦♥ ♦ ♠r♦♠♥♥ ♣r♦ss s♥ ♦♥ ♠♥s♦♥s

r♦t ♥ s♥s♥ ♣♦ssts t t ①♣♥s ♦ ♥ ♠♣♦rt♥t s♥stt② t♦

♠♥ ♥♦s rst♥ r♦♠ ♠♦r ♠♦t♦♥ ♥♠♥t② s②st♠s tt

ss♣t ♥r② r t t s♠ t♠ s♦r ♦ ♥♦s ♥ rs ♦r ♥st♥

t ♥r② ♦ss ♦ ♥ ♦st♦r s ② ♠♣♥ ♠♥s♠s s ♦♥rt ♥t♦

tr♠ tt♦♥ ♦ t ♦ts ♥r♦♥♠♥t ts ♣t ♦rs ♦t ②

♠♥s tt tr♠ tt♦♥ ss ♠♦t♦♥ ♦ t ♦st♦r s s t ♥

♠♥t ♣r♥♣ ♦ t q♣rtt♦♥ t♦r♠ stts tt ♥r② s sr

q② ♠♦♥ ♥rt② ss rs ♦ r♦♠ ♦ s②st♠ s

♦♣ ♥ ❬❪

t s ♦♥sr t r♠♦♥ ♦st♦r s ♥rt Jz ♠♣♥ ♦

♥t D ♥ st♥ss ♦♥t Km ❬r ❪ q♣rtt♦♥ t♦r♠ ♣♣s t♦

♣♦t♥t ♥r② ♥ ♥t ♥r② s♥ t s②st♠ s ② sr ② t♦ r

s r♦tt♦♥ rt Ω ♥ ♥r ♣♦st♦♥ θ r♦ t ♠♣♥ ♠♥s♠

♦r ♥♦s Mn s ♣r♦ ♦r ♥ ①♣rss♦♥ s ♦♣ ♦♥ t ♦♦♥

♦♣♠♥t

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

r ♠♦ t♦ r t ♠♥ ♥♦s

♠♦t♦♥ qt♦♥ ♦ t s②st♠ s

Jzd2θndt2

+Ddθndt

+Kmθn =Mn

r t ssr♣t n srs ♥♦s ♥t♦♥s ♦r r♥♦♠ ♣r♦sss qt♦♥

s rrtt♥ ♥ tr♠s ♦ r♦tt♦♥ rt Ωn =dθndt

♥ t rq♥② ♦♠♥

jωJzΩn +DΩn +Km

jωΩn = Mn

r Ωn ♥ Mn r t ♦rr tr♥s♦r♠s ♦ Ωn ♥ Mn rs♣t② s

♥♦tt♦♥ ♥ ts ♣♣t♦♥s r t ♥ ♣♣♥① ♠♥ sqr r♦tt♦♥

rt t♦ tr♠ ♥♦s s

Ω2n =

M2n

D2 + (ωJz −Km/ω)2

♥ ♥ rrt t qt♦♥ ♥ tr♠s ♦ ♥r rq♥② ω0 ♥ qt②

t♦r Q s ♦♦s

Ω2n =

1

D2

M2n

1 +Q2(ω/ω0 − ω0/ω)2

♥t ♥r② st♦r ♥ rq♥② ♥tr s dK =1

2JzΩ2

ndω s t

♥t ♥r② s ♥ ② ss♠♥ x = ω/ω0

〈K〉 = 1

2Jz

∞∫

0

Ω2ndω =

1

4πD

∞∫

0

M2nQ

1 +Q2(x− 1/x)2dx

♥ qt♦♥s ♦ t r♦tt♦♥ s♥s♦r

♥ ♦rr t♦ t t ♥tr ♥ qt♦♥ ♦♥ ♥ ss♠ tt t qt②

t♦r s ♥♦ s♦ tt t s②st♠ ♥r② s ♦♥♥ ♥r t rs♦♥♥

❬❪ s ♦♥sq♥ t♥ s♠ rq♥② r♥ t ♥♦s s♣tr ♥st②

s ♣♣r♦①♠t② ♦♥st♥t ♥ t ♥tr ♥ s♦ s ♦♦s

〈K〉 = M2n

8D

qt♥ t ♥t ♥r② ①♣rss♦♥ t t tr♠ ♥r② 〈K〉 = 1/2kBT

♦♥ ♥ ♥

M2n = 4kBTD

♦r♥ t♦ qt♦♥ ♦♥ s♦ ♥♦t tt ♠♥ ♥♦s ♦r r♦♥♥

♥♦s s s♠r t♦ ♦♥s♦♥②qst ♥♦s ♥ rsst♦rs ❬❪

♥ t ♠♦♠♥t s♣tr ♥st② ♥♦♥ ♦♥ ♥ r t ♣♦r s♣tr

♥st② ♦ t ♥r ♣♦st♦♥ ♥♦s θn

θ2n =M2

n

D2(Q2 (ω2 − ω0

2) (ω2 + ω02) + (ωω0)

2)

♦♥sr♥ ω ≪ ω0 ♥ ♦r♥ t♦ qt♦♥ t ♥r rt♦♥

♥♦s ♥st② s ♥ ②

Φmn =

√4kBTD

Jz=

√4kBTω0

QJz

[rad

s2√Hz

]

Pr♠♥r② ♦♠♠♥ts ♦♥ t ♠♥ qt♦♥s r tt ♠①♠③♥ t

s♦♥ ♠♦♠♥t ♦ ♥rt ♦ t s②st♠ Jz ♦♥ t rs♥ t ♥tr r

q♥② ω0 ♥rss t ♠♥ s♥stt② ♥ rs t tr♠♦♠♥

♥♦s ♦r ts ♥ ♦t♥ ♦♥② ♦r r ♣ s③s ♦r ② ♣r♦♦ ♠ss

♥ ♠ t ♣r♦ss r② ♥♥

♥ t ♦tr ♥ t ♠♥ ♥♦s s ♥r② ♣♥♥t ♦♥ t ♠♣♥

♦♥t D ♦r ♠♦♥ strtrs t s♠ s③s t r ♠♣♥ s ♣r♦♠

♥♥t ♣♦♥ ♦tr ♦② ♦rs ♥ ts t ♦♠s rr s ♠r♦♠♥

strtrs rs ♥ s③ ❬❪ r♦r st♠t♥ t ♠♣♥ ♦ t s②s

t♠ s ♦♥ ♦ t ♠♦st ♠♣♦rt♥t st♣s ♥ t s♥ ♣r♦ss ♦ ♠r♦♠♥

s r ♠♣♥ ♠♥s♠s r♥t ♥trs ♣♥♥ ♦♥ t

♦♠tr② ♦ ♠♦♥ ♣rts ♥ ♠st r② r ♥ s♥♥ r♦tt♦♥

s♥s♦r ♣r♦t♦t②♣s s st ♥ st♦♥

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

tr♦stt tt♦rs

♥tr③t♦♥ ♦ ♠♥ strtrs ♦s t s ♦ tr♦stt ♦rs

t♦ r ♦r ♦♥tr♦ ♠♦♥ ♣rts ♣♥♥ ♦♥ t ♦♥rt♦♥ ♦ tr♦s

r♥t ts ♠② ♦r tt ♥ trr ♥♦♥ ♥rt② ♦r ♥stt② ♣r♦♠s

♦r ♥ ♣♣r♦♣rt s♥ ♦s t♦ s♣ ts ts ♥ t♦ t ♥ts

r♦♠ t♠ ♥ ♦rr t♦ rss rs♦t♦♥ ♣♣t♦♥s s t♦ ♣t♥

s♥s♥ ♣r♥♣s r st t③♥ ♥ ♥ r ♦r ♣ rs♣t② t♦ t

♦rrs♣♦♥♥ ♥ ♥ ♣t♥

rss ♦ s♥ sss ♥♠♥t ♣r♥♣ ♦ tr♦stt tt♦rs

s t ♥rt♦♥ ♦ ♦♥② ttrt ♦rs ❬❪ ♥ ♦s ♦r r♥

t ♣t♦r s rqr t♦ rt ♦rs ♥ t♦ rt♦♥s ♥ t ♦♦♥

♦♣♠♥t t♦ ♦♥rt♦♥s s♥ r♥t ♣t♦r ♣r♥♣ r ♣rs♥t

tr ♣t♦r ♥ ♣♦s♥ ♣t♦r ♦r s♠♣t② t r♥♥ s ❬❪

♥♦t ♦♥sr ♦r t rt♦♥ ♦ s♥ ♦r♠

tr♣t♦r ♦♥rt♦♥

tr ♣t♦r s ♦♠♣♦s ♦ t♦ ♣t tr♦s ♠♦♥ tr② t

rs♣t t♦ ♦tr s t♦♣♦♦② s st s tr ♣t♦rs

♠♦♥strt ♥r ♦r ♥ rs♦t♦♥ s s♦♥ ♥ ❬❪ ♥ ts st♦♥

t strtr ♣rs♥t ♥ s sss t t t♦♥ ♦ t ♥♦♠♥

♣t♥ ♥ t tr♦stt ♠♦♠♥ts t t ♥ t ♥♥ ♦♥ t s②st♠

qr♠ s ♥②③

r ♠t ♦ s♥ ♣t♦r

tr♦stt tt♦rs

♣t♥ t♦♥ ♥ ♦♥rt♦♥ s♥stt②

t s ♦♥sr ♣r♦♦ ♠ss ss♣♥ ② ♦r s♣r♥s ♥ ♥ t♦ s ♦♥

♦t ss ♣② t r♦ ♦ ♠♦♥ tr♦s ♥ rs♣t② t t

♦ t t st♥ R r♦♠ t r♦tt♦♥ ♥tr stt♦r tr♦ s

♣ t tr ♣ st♥ d ♥ t ♥♦♠♥ ♦r♣ W0 stt♦r s

♦♥♥t t♦ s♣♣② ♦t Va ♥ Vb rs♣t② ♦t♦♣♥ t♥ss

♦ ts s②st♠ s T s♠t ♦ ts ♦s ♣t♦r s s♦♥ ♥ t

r

ss♠♥ t ♣r♣t ♣t♦r ♣♣r♦①♠t♦♥ ❬❪ t ♣t♥s ♥

♥r s♠ ♦s ♥r s♣♠♥t θ ♦ t ♣r♦♦ ♠ss r ♥ ②

Ca = ε0T (W0 +Rθ)

d

Cb = ε0T (W0 −Rθ)

d

❲r ε0 s t ♣r♠ttt② ♦ r ♣t♥ r♥ s t♥

∆C = Ca − Cb = ε02TR

dθ

♥tr♦♥ t ♥♦♠♥ ♣t♥ C0 = ε0TW0/d t ♣t♥ r

♥ ♥ rrtt♥ s

∆C = C02R

W0

θ

s♣♠♥tt♦♣t♥ s♥stt② s ♥② ♦t♥ t

Kθ−C =∂∆C

∂θ= C0

2R

W0

♥ ts ♦♥rt♦♥ t ♣t♥ r♥ s ♥r ♥t♦♥ ♦ t ♣r♦♦

♠ss ♥r ♣♦st♦♥ θ ♥ t♦♥ t s♣♠♥tt♦♣t♥ s♥stt② s

♣r ♦♥st♥t ♣♥♥ ♥r② ♦♥ t ♥♦♠♥ ♣t♥ C0 ♥ t ♠♦♥

tr♦ st♥ r♦♠ t r♦tt♦♥ ♥tr R ♥ t s ♥rs② ♣r♦♣♦rt♦♥ t♦

t ♦r♣ W0 s t♦ ♠①♠③ t s♥stt② ♦♥ s t♦ ♣t tr♦s s r

s ♣♦ss r♦♠ t r♦tt♦♥ ♥tr t ♥ ♠♣♦rt♥t ♥♦♠♥ ♣t♥

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

tr♦stt ♠♦♠♥t t♦♥

tr♦stt ♠♦♠♥ts ♣♣ ♦♥ t ♣r♦♦ ♠ss ♥ r r♦♠ t

tr♦stt ♥r② ♦r♥ t♦ ❬❪

Ma =1

2

∂Ca

∂θVa

2

Mb =1

2

∂Cb

∂θVb

2

ssttt♥ t ♣t♥ ①♣rss♦♥s r♦♠ qt♦♥ ♦♥ ♥ ♥

Ma =1

2

C0R

W0

Va2

Mb = −1

2

C0R

W0

Vb2

rst♥ tr♦stt ♠♦♠♥t s t♥ ♥ ② t ♦♦♥ ①♣rss♦♥

Mel =Ma +Mb =1

2

C0R

W0

(Va

2 − Vb2)

s tr♦stt ♠♦♠♥t ♥ s ♦r ♦r ♦♥tr♦ ♦ t ♣r♦♦

♠ss ♦r ♦♥ ♥ ♥♦t r♦♠ qt♦♥ tt t tr♦stt ♠♦♠♥t

s ♥♦♥ ♥r ♥t♦♥ ♦ ♣♣ ♦ts Va ♥ Vb strt② t♦ ♥r③ t

♠♦♠♥t ss rt rr♥t s VDC ♣♣ t♦ t t♦ stt ♦♠s

♥ s♦ tt t ♥t ♦r ♦♥ t ♣r♦♦ ♠ss s ③r♦ ♥ ♥ tr♥t♥

rr♥t ♦t Vfb s t♦ t s ♦♥ ♦♥ tr♦ ♥

strt r♦♠ t ♦tr tr♦ ❬❪ ❬❪ rtr ts ♦♥ ts

♦t Vfb sss ♥ st♦♥ ♦r♥② t ♦ts Va ♥

Vb ♥ ♦♠♣♦s s ♦♦s

Va = VDC + Vfb

Vb = VDC − Vfb

♥ ♦♥sq♥t②

Mel =2C0R

W0

VDCVfb = Kθ−CVDCVfb

tr♦stt tt♦rs

t ♥ s♥ r♦♠ qt♦♥ tt t ♠♦♠♥t s ♣r♦♣♦rt♦♥ t♦

t ♦t Vfb t s rtr s♥ r♦♠ qt♦♥ tt t ♠①♠♠

♦ t ♦t Vfb s t s ♦t VDC s s s t ♦t Vb♦♠s ③r♦ t ts ♦t s tr♠♥s t ♦♣rt♥ r♥ ♦ t ♥r

r♦♠tr ♥ ♦tr ♦rs t ♠①♠♠ ♦r tt t r♥t ♣t♦r

♥ r♥ s ♥ ②

Melmax= Kθ−CVDC

2

♥♥ ♦ t tr ♣t♦r ♦♥rt♦♥ ♦♥ t ♣r♦♦

♠ss ♠♥ ♦r

♥ ♥ ♥♦t ♦r♥ t♦ qt♦♥ t ♥rt② ♦ t ♣t♥

r♥ t rs♣t t♦ ♥r ♣♦st♦♥ θ t s ♥ s tt t tr

s♥stt② ♥ ♠①♠③ ② ♥rs♥ t ♥♦♠♥ ♣t♥ ♦♥

t ♣tt♥ t ♣t♦r r r♦♠ t ♥tr♦ s♠♣ ② t♦ ♥rs t

♥♦♠♥ ♣t♥ s t♦ s ♦♠ tr♦s tt ♦ t t♦♥ ♦

sr s♠ s♥♣t ♣t♦rs

rt♥ t qr♠ qt♦♥ ♦ t ♥r r♦♠tr r♦♠ qt♦♥

② ♥ t tr♦stt ♠♦♠♥t r♦♠ qt♦♥ ♦♥ ♥ ♥

Jz θ +Dθ +Kmθ︸ ︷︷ ︸♣r♦♦ ♠ss ♠♥ ♦r

= −Jzφ︸ ︷︷ ︸①tr♥ rt♦♥

+ Kθ−CVDCVfb︸ ︷︷ ︸tr♦stt ♠♦♠♥t

s st♦♥ ♣r♦ ♥ tr♦stt st② ♦ ♥ strtr s♥ tr

♣t♦rs t s s♦♥ tt t ♣t♥ r♥ ∆C s ♥r ♥t♦♥

♦ t ♥r ♣♦st♦♥ θ ❲t t ♣rtr ♦t s♣♣② ♥ ♥ qt♦♥

♥ tr♦stt ♠♦♠♥t s ♥tr♦ ♥ t s②st♠ qr♠ tt

♦s ♥♦t ♣♥ ♦♥ θ s qt♦♥ s tr♦stt ♠♦♠♥t

s t♦ ♠♣♠♥t ♦r ♦♥tr♦ tr♦ t ♦t Vfb

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

♣♦s♥ ♣t♦r ♦♥rt♦♥

s♥s♦r s♥ ♣♦s♥ ♣t♦rs t③s ♥ ♦ ♣ t♦ t ♦r

rs♣♦♥♥ ♥ ♥ ♣t♥ ♦♥trr② t♦ tr ♣t♦rs st ♥ t

st st♦♥ ♣ ♥s ♥ rt rt② r s♣♠♥tt♦ ♣t♥

s♥stt② t t ♦st ♦ ♥♦♥♥r rs♣♦♥s tr♦stt ♣r♦♣rts ♦ t

strtr s♦♥ ♥ r r sss t ♣rtr ♦s ♦♥ t ♥♥

♦ t tr♦stt ♠♦♠♥ts ♦♥ t s②st♠ qr♠

r ♠t ♦ ♥♦r♠ ♣t♦r

♣t♥ t♦♥ ♥ ♦♥rt♦♥ s♥stt②

t s ♦♥sr t s♠ s②st♠ s t ♣r♦s st♦♥ ①♣t tt t t

♦ stt♦r tr♦ s ♣ t ♥♦r♠ ♣ st♥ h r

t ♠♦ tr♦ t s Wf stt♦r s ♦♥♥t t♦ s♣♣②

♦t Va ♥ Vb rs♣t② ♦t♦♣♥ t♥ss s T s♠t ♦

ts ♦s ♣t♦r s s♦♥ ♥ t r

♣t♥s ♥ ♥r s♠ ♦s ♥r s♣♠♥t θ ♦ t

♣r♦♦ ♠ss r ♥ ②

Ca = ε0WfT

(h−Rθ)

Cb = ε0WfT

(h+Rθ)

tr♦stt tt♦rs

♥tr♦♥ t ♥♦♠♥ ♣t♥ C0 = ε0TWf/h t ♣t♥ r

♥ ♥ ♥ ②

∆C = C02Rθ/h

1− (Rθ/h)2

♥ ♥ ♥♦t tt ♥ ♣♦s♥ ♦♥rt♦♥ t ♣t♥ r♥ s

♥♦♥♥r ♥t♦♥ ♦ t ♥r s♣♠♥t θ ♥ ts t s♣♠♥tt♦

♣t♥ s♥stt② s ♥♦♥♥r t♦♦ ♦r ss♠♥ s♠ s ♦ θ s♦

tt Rθ/h≪ 1 ♦♥ ♥ ♥tr♦ t ♦♦♥ ♦♥st♥t

Kθ−C ≈ C02R

h

r♦♠ qt♦♥ s♠♣ ② t♦ ♠①♠③ t ♣t♥ ♥ ts ♦♥r

t♦♥ s t♦ ♠♥♠③ t ♥♦r♠ ♣ ♠♥s♦♥ h ♥ t♦ ♠①♠③ t st♥ r♦♠

t ♥tr♦ R ♥ s♦ ♥♦t tt t ♥r③ s♣♠♥tt♦♣t♥

①♣rss♦♥ s s♠r t♦ t ♦♥ ♦t♥ ♦r s♥♣ts ♥ qt♦♥ ②

r♣♥ W0 ② h

tr♦stt ♠♦♠♥t t♦♥

♥ t tr♦stt ♠♦♠♥ts ♣♣ ♦♥ t ♣r♦♦ ♠ss ♥ r r♦♠

t tr♦stt ♥r② ♦r♦r ♥ ♦rr t♦ ♥r③ t rst♥ tr♦stt

♠♦♠♥t ①♣rss♦♥ t rs♣t t♦ ♦♥tr♦ ♦t ♦♥ ♥ ss♠ tt t

♦ts Va ♥ Vb ♥ ♦♠♣♦s ♥ t♦ tr♠s s VDC ♥

♦t Vfb s ♥ ♥ qt♦♥ rst♥ ♠♦♠♥t s t♥ ♥ ②

t ①♣rss♦♥

Mel =Ma +Mb =

2C0R

h

(VDC + Vfb

R

hθ

)(VDC

R

hθ + Vfb

)

(−1 +

R

hθ

)2(1 +

R

hθ

)2

ss♠♥ s♠ s ♦ θ s♦ tt Rθ/h ≪ 1 ♦♥ ♥ rt t s♦♥ ♦rr

♣♣r♦①♠t♦♥ ♦ t ♠♦♠♥t ①♣rss♦♥

Mel ≈ Kθ−C VDCVfb︸ ︷︷ ︸Mel0

+2C0

(R

h

)2 (VDC

2 + Vfb2)

︸ ︷︷ ︸Kel

θ

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

♥ t qt♦♥ ♦♥ ♥ ♥♦t tt t rst♥ ♠♦♠♥t tt ♥

♣♣ s ♦♥st♥t ♦♠♣♦♥♥t Mel0 ♥ s♣r♥ ♦♠♣♦♥♥t Mel1 = Kelθ

r②♥ t t ♥r ♣♦st♦♥ θ ss♠♥ t ♠①♠♠ ♦t

Vfb = VDC t ♠①♠♠ rst♦r♥ ♦r ♥ t ♠①♠♠ tr♦stt s♣r♥

♦♥t r ♥ rs♣t② ②

Melmax= Kθ−CVDC

2

Kel = 4C0

(R

h

)2

VDC2

♦♠♠♥ts t♦ ♠ ♦♥ t tr♦stt ♠♦♠♥ts t ♥ q

t♦♥ ♥ ♥ ♥♦t t ♣rs♥ ♦ ♦♠♣♦♥♥t Mel0 s s♠r t♦

t ♦♥ t ♦r t tr ♦♥rt♦♥ qt♦♥ ♦r t ♥♦♥

♥rt② ♦ t ♣♦s♥ ♦♥rt♦♥ ♥tr♦s ♥ tr♦stt s♣r♥ tr♠

♥rss s t ♥♦r♠ ♣ h rss ♥ s③

♥♥ ♦ t ♣♦s♥ ♣t♦r ♦♥rt♦♥ ♦♥ t ♣r♦♦

♠ss ♠♥ ♦r

s s r♥s ♠♦r ♦♠♣①t② t♦ t ♥♦♥♥r ♣♥♥ ♦ t

♣t♥ r♥ t t ♥r ♣♦st♦♥ θ ♥ ♦r rst ♦rr

♣♣r♦①♠t♦♥ s s♣♠♥tt♦♣t♥ ♦♥t r② s♠r t♦ t

♦♥ ♦t♥ ♥ t s♥♣ts ♦♥rt♦♥ ♥ t ♦♠♣rs♦♥ t♥

qt♦♥ ♥ s♦s tt t ♦r♣ ♣r♠tr W0 ♥ t ♥♦r♠

♣ h t s♠ ♥♥ ♦r tr rs♣t ♦♥rt♦♥ ♦r♦r t

♣ st♥ s s② ♠ s♠r t♥ t ♦r♣ t♥ ♠♦ tr♦s

♥ ① tr♦s ♦r q♥t ♣t♥ t♥ t t♦ ♦♥rt♦♥s

t ♥ rtt♥Kθ−Clateral

Kθ−Cnormal

=h

W0

< 1

r♦♠ t qt♦♥ t ♥r③ ♣♦s♥ ♦♥rt♦♥ s ♠ ♠♦r

s♥st t♦ t tt♦♥ ♦ r♦tt♦♥ ♦ r♦tt♥ ♣r♦♦ ♠ss

rtss st s♥stt② ♥ ♦♥② ♦t♥ ② s♥ ♦♥ ♣t

tr♦ ♥ ♠♣♦rt♥t st♥ r♦♠ t ♥tr♦ R ♥ ts s t rst ♦rr

♣♣r♦①♠t♦♥ s ♥♦ ♠♦r ♥ ♦♥ s t♦ ♦♦ r② t t ♥♦♥♥rt②

♥tr♦ r

tr♦stt tt♦rs

♦ ts ♥ t s ♦♥sr tt t ♣r♦♦ ♠ss s tt ② s♥ ♦t

V t tr♦ V b = 0 ♥ ♣♦st♦♥ ♦ t ♣r♦♦ ♠ss s ♥

②

Mnet =1

2C0V

2

R

h(1− R

hθ

)2 −Kmθ = 0

♦ t s ss♠ s♠ ♣rtrt♦♥s ♦ t ♣ θ + δθ ♥ ♥ rt

δMnet =∂Mnet

∂θδθ

∂Mnet

∂θ> 0 s♠ ♥rs δθ rts ♠♦♠♥t t♥s t♦ ♣ t ♠♦♥

♣t t♦ ♦♥tt t t ① ♣t ♦r st qr♠ t s ♥ssr② t♦

♣∂Mnet

∂θ< 0 qr♠ ♦♥t♦♥ s t♥ ♥ ②

Km > C0V2

(R

h

)2

(1− R

hθ

)3

sttt♥ qt♦♥ ♥ t stt② r♦♥ s ♥ s ♦♦s

θ <h

3R

♥ t qr♠ ♥r ♣♦st♦♥ rss t ♥rs♥ ♦ts tr

s s♣ ♦t r♦♠ t stt② ♥s t s t s♦ ♣♥

t ♦rr♥ t t ♦t Vpi ❬❪ ♣♥ ♦♥t♦♥ stss t ♦♥t♦♥

Mnet = 0 rqrs tt

θpi =h

3R

♥ t ♣♥ ♦t s ♥ ②

Vpi =h

R

√8

27

Km

C0

♥ s♦ ♥♦t tt ♠①♠③♥ t st♥ r♦♠ t ♥tr♦ R r♥s ♠♦r

s♥stt② t t rs s♦ t stt② r♥ t s♠r ♣♥ ♥ θpi♦r♥ t♦ qt♦♥

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

♦ r ♥ ts ♥♦♥♥rt② ♦♣♠♥t ♦ t ♣♦s♥ ♣t♦r ♦♥

rt♦♥ ♦♥② ♦♥sr t stt qr♠ ♦ t r♦tt♦♥ s♥s♦r t

♦♥② ♦♥ tr♦ ♣♦r③ ♥ t ♦♦s t ♦r ♦ t s②st♠ ♥r

t ♥♥ ♦ t t♦ tr♦s ♥ s st ♦ts ♣♣ t t

tr♦s ♥ r ♥t♦♥s ♦ t ♦♠♣♦♥♥ts VDC ♥ Vfb s♦ tt ♥

t ♠♦♠♥t ①♣rss♦♥ ♦ qt♦♥ ♥ t s♥s♦r ②♥♠ qt♦♥

Jz θ +Dθ +Kmθ = −Jzφ+

2C0R

h

(VDC + Vfb

R

hθ

)(VDC

R

hθ + Vfb

)

(−1 +

R

hθ

)2(1 +

R

hθ

)2

♥ ♦rr t♦ s♠♣② t ♣r♦s qt♦♥ ♥ t♦ ♥rst♥ t ♦r ♦

♦tt ♣t♦r t s ♥tr♦ t s♦♥ ♦rr ♣♣r♦①♠t♦♥ ♦ t

♠♦♠♥t ♥t♦♥ r♦♠ qt♦♥ t s

Jz θ +Dθ + (Km −Kel) θ =Mel0

♥ ♥ ♥♦t ♥ qt♦♥ tt t tr s♣r♥ ♦♥trts t ♠

♥ ♦♥ s rtrst s ♠♣♦rt♥t s♥ t rs♦♥♥ rq♥② ♦

t r♦tt♦♥ s♥s♦r s rs ♥ t tr♦s r ♣♦r③ rtr♠♦r

r rs♦♥♥ rq♥② rsts ♥ rr ♠♥ s♥stt② s

♥ ♥ qt♦♥ trs t ♣rs♥ ♦ t tr♦stt tr♠ Mel0

♥ s t♦ ♠♣♠♥t ♦r ♦♥tr♦ ♦ t ♣r♦♦ ♠ss ♣♦st♦♥

r♥t ♣t s♥s♥

r♥t ♣t s♥s♥

♣r♦♦ ♠ss ♥r s♣♠♥ts ♠st ♦♥rt ♥t♦ ♥ tr

s♥ tr♦♥s rtr② s t♦ s♥st ♥♦ t♦ tt s ♥

♥ ♣t♥ ❯s② tt♦♥ rt s♥ r ♠♣r s st♥r

② t♦ ♦t♥ ♥ ♥ ts s♥stt② ❬❪ ♦r s t♥q

♥tr♦s ♥♦ss t ♠♥♠♠ s♥ tt ♦r ♥ ♦tr ♦rs

t rs♦t♦♥ ♦ t ♣♦st♦♥ tt♦♥ ❬❪ s ♥♦s s♦rs ♦♠ r♦♠ t

♦♣rt♦♥ ♠♣r s ♦r t tt♦♥ s t ♦♥t♥s ♥♣t ♦st tr♠

♥♦s t rsst♦rs r ♥♦s 1/f ♥♦s ♥ t ♥♦s s ♥trt ② t

♣t♦r t ♥ t s♥ ♦ r♦♥t♥ tr♦♥s s rt t♦

♦t♥ ♥♦ s♥stt② ♣♥ ♥♦s ♦

♥ t ♦♦♥ ♦♣♠♥t t r♦♥t♥ tt♦r s st t ♣rtr

tt♥t♦♥ ♣ t♦ t t♦ s♥s♥ ♣r♥♣s s♥ ♥ t ♣r♦s st♦♥ tr

♣t♦r ♥ ♣♦s♥ ♣t♦r

r♦♥t♥ tt♦♥ s♥ r ♠♣r

r P♦st♦♥ ♠♣r ♣r♥♣

♣♦st♦♥ ♠♣r s s t♦ tt t ♣t♥ ♥s ♥ t r♥t

s♥s♦r ♠♥t s s♦♥ ♥ r t s ♦♥sr tt ♦t VDC s

♣♣ t tr♦ ♥ tt ♥ ♦t Vfb s t♦ ♦♥ tr♦ ♥

sstrt r♦♠ t ♦tr s♠♣♥ rq♥② ♦ t tt♦r ♣r♦ ②

t s MHz ♣rst ♣t♥ Cp ♦s ♥♦t t t tr♥st♦♥

t t s ♥ s t s ♥ ♥♥ ♦♥ ♥♦s ♣r♦r♠♥ s

st rtr ♥ ts st♦♥

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

s♥s♦r s r♥ ② rq♥② s♥ Vfb ♥ t ♠♣♥

s ♦♠♥t ② t ♣t♦r Cf s rst t ♦t ♦t♣t U ♦ t r♦♥t

♥ rt ♥ ♥t♦♥ ♦ t r rr♥t I s ♥ ②

U = −∫

I

Cf

dt

r rr♥t I s t s♠ ♦ t t rr♥ts ♣ss♥ tr♦ t r②♥

♣t♦rs ♥ t ♣t♥ rt♦♥s r ♦ t ♦rr ♦ ♠♥t ♦ t

s②st♠ ②♥♠s > ms ♥ s♥ t ♦t rt♦♥s r ♦ t ♦rr ♦

♠♥t ♦ t tt♦r s♠♣♥ rq♥② < µs ♦♥ ♥ ss♠ tt t

♣t♥s ♦♣rt ♥ t qsstt r♠ s t qt♦♥ ♥ t

rr♥t I s

I =dVfbdt

(Ca − Cb)

♣♥ t rr♥t ①♣rss♦♥ r♦♠ qt♦♥ t rt♦♥ t♥ t

♣t♥ r♥ ♥ t ♦t♣t ♦t ♦ t r♦♥t♥ rt s

U =∆VfbCf

∆C =2VDC

Cf

∆C = Gamp∆C

r t s ss♠ tt Vfb s sqr s♥ r②♥ t♥ t♦ ♦t s

−VDC ♥ +VDC tr♦r ∆Vfb = 2VDC ♦r♥ t♦ qt♦♥ ♦♥ ♥

r♣ t ①♣rss♦♥s ♦ ∆C t ♦r t t♦ ♦♥rt♦♥s st ♥ t

st st♦♥ s rs ♥

♦♥sq♥t② t ♣t♥ rt♦♥s ♦ t r♦tt♦♥ s♥s♦r r ♠sr

tr♦ t ♦t U t t ♦t♣t ♦ t r ♠♣r ♥ ♦♥ ♥ t

♥ ♥♦t tt t tt♦♥ ♥ t tr ♣t♦r ♦♥rt♦♥ s ♣r②

♥r t ♣r♦♣♦rt♦♥ rt♦♥ t♥ U ♥ θ qt♦♥ ♥ t

♦tr ♥ t tt♦♥ s ♥♦♥♥r ♥ t ♣♦s♥ ♦♥rt♦♥ s s♦♥

♥ qt♦♥ ♦r ♥r s♠ r♦tt♦♥ ♦♥t♦♥ t tt♦♥ ♥

♥r③ ♦r♥ t♦ qt♦♥ ♥② ♦♥ ♥ ♥♦t tt t ♦r♣

W0 ♥ t ♥♦r♠ ♣ h ♣② t s♠ r♦ ♦r tr rs♣t ♦♥rt♦♥

r♥t ♣t s♥s♥

U =2GampC0R

W0

θ

r t♣t ♦t ♦ t r♦♥t♥ rt ♦r s♥♣t ♣t♦rs

U =4C0VDC

Cf

Rθ/h

1− (Rθ/h)2

♦rRθ

h≪ 1, U ≈ 2GampC0R

hθ

r t♣t ♦t ♦ t r♦♥t♥ rt ♦r ♣♦s♥ ♣t♦rs

♦♥ ♦ ♠♣r ♥♦s

s♥stt② s sss t ♥♦s ♦♦r ♦ t ①s t ♠♥♠♠

s♥ t♦ tt s ♥♠♥t rs♦t♦♥ s ♥ ② ♥♦s s♦rs

t♥ t r♥t sts ♦ t s♥s♦r ♦♦♣ ss♥t② ♥♦s ♠♥s♠s r

♥ t♦ r♦♣s ♠♥ ♥♦s ♥ tr ♥♦s rst ♠

♥s♠ s ♥tr♦ ♥ t ♠♥ st♦♥ rs t s♦♥ s st ♥

t ♦♦♥ ♦♣♠♥t ♦ ♠♦r s♣ ♦t tr ♥♦s s♦♠ ♦

t ♥♦s s♦rs r ♦♠♥♥t ♥ ♦♣♥♦♦♣ ♠♦ rs ♦trs r ♦♠♥♥t ♥

♦s♦♦♣ ♠♦ ❬❪ ♥ t ♦♦s r r ♦♥ tr♦♥ ♥♦s ♦ r

♠♣r tt♦r s ♥ ♥ s♦♥ st♣ t ♠♦♥ ♦ t tt♦r ♥♦s

♣r♦ ② t s ♣rs♥t

r t♥qs ♥ s ♥ ♥rt r r♦♠trs t♦ r

♦♦ s♥stt② ♣♥ t ♥♦s ♦ ♦r ♥st♥ st

♣t♥ s rt② s② t♥q ♥t♥ ♦r srt s♠♣♥ s s②s

t♠s ❬❪ ♦r t r ♠♣r s s rsst♦r tt ♥rts t

rr♥t ♥♦s ❲♥ ♥trt ② t ♣t♦r ts ♣r♦s

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

s♣ ♥♦s s♣tr♠ tt ♠st s♣♣rss ② t ♣♦st♦♥ tt♦r t

♦♣rt♥ rq♥s t ♥♦s rss ♦ t tr♠ ♥♦s ♦r t

♥♦s t t s♦ ♦r♥r rq♥② t ts t ♥♦s s ♥♦t q

t♦ t ♦♣rt♦♥ ♠♣r tr♠ ♥♦s ♦♦r s♥ rq♥② ♦♠♣♦♥♥ts

r ♦ t♦ t s♥ t♦ t s♠♣♥ t♦♥ ♥ ♦tr ♦rs t

r t ♥t ♦ t ♠♣r t rr t s♠♣ ♥♦s t t ♦t♣t

s s ② s ♦rrt ♦ s♠♣♥ s ♥ ①t♥s♦♥ ♦

st♣t♦r t♥q ❬❪ ♥ ♦s t♦ r r♠t②

t ♥♦s ♥ ♥♥s t t ♥ ♦ t ♦♣♠♣ rtss t

♥♥♦t s♣♣rss t ♥ ♥♦s t t ♠♣r ♦t♣t ♥ ts ♥♦s

s s t♦ s♥ rq♥s rtr ♦♣♠♥t ♥ t♥qs ♥

♦♥ ♥ ❬❪

t s ♦♥sr ♥ q♥t ♥♦s ♠♦ ♦r t r ♠♣r ♣rs♥t ♥

r ♥ ♣rtr t s ss♠ tt t ♦♥trt♦♥ ♦ ♠♣t♦♥ sts

♥ r♣rs♥t s ♥ q♥t ♥♦s s♦r t t ♠♣r ♥♣t Vn2 ♥

t s ss♠ tt t ♥♦s ♦♥trt♦♥s t t ♠♣r ♦t♣t s ♠♦ ②

♠♣ ♣r♠tr Rdet

r q♥t ♠♣r ♥♦s ♠♦

♦♥sq♥t② t ♠♣r ♥♦s s ♥ ②

Vamp2 = Gn

2Vn2

r Gn =2C0 + Cp + Cf

Cf

s t ♥♦s ♥ ♦ t ♠♣r

r♥t ♣t s♥s♥

♥ t t ♥♦s s♣tr♠ rt t t ♦t♣t ♦ t tt♦r s

V 2det = 4kBTRdet

s rst t q♥t ♥♦s ♦ t ♣♦st♦♥ tt♦r ♣r♦ ② t s

√Veq

2 =

√Vamp

2 + V 2det

② r♣♥ qt♦♥s ♥ ♥ ①♣rss♦♥ t q♥t

tr ♥♦s s ♥ ♥② ②

√Veq

2 =

√(2C0 + Cp + Cf

Cf

)2

Vn2 + 4kBTRdet

rr♥ t♦ tr s♥stt② ♦t♥ t qt♦♥ ♦♥ t t tr

♥♦s ①♣rss♦♥ ♦♥ ♥ ♦t♥ t s♥t♦♥♦s rt♦ ♦ t ♥tr

rt ♦ t ♦♣♥♦♦♣ ♠♦ s ♦♦s

SNR =2VDC∆C

Cf

1√Gn

2Vn2 + 4kBTRdet

t s ♥trst♥ t♦ ①♣rss t tr ♥♦s t ♥tsrad

s21√Hz

s ♥

♠ ② tr♥s♣♦rt♥ t ♥♦s ♥st② tr♦ t tr ♥ ♠♥

♠♣t♦♥ ♥② t tt♦r ♥♦s s

Φen =

√(G2

nVn2 + 4kBTRdet

) 1

GmechGdet

[rad

s21√Hz

]

❲r Gmech s t ♠♥ ♥ ♥ ♥ ♥ Gdet s t tt♦r ♥

♥ s

Gdet =2VDC

Cf

Kθ−C = GampKθ−C

sr♥ qt♦♥ t st rs♦t♦♥ s ♦t♥ ♦r ♠♥

♥ Gmech ♥ tt♦r ♥ Gdet ♦♥sq♥t② ♦♥ s t♦ ♣rr strtrs

t ♦ rs♦♥♥ rq♥② ♥ ♥♦♠♥ ♣t♥ s

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

t ♦r ♦♥tr♦ ♦♦♣

rs♦t♦♥ ♣t s♥s♦rs r s② ♦♣rt ♥ t ♦s♦♦♣ ♠♦

t♦ ♥rs tr ♥t ♥ ♣r♦r♠♥ ♥ ts ♠♦ t ♦t♣t ♦t

♦ t ♣t♥ tt♦♥ rt s s♥t t♦ t ♣r♦♦♠ss ♥rt♥

rst♦r♥ tr♦stt ♦r ♠♥t♥s t ♣r♦♦ ♠ss ♦s t♦ ts ③r♦ ♣♦

st♦♥ ♦r♦r t s♠ ♠♣ts ♦t♥ tr♦ ts ♦♥tr♦ ♠♣r♦ t

♥rt② ♦ t s②st♠ s♣② ♥ ♣♦s♥ ♣t♦rs r s ♠♥

ss ♥ s♥♥ ♦♥tr♦ ♦♦♣ ♦r ♣t s♥s♦r s tt t tr♦stt

♦r ♥rt s ♥♦♥♥r ♥t♦♥ ♦ t ♦t s ♦♥sq♥ ♥r③

t♦♥ t♥qs r ♥ ♥ t ♣r♦ t s♥ Σ∆

♠♦t♦r s ♠♣♠♥t

s st♦♥ s r r ♦♥ ♦♥tr♦ ♦♦♣ s♥ Σ∆ ♠♦t♦♥ ♦♦

② st② ♦ t ♥trt♦♥s ♦ s ♦♥tr♦ t t r♦tt♦♥ s♥s♦r

Σ∆ ♠♦t♦♥

Σ∆♠♦t♦♥ ❬❪ s ♠t♦ ♦r ♥♦♥ ♥♦ s♥s ♥t♦ t s♥s

♦r ♥ ♦tr ♦rs rrs♦t♦♥ t s♥s ♥t♦ ♦rrs♦t♦♥ t s

♥s Σ∆ ♥♦t♦t ♦♥rtr s ♣r♦r♠ s♥ rr♦r

r t r♥ t♥ t t♦ s♥s s ♠sr ♥ s t♦ ♠♣r♦ t

♦♥rs♦♥ ♥② ♦ t s②st♠ rs ♦♥ t s ♦ ♦rrs♦t♦♥

rq♥② s♥ ♦rs♠♣♥

♦r♥ t♦ r t ♥♣t t♦ t rtx(t) s t♦ t q♥t③r

♥ ♥trt♦r Σ ♥ t q♥t③ ♦t♣t y[n] s t♦ strt

r♦♠ t ♥♣t s♥ ∆ s ♦rs t r ♦ t q♥t③

s♥ t♦ tr t r ♥♣t ♥② ♣rsst♥t r♥ t♥ t♠ ♠

ts ♥ t ♥trt♦r ♥ ♥t② ♦rrts ts ❬❪ t tt♦♥♦

♦♥rtr s t s r♣ ② ♥t② ♥ tr♥sr ♥t♦♥ s♦ tt

t ♦rrs♣♦♥♥ t♠ ♦♠♥ ①♣rss♦♥ ♦ t ♠♦t♦r ♦t♣t s

y[n] = x[n− 1] + e[n]− e[n− 1]

❲r e[n]− e[n− 1] s t rst ♦rr r♥ ♦ e[n] s t q♥t③t♦♥

rr♦r

t ♦r ♦♥tr♦ ♦♦♣

r Pr♥♣ ♦ Σ∆ ♠♦t♦♥

r ♦s s♣tr♠ ♦ r♥t r♦♠ ♥ ♦rs♠♣ q♥t③r t♦ t♦rr Σ∆♠♦t♦r

Σ∆♠♦t♦♥ ♥ s♣ t q♥t③t♦♥ ♥♦s rst♥ ♥ tt♥t ♥♦s

♥ t ♥ ♦ ♥trst rr t ♥trt♦r ♦rr t ♦r t ♥♦s ♥ t

♥ ♦ ♥trst s strt ♥ r rst ♦rr ♠♦t♦rs r ♥♦♥

t♦♥② st ♥ ♠♦t♦rs t r ♥trt♦r ♦rrs ♦♥sq♥t②

♦♥ s t♦ ♣② tt♥t♦♥ t♦ stt② ♦r r ♦rr ♠♦t♦rs ♥② t

♥♦s t r rq♥s ♥ ♠♥t s♥ t trs ♥ ♠t♦♥

rst♥ ♥ t s♥ t ♦ q♥t③t♦♥ ♥♦s

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

♠♣♠♥tt♦♥ ♦ t t t t r♦t

t♦♥ s♥s♦r

r trtr ♦ t ♥rt s♥s♦r

s♠t ♠♦t♦r ♦♥tr♦r ♣r♦ ② t ♥ s t♦

s♥ t ♦s♦♦♣ r♦tt♦♥ s♥s♦r r s♦s t strtr ♦

t r♦tt♦♥ s♥s♦r s♥ Mel ♦rs s t ♦ t

s②st♠ ♦♣♣♦s♥ t♦ t s♥ Φ ♥ t s♥s♦r s t ②♥♠s ♦ s♦♥

♦rr s②st♠ ♦♥tr♦r s s t♦ ♥♦r t stt② ♦ t ♦ s②st♠ s

s t♦ r t ♥♦s ♥ t ♥ ♦ ♥trst ③ ③

s strtr ♣rs♥ts ♥♠r♦s ♥ts ♦r t ♥♦ ♦s ♦♦♣ ♠

♣♠♥tt♦♥ s st ♥ ❬❪ ♦♠ r t r

♦t♣t s♥ s rt② t ♥♦ ♥ ♦r ♥ ①tr♥ tt♦

♥♦ ♦♥rtr

r♦ t♥ r② ♥ ♥t s ♣♦ss

♣r♦r stt② ♦♠♣r t♦ ♥♦ ♠♣♠♥tt♦♥ ♦ ♦s ♦♦♣

♠♥t♦♥ ♦ t ♥♦♥♥rt② t♥ ♦t ♥ tr♦stt ♦r

♥ st♦♥ ♥ tr♦sttMel ♠♦♠♥t s ♥t ♦r t ♠♣♠♥tt♦♥

♦ ♦r ♦♥tr♦ s tr♦stt ♠♦♠♥t ①♣rss♦♥ s ♥ ♥

qt♦♥s ♥

Mel = Kθ−CVDCVfb

♥ ♦rr t♦ ♦s t ♦♦♣ ♦♥ s t♦ ♥rst♥ t ♥rt♦♥ ♦ t

s♥ Vfb ② t Σ∆ ♦♥tr♦r ♥ ♦ t s t♦ ♥r③ t ♦♥tr♦ ♠♦♠♥t

Mel s s t ♠ ♦ t ♥①t st♦♥

t ♦r ♦♥tr♦ ♦♦♣

tstr♠ ♦♥rs♦♥ ♦r ♥r③

tstr♠ ♦t♣t r♦♠ t Σ∆♦♥rtr r♣rs♥ts t ♥♦ s♥ ♥

♦ ♥ ♣s ♥st② ♠♦t♦♥ P s♥ ♥ r ♦♥ ♥ ♥

t tstr♠ r♣rs♥tt♦♥ ♦ s♥ s♥ ♥ ts strt♦♥ ♦♥ ♥ ♥♦t

tt t s♠♣♥ rq♥② s t♠s r t♥ t s♥ rq♥②

♠♣♠♥tt♦♥s ♥ r ♥ ♦rs♠♣♥ rt ♦ ❬❪ s ①♣♥

♦r ts tstr♠ ♥ ♦♣ss tr ♦r r t♦ r♦r t ♥♦r

♠t♦♥ ♥♦

♥ t♦♥ t tstr♠ s s♦ ♦r ♠♦t♦r ♦♥tr♦ t

♦t Vfb s ♦t ♥ t t♦ s ♣♥♥ ♦♥ t t

VDC t ♦r −VDC t s rst ♦♥ ♥ rt t

♦t t t ♦t♣t

Vfb = Dc s♥(bit)VDC

❲r Dc s t②② ♣r♠tr ♦♥tr♦♥ t tr♥t♦♥ t♥ tt♦♥

♥ s♥s♥ r ♦t s ♥ ② t ♥trt♦♥ ♦ Vfb ♦r

♣r♦ ♦ t s♥s♥ ♠♥t T0 ≫ Ts r Ts s t s♠♣♥ ♣r♦

♥ rtt♥ s ♦♦s

Vfb = DcVDC

∫ T0

0

s♥(bit)dt = DcVDC ν

r♦ qt♦♥ ♦♥ ♥ ♥♦t t ♥r③t♦♥ ♦ t ♦♥tr♦ t r

s♣t t♦ t ♦♥tr♦ ♣r♠tr ν ∈ [−1; 1] ♥ t♦♥ ♦♥ s♦ ♥♦t tt

t tr♥t♦♥ ♦ Vfb t♥ VDC ♥ −VDC ♦s ♥♦t ♥♥ ts sqr

r♠♥s t VDC2

t s t♥ ♣♦ss t♦ t t r ♦r ♦ t t ♦♥

tr♦r s♥ t ♥r tr♦stt ♠♦♠♥t ①♣rss♦♥s ♦t♥ ♥ qt♦♥s

♥

Mel = Kθ−CVDCVfb = Kθ−CDcVDC2 ν

s rst ♦♥ ♥ ♥ t ♥ s ♦♦s

Kfb =Mel

Jzν=Kθ−CVDC

JzVfb =

Kθ−CDcVDC2

Jz

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

♦ ♦♥ ts ♦♣♠♥t ♥r③ tr♦stt ♠♦♠♥t s t

t rs♣t t♦ ♦♥tr♦ ♣r♠tr ν s ♦♥tr♦ ♣r♠tr rsts r♦♠ t

♠t♦♥ ♦r t r♥ ♦ t tstr♠ ♦t♣t ♥ ② t Σ∆ ♠♦t♦r

♥② ♥ Kfb s ♦t♥ r♣rs♥ts t s ♦ t

r♦tt♦♥ s♥s♦r ♦r ♥ ♦tr ♦rs t ♠①♠♠ ♥r rt♦♥ tt ♥

♦♥tr♦ ② t s②st♠

r ♥♦ s♥ ♥ ts tstr♠ ♦♥rs♦♥

♦♥ ♦ ♥♦s ♥ t ♦s♦♦♣ ♠♦

t♦♥ ♥♦s s♦rs ♦r ♥ t s♥s♦r ♦♣rts ♥ ♦s♦♦♣ ♠♦

♥t③t♦♥ ♥♦s s ♦♥ ♦ ts ♥♦s s♦rs t t s ♥♦t ♣r♦♠♥♥t s♥

t Σ∆ strt② s ♠♣♦② ❬❪ ♥♦tr s♦r s t ♣r♦♦ ♠ss rs ♠♦

t♦♥ rst♥ r♦♠ t tr♦stt ❬❪ ❲♥ ts s ♣♣

tr♦ t ♣s tr♥ t rsts ♥ ♣r♦ ♠♦t♦♥ ♦ t ♣r♦♦ ♠ss

r♦♥ ts qr♠ ♣♦st♦♥ ♥ ♥r ③r♦ ①tr♥ ①tt♦♥ s ♥♦s s

♥rs② ♣r♦♣♦rt♦♥ t♦ t sqr ♦ t s♠♣♥ rq♥② tr♦r t ♦

♦♠ ♦♠♥♥t ♦r ♦ s♠♣♥ rq♥② ♥ s♠♣♥ rq♥② ♦

MHz s ♣♣ ② t ts s♦r s ♥♦t ♣r♦♠♥♥t ♥ t ♦s♦♦♣

♠♦ ♦ t r♦tt♦♥ s♥s♦r

♥ ♠♣♦rt♥t ♥♦s ♦♥trt♦♥ ♦♠s r♦♠ t ♥ t tstr♠ ♦t

♣t s ♦♥rt ♥t♦ ♥ ♥♦ sqr s♥ ♦ ♠♣t VDC ♥ s♠

♦t rt♦♥s ♦r ♥♦s r ♦sr r ♥t ♥ t s♥s♦r ♦♦♣

♦♥sq♥t② t ♥♦s ♦♠♣♦♥♥t ♥ t ♦s♦♦♣ ♠♦ ♦ t ♣r♦

t ♦r ♦♥tr♦ ♦♦♣

♥ ♠♦ ② ♠♣ ♣r♠tr Rdac t t tt♦♥♦ ♦♥rtr

♥rt♥ t ♥♦s s♣tr♠ ♦√4kBTRdac s tr♦♥ ♥♦s rsts

♥ st ♥s ♥ t ♦t ♣♣ t♦ ♦♥tr♦ tr♦s tr♦r

ts ♥♦s s ♥t ♥ t s♥s♦r ♦♦♣ r♥ t ♦rr♥♥ ♦ t ♣r♦♦

♠ss ♥♦s ♥ ①♣rss ♥ ♥tsrad

s21√Hz

② tr♥s♣♦rt♥ t

♥♦s s♣tr♠ tr♦ t ♦♥t s s

Φfn =√4kBTRdacKfb

[rad

s21√Hz

]

ts ♥♦s ♣♥s ♦♥ t ♥ Kfb ♠♥s tt t s②st♠

s ♥s t♦ ♠t ♦r ttr ♣r♦r♠♥s ♦r t s♠ tr♦s

r s ♦r ♦t tt♦♥ ♥ tt♦♥ s s♠r s rst ♥

♦r tt♦♥ ♥ s♥ t② ♣♥ ♦t ♦♥ t ♦♥st♥t Kθ−C

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

♣tr s♠♠r② ♥ ♦♥s♦♥s

s ♣tr r t s♥ ♣r♥♣s t♦ ♦♣ rs♦t♦♥

s♥stt② s r♦tt♦♥ s♥s♦r ♠♥ ♠♣t♦♥ ♦ ♥

♥rr♦♠tr strtr s ♥ ♥ t♦ ♣t s♥s♥ ♣r♥♣s

s♥ tr ♣t♦rs ♥ ♣♦s♥ ♣t ♣t♦rs rs♣t② r st

t ♣rtr ♦s ♦♥ tt♦♥ ♥ ♦♥tr♦ ♣② t s ♦♥ tt

tr ♣t♦rs r ss s♥st t♦ ♣r♦♦ ♠ss ♥r s♣♠♥ts t♥ ♣

♦s♥ ♣t♦rs ♦r t ttr ♦♥rt♦♥ ♥ s♦ ♥st ♦r

♦r ♠♣♦rt♥t ♥r s♣♠♥ts ts ♦♣rt♥ t r♦tt♦♥ s♥s♦r ♥ t

♦s♦♦♣ ♠♦ s ♦♥ ♣rr ♥ ♦r ♦♥tr♦ ♣s t

♣r♦♦ ♠ss ♦s t♦ ts ③r♦ ♣♦st♦♥ ♥ s ♦♥sq♥ t ♥rss t ♥

rt② ♥ t stt② ♦ t s②st♠ t st ♦♥ t♦ ♣② tt♥t♦♥ t♦ ♥♦s

♠♥s♠s s♥ t② r rt t♦ t s♥s♦r ♥♦s ♦♦r s ♥♦s ♦♦r s t

♠♥♠♠ s♥ tt t r♦tt♦♥ s♥s♦r ♥ tt ♥ t s t♦ s ♦ s

♣♦ss

t♦ ♦♥rt♦♥s r r♣rs♥t t t ♦♥tr♦ tr♦♥s ♥ rs

♥ s s tr rs♣t s♥ ♦r♠s s♠♠r③ ♥ ts

♥

♥ t s♥ ♣r♠trs ♥ t s ♣♦ss t♦ ♣r♦♣♦s r♥t ♣r♦t♦t②♣s

♠t♥ t rqr♠♥ts ♦ ss♠ ①♣♦rt♦♥ s♥♥ ts ♣r♦t♦t②♣s

♦♦ t s♠ ♦ s ts ♣tr s♥ tr♦s t♥ s♥stt② rs♦t♦♥

♥ stt② ♠♦r ♦♥srt♦♥

♥①t ♣tr ♣rs♥t ♥ ♦♠♣r t♦ r♦tt♦♥ s♥s♦r s♥s ♦♥

♦r♥ t s♥♦♠ tr♦s ♥ ♥♦tr ♦r♥ t ♣r ♣♦s♥

tr♦s

♣tr s♠♠r② ♥ ♦♥s♦♥s

♦s♦♦♣ s♥ ♦r♠ ♦ s♥♣t ♣t♦rs

r ♠t ♦ t s♥s♦r ♦♦♣ t s♥♣t ♣t♦rs

♥s♦r ♣r♠trs

♥ ♥ Gmech =1

ω02

[rad

rad/s2

]

♣t ♥ Kθ−C =2C0R

W0

[F

rad

]

tr ♥ Gdet =2VDCKθ−C

Cf

[V

rad

]

♥ Kfb =Kθ−CDcV

2DC

Jz

[rad

s21

V

]

♦s ♣r♠trs

♦s ♥ Gn =2C0 + Cp + Cf

Cf

♥ ♥♦s Φmn =

√4kBTω0

JzQ

[rad

s21√Hz

]

tt♦♥ ♥♦s Φen =

√(G2

nVn2 + 4kBTRdet

) 1

GmechGdet

[rad

s21√Hz

]

♥♦s Φfn =√4kBTRdacKfb

[rad

s21√Hz

]

t ♣r♠trs ♥ q♥t ♥♦s s♦rs ♦r r♦tt♦♥ s♥s♦rt s♥♣t ♣t♦rs

♣tr ❲♦r♥ ♣r♥♣s ♦ ♣r♦r♠♥ ♣t ♠r♦♠♥ r♦tt♦♥ s♥s♦r

♦s♦♦♣ s♥ ♦r♠ ♦ ♣r♣t ♣t♦rs

r ♠t ♦ t s♥s♦r ♦♦♣ t ♣r♣t ♣t♦rs

♥s♦r ♣r♠trs

♣t ♥ Kθ−C =2C0R

h

[F

rad

]

tr ♥ Gdet =2VDCKθ−C

Cf

[V

rad

]

♥ Kfb =Kθ−CDcVDC

2

Jz

[rad

s21

V

]

tr s♣r♥ Kel = 4C0VDC2

(R

h

)2 [N.m

rad

]

♠♦ rq♥② ω0m =

√ω0

2 − Kel

Jz

[rad

s

]

♥ ♥ Gmech =1

ω0m2

[rad

rad/s2

]

♦s ♣r♠trs

♦s ♥ Gn =2C0 + Cp + Cf

Cf

♥ ♥♦s Φmn =

√4kBTω0

JzQ

[rad

s21√Hz

]

tt♦♥ ♥♦s Φen =

√(G2

nVn2 + 4kBTRdet

) 1

GmechGdet

[rad

s21√Hz

]

♥♦s Φfn =√4kBTRdacKfb

[rad

s21√Hz

]

t ♣r♠trs ♥ q♥t ♥♦s s♦rs ♦r r♦tt♦♥ s♥s♦rt ♣r♣t ♣t♦rs

♣tr

s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♥ ♦♥str♥ts

♥ st② ♦ t r♦tt♦♥

♠♣♥ ♥②ss

tr ♠♦ ♦ r♦tt♦♥ s♥s♦r s♥s

♥♥ ♦ ♥♦♥♥rts ♦♥ t rs♣♦♥s

♣t♠③t♦♥ ♦ r♦tt♦♥ s♥s♦r s♥s

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

s ♣tr ♦♣s t♦ s♥s ♦r ♥ r♦tt♦♥ s♥s♦r ♥t♥

♦r ss♠ ①♣♦rt♦♥ s ♦♥ t s♥s♥ ♣r♥♣s ♣rs♥t ♥ ♣tr

② trs t r s t♦ s♥ t♦ strtrs s ♦♥ t♦

♣t♦r ♦♥rt♦♥s ♦♥ s♥ s♥♦♠ ♣t♦rs ♥ t ♦tr ♦♥

s♥ ♣r ♣♦s♥ ♣t♦rs ♦r ♥ t t s♥ t t♥

♦♥str♥ts ♠♣♦s ② t t ♠♥tr♥ ♣r♦ss ♥ t ♣♥

r ♣r♦ ♥ tr ♠♥ ♥②ss r ♣r♦r♠

rst t ♠♥ st② t t t♦♥ ♦ s♣r♥ st♥ss ♦♥ts

♥ rst ♠♦ rq♥s

♦♥ ♠♣♥ ♥②ss ♥ ♦rr t♦ t t qt② t♦r ♦ t

♦♥rt♦♥s ♥ t♦ ♥ t ♣rssr ♥ t♦ ♠t t ♠♥

♥♦s

r t tr st② t t t♦♥ ♦ ♥♦♠♥ ♣t♥s ♥

tr♦stt ♠♦♠♥ts r ♠♣♦rt♥t t♦ t t tt♦r ♥ t

♥s ♦ t s②st♠

♥ ♥♦♥♥r st② ♦ t r♦tt♦♥ s♥s♦r s ♣r♦♣♦s t♦ ♣rt ts ♦r

♥ ♦♣rt♥ t r ♠♣ts ♦ t ss♠ ♠ss ♥② ♥ ♦♣t♠③t♦♥

st② s ♦♥ t♦ ①trt t s♥ ♣r♠trs ♥ t♦ st ♣r♦r♠♥s

s♥s st r s♠t t♦ ♦rs tr ②♥♠ ♦rs s s tr

♥♦s strt♦♥s ♥ t rq♥② ♦♠♥

♥ ♦♥str♥ts

♥ ♦♥str♥ts

♦r ♥♥♥ t ♠♦♥ ♣s ♦♥ s♦ st t r♥t t♥

♦♥str♥ts ♥ ♦rr t♦ ♥ t♦♣♦♦② ♦r s♥ t st②

rst s♣t♦♥s ♦♥ t s♥ r rt t♦ t ♠♥s♦♥s ♦ t

t♦ ♣r♦ss r♦tt♦♥ s♥s♦r ♠♥tr ♦r♥ t♦ s♣

♣r♦ss ♦♣ s♦ r ♦r r♦♠trs ♦r s♣② t r

t♦♥ ss ♦♣t♠③ ♣ t ♦♥ t♥ ♣r♦ss ♦ ♦♥♥

♥st♦r rs t t♥ss ♦ µm ♦♥sq♥t② t s♠st ♣

tt ♥ ♣r♦ss s µm ♥ t s♠st s♣r♥ t s st t

µm rs♥ ♣r♦ss ♥s t ♣rs♥ ♦ ♦s ♥ ♠♦ ♣rts ♥

t♦ r ♠tr ♥st② s ♦♥ s t♦ ♦♥sr ♥ s♦♥ ♥st② ♥

t ♠♦s s r ② rt♦ ♦ % ♥ ρ = 1864 kg/m3

♥ t s♦♥ s ♥ ♥s♦tr♦♣ ♠tr ♦♥ s♦ r ♦ t ♦r♥

tt♦♥ ♦ ♠s ♦♥ t r rs r ♦r♥t s s ♣rs♥t ♥

r ♠s r ♦r♥t ♦♥ t [] r②st♦r♣ ①s s♦ tt t

s♦♥ ❨♦♥ ♠♦s s t s♠st ♣♦ss ♦r r ♠♥ s♥stt②

rst♥ ❨♦♥ ♠♦s Ey s ♦ GPa

r r②st♦r♣ ①s ♦ rs s ♦r t r♦tt♦♥ s♥s♦r ♣r♦ss

♥ s♦ r ♦ ♣♦t♥t ♦rt♥ ♦ t s♥st ♠♥ts r♥

t ♣r♦ss ♥ ♥ ♦rt♥ ♥ ♠♦② t rt ♣r♠trs ♦ t

s♥ s s ♠ t ♦r r ♣ t♥ tr♦s ♠♥s♦♥ ♥②ss

s♦♥ ♥ t ♥①t ♣tr t♦ q♥t② ts ♦rt♥ ♦r rtr ts

t ♠♥tr♥ ♣r♦ss s ♣rs♥t ♥

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♦ t♦ ♣ t ♣s ♥ t♦ tst t♠ t t ♣r♦

t s♥st ♠♥t s③ s ① t mm × mm ♦r♦r t ♥tr

s♣♣♦rt♥ ♥♦r Ra s ① s③ t♦ ♥sr t tr ♦♥♥ ♥ t s

st t µm

②♦♥ ts ♦♥srt♦♥s ss r♦♠ t ♣r♦ss ♦♥ ♥ s♦♠ r

qr♠♥ts rt t♦ t ♦♥t♦♥s ♦ s ♦ t tr r♦tt♦♥ s♥s♦r rst

♦♥ s t t rs♦♥♥ rq♥② s t♦ ♦ kHz t♦ ♠t t

♠♥ ♥♦s s ♦♣ ♥ qt♦♥ s♦ t tr♦♥s ♥s

♠♥♠♠ ♥♦♠♥ ♣t♥ t♦ ♦r ♣r♦♣r② ♦ ts ♥tr♥s ♥♦s r

♦r t ♥♦♠♥ ♣t♥ s t♦ rr t♥ pF

s rqr♠♥ts s♠♠r③ ♥ t r t t ♦r ♦ t s♥

s♥ t t♦♣♦♦s s t♦ ♦♣ ♦r ♣r♦t♦t②♣s ♥rt r♦♠ t♠ ♥

t♥ sr r ♦ 3.2× 3.2 mm2 ♦♥ s t♦ s♥ strtr s

rt② s♠ rs♦♥♥ rq♥② t s♦t s♣r♥s ♥ ② ♣r♦♦

♠ss ①♥ t ♥♦♠♥ ♣t♥ t s♣ ② ♥rs♥

t ♥♠r ♦ tr♦s s ♦r ♠♥♠③♥ t rs♦♥♥ rq♥②

♠①♠③♥ t ♣t♥ r ♦♣♣♦st ♠♥s♠s ♥ tr♦ ♠st

♣t t s♦♠ ♣♦♥t

t♦ s♥ ♣r♥♣s ♥ s♥ ♥ rs ♥ ♥ t ①

♠♥ts ♥ t ♣r♦♦ ♠ss r t s♠ ♦r t t♦ ♦♥rt♦♥s ♦♥ ♥

r t st♥ss ♦♥t ♦r ♦t strtrs ♦r s♣rt t♦♥s

♦r ♦r t tr♠♥t♦♥ ♦ t ♠♣♥ ♦♥t ♥ t tr ♣r♦♣rts

♥ ♦♥str♥ts

♣t♦♥s Pr♠tr ♥♠ ❱

♥st ♠♥t s③ Csize < mm

♣♣♦rt♥ ♥♦r rs Ra µm

❲r t♥ss µm

rt ♣ ♠♥s♦♥ lc > µm

♣r♥ t Wb > µm

trtr rs♦♥♥ rq♥② f0 < kHz

♦♠♥ ♣t♥ C0 > pF

♥ s♣t♦♥s

r s♥ t s♥♦♠ ♣t♦rs

r s♥ t ♣♦s♥ ♣t♦rs

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♥ st② ♦ t r♦tt♦♥

s st♦♥ s t t ♠♥ st② ♦ t r♦tt♦♥ s♥s♦r ♥ rst

st♣ t st♥ss ♦♥ts ♦ t rst ♦r♠t♦♥ ♠♦s r ♥ r♦tt♦♥ ♥

t ①② ♣t ③①s tr♥st♦♥ ♥ r♦tt♦♥ ♥ t ②③ ♣♥ ♥ ts st♥ss

♦♥ts ♦♣ t t ♥rt ♣r♠trs ♦ t ss♠ r♥ ♣r♦ t

rq♥② s ♦ t rst ♠♦s t♦♥ ♦ t rst ♠♦ rq♥s

s ss♥t ♦r t t♦♥ ♦ t qt② t♦r ♥ t ♠♥ ♥♦s

tt ♠♦

♥ t stt st② t ♠ qt♦♥ ♥r r♥t ♦♥r② ♦♥t♦♥s s

s♦ t♦ tr♠♥ t st♥ss ♦♥ts ♦ t s♣♣♦rt♥ s♣r♥s ♥ t♦♥

t ♠ qt♦♥ s r ♦♥sr♥ sr ②♣♦tss

♠tr s ss♠ t♦ s♦tr♦♣ t ♥♦ ♦♥srt♦♥ ♦ P♦ss♦♥

t

s♣♣♦rt♥ ♠s ♦♣rt ♥ t s♠str♥ s♠t♦♥ r♠

♥ s♣

♠ ♥rt ♥ sr♥ ts r s♣♣♦s ♥

♥② t ss♠ r♥ s ss♠ t♦ ♣rt② r

♦r t t♦♥s r♥t ♣r♠trs r ♥tr♦ ♥ t

♠ ♥t Lb

♠ t Wb

trtr t♥ss T

♥tr ♥♦r rs Ra

♥ ♥♥r rs Ri

♥ ①tr♥ rs Re

♠ t♦♥ ♥ t ①② ♣♥ v(x)

♠ t♦♥ ♥ t ③① ♣♥ w(x)

Pr♠trs s ♥ t rt♦♥ ♦ t st♥ss ♦♥ts

♥ st② ♦ t r♦tt♦♥

♦tt♦♥ ♥ t ①② ♣♥

r ♠♦ ♦ ♥ s♦t ♠ t ts ♦♥r② ♦♥t♦♥s ♦r t r♦tt♦♥♥ ①② ♣♥

r♦tt♦♥ ♥ t ①② ♣♥ s t ♠♥ ♠♦t♦♥ s♥ t strtr s t♦

s♥st t♦ ♥r rt♦♥s r♦♥ t ③ ①s ♥ ♦rr t♦ t t

st♥ss ♦♥t ♦♥ s t♦ s♦t ♦♥ s♣r♥ r♦♠ t strtr ♥ s♦ t

♠ t♦♥ qt♦♥ t t ♣♣r♦♣rt ♦♥r② ♦♥t♦♥s r

s t ♦r s♣r♥s r ♠♦♥t ♥ ♣r t t♦t st♥ss ♦ t strtr s

♦t♥ ② s♠♠♥ t ♦♥trt♦♥s

♦r ♥ s♦t ♠t ♥♠t ♦♥t♦♥ t t r ①tr♠t② s ♥ ②

v(Lb) = λ = (Lb +Ra)θ

♥ t ss♠♣t♦♥s ♣rs♥t t t ♥♥♥ t ♠ t♦♥ s rt t♦

t rt♦♥s ♦rs t t ① ♣♦♥t tr♦ t ♦♦♥ r♥r② r♥t

qt♦♥ ❬❪d2v

dx2=M1 − F1x

EyIz

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

❲r M1 s t ♥♥ rt♦♥ ♠♦♠♥t ♥ F1 s t ♥♥ rt♦♥

♦r t t ① ①tr♠t② Ey s t ❨♦♥ ♠♦s ♦ t ♠tr ♥ Iz s t

qrt ♠♦♠♥t ♦t ③①s ♥ ②

Iz =TWb

3

12

♦♥r② ♦♥t♦♥s ♦r ts ♣rtr ♠♦t♦♥ r

v(0) = 0

dv

dx

∣∣∣∣x=0

= 0

v(Lb) = (Lb +Ra)θ

dv

dx

∣∣∣∣x=Lb

= θ

❯s♥ t ♦♥r② ♦♥t♦♥s t t ① ①tr♠t② t t♦♥ ♥t♦♥ s

♥ ② t rt♦♥

v(x) =x2

EyIz(M1

2− F1

6x)

❯s♥ t ♦♥r② ♦♥t♦♥s t t r ①tr♠t② t rt♦♥ ♦rts r

M1 =2EyIz(2Lb + 3Ra)

L2b

θ

F1 =6EyIz(Lb + 3Ra)

L3b

θ

♥ ♦rr t♦ ♥ t s♣r♥ ♦♥st♥t ♦r ts ♣rtr ♠♦t♦♥ ♦♥ s t♦ tr♥s♣♦rt

t rt♦♥ ♦rs ♥ ♠♦♠♥ts t♦ t ♥tr♦ ♦♥sr♥ tt t s♥s♦r s

♦♠♣♦s ♦ ♦r s♣r♥s t ♥♥ ♠♦♠♥t ①♣rss t t ♥tr♦ s

Mcenter = 4 (M1 + F1Ra) =4

3

EyTW3b (L

2b + 3LbRa + 3R2

a)

L3b

θ

♥ ♥ ①trt t s♣r♥ ♦♥st♥t ♦r ts ♣rtr ♠♦t♦♥

Km =4

3

EyTW3b (L

2b + 3LbRa + 3R2

a)

L3b

♥ st② ♦ t r♦tt♦♥

♥♥ ♦ r t♦♥s

t♦♥ ♦ ♠ ♥r ♥♥ ♦rts s t♦ s♠ ♦♥t♦♥ ♥

t s r t t♦♥ s r t trt♦♥ ♦r ♥rt ② ts ♦♥

t♦♥ s ♥♦ ♠♦r ♥ ♥ ♥♦tr ♥♥ ♦♥trt♦♥ s t♦ ♦♥sr

s ♠♦ ② t t♦♥ ♦ ♥ tr♠ T1 trt♦♥ ♦r

d2v

dx2− T1EyIz

=M1 − F1x

EyIz

r t ♦♥r② ♦♥t♦♥s r t s♠ s ♥ t ♣r♦s st♦♥ ♥ ♥

♥tr♦ t r k ♥ ② t ①♣rss♦♥

√T1EyIz

❯s♥ t ♦♥r② ♦♥t♦♥s t t ① ①tr♠t② t t♦♥ qt♦♥ s

♥ ② t ♦♦♥ ①♣rss♦♥

v(x) =kM1(cosh(kx)− 1) +R1x(k − sinh(kx))

k3EIz

rt♦♥ ♦rs ①♣rss♦♥s r ♦t♥ ② s♥ t ♦♥r② ♦♥t♦♥s t

t r ①tr♠t②

M1 = kEyIzcosh(kLb)k(Lb +Ra)− sinh(kLb)− kRa

2(1− cosh(kLb)) + kLb sinh(kLb))θ

F1 = k2EyIzsinh(kLb)k(Lb +Ra)− cosh(kLb) + 1

2(1− cosh(kLb)) + kLb sinh(kLb))θ

t ♥ ♥♦t tt t rt♦♥ ♦rs r ♥♦♥♥r s♥ t② ♣♥ ♦♥ t

r ♦♥t♥s t t♥s ♦r ♣r♠tr ② t♥ t ♠t ♥

s ♦s t♦ t rt♦♥ ♦rs ①♣rss♦♥s r

limk→0

M1 =2EyIz(2Lb + 3Ra)

L2b

θ

limk→0

F1 =6EyIz(Lb + 3Ra)

L3b

θ

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

s ♠ts ♦rrs♣♦♥ t♦ t ①♣rss♦♥s ♦♥ ♥ qt♦♥ ♦♥r♥♥

t t♥s ♦r ①♣rss♦♥ ♦♥ s t♦ t t t♦t ♠ ♦♥t♦♥ s♥

T1 = Sσx = ESǫx =EyS

Lb

∆Lb

r S s t ♠ st♦♥ σx s t strss ♦♥ ①①s

t s ♦♥sr ♥ ♥♥ts♠ ♥t dx ♥s t q♥tt② dv

♦♥sq♥t② t ♥t ♦ ts ♠♥t dx ♥rss ♥ ♦♠ dx+∆Lb ♠♣

♦♠tr ♦♥srt♦♥s t♦ t q♥

d∆Lb

dx≈ 1

2

(dv

dx

)2

♦♥ t♦ t t♥s ♦r ①♣rss♦♥

T1 =EyS

2Lb

∫ Lb

0

(dv

dx

)2

dx

s rt♦♥ s str♦♥② ♥♦♥♥r ♥ ♥♥♦t s♦ ♥②t② t t s

♣♦ss t♦ ♥ s♦t♦♥ s♥ t♦♥♣s♦♥ ♥♠r ♠t♦ rtss

t s ♣♦ss t♦ ♥ ♥ ♣♣r♦①♠t♦♥ ♦ t t♥s ♦r T1 ♦r s♠ s ♦ k

T1 =1

30

EyTWb(17L2b + 18R2

a + 33LbRa)

L2b

θ2

♥ r ♦♠♣rs♦♥ ♦ t ♥♥ ♠♦♠♥t t t strtr ♥tr♦

Mcenter s s♦♥ ♦r t s♠ t♦♥ ♥ t r t♦♥ t♦rs

♥ ♥ ♥♦t tt t t♥s ♦r T1 s r ♥♥ ♦♥ t rt♦♥

♠♦♠♥t ♦r ♥st♥ ss♠♥ ♠ t ♥t ♦ µ♠ t ♦ µ♠

♥ t♥ss ♦ µ♠ t rt♦♥ ♠♦♠♥t s tr t♠s rr tt t ♦

①♣t r♦♠ t s♠ t♦♥ t♦r② ♦r θ mrad

❯s♥ srs ①♣♥s♦♥ ♦ t t♦♥ ♥t♦♥ ♦r k ♦s t♦ ③r♦ t s ♣♦ss

t♦ ♥ t t② ♦♠♥ ♦ t s♠ t♦♥ ss♠♣t♦♥ s t②

♦♠♥ s ♥ ② t ①♣rss♦♥

k2 ≪ 30(L2b + 3RaLb + 3R2

a)

L2b(L

2b + 9RaLb + 9R2

a)

♥ st② ♦ t r♦tt♦♥

r r t♦♥ s s♠ t♦♥ ss♠♣t♦♥

sttt♥ t t♥s ♦r ①♣rss♦♥ t♦ qt♦♥ s

1

75

(θ

Wb

)2(17L2

b + 33RaLb + 18R2a)(L

2b + 9RaLb + 9R2

a)

(L2b + 3RaLb + 3R2

a)≪ 1

qt♦♥ s ♥♦t r ♦♥ s t♦ ♦♥sr r ♦rr tr♠s ♥ t s♣r♥

♦r ①♣rss♦♥ ♥ ♦rr t♦ ♥ ts s♣r♥ ♦r ①♣rss♦♥ ♦♥ s t♦ tr♥s♣♦rt

t rt♦♥ ♦rts t♦ t ♥tr♦ s s

Mcenter = 4 (M1 + F1Ra)

sttt♥ qt♦♥ t♦ qt♦♥ ♥ t♥ t ②♦r ①♣♥s♦♥

t♦ t tr ♦rr t s♣r♥ ♦r ♥ ♣♣r♦①♠t ②

FNonLinear =4

3

EyTW3b (L

2b + 3LbRa + 3R2

a)

L3b

θ

+4

225

EyTWb(17L2b + 33LbRa + 18R2

a)(Lb2 + 9LbRa + 9R2

a)

L3b

θ3

s ①♣♥ ♦ t ♥♦♥♥r t ♠s t s♣r♥ str ♦r r

t♦♥s ♥ t ②♥♠ ♣r♦♣rts s ♦♥s♦♥ ♦♣rt♥ ♥ t ♥r

r♠ ♥s r s♣r♥ t s t ♦s t ♦ rq♥②

s ①♣♥s ② ♦♥tr♦ s ss♥t t♦ ♠t t ♠♣t ♦ r♦tt♦♥

θ ts ♥sr♥ ♠♥ ♥r ♦r

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

❩①s tr♥st♦♥

r ♠♦ ♦ ♥ s♦t ♠ t ts ♦♥r② ♦♥t♦♥s ♦r t tr♥st♦♥ ♦t ③①s

♣rst ♠♦t♦♥ ♦ t ss♠ ♠ss s t tr♥st♦♥ ♠♦t♦♥ ♦♥ t ③

①s r ♥ t ♦♦♥ ♦♣♠♥t s♠ t♦♥ ss♠♣t♦♥ s

♠ ♥ s t♦ ♣② tt♥t♦♥ t♦ t ♥♦♥r♦tt♦♥ ♥♠t ♦♥t♦♥ t t

♠ r ♥ qt♦♥ sr♥ t ♦t ♦ ♣♥ t♦♥ s ts ♥

②dw2

d2x=M2 − F2x

EyIy

♦♥sr♥ t ♦♦♥ ♦♥r② ♦♥t♦♥s

w(0) = 0

dw

dx

∣∣∣∣x=0

= 0

w(Lb) = δ

dw

dx

∣∣∣∣x=Lb

= 0

❲r M2 s t ♥♥ rt♦♥ ♠♦♠♥t ♥ F2 s t ♥♥ rt♦♥ ♦r

t t ① ①tr♠t② Ey s t ❨♦♥ ♠♦s ♦ t ♠tr ♥ Iy s t

qrt ♠♦♠♥t ♦t ②①s ♥ ②

Iy =WbT

3

12

♥ st② ♦ t r♦tt♦♥

t♦♥ ♥t♦♥ w ♥ ♦♥ ② ♥trt♦♥

w(x) =x2

EyIy(M2

2− F2

6x)

M2 ♥ F2 r tr♠♥ ② t ♦♥r② ♦♥t♦♥s t t r ①tr♠t②

M2 =6EyIyL2b

δ

F2 =12EyIyL3b

δ

♥② t st♥ss ♦♥t ♦r ts ♣rtr ♠♦t♦♥ s

KmZ =4EyT

3Wb

L3b

tr♠ ♥ qt♦♥ s t strtr t♥ss T rs t

tr♠ ♥ t st♥ss ♦♥t ♦r r♦tt♦♥ ♥ t ①② ♣♥ sWb qt♦♥

♥ T s rr t♥Wb ② rt♦ ♦ s t t ♦t♦♣♥ ♦r♠

t♦♥ ♠♦ s t rq♥② ♠ rr t♥ t ♥♣♥ ♦r♠t♦♥ ♠♦ s

rst t strtr ♦ t r♦tt♦♥ s♥s♦r s s♥st t♦ ♥r rt♦♥s ♥

ts rr♥ ♣♥ rs t trs ♣rst ♠♦t♦♥s s s tr♥st♦♥s ♥♦r♠

t♦ ts rr♥ ♣♥

♦tt♦♥ ♥ t ②③ ♣♥

♥♦tr ♣rst ♠♦t♦♥ ♦ t ss♠ ♠ss s t r♦tt♦♥ ♠♦t♦♥ ♥ t

②③ ♣♥ ♦r ♥ t ①③ ♣♥ ♥ t ♦♦♥ ♦♣♠♥t s♠ t♦♥

ss♠♣t♦♥ s ♠ t s♦ ♥♦t tt t♦ ♠s ♥ ♦t ③①s ♥

t♦ ♠s tst r♦♥ ① ①s r s ♦♥sq♥ t st② s

♥t♦ t♦ ♣rts ♦♥ ♦r t ♥♥ ♦r♠t♦♥ ♥ ♥♦tr ♦♥ ♦r t t♦rs♦♥

♦r♠t♦♥

♥♥ ♦♥st♥t s ♦t♥ ♥ t s♠ ② s t r♦tt♦♥ ♥ t ①

② ♣♥ r♦r t ♦♥trt♦♥ ♦ t t♦ ♥♥ ♠s s ♥ ② t

♦♦♥ ①♣rss♦♥

Kϕ1=

2

3

EyT3Wb(L

2b + 3LbRa + 3R2

a)

L3b

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

r ♠♦ ♦ ♥ s♦t ♠ t ts ♦♥r② ♦♥t♦♥s ♦r t r♦tt♦♥♥ ②③ ♣♥

♥②ss ♦ t t♦rs♦♥ ♦♥st♥t ♦ rt♥r r s qt ♦♠♣t

♦r♥ t♦ ❬❪ t t♦rt ①♣rss♦♥ ♦r t t♦rs♦♥ ♦♥st♥t s

Kϕ2=

2GW 3b T

Lb

β

(T

Wb

)

β(η) =1

3

(1− 192

π5

1

η

∑

n=1,3,5

1

n5tanh(

nπη

2)

)

r G s t ♠tr sr ♠♦s ♥ t ♦♠♥ s♣r♥ ♦♥st♥t ♦r

ts ♣rtr ♠♦t♦♥ s

Kmt= Kϕ1

+Kϕ2=

2

3

EyTWb ((TLb)2 + 3T 2LbRa + 3(TRa)

2) + 3GW 2b β(

TWb

)L2b

L3b

♥ t tr♠ s t strtr t♥ss T ♥ qt♦♥ t rq♥②

♦ ts ♦r♠t♦♥ ♠♦ s rr t♥ t ♦♥ ♦r r♦tt♦♥ ♥ t ①② ♣♥

♦♥sq♥t② t strtr ♦ t r♦tt♦♥ s♥s♦r trs ts ♠♦t♦♥ t②♣

♥ st② ♦ t r♦tt♦♥

rst ♠♦ rq♥s

♥ ♦rr t♦ t t rq♥s ♦ t rst ♦r♠t♦♥ ♠♦s ♦♥ ♥

♦♥sr ♦♥② t ♥rt ♦ t ss♠ r♥ s rst t ♥rt ♣r♠trs ♦

t ss♠ r♥ ♠♦♠♥ts r♦♥ t ③①s ♥ t ①①s s s t ♠ss

r ♥ ②

M = ρπT(Re

2 −Ri2)

Jz =M

2

(Re

2 +Ri2)

Jx =Jz2

r ρ s t ♠tr ♥st② ♥ st♥ss ♦♥st♥ts t ♥ qt♦♥s

♥ t s ♣♦ss t♦ t t rst ♠♦ rq♥s ♦ t

r♦tt♦♥ s♥s♦r

fθ =1

2π

√Km

Jz=

1

2π

√4

3

EyTW 3b (L

2b + 3LbRa + 3R2

a)

JzL3b

fφ =1

2π

√Kmt

Jx=

1

2π

√2

3

EyTWb((TLb)2 + 3T 2LbRa + 3(TRa)2 + 3GW 2b β(

TWb

)L2b)

JxL3b

fz =1

2π

√KmZ

M=

1

2π

√4EyT 3Wb

ML3b

rq♥② ①♣rss♦♥s ♣rs♥t ♥ t♦ t ♥ ♦♠

♣r t ♥t♠♥tt♦ s♠t♦♥s t♦ ♦♥ ♦♥ t ♠♦

t② t s ss♠ ss♠ r♥ ss♣♥ ② ♦r s♣r♥s t ♣r♠tr

s ♥ ♥ t r ♥♠r ♠♦ s ♠ t

t♣②ss © ♥ ♦♠♣rt rsts r s♦♥ ♥ t t ♥ s♥ tt

t t s r♠r② ♦♦ rtr♠♦r ♦♠♦rt♥ ♦srt♦♥ s tt t ♣r

st ♠♦t♦♥s rs♦♥♥t rq♥s ♠ r t♥ t ♦♥ ♦ t ♠♦t♦♥

♦ ♥trst ♦r ♥st♥ t ♦t♦♣♥ r♦tt♦♥ ♠♦ s rs♦♥♥t rq♥②

s s①t♥ t♠s rr t♥ t ♥♣♥ r♦tt♦♥ ♠♦ ♥ t ♦t♦♣♥

tr♥st♦♥ ♠♦ s rs♦♥♥t rq♥② s ♠♦r t♥ t♥t② t♠s

rr t♥ t ♥♣♥ r♦tt♦♥ ♠♦ r♦r t r♦tt♦♥ s♥s♦r strtr

s t♦ tr ♣rst ♠♦t♦♥s ♥ s♥st t♦ ♥r rt♦♥s ♦

ts rr♥ ♣♥

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

s ♥ r♠r ♦♥ ♥ ♥♦t tt t rs♦♥♥t rq♥s ♣♥ str♦♥②

♦♥ t ♠ t Wb s ♥♥ ② ♦rt♥ r♥ ♣r♦ss♥ ♥

♦♥s♦♥ ♦♥ t♦ ①♣t s♠r ♠ t ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦

t②♣s ts ♦r rs♦♥♥t rq♥s ♦ t rst ♠♦s

Pr♠tr ❱ ❯♥t

Lb µm

Wb µm

T µm

Ra µm

Ri = Ra + Lb µm

Re µm

Jz 8× 10−14 kgm2

M nkg

r ♠♦ ♦r t t♦♥ ♦ rst ♠♦ rq♥s

♠♥ rq♥② ♥②t rst Hz rst HzfCOMSOL

fanalytical

♦tt♦♥ ①② ♣♥

♦tt♦♥ ②③ ♣♥

r♥st♦♥ ③①s

♠r ♥②ss rsts

♠♣♥ ♥②ss

♠♣♥ ♥②ss

♦r ♠♦♥ strtrs t s♠ s③s t sr ♦rs s♦s ♦r ♦♠

♥♦♥♥ t rs♣t t♦ t ♦♠ ♦rs rt② ♥ ts t ♦♠s

rtr s ♠r♦♠♥ strtrs rs ♥ s③ ♥ ♣rtr ♣t

♠r♦♠♥ strtrs s ♣r♣t ♣t♦rs r ♠♦ tr♦

♥trts t t s ♥♣st t♥ ♠♦♥ ♥ ① tr♦s t

ts t♦ ♠♥s♠s ♥ ♦r t s♦s tr ♠♣♥ ♦r s♠

♠♣♥ ♥ t sq③♠ ♠♣♥

♠ ♠♣♥ ♦rs ♥ t♦ ♣r ♣ts ♠♦ t♥♥t② t

rs♣t t♦ ♦tr t♦ s♦st② ts t t sstrtr ♥tr t

①rts ♦r ♦♥ t ♠♦♥ ♣t tt ♦♣♣♦ss t rt ♠♦t♦♥ s

♠♣♥ ♦r s ♥t♦♥ ♦ t ♦t② r♥t ♥ t ♥t② ♦ t ♠♦♥

♣t t s♦st② ♦ t s ♥ t ♦r♣ r t♥ ♠♦♥ ♥ ① ♣t

s ♠♣♥ ♠♥s♠ s ♦♠♥♥t s♦r ♥ tr②r♥ strtrs

♦♠r♥ s②st♠s s s ♦♥ ♦ ♦r r♦tt♦♥ s♥ t s♥♦♠

♦♥rt♦♥

♥ t ♦tr ♥ ♥ s ♠ t♥ t♦ ♣r ♣ts s sq③ ②

t rt ♠♦t♦♥ ♦ ts srs s ♦ s ♣r♦ rt♥ ♣rssr

t♦♥ ♥ t t② s s t s♦ sq③♠ ♠♣♥ sq③ ♠

♠♣♥ s rtr③ ② ♣②s ♠♥s♦♥s t ♥t ♥ t♥ss ♦

t s ♠ rtr♠♦r ♦tr ♣r♠trs s s t ♠♥t ♣rssr ♥ t

s♦st② ♦ t s ♣② ♠♣♦rt♥t r♦ ♥ ts t②♣ ♦ ♠♣♥ s ♠♥s♠

s ♦♠♥♥t ♦r r♥ strtrs s♥ ♣♦s♥ tr♦s

♦♦♥ st♦♥ s r ♦♥ ♠♣♥ ♠♥s♠s ♦♦ ② t

t♦♥ ♦ t qt② t♦r ♦r t t♦ ♦♥rt♦♥s st s♥♦♠

♣t♦rs ♥ ♣♦s♥ ♣t♦rs qt② t♦r ①♣rss♦♥s r t♥ s

t♦ tr♠♥ t ♣rssr ♠ts t ♠♥ ♥♦s ♦ t r♦tt♦♥

s♥s♦r s♥s

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♠♣♥ ♠♥s♠s ♦r t s♥♦♠ ♦♥r

t♦♥ ♦ t r♦tt♦♥ s♥s♦r

r ♠♣♥ ♠♥s♠s ♥ s♥♣t r♦tt♦♥ s♥s♦r t s♦♠tr t t♦♣

s♥♣t♦r s♥ ♥♦s t t♦ ♠♣♥ ♠♥s♠s ①♣♥

♦ ♥ ♦♥ ♥ ♥♦t ♦♥ r tt s♠ ♦rs t t tr

♦♥rs rs sq③♠ ♦rs t t ①tr♠t② ♦♥r② ♦r ♥ ♥

r tr♦ ♦♠tr ♣r♠trs ♦ t ♠♣r r T t strtr

t♥ss Wf t ♥r t W0 t tr♦ ♦r♣ d t tr ♣ h0 t

♥♦r♠ ♣ ♥ t vi t ♦t② ♦ t t tr♦ ❲ ss♠ tt ♥r

tr♦s r str♣ ♣ts s♥ T ≫ Wf

♥ ♦♥ ♥ tr s ♦♥♥♠♥t ♦ t s ♠ t♥ ① ♥rs r

t♥ s ♦ ♦♥ t ♦t♦♣♥ rt♦♥ s rst ♦♥ s♦ ♦♥sr

t ♣r♠tr T ♥ h0 s t rtrst ♠♥s♦♥s ♦ t sq③ ♠♣r

♥ t ♦tr ♥ t sr♥ ♦ t s ♦rs ♦♥ t ♦r♣ t♥ ♠♦

♥ ♥ ① ♥rs rtrst ♠♥s♦♥s ♦ ts s ♠♣r r t

♣r♠trs W0 ♥ d

♥ t ♦♦♥ ♦♣♠♥t ♠♣♥ ♠♦ s r s♣rt② t

♣rtr ♦s ♦♥ t ♥♥ ♦ s rrt♦♥ ts

♠♣♥ ♥②ss

r ♦ ♦ sq③♠ ♠♣r

q③♠ ♠♦

♥ t sq③♠ ♠♣r s♦♥ ♥ r t ♥rt t s ♥

t♦ r② s♠ ♦♠trs ♥ ♥r s♦tr♠ ♦♥t♦♥s t ♦r ♦ t

sq③ ♠ s ♦r♥ ② t ♥♦♥ ②♥♦s qt♦♥ ♥ ② ❬❪

∇(ph3

η∇p)

= 12∂(hp)

∂t

r η s t ②♥♠ s♦st② ♦ t s p t ♣rssr ♥s t t② ∇ s

t r♥t ♦♣rt♦r ♥ ♥② h t ♠ ♣

❯♥r s♠ rt♦♥s ♦ ♣rssr p ♥ ♣ ♠♥s♦♥ h ♥r③ ♦r♠ ♦

qt♦♥ s ♣r♦♣♦s ♥ ❬❪ s t♦ t ♠♣♥ ♦r ①♣rss♦♥ ♦r

str♣ ♣t s s

Fd =96ηab3

π4h03 v

r a s t ♠♣r ♥t b s t ♠♣r t h0 s t ♥♦♠♥ ♠ ♣

♥ v t ♠♦♥ ♣t ♦t② ♠♣t

q③♠ ♠♣♥ ♦♥t ♦ t r♦tt♦♥ s♥s♦r s♥

♥ t r♦tt♦♥ s♥s♦r s sq③♠ ♠♣♥ ♦rs t t t♣ ♦

tr♦ ♥r rt♥ ♠♣♥ ♠♦♠♥t ♦t t ♥tr♦ ♥ t♦♥ ♦♥

♥ ♥♦t r♦♠ r tt t s ♠ s ♦♥♥ t♥ ① ♦♠ ♥rs

rt♥ s ♦ ♦♥ t ♦t♦♣♥ rt♦♥

t s ♦♥sr t ♠♣♥ t♦♥ rt t t t tr♦ ♥ r

♥r t s s♠ ♥♦ s♦ tt ♦♥ ♥ ①♣rss t ♥r ♦t② s

♦♦s

vi = RiΩ

r Ri s t st♥ r♦♠ t ♥tr♦ ♥ Ω s t r♦tt♦♥ rt ♦ t ♣r♦♦

♠ss

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

r ♠♠t♦♥ ♦ ♠♣♥ t♦♥s ♦r ♦♠

s rst t ♠♣♥ ♠♦♠♥t t t t ♥r s ♥ ②

Mi =96ηWfT

3Ri2

π4h03 δΩ

♦ t t ♠♣♥ ♠♦♠♥t ♦r ♦♠ ♦♥ s t♦ s♠ ♦♥tr

t♦♥s r♦♠ ♠♦♥ ♥rs ss♠♥ Nf ♥rs ♦♥ ♦♠ t ①♣rss♦♥ ♦ t

♠♣♥ ♦r s ♥ ②

Dsqueeze =

2Nf−1∑

i=1

Ri296ηT

3Wf

π4h03

r Ri = R1 + i (d+Wf ) = R1 + iLp s♠♠t♦♥ s t st

Dsqueeze = R096ηT 3Wf

π4h03

t t ♥tr♦t♦♥ ♦ t ♦♥st♥ts R0 s s

R0 =8

3Nf

((1

8+ Nf 2 − 3

4Nf

)Lp2 +

3

2

(Nf − 1

2

)R1 Lp+

3

4R1

2

)

♠♣♥ ♥②ss

s rrt♦♥ t

♥ ♦rr t♦ ♠♥♠③ t ♠♣♥ t ♦♥ s♦ r t s ♣rssr

♥ t strtr t② ♦r s ♣rssr ♠♥t♦♥ ♠s t ♦♥t♥♠

♦r ♦ t s ♠ ♥♦ ♠♦r ♥ ts s rrt♦♥ ♦rrt♦♥ ♠st

t♥ ♥t♦ ♦♥t ♥ t ♠♦ s s♣ ♥ ❬❪ ♥ ❬❪ t s rrt♦♥

t ♥ ♥tr♦ tr♦ t ♥s♥ ♥♠r ♥ s ♦♦s

Kn =λ0h0

r λ0 s t ♠♥ r ♣t ♥ ♥ ♥t♦♥ ♦ t s ♦♥st♥t R t ♠♦

r ♠ss Mm ♥ t t♠♣rtr T0 ②

λ0 =η

Pa

√2RT0Mm

❲t ts ♠ ♣r♠tr Kn t s ♣♦ss t♦ rt ♠♦ s♦st② ♠♦

ηmodified =η

Qpr

r Qpr s ♦ rt ♦♥t ♥t♦♥ ♦ t ♥s♥ ♥♠r Kn ♦r

♦♥t♥♠ ♦ ts s rs t ♥rss s♥♥t② ♦r r ♥s♥

♥♠r ♦r r ♠ ♦ rt ♦♥t t♦♥ rqrs t s♦

t♦♥ ♦ t ♦t③♠♥♥ qt♦♥ s ♦♠♣t ♥ ♦r s♠♣ t♦♣♦♦s

t rs t r♥t ♦ r♠ ♥ t ss♦t ♣♣r♦①♠

t♦♥ ♦ Qpr sttt♥ Qpr ♥ qt♦♥ ♦♥ ♥ ♦t♥ t sq③♠

♠♣♥ ♦♥t ♦ t r♦tt♦♥ s♥s♦r t s rrt♦♥ t

Dsqueeze = R096ηT 3Wf

Qprπ4h03

♦ r♠ ♦♥t♥♠ ♦ s♣ ♦ tr♥st♦♥ ♦ ♠♦r ♦

♦♥t♦♥s ♦♥ Kn Kn < 0.001 0.001 < Kn < 0.1 0.1 < Kn < 10 Kn > 10

Qpr ♥t♦♥ 1 + 6Kn 1 + 9.638K1.159n

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♥ ts ♥ sq③♠ ♠♣r

♠♣♥ ♦♥t ♥ s ♥r tr ♦♥r② ♦♥t♦♥s t

t ♥r tr♦ ♦♥rs s ♦♥t♦♥ s ♦♦ ♣♣r♦①♠t♦♥ ♦♥②

t ♦st♥ ♥r ♠♥s♦♥s r ♠ rr t♥ t ♠ ♣ T,Wf >> h0

♦r ♥ ♣rt t s♣t rt♦ s s♠ ♥♦ s♦ tt ♦rr ts ♥

♣② ♥ ♠♣♦rt♥t r♦ ♥ t ♠♣♥ t ♥ ♦st ♦rr ♦♥t♦♥ s t♥

s t♦ ♦rrt ts t s ①♣♥ ♥ ❬❪ s ♠♦ ①t♥s♦♥ ♥s t

t♦♥ ♦ t ♣t ♠♥s♦♥s ♥ ♥ s ♦♦s

T ′ = T

√1 + 3AT

(1 + 4AWf

)3/8√

1 + 3AWf(1 + 4AT )

1/8

Wf′ = Wf

√1 + 3AWf

(1 + 4AT )3/8

√1 + 3AT

(1 + 4AWf

)1/8

r t ♦♥ts AT ♥ AWfr

AT =8

3π

1 + 2.676Kn0.659

1 + 0.531Kn0.5(h0/T )0.238

h0T

AWf=

8

3π

1 + 2.676Kn0.659

1 + 0.531Kn0.5(h0/Wf )0.238

h0Wf

♠♣♥ ♥②ss

r ♦ ♦ s♠ ♠♣r

♠ ♠♣♥ ♠♦

t rt② s♦ ♦ts t s s ①t ② t sr ♦r ①rt ②

♠♦♥ ♣ts r ♦r ♦ rq♥② ♦st♦♥s ♥ s♠ ♣rssr

rt♦♥s r♦ss t sr ♦ t ♠♣r t s ♦ ♥ ♠♦ ② t

s♦♥ qt♦♥ ❬❪∂v

∂t= η u(z)

r u s t t s ♦t② strt♦♥ ♥ t ♣ ♦♣rt♦r ♦r

② sts ♦ t s ♦ ♥ ♦♥sr ♦tt ♦ t ♥r

♦t② strt♦♥ t t ♠♦♥ ♣t ♦rrs t ♠♣♥ ♦r s ①♣rss

② ❬❪

Fshear =ηA

dv

r A s t r ♦ t ♠♦♥ ♣t ♥ d t t♥ss ♦ t s ♠

♠ ♠♣♥ ♦♥t ♦ t r♦tt♦♥ s♥s♦r s♥

♦♥sr♥ t t ♠♦♥ ♥r ♦rr r ♥ ♥ qt♦♥

t s♠ ♠♣♥ ♦♥t s ♥ ②

DRi=ηRi

2W0T

d

❲r d s t tr ♠ t♥ssW0 t sr♥ ♥t ♦r t ♦r♣ t♥

♣ts ♥ Ri t st♥ ♦ t ♠♣r r♦♠ t ♥tr♦ ♠♠♥ t

♦♥trt♦♥s ♦r ♦♠ t t♦t ♠♣♥ ♦♥t ♦ t s ♠ ♠♥s♠

s ♥ ②

Dslide = R0ηW0T

d

r R0 t ♦♥st♥t ♥ ♥ qt♦♥

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

r s♠ ♠♣♥ ♦♥t ♦ t r♦tt♦♥ s♥s♦r

♣♣r♦①♠t♦♥ Qpr2 r②

♣ ♦ Kn2 < 1 1 + 2Kn2 −3%

♥② ♦ 1 + 2Kn2 + 0.2Kn20.788e−Kn2/10 ±1%

♣♣r♦①♠t♦♥s ♦r Qpr2 ♥ s♠ ♠♣♥

s rrt♦♥ t

s rrt♦♥ s ♥ ♠♣t ♦♥ t ♦ ♣r♦ t t ♦♥t Qpr

s ♦r t sq③♠ ♠♣r s ♥♦t ♦r ts ♣rs♥t s rtss

♥♦tr ♦♥t Qpr2 ♥ ♥tr♦ ❬❪ s ♥t♦♥ ♦ t ♥s♥

♥♠r ♦ t s♠ ♣r♦♠ Kn2 ♥ ♥ s

Kn2 =λ0d

♥ ♥ ♥ ♥ t ♣♣r♦①♠t♦♥s ♦ Qpr2 s t ♠♣♥ ♦♥t

r♦♠ qt♦♥ ♥ rrtt♥ s s

Dslide = R0ηW0T

Qpr2d

♠♣♥ ♥②ss

♥ ts ♥ s ♠♣rs

rr♥s st② t ♥ ts ♦ s ♠♣rs rtss s♠♣

♦♥t♦♥ ♠♦ s ♣rs♥t ♥ ❬❪ r ♠♦ ♣ s ♥tr♦ ② t

♦♦♥ ①♣rss♦♥

d′ =d

1 + 8.5d

a

r a s t rtrst ♥t ♦ t ♠♣r s ♥ ♦r s ♥

② W0

♦t ♠♣♥ ♦♥t ♦ t s♥♦♠ ♦♥rt♦♥

♥ s♦ ♥♦t tt t sq③♠ ♠♣♥ ♦♥t s ♣r♦♣♦rt♦♥ t♦

1/h03 rs t s♠ ♠♣♥ ♦♥t s ♣r♦♣♦rt♦♥ t♦ 1/d ♦♥s

q♥t② t sq③♠ ♠♥s♠ s ♦♠♥♥t ♦r t s♠ ♦♥ ♥

qt♦♥s ♥ ♦♥ ♥ t t t♦t ♠♣♥ ♦♥t ♥

s ♦♦s

D = R0

(96ηT ′3Wf

′

Qprπ4h03 +

ηW0T

Qpr2d′

)

♦♥sr♥ Nc ♦♠s ♦r ♠♣rs ♦♥ ♥ ♥② rt t ①♣rss♦♥ ♦r t

qt② t♦r

Q =Jzω0

D=

Jzω0

NcR0η

(96T ′3Wf

′

Qprπ4h03 +

W0T

Qpr2d′

)

♥ t s♥♦♠ ♦♥rt♦♥ t qt② t♦r ①♣rss♦♥ rss r♦♠ t

s♠♠t♦♥ ♦ t♦ ♠♣♥ ♠♥s♠s s♠ ♠♣♥ ♥ sq③♠

♠♣♥ ♦♥sr♥ tt t qt② t♦r ♣♥s ♦♥ t ♦ t ♥♦r

♠ ♣ ♠♥s♦♥ h0 strtrs t r s ♦ h0 ♠♣② r qt②

t♦r s

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♠♣♥ ♠♥s♠s ♦r t ♣♦s♥ ♦♥r

t♦♥ ♦ t r♦tt♦♥ s♥s♦r

r ♠♣♥ ♠♥s♠s ♥ ♣♦s♥ r♦tt♦♥ s♥s♦r

♣♦s♥ s♥ ♦♥sr ♥♦ s ♠♦r s♠♣ s♥ t ♠♣♥ s

♦♠♥t ② sq③♠ ♠♣♥ ♦r♥ t♦ r ♦♥ ♣t ♠♦s

t ♦t② strt♦♥ v ♦r t ♠♦♥ ♣t ♦ s♠♣② t ♠♦ ♦♥

♥ ♦♥sr tt v s ♦♥st♥t ♦r t ♣t ♥ ♥ ♣♣r♦①♠t ②

v ≈ RmΩ

❲r Rm s t ♣♦st♦♥ ♦ t ♣t ♥tr ♥ Ω s t ♣r♦♦ ♠ss r♦tt♦♥ rt

t t♦♥s ♦ t ♠♣♥ ♦r ♦r rt♥r ♣t ♥ ♦♥

♥ ❬❪ t r s ♣rt ♣♣r♦①♠t♦♥ ♦ t ♠♣♥ ♦r t

s rrt♦♥ ts ♥ ♥ ❬❪

Fd =(ab)2η

Qprh03

1

f

(b

a

) +1

f(ab

)

−1

v

t f(ξ) = ξ − 0.63094ξ2 + 0.47456ξ8.138

r a ♥ b t ♣t ♠♥s♦♥s ♦♥sr♥ t ♣♣r♦①♠t♦♥ ♥ ♥

qt♦♥ ♥ ss♠♥ tt t ♠♣♥ t♦♥ s ♠♦ ② s♥

♦r t t st♥ Rm r♦♠ t ♥tr♦ t ♠♣♥ ♦♥t ♦r t r♦tt♦♥

♠♣♥ ♥②ss

♠♦t♦♥ s ♥ ②

D =T 2(R2 −R1)

2Rm2η

Qprh03

1

f

((R2 −R1)

T

) +1

f

(T

(R2 −R1)

)

−1

r R1 ♥ R2 t ♣♦st♦♥s ♦ t ♠♣r ①tr♠ts T t ♣t t♥ss

♥ Qpr t rt ♦ rt ♦♥t ♣♥♥ ♦♥ t ♥s♥ ♥♠r Kn

♦♥sr♥ Nc ♠♣rs ♦♥ ♥ ♥② rt t qt② t♦r ♦ ts s♥

s s s

Q =Jzω0

D=

Jzω0Qprh03

NcT 2(R2 −R1)2Rm2η

1

f

((R2 −R1)

T

) +1

f

(T

(R2 −R1)

)

♥ t ♣♦s♥ ♦♥rt♦♥ ♦♥② ♦♥ ♠♣♥ ♠♥s♠ s ♥♦

s t sq③♠ ♠♣♥ ♥rs♥ t qt② t♦r ♥ ♦t♥ ②

♠♣♦②♥ s♠ ♣ts s s r ♥♦r♠ ♣ ♠♥s♦♥ ♦r ts ♥

♦st ♦♥ t tr ♣r♦♣rts sss rtr

♠♠r② ♦♥ t ♠♣♥ ♥②ss

♥ ts ♦♣♠♥t t ♦♠♣t ♠♣♥ ♠♦s ♦r t t♦ ♦♥rt♦♥s

st r ♥ t♦ t t qt② t♦r qt② t♦r s ♥ ♠

♣♦rt♥t s♥ ♣r♠tr s♥ t s rt t♦ t ♠♥ ♥♦s ♥ t s♥s♦r

♦♦♣ s s♦♥ ♥ t ♣r♦s ♣tr r s♠♣②♥ ss♠♣t♦♥s s s

s♠♥②t ♠♦s r s t♦ ♣r♦ ♥②t ①♣rss♦♥s ♥ t

♠♣♥ ♦♥ts ♥ qt♦♥s ♥ r ♦t♥ tr♦ ♦♥t♥

♠ ♦ ②♣♦tss s ♥♦ ♠♦r ♥ ♠♦r r♠ t ①♣♥s

② ♥tr♦ t rt ♦ rt ♦♥ts ♦r ♠♣♥ ♠♥s♠s

t♦ ①t♥ t t② ♦♠♥ ♦ ♥②t ♦r♠ ♦♥sq♥t② t qt②

t♦r ①♣rss♦♥s s ♦♥② t♦ ♥ ♦rr ♦ ♠♥t ♦ t ♠♥

♥♦s ♦r s♥ ♦r st ♣r♦r♠♥s t ♠♥ ♥♦s s t♦

s ♦ s ♣♦ss ts r② qt② t♦r s r ♥ ①♠③♥

t qt② t♦r ② ♦♣t♠③♥ t ♦♠tr rtrsts ♦ t ♠♣rs s

♦♦ ♥t strt② t ♦♥ s♦ ♦♥sr t♦ r t ♠♥t ♣rssr ♥

t t② ♦r ttr rsts

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♥t♦♥ ♦ t ♣rssr ♥ ♦r ♦ ♠

♥ ♥♦s

t② t♦r t♦♥

♥ t ♦♦s t rt♦♥ ♦ t qt② t♦r s ♥t♦♥ ♦ t ♠♥t

♣rssr Pa s sss t s ♦♥sr t ♦♠tr ♣r♠trs ♦ t t♦

s♥ ♦♥rt♦♥s s♦♥ ♥ ♣♣♥s ♥ s ♦♥sr s

r② r t r ♠♥ ♣t λ0 ♦ 70 nm t t♠♦s♣r ♣rssr ♦r♥ t♦

qt♦♥ ♥ ♦♥ ♥ ♦sr ♥ r t qt② t♦r ♦r t

t♦ s♥s ♥ ts ♦t♦♥ t ♦ ♣rssr s♥ ♣t s♥ s ttr

②♥♠ ♣r♦♣rts t r t♦r ♦r ♥ ♣rssr rtr♠♦r ♦♥

♥ ♥♦t tt t t♦r ♥rss ♥r② ♥ ♦rt♠ s ♦r rs♥

♣rssr s ♥ ♦r ♣rssr ♦ Pa Q s rr t♥

♥ ♦♥ s rst t ♣rssr r♥ ♦ ♥trst ♦ Pa ♦r

rtr t♦♥s t s st t ♣rssr t Pa ♥ t♦♥ t♦ ♣r♦♥

qt② t♦r ts ♣rssr s ♦s♥ s t s t ♠♥♠♠ tt

♥ r ♥ t ♦rt♦r② ①♣r♠♥ts t ♥ t ♥①t ♣tr

r t♦r ♦♠♣rs♦♥ ♦r t t♦ s♥s st

♠♣♥ ♥②ss

♥ ♥♦s t♦♥

♥ t ♣rssr ♣♣r ♠t ♥ ♦♥ ♥ ♥♦ t t ♠♥ ♥♦s

♦r t t♦ s♥s ♦♥sr ♥ ♥ r t ♠♥ ♥♦s ①♣rss♦♥

♥ ♥ t ♦r♠r ♣tr qt♦♥

Φmn =

√8πkBTof0JzQ

❯s♥ t t♦r s ♦t♥ t t ♣r♠trs ♥ ♥ ♣♣♥s

♥ t ♠♥ ♥♦s ♥ t ♥ t s s♦♥ ♥ r

s♥ ♣t s♥ s ♦r ♠♥ ♥♦s ♥ s♦

♣rr ♥ tr♠s ♦ rs♦t♦♥ t ♥♦s ♦♦r t µrad/s2/√Hz ♥st

µrad/s2/√Hz ♦r t ♣♦s♥ s♥ ♦r ♦♥ s t♦ ♦♥sr t

♦r s♥s♦r ♦♦♣ ♦r ♦r ♦♦s♥ t ttr ♦♥rt♦♥

r ♥ ♥♦s ♦♠♣rs♦♥ ♦r t t♦ s♥s st

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

tr ♠♦ ♦ r♦tt♦♥ s♥s♦r s♥s

♥ ts st♦♥ t tr ♣r♦♣rts ♦ t r♦tt♦♥ s♥s♦r s♥s r s

ts rst t st② ♦ t s♥♦♠ ♦♥rt♦♥ s ♣rs♥t

t t ♣rs♥ ♦ tr ♣t♦rs s s ♣♦s♥ ♣t♦rs ♥

t tr ♣r♠trs ♦ t s♥ s♥ ♣♦s♥ ♣ts r ♣r♦

♥♦♠ ♣t♦rs

♥ ♦rr t♦ t t tr rtrsts ♦ t s♥♦♠ s♥

♦♥ ♥ ♦♥sr t ♠♦ ♣rs♥t ♥ r ♦♠tr ♣r♠trs

s ♦r t♦♥s r st ♥ t

❱♠ ♣r♠ttt② ε0

trtr t♥ss T

tr♦ ♦r♣ W0

♥r t Wf

tr ♣ d

♦r♠ ♣ h

♦♠tr ♣r♠trs rtr③♥ t tr ♣r♦♣rts ♦ ts♥♦♠ s♥

♦♥sr♥ t t ♥r tr♦ r♥t ♣t♦r ♦♥rt♦♥s ♥

♦♥sr ♦r ♥st♥ tr r t♦ s♥ ♦♠♣♦♥♥ts Ci,1 ♥ Ci,2 ♥ t♦

♣♦s♥ ♦♠♣♦♥♥ts Cfr,i ♥ Cfs,i ❯s♥ t ♣r♣t ♣♣r♦①♠t♦♥

t ♣t♥ ①♣rss♦♥s r ♥ ②

Ci,1 = Ci,2 =ε0T (W0 +Riθ)

d

Cfr,i = Cfs,i =ε0TWf

h−Riθ

r θ s t ♥r ♣♦st♦♥ ♦ t ♣r♦♦ ♠ss ♥ Ri t st♥ ♦ t t

tr♦ r♦♠ t ♥tr♦ ♦♥sr♥ Nf ♥r ♦♥ ♦♠ tr♦ ♥ Nc

tr ♠♦ ♦ r♦tt♦♥ s♥s♦r s♥s

r tr ♠♦ ♦r s♥♦♠ ♣t♦rs

♣t♦rs t t♦t ♣t♥ s ♥ ② t ♦♦♥ ①♣rss♦♥

CA =

2Nf−1∑

i=0

Ncε0T (W0 + (R1 + iLp)θ)

d+

2Nf−1∑

i=0

Ncε0TWf

h− (R1 + iLp)θ

r Lp = d +Wf ②♦r ①♣♥s♦♥ ♦ qt♦♥ s t ♦♦♥

♣♣r♦①♠t♦♥ ♦r t ♣t♥ CA

CA ≈ C01 (1 + a11θ) + C02

(1 + a21θ + a22θ

2)

r t r♥t ♦♥st♥ts ♥tr♦ ♥ qt♦♥ r ♥ ②

C01 = Nc(2Nf − 1) ε0TW0

d

C02 = Nc(2Nf − 1) ε0TWf

h

a11 =R1 +NfLp

W0

a21 =R1 +NfLp

h

a22 =4Lp

2Nf2 + (6R1 − Lp)LpNf + 3R1

2

3h2

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♥ ♦ s ♣t♦r ♦♥rt♦♥ s s ♦♥ ♥ t

♣t♥ ♦ t ♦♣♣♦st ♦♠ tr♦ Cb

CB ≈ C01 (1− a11θ) + C02

(1− a21θ + a22θ

2)

♥② t ♣♦st♦♥t♦♣t♥ ♦♥st♥t ♦r ts ♣rtr s♥ s

Kθ−C = 2 (a11C01 + a21C02)

♣♦st♦♥t♦♣t♥ ♦♥st♥t rss r♦♠ t ♦♥trt♦♥ ♦ t♦ ♣

t♥ ♠♦s

rst ♦♥ t③s ♥ ♥ t tr r ♦ ♥r tr♦s s

♠♦ s ♣r② ♥r ♥ t s rtr③ ② t ♥♦♠♥ ♣t♥ C01

♥ t ♣r♠tr a11

s♦♥ ♦♥ t③s ♥ ♥ ♣ t t t♣ ♦ ♥r tr♦s s

♠♦ s ♥♦♥♥r ♥ t s rtr③ ② t ♥♦♠♥ ♣t♥ C02

♥ t ♣r♠trs a21

♦r♦r ♦♥ ♥ t t tr♦stt ♠♦♠♥t ♣♣ t♦ t strtr

s♥ t ♦t strt♦♥ s♦♥ ♥ qt♦♥

Mel = Kθ−C (VDCVfb) + 2a22C02

(VDC

2 + Vfb2)θ

♦♥sr♥ t ①♣rss♦♥s r♦♠ qt♦♥s ♥ s s t

♦t Vfb ♦♣ ♥ qt♦♥ ♦♥ ♥ t t ♠♣t♦♥

♥ ♦ t ♣t tt♦♥ ♥ t ♥ ♦ t ♦♥tr♦ ♦♦♣ r

♦r t ♣r♠trs ♦ t s♥♣t ♣t♦r s♥ r ♥ ②

Gdet = GampKθ−C

Kfb =Kθ−CDcVDC

2

Jz

r Gamp s t ♠♣r ♥ Dc t t② ② ♣r♠tr VDC t rr♥

♦t ♣♣ t♦ t s②st♠ ♥ Jz t ♠♦♠♥t ♦ ♥rt ♦ t strtr

s♦♥ tr♠ ♥ qt♦♥ s q♥t t♦ t tr s♣r♥ ♦♥t

tr ♠♦ ♦ r♦tt♦♥ s♥s♦r s♥s

♥tr♦ ♥ ♥ t s ♥ ② t ♦♦♥ ①♣rss♦♥

Kel = 4a22C02VDC2

t s ♥trst♥ t♦ ♥♦t tt ♥ t♦ r s♥♥ s♥♣t♦r

♦♥rt♦♥ ♦r♥ ♣r♥♣② t ♥ ♥ t tr♦ ♦r♣ W0

♣♦s♥ t s ♥tr♦ tr♦ t ♥r t♣s s ♦♠♣♦♥♥t ♥

♠♥♠③ ② ♥rs♥ t ♥♦r♠ ♣ h ♥ ts s t r♦tt♦♥ s♥s♦r ♦rs

t ♣r s♥ ♣t♦rs trs ♦♥ ♥ ♠♥♠③ t ♥♦r♠ ♣ h ts

rt♥ ②r s♥ ♠①♥ s♥ ♣t♦rs ♥ ♣ ♦s♥ ♣t♦rs

♣♦s♥ ♣t♦rs

s♠ st② s ♣r♦r♠ t♦ t t tr ♣r♠trs ♦ ♣

♦s♥ ♣t♦r s♥ ♣rs♥t ♥ r ♦♠tr ♣r♠trs

rtr③♥ ts s♥ ♥ tr♠s ♦ tr ♣r♦♣rts r s♠♠r③ ♥ t

❱♠ ♣r♠ttt② ε0

trtr t♥ss T

tr♦ sr W0

♦r♠ ♣ h

♦♠tr ♣r♠trs rtr③♥ t tr ♣r♦♣rts ♦ t♣♦s♥ s♥

♣t♥ ①♣rss♦♥ rst♥ r♦♠ Nc ♦♥♣t tr♦s s ♥ ②

CA = Nc

∫ R2

R1

ε0T

h− rθdr =

Ncε0T

θ(ln(R2θ + h)− ln(R1θ + h))

r R2 = R1 + W0 t W0 t ♦r♣ t♥ t ♠♦♥ ♥ t ①

tr♦ ②♦r ①♣♥s♦♥ ♦ qt♦♥ s

CA ≈ Ncε0TW0

h

(1− (2R1 +W0)θ

2h+

(3R12 + 3R1W0 +W0

2)θ2

3h2

)

r♦ t ♣♣r♦①♠t♦♥ ♥ ♥ qt♦♥ ♥ s♥ t s♠ ♠t♦

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

r tr ♠♦ ♦r ♣♦s♥ ♣t♦rs

♦♦② s ♦r t s♥♦♠ s♥ ♥ t ♣r♦s st♦♥ ♦♥ ♥ t t

tr ♣r♠trs ♦ t ♣♦s♥ ♣t♦r s♥

C0 = Ncε0TW0

h

Kθ−C = C0

((2R1 +W0)

h

)

Gdet = GampKθ−C

Kfb =Kθ−CDcVDC

2

Jz

Kel = 4C0VDC2 (3R1

2 + 3R1W0 +W02)

3h2

s s♥ ♦♥rt♦♥ s s ♦♥ ♣r ♣♦s♥ tr♦s ♥ t ♣

t♥ s st ② t tr♦ ♠♥s♦♥s s rst ♦♥ s t♦ ♣rr ♦♥

tr♦s t♦ ♦t♥ ♥rs ♣t♥ s

tr ♠♦ ♦ r♦tt♦♥ s♥s♦r s♥s

♠t♦♥ ♦ t ♥♦♠♥ ♣t♥

♣r♣t ♣♣r♦①♠t♦♥ s s t♦ t t tr ♣r♦♣rts

♦ t t♦ r♦tt♦♥ s♥s♦r ♦♥rt♦♥s ♥ ts st♦♥ s♠t♦♥s r

♦♥ s♥ t♣②ss © t♦ t ts ss♠♣t♦♥ ② ♦♠♣r♥ t

s♠t♦♥ ♦ t ♥♦♠♥ ♣t♥ t t ♥②t qt♦♥s r♦♠ q

t♦♥s ♥ s ♦ t ♦♠tr ♣r♠trs s ♦r t

t♦♥s r ♣rs♥t ♥ t

♥♦♠ s♥ ❱ ❯♥t

T [µm]

W0 [µm]

Wf [µm]

d [µm]

h [µm]

Nf

Nc

♣♦s♥ s♥ ❱ ❯♥t

T [µm]

W0 [µm]

h [µm]

Nc

❱s ♦ t ♦♠tr ♣r♠trs s ♦r t♦♥s

♥♦♠♥ ♣t♥ s r s♠♠r③ ♥ t ♥ s♦ tt t

♣♦s♥ ♠♦ t t s♠t rs tr s ♥ ♠♣♦rt♥t r♥

♦r t s♥♦♠ ♠♦ s ♥ ①♣♥ ② t ♥♥ ♦ t r♥♥

s tt rt ♥ ♠t♦♥ ♦ tr rs t tr♦ ①tr♠ts

♥ ♥ t ♣♦s♥ s t ♣t♦r s r r ♥ t

tr♦stt ♥r② s tr♠♥ ② t ♠♦♥t ♦ tr rs ♠t

t♥ t tr♦s ♥ t ♦♥trr② ♥ t s♥♦♠ s t tr♦s

s♠ ♠♥s♦♥s ♥ t r♥♥ s rr ♥♥ ♦r♥ t♦

r ♥ ♥ ♦sr ♥ ts ♣♦t tt ♥ ♠♣♦rt♥t tr♦stt ♥r②

s ♠t t ♥r ♥s s ♥♦t ♥ ♦♠♣r t♦ t t

tr♦stt ♥r② t♥ ♥rs

s ♥ r♠r ♦♥ ♥♦♠♥ ♣t♥ t ♣ ♣r♠trs d ♥ h r s♥

st t♦ ♦rt♥ r♥ ♣r♦ss♥ s t♦ ♦♣rt s② t t

♦♥ s t♦ s♥ ♣r♦t♦t②♣s t rr ♥♦♠♥ ♣t♥ t♥ t ♦♥ ♥

♥ t t♥ ♦♥str♥ts r♦♠ t

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

s♥ s C0 [F ] ♥②t C0 [F ] t r♥

♥♦♠ 3× 10−13 4.2× 10−13 %

♣♦s♥ 1.05× 10−13 1.15× 10−13 %

♦♠♣rt t ♦ t ♥♦♠♥ ♣t♥ t t ♥ t ♥②t ♦r♠s

r ♠t♦♥ ♦ t tr♦stt ♥r② ♦r ♦♠ strtr

♥♥ ♦ ♥♦♥♥rts ♦♥ t rs♣♦♥s

♥♥ ♦ ♥♦♥♥rts ♦♥ t r

s♣♦♥s

r♦♦t t t s♥ ♦ t r♦tt♦♥ s♥s♦r r♥t ♣♣r♦①♠t♦♥s

♥ ♠ ♦♥sr♥ s♠ ♠♣ts θ ♦ t ss♠ ♠ss ♦r ♥st♥

ts ♦ s t♦ sts s♠♣ ①♣rss♦♥s ♦ t ♣t♥ s s♦♥ ♥

qt♦♥s ♥ rst♥ ♥ rst ♦rr ①♣rss♦♥s ♦ t tr♦stt

♠♦♠♥ts ♥ t s②st♠ s ♦♣rt ♥ ♦s♦♦♣ ♠♦ t ♣♣r♦①♠t♦♥s

♠ r rs♦♥ ♦r ♦♣♥♦♦♣ ♦♣rt♦♥s ♦ t r♦tt♦♥ s♥s♦r ♠②

♥♥ ② ♥♦♥♥r tr♠s s t ♥♦t ♥ st♦♥

①♣r♠♥t② ♥♦♥♥r ♦r ♦ t r♦tt♦♥ s♥s♦r ♠② ♦r t

rs♦♥♥ ♣ st♦rt ♥ ♦r ♦r r rq♥② ♦r str♦♥ ♠♣ts ♦

t ♣r♦♦ ♠ss ♥ ♦♣♥♦♦♣ ♠♦ ♥ t s ♣♦ss t♦ ♦sr t ♥♥

♦ t ♥♦♥♥r s♣r♥ ♦♥t ♦♣ ♥ qt♦♥ s s r

♦rr tr♠s ♦ θ ♥ t tr♦stt ♠♦♠♥t ①♣rss♦♥s ♥ ♦rr t♦ ♥rst♥

t ♥♦♥♥r ♦r ♦ t r♦tt♦♥ s♥s♦r ♦♥ s♦ ①♣♥ t ♥♦♥♥r

tr♠s t♦ r ♦rrs ♥ st② t ♦♥sq♥s ♥ t ♠♥ ♥♦♥♥r

♦♥ts r str♦♥r t♥ t tr ♥♦♥♥r ♦♥s ♥ rs

♥ t ♦♦s ♥♦♥♥r ♠♦ ♦ t r♦tt♦♥ s♥s♦r s r ② ♦♥sr

♥ ♥r ♥♦♥♥r tr♠s ♥ ♥ s♦♥ st♣ t ♥r tr♠s r r♣

② t t ♦♥st♥ts ♦ r♦tt♦♥ s♥s♦r s♥s t♦ ♣rt t ♦♠♥♥t ♥♦♥

♥r ♠♥s♠ ♦r ♦♥rt♦♥ s♥♦♠ ♦r ♣♦s♥ tr♦s

♦♥♥r ♠♦ ♦ t r♦tt♦♥ s♥s♦r

t s ♦♥sr tt ♥r ♥♦♥♥r tr♠s ♠♦② t ♠♦t♦♥ qt♦♥ s

♦♦s

Jzd2θ

dt2+D

dθ

dt+Kθ +K1θ

2 +K2θ3 =Mel0

ss♠♥ ♥♠♣ ♥ ♥♦r rt♦♥s r♠ ② stt♥ D = 0 ♥Mel0 =

0 t qr♠ qt♦♥ ♥ ①♣rss ♥ ♥♦♥ ♦r♠

d2θ

dt2+ ω0

2θ + αεθ2 + βε2θ3 = 0 ε > 0

♥ t ♦♦♥ ♦♣♠♥t s ♥stts ♠t♦ ❬❪ s ♣r

trt♦♥ ♥②ss r♦♥ ♥r ♦st♦♥s t t ♥r rq♥② ω0

strt② s t♦ ♣r♦♠♣t rt♦♥s♣ ♥t♦ t ♣♣r♦①♠t s♦t♦♥

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♦ t ♥♦♥♥r qt♦♥ rst ♦♥ s t♦ ♠ ♥ ♦ rs s ♦♦s

τ = ωt r ω = ω0 + εω1 + ε2ω2 +©(ε3)

①t ①♣♥ θ ♥ ♣♦r srs ♦ ε

θ(τ) = θ0(τ) + εθ1(τ) + ε2θ2(τ) +©(ε3)

sttt♥ qt♦♥s ♥ t♦ ♦♥ ♥ ♥ t ♦♦♥ q

t♦♥ s♦rt t rs♣t t♦ t ♣♦rs ♦ ε

[ω0

2

(θ0 +

d2θ0∂τ 2

)]+

ε

[ω0

2

(θ1 +

d2θ1∂τ 2

)+ 2ω0ω1

d2θ0∂τ 2

+ αθ02

]+

ε2[ω0

2

(θ2 +

d2θ2∂τ 2

)+ 2ω0ω1

d2θ1∂τ 2

+d2θ0∂τ 2

(ω1

2 + 2ω0ω2

)+ 2αθ0θ1 + βθ0

3

]

+©(ε3)= 0

♦ sts ♦r ♥② ε 6= 0 t tr♠s ♥s rts ♥ qt♦♥ t♦

♥s s rsts ♥

θ0 = A cos(τ)

❲r s ♥ ♥trt♦♥ ♦♥st♥t r♣rs♥t♥ ♦st♦♥ ♠♣t sttt

♥ qt♦♥ t♦ s

ω02

(θ1 +

d2θ1∂τ 2

)= 2ω0ω1A cos(τ)− α

2A2(1 + cos(2τ))

♣rt♣t♦♥ ♦ t tr♠ ♣r♦♣♦rt♦♥ t♦ cos(τ) ♥ t rt ♥ s ♦

qt♦♥ ♥rts tr♠ ♥ τ sin(τ) ♥ t ♣rtr s♦t♦♥ ♦ θ1 ts

s s♦ sr tr♠ ♥ t ♥s t♦ ♥s ♥ ♦rr t♦ ♣ t s♦t♦♥

♣r♦ s ♦♥sq♥ ♦♥ s♦ r♠♦ t sr tr♠ ② stt♥ ω1 = 0

♥② qt♦♥ ♥ s♦ s ♦♦s

θ1(τ) =αA2

3ω02cos(τ) +

αA2

6ω02(cos(2τ)− 3)

♥♥ ♦ ♥♦♥♥rts ♦♥ t rs♣♦♥s

r♦♠ qt♦♥ rst ♦rr ♣♣r♦①♠t♦♥ ♦ θ s♦s t ♣♣rt♦♥ ♦ t♦

t♦♥ rq♥② ♦♠♣♦♥♥ts tr♠ ♥ r r♠♦♥ tr♠ t t

t ♦st♦♥ rq♥②

s♠ ♣r♦ss ♥ r♣t ② ssttt♥ qt♦♥s ♥

t♦ r♠♦ ♦ sr tr♠s s t ①♣rss♦♥ ♦ ω2 s s

ω2 =A2

24ω03

(9βω0

2 + 10α2)

♥② t ♠♦ ♥r rq♥② ♥t♦♥ t♦ ♥♦♥♥r tr♠s s ♥

②

ω = ω0 + ε2ω2 = ω0 + γA2

r t ♦♥t γ ♣♥s ♦♥ t ♦♥ts K K1 ♥ K2 ♥ ♥ q

t♦♥ ♥ ①♣rss ②

γ =3

8

K2

Kω0 −

5

12

K12

K2ω0

♥trst♥ ♦♠♠♥ts ♥ ♠ r♦♠ qt♦♥s ♥ ♥

♣♥♥ ♦♥ t s♥ ♦ γ t ♥r rq♥② ♦ t s②st♠ ♥ st t♦

♦r ♦r r rq♥② ♦r rt♦♥ ♠♣t s s♦♥ ♥ r t

♦ ♥trst♥ t♦ t t ♥♦♥♥r tr♠s ♦ t r♦tt♦♥ s♥s♦r ♦t

tr ♥ ♠♥ ♥ t t ♦♥st♥t γ t♦ tr♠♥ ♥

rt♦♥ t rs♦♥♥ ♣ s st♦rt ♥ t♥ ♦♥♥ ♦♥ t ♦♠♥♥t

♥♦♥♥rt② s♦r s s ♣r♦r♠ ♥ t ♥①t st♦♥

r strt♦♥ ♦ t rs♦♥♥ ♣ st t♦ ♥♦♥♥r ♠♥s♠s♥tr♦ tr♦ t ♦♥t γ t γ > 0 t γ < 0 r♥♥ r rs r ♦t♥ ♦r s♠ ♠♠ ♥ str♦♥ rt♦♥ ♠♣t Ars♣t②

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

Prt♦♥ ♦ t ♦♠♥♥t ♥♦♥♥r ♠♥s♠ ♦

t r♦tt♦♥ s♥s♦r ♦♥rt♦♥s

♥ ts st♦♥ s t tr ♦r♠ t ♥ st♦♥s ♥

t t srs ①♣♥s♦♥ t♦ t tr ♦rr ♥ θ ♦♥sr♥ s♥s

s♥ ♦♠ tr♦s t rst ♦rr ♦♥t Kec1 s s t s♦♥ ♦rr

♥ t tr ♦rr tr♠s Kec2 ♥ Kec3 rs♣t② r ♥ s ♦♦s

Kec1 =C02VDC

2

3

16Lp2Nf

2 − 4Lp (Lp − 6R1 )Nf + 12R12

h2

Kec2 = 12C02VDC2 (Lp Nf + R1 )

((Nf

2 − 12Nf

)Lp

2 + Lp Nf R1 + 12R1

2)

h3

Kec3 =C02VDC

2

15h4[(384Nf

4 − 288Nf3 + 16Nf

2 + 8Nf

)Lp

4

+960

(Nf −

1

2

)Nf

2R1 Lp3 + 960Nf

(Nf −

1

4

)R1

2Lp2

+480Lp Nf R13 + 120R1

4]

♦♥sr♥ s♥s s♥ ♣♦s♥ tr♦s t rst ♦rr ♦♥tKeg1 s

s t s♦♥ ♦rr ♥ t tr ♦rr tr♠s Keg2 ♥ Keg3 rs♣t②

r ♥ s ♦♦s

Keg1 =4C0VDC

2

3

(3R1

2 + 3R1W0 +W02)

h2

Keg2 =3C0VDC

2

2

(2R1

2 + 2R1W0 +W02)(W0 + 2R1)

h3

Keg3 =8C0VDC

2

5

(5R1

4 + 10R13W0 + 10R1

2W02 + 5R1W0

3 +W04)

h4

♥ t ♠♥ s♣r♥ tr♠s tr♠♥ ♥ st♦♥ ♦♥ ♥ rt

t rst ♦rr ♥ t tr ♦rr tr♠s Km ♥ Km3 rs♣t② s ♦♦s

Km =4

3

EyTW3b (L

2b + 3LbRa + 3R2

a)

L3b

Km3 =4

225

EyTWb(17L2b + 33LbRa + 18R2

a)(Lb2 + 9LbRa + 9R2

a)

L3b

♥♥ ♦ ♥♦♥♥rts ♦♥ t rs♣♦♥s

♥② ♦♥ ♥ t t ♦♥st♥ts K K1 ♥ K2 s t♦ t γ ♥

qt♦♥

K = Km−Ke1

K1 = −Ke2

K2 = Km3 −Ke3

rKe1 = Kec1 ♦rKeg1 Ke2 = Kec2 ♦rKeg2 Ke3 = Kec3 ♦rKeg3 ♣♥♥

♦♥ t s♥ s ♦♥sr

♥ t ♦♦s t t♦ ♦♥rt♦♥s ♦ t r♦tt♦♥ s♥s♦r s♥♦♠

♣t♦r ♥ ♣♦s♥ ♣t♦r r ♥②③

♥♦♠ ♣t♦rs

♥ s ♦ r ♥♦r♠ ♣ h t t ♥r t♣s t ♥♦♥♥r ♦r s

♦♥② ♥ ② t ♠♥ tr♠ Km3 s♥ Kec1 = Kec2 = Kec3 = 0 ♥

qt♦♥ s ♦♥sq♥ t rs♦♥♥ ♣ s♦ st t♦ t ♣♣r

rq♥s ♦r ♦♥ ♦♥srs t ♦♠tr ♣r♠trs s♦♥ ♥ ♣

♣♥① r t ♥♦r♠ ♣ h s t s♠ s t tr ♣ d t

♥♦♥♥r tr tr♠s r ♥♦ ♠♦r ♥ ♦r♦r t ♦♥t γ ♦

qt♦♥ ♦♠s ♥t ♠♣②♥ st ♦ t rs♦♥♥ ♣ t♦ t

♦r rq♥s

♣♦s♥ ♣t♦rs

♥ t ♣r ♣♦s♥ s t ♥♦♥♥r tr tr♠s r ♦♠♥♥t ♦r

t ♠♥ ♦♥ ♦r ♥st♥ ♦♥sr♥ t ♦♠tr ♣r♠trs s♦♥

♥ ♣♣♥① t ♦♥t γ s ♥t ts t rsts ♥ st ♦ t rs

♦♥♥ ♣ t♦ t ♦r rq♥s

s ♣rt ♦rs ♦♥r♠ ♥ st♦♥

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♣t♠③t♦♥ ♦ r♦tt♦♥ s♥s♦r s♥s

♥ t ♦♦♥ st♦♥ t s♥ ♦r♠ ♦t♥ tr♦ t r♥t

♥②ss r ♦♠♥ t♦ ♥ ♥ ♦♣t♠ strtr t t st ♣r♦r♠♥s

♠t♥ t t♥ ♦♥str♥ts t ♥ t ♥ ♦rr t♦ t

t♦rt rs♦t♦♥ ♥ s♥stt② ♦ r♦tt♦♥ s♥s♦rs ♣r♦t♦t②♣s ♦♥ s♦

♦♥sr ♦♣rt♦♥ ♣r♠trs ♠sr ♦♥ t tr♦♥s tt s t♦

♦♥tr♦ t s♥st ♠♥t ♦s ♣r♠trs r ♥ ♥ ts

♥ ♥ tr s ♥ ♦♥ ♥ t

♦r t t♦♥ ♦ t r♦tt♦♥ ♣r♦r♠♥s ♦s ♦♥ ♦r

♦t♣t ♣r♠trs t ♥♦s ♦♦r NF t ♠♥ s♥stt② Gmech t

tt♦r s♥stt② Gdet ♥ t ♥♦♠♥ ♣t♥ C0 rs♣t② ♥

② t ♦♦♥ ①♣rss♦♥s

NF =

√√√√(G2

nVn2 + 4kBTRdet

)

(GmechGdet)2+

4kBTω0

JzQ+ 4kBTRdacKfb

2

Gmech =1

ω02 − Kel

Jz

Gdet =2VDCKθ−C

Cf

C0 = Nc (2Nf − 1)

[ε0TW0

d+ε0TWf

h

]

︸ ︷︷ ︸qt♦♥

♦r Ncε0TW0

h︸ ︷︷ ︸qt♦♥

♣t♦♥s Pr♠tr ♥♠ ❱

tr♦♥s s♣♣② ♦t VDC [V ]

t②② ♣r♠tr Dc

♠♣r ♥♦s ♥♣t Vn nV/√Hz

♠♣r ♥♦s rsst♦r Rdet MΩ

♥♦s rsst♦r Rdac kΩ

Prst ♣t♥

♦ t

Cp pF

sr ♣r♠trs ♦r ♦♣rt♦♥s t t tr♦♥s

♣t♠③t♦♥ ♦ r♦tt♦♥ s♥s♦r s♥s

r ♦ t r♦tt♦♥ s♥s♦r s♥st ♠♥t t ♥♦r rs♥ t s♥st ♠♥t s③ r ① ② t ♣r♦ss

t② ♥ t ♦♣t♠③t♦♥ s t ♦♥trt♥ r♦s ♦ t r♥t

s♥ ♠♥ts ♠♥ ♥ tr t t ♣ s③ ① t mm

♥ ♦♥sr♥ ① ♥♦r rs t µm ♦r tr ♦♥♥ s r

♦r ♥st♥ ② ♦sr♥ qt♦♥ ♦♥ s♦ rs t st

♥ss ♦♥t ♥ ♥rs t strtr ♥rt t t ♣ ♦ ♦♥r s♣r♥

♥t Lb ♥ r r♥ t WR s♦ tt t ♥♦s ♦♦r s ♠♥♠③

t ♠♥ s♥stt② s ♠①♠③ ♦r ts r t tr

tt♦♥ s♥ Kθ−C ♣♥s ♦♥ t tr♦ ♥t Lc

♦♣t♠③t♦♥ ♣r♦ss ♣r♦r♠ s ♦♦s t r♥ t ♥ ♠♥

t♥ t s♣ s t♥ µm ♥ µm t♥ t r②♥ ♣r♠tr

t ♠ ♥t r♥♥ t♥ µm ♥ µm tr♦

♥t Lc s t♦♠t② ♣t s♦ tt t t♦t s③ s ① t µm

♥♦♠ s♥s

s st♦♥ s t t ♦♣t♠③t♦♥ ♦ s♥♦♠ s♥s ♥ rst

st♣ ♣r s♥♣t♦r s st ② t♥ r ♥♦r♠ ♣ t t ♥r

t♣ t♦ ♦ ♥♦♥♥r ts ♥ ♥ s♦♥ st♣ ②r s♥ s st

♠①♥ s♥ ♣t♦rs ♥ ♣ ♦s♥ ♣t♦rs

Pr s♥♣t ♣t♦rs

s st♦♥ s t t ♦♣t♠③t♦♥ ♦ s♥ t ♣r s♥♣t

♣t♦rs ♥ ♦tr ♦rs t ♥r t♣s r ♣♦st♦♥ r r♦♠ t ① ♦♠

s♦ tt tr♦stt ts r ♥tr♦ ♦♥② tr♦ tr s ♦ ♥r

tr♦s ♦r♥ t♦ t ♣r♠trs ♥ t ♦♥st♥ts ♥ ♥ st♦♥

t s ♦♥sr tt t ♥♦r♠ ♣ h s st t ♠r♦♥s rs t tr ♣

d s st t ♠r♦♥s r♥ t s ① t t♦ s µm ♥

µm rs t s♣r♥ ♥t rs t♥ µm ♥ µm ♦ ♥sr t

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♦♥str♥t ♦♥ t ♣ s③ t ♥♠r ♦ ♥rs Nf ♥ ♦♠ s ♣t t

st♣

rt♦♥s ♦ t ♦t♣t ♣r♠trs t rs♣t t♦ t s♣r♥ ♥t r

s♦♥ ♥ r t s ♥♦t sr♣rs t♦ ♦sr ♦♣♣♦st rt♦♥s ♦ t

♠♥ s♥stt② ♥ t tr s♥stt② t rs♣t t♦ Lb ♦r♦r

♦♥ ♥ ♥♦t tt t ♥♦s ♦♦r s ♦r s ♦r r r♥ ♦♥ t

st♣r s♦♣s ♦r ♣t♥ ♥ tr s♥stt② ♦ ♦♣rt t t ♦♥tr♦

tr♦♥s ♦♦s t♦ s♥s r♣rs♥t ② t ♥s ♥ ♥ t rs

♣r♦r♠♥ s r♦♠ ts t♦ s♥s ♥ s♥ ♥ t

♥ ts s♥ ♥②ss ♦s♥ strtrs ♦r♥ ♥ ♣r s♥

♠♦ ♥ ♦tr ♦rs t tr ♣r♠trs r ♣rt② ♥r s♥ t

♦♥t Kθ−C s ♦♥st♥t s st♦♥ ♦r t ♦ ♥trst♥ t♦

st② t ♥♥ ♦ ♥r t♣s ♥ t② t ♦sr t♦ t ♦♣♣♦st ① ♦♠

tr♦ s ♣♦♥t s st ♥ t ♥①t st♦♥

Pr♠tr ♥♠ s♥ s♥

C0 [pF ]

Gmech [µrad/(mrad/s2)] 0.54× 10−4 0.94× 10−4

Gdet [mV/µrad]

NF [mrad/s2/√(Hz)]

Pr♦r♠♥ ♦ ♣r s♥ ♦♠s

♣t♠③t♦♥ ♦ r♦tt♦♥ s♥s♦r s♥s

r ♥②ss ♦ ♣r s♥ ♦♠s

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

②r ♣t♦rs

♦r t st② ♦ t ②r s ♠♦② t ♣r s♥ s♥s ② st

t♥ t ♥♦r♠ ♣ ♠♥s♦♥ h t ♠r♦♥s rst♥ r s s♦♥ ♥

r ♥ s♦ ♥♦t tt t t ♦♣t♠♠ ♣♦♥t ♦t♥ ♦r Lb =

µm t ♦r ♣r♦r♠♥s r s♥♥t② ♥rs s ♣rs♥t ♥ t

♥ t ♥♦s ♦♦r s r ② t♦r ♦ t ♠♥ ♥ t

tr s♥stt② r ♥rs s ♥ ①♣♥ ② t ♥♥ ♦ t

tr♦stt s♣r♥ ♦♥ t ②♥♠ ♦r ♦ t strtr ♥ ♦♥ s♦

r♠♠r tt ♣♦s♥ ♣t♦rs rt ♥t tr♦stt s♣r♥

♦♥trts t ♠♥ s♣r♥ ♥ rst♥ ♥ rr ♠♥ s♥stt②

ts ♦r ♥♦s ♦♦r s st♦♥ ♥ t ♦r t♦ t s♠

♠♥s♦♥s ♦ ♥r tr♦s ts tr♦stt s♣r♥ s t♦♦ t♦ ♥ ♦♠

♣t② t ♠♥ s♣r♥ ♦r ♥ ♠♦r ♣r♦r♠♥s

♥ s♣t ♦ ♥r ♦r ♣r s♥♣t♦r s♥s s♦ ♦r ♣r♦r

♠♥s t♥ ②r s♥s ♥ tr♠s ♦ s♥stt② ♥ rs♦t♦♥ s s ①

♣♥ ② t ♥♥ ♦ t tr♦stt s♣r♥ t ♥tr♦ ② ♣♦s♥

tr♦s ♦r ts ♥t s♣r♥ tr♥s ♦t t♦ t♦♦ ♦r ♣r

t ♠t♥ t t ♠♥ s♣r♥ ♦♥t ♥ ♥♦♥♥r ts r

str♦♥r ♥ t ♣r ♣♦s♥ ♦♥rt♦♥ ♦♥ s♦ ①♣t ttr ♣r♦r

♠♥s ♦r ts s s st ♥ t ♥①t st♦♥

Pr♠tr ♥♠ s♥

C0 [pF ]

Gmech [µrad/(mrad/s2)] 4× 10−4

Gdet [mV/µrad]

NF [mrad/s2/√(Hz)]

Pr♦r♠♥ ♦ ②r s♥ ♦♠s

♣t♠③t♦♥ ♦ r♦tt♦♥ s♥s♦r s♥s

r ♥②ss ♦ ②r s♥ ♦♠s

♣♦s♥ s♥s

s st♦♥ s t t ♦♣t♠③t♦♥ ♦ s♥ t ♣♦s♥ ♣

t♦rs ♦r♥ t♦ t ♣r♠trs ♥ t ♦♥st♥ts s ♥ t st♦♥ t

s ♦♥sr tt t ♣ t♥ ♠♦♥ ♥ ① tr♦s s st t ♠r♦♥s

r t r♥ t s ① t t♦ s♣ s µm ♥ µm t

♠ ♥t rs t♥ µm ♥ µm

rt♦♥s ♦ t ♦t♣t ♣r♠trs ♦ ♥trst t rs♣t t♦ Lb r s♦♥

♥ r ♥ ♥ ♥♦t ♥ ♥trst♥ ♦r ♦ t ♥♦s ♦♦r s

♦ ♠♥♠♠ t t s♠ s♣♦t s sr♣ ♣ ♦r t ♠♥ s♥st

t② s s♣♦t ♦rrs♣♦♥s t♦ t t ♠♥t♦♥ ♥ t s♥ ♣t♦r s

r t ♠t♥ t♥ t tr♦stt s♣r♥ ♥ t ♠♥ s♣r♥ s

♣rt ♥ t♦ ♥ ♥♥t ♠♥ ♥ s Gmech ①♣rss♦♥ ♥ t

s ♣ ♦ t ♠♥ s♥stt② s t♦ ♠♥♠♠ ♦ t ♥♦s

♦♦r ♦r♥ t♦ qt♦♥ s♥ t tt♦♥ ♥♦s ♦ t r ♠♣r

s s♥♥t② r ♥② ♦♥ ♥ ♥♦t tt ♥ ♦ t r♥ t

♠s t s♣♦t st ♦♣t♠♠ s♥s r ♥t ♥ tr ♣r♦r♠♥s

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

r ♣rs♥t ♥ t

Pr♠tr ♥♠ s♥ s♥

C0 [pF ]

Gmech [µrad/(mrad/s2)] 2.1× 10−3 6.8× 10−3

Gdet [mV/µrad]

NF [mrad/s2/√

(Hz)]

Pr♦r♠♥ ♦ ♣♦s♥ ♣t♦rs

s ①♣t t ♠t♥ ♦ t tr♦stt s♣r♥ t t ♠♥ ♦♥

♣r♦s t st s♥r♦ t♦ s♥ s♥stt② rs♦t♦♥ r♦tt♦♥ s♥

s♦rs ♥ t ♥♦s ♦♦r s t♥ t♠s ttr t♥ ♦r ♣r s♥♣t♦r

s♥s ♥ t s♥stt② ♠♥ ♥ tr s s♥♥t② ♠♣r♦

♦♥sr♥ t ♦♠tr ♣r♠trs ♦ t r♥t s♥s st ♦♥

s t♦ ♠ sr tt t rst♥ s②st♠s r ♦♣r t t ♣r♦

s s ② ♦ s♠t♦♥ ♦ t s♥s♦r ♦♦♣ s t♦ ♣r♦r♠ t♦

t r♦tt♦♥ s♥s♦r s♥s r ♦♥tr♦ ② t tr♦♥s s s t ♠

♦ t ♥①t st♦♥

♣t♠③t♦♥ ♦ r♦tt♦♥ s♥s♦r s♥s

r ♥②ss ♦ ♣♦s♥ ♣t♦rs

♣tr s♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♦s♦♦♣ s♠t♦♥ ♦ t ♦♣t♠♠ s♥s ♥

t

♠♥ ♥tr s ♥ ♦♣ t♦ s♠t t r♦tt♦♥ s♥s♦r t

ts ♦♥tr♦ ♦♦♣ r s♥s ♣rs♥t ♥ t st♦♥s ♥ r ♥

t ♥t♦ t s♠t♦r ♦r ♣rs② t ♣r s♥ s♥ t

②r s♥ s♥ ♥ ♣♦s♥ s♥ ♦t♣t tstr♠

♥rt ② t s♠t tr♦♥s s t♥ ♣r♦ss ② t♥ ts ♦♥s

P♦r ♣tr ♥st② P rs♣♦♥s s s♦♥ ♥ r t ♥♦ ①tr

♥ ①tt♦♥ ♣♣ t ♠♣t ♥ t r♣ s ①♣rss ♥ dB ♦ V/√Hz

♥ ♥ ♥♦t t ♥ ♦ ♥♦s ♥ ♦ rq♥② ♥t t♥

Hz ♥ Hz ♥ r ♥♦s rs♥ tr kHz s r ♥♦s

tr kHz s t rst ♦ t Σ∆ ♠♦t♦♥ s st♦♥ ♥♦s

♥ t ♦ rq♥② ♥t s t ♥♦s ♦♦r ♦r ♥ s♥ ♥ ♥

r ♥♦s t ♦r t s♥ ♦r t s♥ ♥

♦r t s♥ ♥ ♥trst♥ ♦srt♦♥ s t ♣rs♥ ♦ ♥♦t ♥ t

s♥ s♥s r♥ t strtr rs♦♥♥ s♣♦t ♥ t ♣♦s♥ s♥

ts ♥♦t ♦s ♥♦t ♣♣r ♥ t P ♣♦t ♠♥♥ tt t ♦♥tr♦ ♦♦♣ ♥

t s②st♠ rs♦♥♥ s s ♦r♥ t st rs♦t♦♥

♦ ♦♥ ts ♣tr ♦♥ ♥ s② tt s♥s t ♣♦s♥ ♣

t♦rs r ♠♦r st ♦r ♣r♦r♠♥ s♥stt② r♦tt♦♥ s♥s♦r

♠t♥ t♥ ♠♥ s♣r♥ ♥ tr♦stt s♣r♥ s t♦ t ♣♣r

♥ ♦ ♥ ♦♣t♠③t♦♥ s♣♦t r t ♠♥ s♥stt② s ♠①♠③

t ♥♦s ♦♦r s ♠♥♠③ ♦ t ts stt♠♥t t s♥s st ♥

ts ♣tr ♣r♦ss ♥ ♠sr t ♦r ♦♥tr♦ tr♦♥s ♦r s

♦ rt② t s♥s st r r♥♠ t t ♦♦♥ rt♦♥s

s♥ ♦r s♥ ♦♠s

s♥ ♦r ②r ♦♠s

s♥ ♦r ♣♦s♥ tr♦s

♦♠tr ♣r♠trs ♦ t tr s♥s ♥ ♦♥ ♥ ♣♣♥s

♥

♣t♠③t♦♥ ♦ r♦tt♦♥ s♥s♦r s♥s

r ♠t P ♦ t tr s♥s st ♦♣ s♥ s♥ ♦tt♦♠ s♥

s ♣ s ♥t♥t♦♥② t ♥

♣tr

sr♠♥ts ♥ rtr③t♦♥

♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

Pr♦ss♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♣t♥ s ❱♦t ❱ rtr③t♦♥

♣♥♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

t♣ ♦r t ♦♣♥♦♦♣ rtr③t♦♥

s♦♥♥ rq♥② ♥ t② t♦r ♠sr♠♥t

♦♥♥r ♦r ♥ ♦♣♥♦♦♣ ♠♦

♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

tr♦stt s♣r♥ rtr③t♦♥

①♣r♠♥t st♣ ♦r ♣r♦r♠♥ rtr③t♦♥

①♣r♠♥t ♣r♦r♠♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♦♠♣rs♦♥ t ♦tr r♦tt♦♥ s♥s♦rs

♦♣ r♦♠trs ♦r ♥r ♠sr♠♥ts

tr♦♠ s♥s♦r ♥t

♠♠r② t

♦♥s♦♥ ♦♥ ①♣r♠♥ts

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♣r♦s ♣tr s t♦ ♦♣t♠♠ strtrs tt ♥ t♦ ♣r♦ss

♦r ①♣r♠♥t rtr③t♦♥ r strtrs r ♥t

Pr s♥♦♠ s♥

②r♦♠ s♥

Pr ♣♦s♥ s♥

♥ ts ♣tr s♥s ♥ r rtr③ ♥ ts ♥ ①♣r

♠♥t ♠sr♠♥ts r ♦♠♣r t♦ t ♥②t sts ♥ ♣tr ♦r

♣rs♥t♥ t ♠sr♠♥ts t ♣r♦ss t③ t♦ ♠♥tr t r♦tt♦♥

s♥s♦r ♣r♦t♦t②♣s s sr ♥ t q♥tt♦♥ ♦ t ♦rt♥ ♦ rt

♣r♠trs s ♦♥ s♥ ♠r♦s♦♣ ♠♥ trrs t rtr③t♦♥ s

♦r♥③ ♥ sr st♣s

rst t ♥♦♠♥ ♣t♥ s s t ♣rst ♣t♥ r ♠

sr ♥ t rt♦♥ ♦ t ♣t♥ t rs♣t t♦ t ♦t s♣♣② s

♥

♥ s♦♥ st♣ ♥ ♦♣♥♦♦♣ rtr③t♦♥ s ♣r♦r♠ ♥ ♦rr t♦ tr

♠♥ t rs♦♥♥ rq♥② ♥ t qt② t♦r ♦ ♦r s♥s srt♦♥s

♦ ♥♦♥♥r ♦rs s♦rt② ♣rs♥t

♥② t ♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r s ♣r♦r♠ ♥

t ①♣r♠♥t ♥♦s ♦♦r ♥ s♥stt② r tr♠♥ ♣r♦r♠♥s ♦

t r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s r s♦ ♦♠♣r t♦ ♦tr r♦tt♦♥ s♥s♥ s②st♠s

♠sr ♥ t s♠ ♦rt♦r② ♦♥t♦♥s

Pr♦ss♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

Pr♦ss♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

s♣ ♣r♦ss ♦♣ s♦ r ♦r r♦♠trs s s ♦r

s♣② t rt♦♥ ss ♦♣t♠③ ♣ t ♦♥ t♥

♣r♦ss ♦ ♦♥♥♥st♦r rs t t♥ss ♦ µm

rst♥ ♣ s③ s × × mm3 ♣r♦ss ♦ s strt ♥ r

trt♥ ①t♦♥ P♦t♦t♦r♣②

t ♣♦st♦♥ P♦t♦t♦r♣②

♣♦r rs

ss ♦♥♥

r r♦tt♦♥ s♥s♦r ♣r♦ss

tr ♣r♦t♦t②♣s t♦ rtr③ r ♠♥tr s ♦♥ ts ♣r♦ss

srt♦♥s ② ♥♥♥ tr♦♥ r♦s♦♣② ♦ t tr strtrs ♥

♦♥ ♥ rs ♥

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

r s♥ ♣r s♥ ♦♠s

r s♥ ②r ♦♠s

r s♥ ♣♦s♥ tr♦s

Pr♦ss♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♥ s♦ r ♦ ♣♦t♥t ♦rt♥ ♦ t ♦♠tr② r♥ t

♣r♦ss ♥ ♥ ♦rt♥ ♥ ♠♦② t rt ♣r♠trs ♦ t s♥

s s t ♠ tWb ♦r t r ♣s d ♥ h t♥ tr♦s ♠♥s♦♥

♥②ss ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s ♥ s♥ ♥ r ♥ ♥ ♥♦t ♥

♦rt♥ ♦ µm ♦♥ ♦t ss ♦ ♥r tr♦s s rst t ♥r

s③ s r ② µm rs t tr ♣ s ♥rs ② µm s♠r

♥②ss ♥ ♣r♦r♠ ♦♥ t s♣r♥ t s ♥ r ② µm

r rt♥ ♦ tr♦s

♦♥s♦♥ tt ♥ r♥ s tt t s♥st ♠♥ts ♦ t r♦t

t♦♥ s♥s♦r s♠r rs♦♥♥ rq♥s t♥ ①♣t ② ♥②t

t♦♥s ♦♥ t ♠♦ tr ♣r♦♣rts ♦r ♥♦♠♥ ♣t♥

♥ ♦r tr♦stt ♠♦♠♥ts r♦♠ ts ♠♥s♦♥ ♥②ss t s ♣♦ss

t♦ ♣t ♦r ♠♦s t ♠♦ ♦♠tr ♣r♦♣rts ♦r ♦♠♣rs♦♥s t

①♣r♠♥t ♠sr♠♥ts

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♣t♥ s ❱♦t ❱ rtr③t♦♥

r strt♦♥ ♦ ❱ rtr③t♦♥ ♦♥ s♥ s

♣t♥♦t rt♦♥s♣ s s ♦♥ t stt rs♣♦♥s ♦ t

t rs♣t t♦ ♦t ♥♣t ♣♦r③ ♦♥② ♦♥ st ♦ tr♦s

r t ss♠ ♠ss r♦tts t♦ t rst♥ tr♦stt ♠♦♠♥ts

♥ t r♦tt♦♥ ♠♣t θ ♥ ♠♣♦rt♥t ♦♥ s t♦ ♦♥sr t ♥♦♥

♥r tr♠s ♠♥ ♥ tr sts ♥ st♦♥ stt

qr♠ ♦ t r♦tt♦♥ s♥s♦r s rtt♥ s

(Km − Ke1

4

)θ − Ke2

4θ2 +

(Km3 −

Ke3

4

)θ3 =

Kθ−C

4VDC

2

♥♦♠♥ ♣t♥ s ♠sr ♦r ♣r♦t♦t②♣ ♥ ♦♠♣r t

t♦rt rsts r♦♠ ts ♥ rsts r ♣rs♥t ♥

t ♥ ♥ ♥♦t tt s♣t t ♦rt♥ ♦ tr♦s t ♠sr

♥♦♠♥ ♣t♥s ♥ ♣t ♦♥sr♥ t t♥ ♦♥str♥t

♦ t ♠♣♦ss rr t♥ pF

♥ t ♦tr ♥ t ❱ ♣r♦ ♦ s♥ s s♦♥ ♥ r

♣s r♣rs♥tt♦♥ ♦ t ♣t♥ ♣♥♥ ♦♥ ♥rs♥ ♦r rs♥

♦t rt♦♥s s ♠ ♦r♦r s♠t♦♥s r ♣r♦r♠ t ♣t

♣r♠trs t ♥t♦ ♦♥t t ♠♦ ♦♠tr② t♦ ♦rt♥

♥ ♥ ♥♦t ♦♦ ♠t♥ t♥ ♠sr♠♥ts ♥ s♠t♦♥s tr

♣t♥ t ♠♦s s ①♣t t s♥ ①♣r♥s ♦♥② ♥r tr

♦r ts t ♦s ♥♦t s♦ ♣♥ t ♥ s♥s ♥

tr ♣♥ ♦ts t ❱ ♥ ❱ rs♣t② ♥♦tr ♦♠♠♥t

♦♥ s♥s ♥ s tt t rs♥ ♦ t tr ♣♥ ♦rs t

r♥t ♦ts ♥② s♥ ♣rs♥ts r♥t ❱ ♣r♦s ♦r ♣♦st

♣t♥ s ❱♦t ❱ rtr③t♦♥

♥ ♥t ♦ts ①♣♥ ② ♥ s②♠♠tr② ♦ t s♥st ♠♥t t♦

t♥ ♣r♦ss

r ♦♠♣rs♦♥ t♥ ❱ ♠sr♠♥ts ♥ s♠t♦♥s ♦♣ ts♥ ♦♣ rt s♥ ♦tt♦♠ s♥

♣t♥s C0 ♠sr ❬pF ❪ C0 t ❬pF ❪ r♥ Cp ❬pF ❪

s♥ %

s♥ %

s♥ %

♦♠♥ ♣t♥ ♥ ♣rst ♣t♥ ♠sr♠♥ts

♥ ♦♥s♦♥ t t♦r♦ ♠♦♥ ♦ t r♦tt♦♥ s♥s♦r ♣r♦r♠ ♥ ♣

tr s rst♥ ♥ ♦♦ tt♥ t♥ ♠sr♠♥ts ♥ s♠t♦♥s ♦ t

stt rs♣♦♥s ♥①t st♣ s t rtr③t♦♥ ♦ t ②

♥♠ ♣r♠trs s t ♦s ♦ t ♥①t st♦♥

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♣♥♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥

s♦r

♥ ts st♦♥ t ♦♣♥♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

s ♣r♦r♠ tr ♣rs♥t♥ t st♣ t tr♦stt tr♥sr ♥t♦♥ ♦

s♥ ♥ s ♠sr t♦ ①trt ts ②♥♠ ♣r♠trs

rs♦♥♥ rq♥② ♥ qt② t♦r

t♣ ♦r t ♦♣♥♦♦♣ rtr③t♦♥

s rtr③t♦♥ s s ♦♥ t ②♥♠ rs♣♦♥s ♦ t tr♦

♥ tr♦stt tt♦♥ strt ♥ r t♦ tr♦s ♥

r ♣♦r③ t ♦t VDC ♥ t t t♦♥ ♦ ♥ ♦t

VAC sin(ωt) t ♦♥ tr♦ ♥ t strt♦♥ ♦ VAC sin(ωt) t t ♦tr

r strt♦♥ ♦ t ♦♣♥♦♦♣ rtr③t♦♥

♦t VDC s st ② t tst tr♦♥s t V ♦ ♦♣rt t

♥ ts ♥r r♠ s♠ ♦t VAC s ♣♣ ♥② ts ①♣r♠♥t ♥

sr ② t ♦♦♥ qt♦♥

θ +ω0

Qθ +

(ω0

2 − Kel

Jz

)θ = Kθ−CVDCVACsin(ωt)

r Kel ♥ Kθ−C r t tr ♣r♠trs sts ♥ st♦♥s ♥

♣♥♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

r Ptr ♦ t ♠ ♠r s ♦r ♦♣♥♦♦♣ rtr③t♦♥

r♦♠ st♦♥ t ♠♥t ♣rssr ♥s t t② s rt

♥♥ ♦♥ t qt② t♦r s s ② t st♣ s ♣t ♥s ♠ ♠

r s ♣rs♥t ♥ r t ♣rssr ♠♦♥t♦r t Pa ♦r mTorr

♦r♥ t♦ qt♦♥ t ♥t s♣r♥ ♦♥st♥t ♥ ♣② ♥ ♠♣♦rt♥t

r♦ ♦r s♥s t ♣♦s♥ t ♥ s♦ r t tr ♠♥ rs

♦♥♥ rq♥② s tr♦stt ♦♥st♥t rtr③ rtr t

s ♥st t ♥②t ♦r♠s ♥ ♥ qt♦♥s ♥

t♦rt tr♦stt s♣r♥ s t♥ strt r♦♠ t ♠♥ s♣r♥ tr♠

♥ ♥ qt♦♥ t♦ t t tr♦♠♥ rs♦♥♥ rq♥②

s t♦rt ①♣rss♦♥ s t t ♣t ♦♠tr ♣r♠trs r♦♠

♣r♦ss ♥ t♥ ♦♠♣r t ♠sr♠♥ts

s♦♥♥ rq♥② ♥ t② t♦r ♠sr♠♥t

♥ ♥ ♦sr ♥ t t ♦♠♣rs♦♥ t♥ ♠sr ♥ s♠t

rs♦♥♥ rq♥② s ❲t t ♣t♥ ♦ t r♦tt♦♥ s♥s♦r ♠♦s t

♥ ♦♠tr ♣r♠trs t ♥ ♦sr rt② ♦♦ r♠♥t

t♥ ♠sr ♥ s♠t rs♦♥♥ rq♥② fres ♦r t s♠t

s ♦ t t♦r r s♥♥t② r♥t r♦♠ ♠sr♠♥ts r♥ t

♦ rt② ♦ ♠♣♥ ♠♦s ♦♣ ♥ rtss t ♥

s♥ tt t ♠♣♥ ts r ♠♦r ♠♣♦rt♥t ♥ s♥s s♥ ♣♦s♥

ts r t ♥②ss ♥ st♦♥

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

fres ❬Hz❪

♠sr

fres ❬Hz❪

t♦rt

t

r♥

Q

♠sr

Q

t♦rt

t

r♥

s♥ % %

s♥ % %

s♥ % %

♦♠♣rs♦♥ ♦ ♠sr tr♦♠♥ rs♦♥♥ rq♥② ♥qt② t♦r ♦r t tr s♥s ♦♥sr

♥ ♦♥s♦♥ ♦♥ ♥ t t r♦tt♦♥ s♥s♦r ♠♦s ♦♣ ♥ ♣tr

s♥ t② ♦rr♦♦rt ♦♣♥♦♦♣ ♠sr♠♥ts ♥ tr♠s ♦ tr♦♠♥

rs♦♥♥ rq♥② ♦r t ♠♦♥ ♦ t qt② t♦r s ♦♥ t♦

♥rt t② ts ♥♦t rt ♥② sss s♥ ♦ ♣rssr

s ♥ ♦s♦♦♣ rtr③t♦♥s ♥ ♦♥ ♥s t qt② t♦r t♦

s r s ♣♦ss t♦ ♠ t ♠♥ ♥♦s ♥ r♥ ♠sr♠♥ts

♦♥sq♥t② ♣rssr ♦ Pa s♦ ♥♦ t♦ ♦♥sr t ♠♥

♥♦s s♠r t♥ tr♦♥ ♥♦s

♦♥♥r ♦r ♥ ♦♣♥♦♦♣ ♠♦

r♦♠ st♦♥ ♣rt♦♥s r ♠ ♦♥ t ♦♠♥♥t ♥♦♥♥r ♠

♥s♠ ♠♥ ♦r tr ♦ t r♥t ♦♥rt♦♥s st t s s

tt ♣rs♥ ♣t♦rs r ♦♠♥t ② ♠♥ ♥♦♥♥rt② rs

strtrs s♥ ♣♦s♥ tr♦s r ♦♠♥t ② tr ♥♦♥♥rt②

s ♣rt♦♥s r r ♥ ts st♦♥ t ♥ ♦srt♦♥ ♦ t ♥♦♥♥r

♦r ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

tr♦♥ ♦t ♥♣t VAC s s ♦r ♣rssr s r ♥ssr② t♦ ♦r

t ♥♦♥♥r r♠ ♦ t r♦tt♦♥ s♥s♦r ♥♦♥♥r ♦r ♦sr

r ♣rs♥t ♥ r ♥ ♦♥ ♥ t s♥ s rs♦♥♥ ♣

s st♦rt t♦r ♣♣r rq♥s t♥ t ♦♠♥♥ ♦ ♠♥

♥♦♥♥rt② ♥ t ♦tr ♥ t rs♦♥♥ rq♥s ♦ s♥ ♥

r st♦rt t♦ ♦r rq♥s ♥ s♥ ts strtrs s ♣

♦s♥ tr♦s t ♥♦♥♥r ♦r s ♥ ② tr ♥♦♥♥rt②

♥♦♥♥r ♦r ♦ t r♦tt♦♥ s♥s♦r s ♥ s ♥r ♦srt♦♥

s♥ t s②st♠ s ♣♥♥ t♦ ♦♣rt ♥ ♦s♦♦♣ ♠♦

♣♥♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

r sr♠♥ts ♦ ♥♦♥♥r tr♥sr ♥t♦♥s ♦♣ t s♥ ♦♣ rt s♥ ♦tt♦♠ s♥

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥

s♦r

♥ ts st♦♥ t rs♦t♦♥ ♥ t s♥stt② ♦ t r♦tt♦♥ s♥s♦r s st

② ♠♥s ♦ ♠sr♠♥ts ♦ t ♥ ts ♦♥tr♦ ♦♦♣ s ♦♥tr♦ ♦♦♣

♣s t ♣r♦♦ ♠ss ♦s t♦ ts ③r♦ ♣♦st♦♥ s♦ tt t ♠♥t ♦rs

♥ t ♥r r♠ ♥♦ ♥♥ ♦ t ♥♦♥♥r s♣r♥ t s s ♥♦ ♥

♥ ♦ t r ♦rr tr♦stt tr♠s ♥ ts ①♣r♠♥t ♥ ♠♣♦rt♥t

♣r♠tr s t rr♥ ♦t VDC ♣♣ t♦ t ♠♥t s♥

t ♥♥s s♥♥t② t ♥t tr♦stt s♣r♥ ♦ s♥s ♥

s rtr③t♦♥ ♦ ts t ♠st ♦♥ ♦r t♥ t ♣r♦r

♠♥s tr t rtr③t♦♥ ♦ t tr♦stt s♣r♥ t ♣♦ss

t♦ t t r ♣r♦r♠♥s ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

r♦♦t ts st♦♥ t P ♦ t ♦t♣t ♥②③ ♦r

rtr③t♦♥s t②♣ P rs♣♦♥s ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s s ♣r

s♥t ♥ r

r ②♣ P rs♣♦♥s ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♥ s♦ ♥♦t t ♦♦ r♠♥t t t s♠t♦♥s s♦♥ ♥ r

①♣t rs♥ s♣tr♠ t rq♥s ♦ ③ s tr s s

② t s♥s♦r ♦st s♥ t strtr ♥ ♥♦t ♣rt② s②♠♠tr t♦ ♥♦♥

♦♠♦♥♦s t♥ r♥ t ♣r♦ss tr t r♠ t P rss

t♦ r t ♥♦s ♦♦r ♦♥r t♠ qst♦♥s ♦ t♦ ♠♥♠③ ts

♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

♠sr♠♥t rtt rtr♠♦r ♦♥ ♥ ♥♦t ♣ t ③ r♣rs♥t♥

tr♠♥st ♥♦s ♥ t ♦rt♦r② ♥② t ♥♦t ♥ t P ♣♦t ♥ts

t tr♦♠♥ rs♦♥♥ rq♥② ♦ t ♥ ♦rr t♦ ♣♦t t ♥♦s

♥st② ♦ t s♥s♦rs st ♦♥sr rq♥② ♥ ♦ ♥trst s

t♥ Hz ♥ Hz

tr♦stt s♣r♥ rtr③t♦♥

rs♦♥♥ rq♥② s♣♦t s ♥t♦♥ ♦ t t st♥ss ♦ t

tst s s♣♦t ♥ s t♦ rtr③ t tr♦stt s♣r♥ s♥ t

♣♥s ♦♥ t ♦t VDC ♥ rt♦♥s ♦ VDC ♠ t rs♦♥♥

rq♥② st t♦ ♦r ♦r r rq♥s ♥ ♠sr♥ ts st ♦s t♦

t tr♦stt ♣r♠trs

♦ ts ♥ t s ♦♥sr t♦ ♦t s E1 ♥ E2 ♥r r

q♥s ω1 ♥ ω2 ♦ t tr♦♠♥ rs♦♥♥ r ♥ ② s

ω1 =

√(Km −Kel1)

Jz

ω2 =

√(Km −Kel2)

Jz

r Km s t ♠♥ st♥ss Jz t ♠♦♠♥t ♥rt ♦ t strtr Kel1

t tr♦stt s♣r♥ ♦rrs♣♦♥♥ t♦ t ♦t VDC1 ♥Kel2 t tr♦

stt s♣r♥ ♦rrs♣♦♥♥ t♦ t ♦t VDC2 ♦r♥ t♦ t ♥t♦♥s

♦ t tr♦stt s♣r♥ ♥ ♥ ♦♥ ♥ rt

Kel = AelVDC2

r Ael s ♦♥st♥t ♣♥♥ ♦♥ tr♦ rttr ♦♠♥ t♦

qt♦♥ ♦♥ ♥ rt

|ω22 − ω1

2| = Ael

Jz|VDC1

2 − VDC22|

s rst ♥ ♦rr t♦ rtr③ t ♦♥st♥t Ael ♦♥ ♥s t♦ ♠sr t

rs♦♥♥ rq♥② ♦r t♦ ♦t s ♥ t♦ t t ♦♦♥ q

t♦♥

Ael = Jz|ω2

2 − ω12|

|VDC12 − VDC2

2|

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

P s♣tr♠ ♦ t tr s♥s st r ♣rs♥t ♥ r

rst ♦♠♠♥t s tt t rs♦♥♥ ♣ st②s t t s♠ s♣♦t ♦r t s♥

s ♦♠♦rt♥ ♦r s♥ t s s ♦♥ ♣rtr ♣t♦rs t

♥♦ tr s♣r♥ t ①t ♦♥ ♥ ♦sr ♠♦♥ rs♦♥♥ ♣ t

rs♣t t♦ t ♦t VDC ♦r t s♥s ♥ ❯s♥ t qt♦♥

♦♥ ♥ t t tr♦stt s♣r♥ ♦r s♥ rsts r s♦♥

♥ t ♦r ♦t VDC ♦ V ♥ ♥ ♥♦t ♦♦ r♠♥t

t♥ ♦r ♠♦s ♥ ♠sr♠♥ts

♦r ♥r② ♦♥ ♥ ♥♦t t ♥♦s ♦♦r ♠♥t♦♥ t rs♣t t♦ ♥

rs♥ ♦ts st rs♦t♦♥ ♥ ♦t♥ ♥ t ♥♦t ♥ss

♦♠♣t② r♦♠ ♠sr♠♥ts ♥ ♦tr ♦rs t st rs♦t♦♥ s ♦t♥

♥ t tr♦stt s♣r♥ ♠ts t ♠♥ s♣r♥ s stt♠♥t ♦r

r♦♦rts t s♥ ♥②ss ♣r♦r♠ ♥ st♦♥

VDC V s♥ s♥

sr Kel [N.m] 5× 10−6 7.5× 10−6

♦rt Kel [N.m] 6× 10−6 8.6× 10−6

♦♠♣rs♦♥ t♥ ♠sr ♥ s♠t s ♦ t tr♦stts♣r♥

♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

r ♥♥ ♦ t ♦t ♦♥ t P rs♣♦♥s ♦♣ s♥ s♥ ♦tt♦♠ s♥

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

①♣r♠♥t st♣ ♦r ♣r♦r♠♥ rtr③t♦♥

♥ ts st♦♥ t ♦t VDC s st t 1.5 V t♦ ♥sr t ♠t♥ ♦

t tr♦stt s♣r♥ t t ♠♥ ♦♥ ts ♦♥ ttr rs♦t♦♥s

♥ ♦rr t♦ tr♠♥ t ♣r♦r♠♥ ♦ t r♦tt♦♥ s♥s♦r s♥s s

rs♦t♦♥ rt t ♣ ♦ ♥rt♥ ♦rq♥② ♦♠♣t ♥r

rt♦♥ s♥s s rt t s s t tr♦♥ ♦r r s♦♥ ♥

r

r t♣ s ♦r t ♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦rt t r♦tt♦♥ t t t tr♦♥ ♦r t t ♠♥t

♣r♦r♠♥ ♣r♠trs t r t s ♥ t ♥♦s ♦♦r

s s t ♠①♠♠ ①tr♥ ①tt♦♥ tt ♥ t♦rt②

♦♥tr♦ ② t

♥♦s ♦♦r s t ♠♥♠♠ ♥r rt♦♥ tt ♥ ♠sr

①♣r♠♥t s♥ ♦♣ t♦ rtr③ t ♣r♦t♦t②♣s s ♦r♥③ s

♦♦s

♣r s♥ ♥♣t r♦♠ t rt t s ♣♣ t♦ t r♦tt♦♥ s♥s♦r

♠♣t ♦ ♥r rt♦♥s s st t rad/s2 t rq♥② ♦

Hz

♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

♠♣t ♦ t rst♥ ♣ ♥ t P s♣tr♠ s ♠

sr r rt♦ ♦ ts ♠sr t t rt♦♥

♠♣t s t st♦r ♦ t ♣r♦t♦t②♣

s s t♦r s t♥ s t♦ t t s s ♦t♥ ♦r

t ♠①♠♠ ♠♣t ♦ t tstr♠ ♦t♣t t dB

♥② t P s♣tr♠ s ♠t♣ ② t s t♦ ①♣rss t ♥

♠♥ ♥ts mrad.s−2.Hz−1/2

r ①♣r♠♥t s♥ ♦r ♣r♦r♠♥ t♦♥

s r♠r ♦♥ t ①♣r♠♥t s♥ t ①♣rss♦♥ rt♥ t ♦s ♥st②

①♣rss ♥ mrad.s−2.Hz−1/2 ♥ t ♥♦s ♥st② ①♣rss ♥ V.Hz−1/2

s

♦s ♥st②[mrad.s−2.Hz−1/2

]= × ♦s ♥st②

[V.Hz−1/2

]

︸ ︷︷ ︸sr P

r s t s ♦ t ♣r♦t♦t②♣

♥ ♦♥s♦♥ rs♦t♦♥ r♦tt♦♥ s♥s♦r ♥s ♦ ♥♦s ♦♦r t s♦

♦ s t♦ ♠sr t s♠st ♥r rt♦♥ s

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

①♣r♠♥t ♣r♦r♠♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦

t②♣s

♠sr P t ♥♦ ①tr♥ r♦tt♦♥ ♥♣t r s♦♥ ♥ r ♦r

t tr r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s ♦♦♥ t ①♣r♠♥t s♥ t

♥ t ♣r♦s st♦♥ t ♣r♦r♠♥ ♦ ♣r♦t♦t②♣s s ♥② sts

♠sr ♣r♦r♠♥s r ♣rs♥t ♥ t ♥ t ♥♦s ♥st② ♣♦t s

♣rs♥t ♥ r

Pr♦r♠♥ ♣r♠trs s♥ s♥ s♥

♦s ♦♦r [dB(V.Hz−1/2)

]

s

[rad

s2

]

s♦t♦♥

[mrad

s2√Hz

]

sr ♣r♦r♠♥s ♦ t tr s♥s st

r ♥♦s ♥st② ♦ t tr s♥s

♥ ♦♥ ♥ t ♣r s♥ s s♥ s rt② ♦ s

t s t ♦s ♥♦t t ♥t r♦♠ t tr♦stt s♣r♥ t t ♠♥

rs♦♥♥ s ♥♦t ♥ ♥ t ♥♦s ♦♦r s r t ♦

mrad/s2/√Hz ♥ t ♦tr ♥ t ♣♦s♥ s s♥ s ♥

♠♣♦rt♥t tr♦stt s♣r♥ ♦♥ t r s ♥ ts s t rs♦

♥♥ rq♥② s ♥ ♥ t rs♦t♦♥ s mrad/s2/√Hz

♦s♦♦♣ rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r

st rst ♦♠s r♦♠ t ②r s s♥ ♠♦♥strts ♥♦s

♦♦r t t s♠ s s♥ ♦r t s ♦ s♥ s t

s ♦ s t s ♦ s♥ rst♥ ♥ ttr ♥♦s ♥st② t

µrad/s2/√Hz

♦ ♠①♠③ t ♣r♦r♠♥ ♦ t r♦tt♦♥ s♥s♦r ♦♥ s t♦ ♥ t rs

♦♥♥ rq♥② ② t s ♦ t tr♦stt s♣r♥ ♥tr♦ ② ♣♦s♥

tr♦s ♦r ♦♥ s t♦ ♠t s♦ t s s♦ tt t rs♦t♦♥ s

♠♣r♦ s s♦♥ ♥ qt♦♥ s rst t ♦♠ rttr ♦♣

♥ s♥ s ttr ♦r rs♦t♦♥ ♣r♣♦s s♥ t ♥s t ♠♥

rs♦♥♥ ♦r♥ ♦r s

♥ ♦♥s♦♥ t rs♦t♦♥ ♦r t rq♥② ♥ Hz Hz s

♣rs♥t ♥ t ♥ ♦♠♣r t t s♣t♦♥s ♥ ♥ st♦♥

♥ ♣r♦♣♦s ♥ ts P ssrtt♦♥ s ♥ ♦r♦♠ ② ♥

t s♥ ♦ ♣r♦r♠♥ ♥r r♦♠tr s ♦♥ t♥♦

♦②

s♥ s♥ s♥ ♣t♦♥s

s♦t♦♥

[mrad

s2

]

P♦r mW

rs♦t♦♥ ♦ t tr s♥s st

♦ ♦♠♣t t rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦rs ♦♠♣rt

st② s ♣r♦r♠ t t rtr③t♦♥ ♦ ♦tr r♦tt♦♥ s♥s♥ s②st♠s ♥

t s♠ ♦rt♦r② ♦♥t♦♥s s s t ♦t ♦ t ♥①t st♦♥s

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

r ♣t♠③ P rs♣♦♥ss t ♦t VDC st t V ♦♣s♥ s♥ ♦tt♦♠ s♥

♦♠♣rs♦♥ t ♦tr r♦tt♦♥ s♥s♦rs

♦♠♣rs♦♥ t ♦tr r♦tt♦♥ s♥s♦rs

♣r♣♦s ♦ ts st♦♥ s t♦ ♦♠♣r t r♦tt♦♥ s♥s♦rs ♦♣

♥ ts rsr t ♦tr t♥♦♦s ♦♠♣rs♦♥ ♦♥t ♥ t♦

st♣s rst ♦♠♣r t r♦tt♦♥ t ♠sr♠♥ts r♦♠ ♦♣

r♦♠trs ♥ ♦rr t♦ rrt ♥ t st♣ ♣r♦♣♦s ♥ st♦♥

♥ ♥ s♦♥ st♣ ♦♠♣r t r♦tt♦♥ s♥s♦r t t

tr♦♠ s♥s♦r r♦♠ ♥t ♣rs♥t ♥

♦♣ r♦♠trs ♦r ♥r ♠sr

♠♥ts

r tr♦♥ ♦r t t♦ r♦♠trs ♦♥ ♦t ss ♦ r♦tt♦♥ s♥s♦r

r♦tt♦♥ s♥s♦r ♦rs t ♥ ♥ s s♦ t♦ ♦♥tr♦

r♥t ♣t r♦♠trs s s♦♥ ♥ r t♦

r♦♠trs r s♣rt ② st♥ ♦ cm t r♦tt♦♥ s♥s♦r ♥ t

♠ ♥♦r♠t♦♥ ♣r♦ ② ts tr s♥s♦rs s ♦♥str♥ ② t

♦♦♥ qt♦♥

φ =a2 − a1L

r φ s t ♥r rt♦♥ ♠sr ② t r♦tt♦♥ s♥s♦r a1 ♥ a2 r

t ♦r③♦♥t rt♦♥s ♠sr ② t r♦♠trs ♥ rs♣t②

♥ L s t st♥ t♥ t t♦ r♦♠trs ♦r♥ t♦ qt♦♥

t rs♦t♦♥ ♦ t r♦♠trs ♥ t st♥ L tr♠♥s t rs♦t♦♥

tt ♥ ♦t♥ ♥ t ♥r ♠sr♠♥ts P rs♣♦♥s ♦ ♦♣

r♦♠trs s ♣rs♥t ♥ r t s ♥trst♥ t♦ ♦sr tt

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

ts ♥r ♠sr♠♥t s ♠♦r s♥st t♦ ♠♥t ♥♦s t t ♣rs♥ ♦

♦t ♦ ♣s ♥ t rq♥② ♥ Hz Hz ♦♠♣r t♦ t r♦tt♦♥

s♥s♦r

♦r♦r t r♦♠trs r rt s♦ tt t ♥♦s ♥st② ♦ ts t②♣

♦ ♠sr♠♥t ♥ ♦♠♣r t t ♦♥s t ♥ t ♣r♦s st♦♥

♣♦t s s♦♥ ♥ r ♥ ♥ ♥♦t tt ♥r ♠sr♠♥ts

t ♦♣ r♦♠trs ♥ t st rs♦t♦♥ ② r♦tt♦♥

s♥s♦r ♣r♦t♦t②♣s ♦r t s♥stt② ♦ r♦♠trs t♦ tr♥st♦♥ ♥♦s

r♣rs♥ts t ♠♥ ♠t ♦ ts t②♣ ♦ ♠sr♠♥ts rs t r♦tt♦♥ s♥s♦r

s s♥ t♦ tt♥t ♦t♦♣♥ ♠♦t♦♥s ♦ t s♥st ♠♥t t♥s t♦

qrt ♠♦♠♥t ♦ t ss♣♥s♦♥ ♠s ❯♥♦rt♥t② r♦sss♥stt②

♥②ss ♦ t r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s ♥♦t ♥ ♣r♦r♠ r♥ t

tss ♥ t ♦ r♣rs♥t ♥ ♠♣♦rt♥t ♠sr♠♥t ♦r tr ♦rs ♦♥ ts

st

r ♥②ss ♦ ♦♣ r♦♠trs ♦r ♥r ♠sr♠♥tst P ♣♦t t ♥♦s ♥st② ♣♦t

♦♠♣rs♦♥ t ♦tr r♦tt♦♥ s♥s♦rs

tr♦♠ s♥s♦r ♥t

r Prs♥tt♦♥ ♦ t ♥t

♥ tst s t♦ ♦♠♣r t r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s t t

rr♥ s♥s♦r ♥ r♦tt♦♥ ss♠♦♦② t r♦tt♦♥ ss♠♦♠tr ♥t

s♦♥ ♥ r rt♦♥ ♦ t s♥s♦r s ♣r♦r♠ t Hz ♥ ts

♥♦s ♥st② s ♦♠♣t ♥ t s♠ ♥r♦♥♠♥t ♦r ♦♠♣rs♦♥ ♥②ss

t r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s ♥♦s ♥st② ♣♦t s s♦♥ ♥ r

♥ ♥ ♥♦t tt t ♥t ♥♦s ♦♦r s r ttr t♥ ♦tr s♥s♦rs

t ♦ 50 µrad/s2/√Hz ♦r s ①♣♥ ♥ st♦♥ ts

s♦t♦♥ s ♥♦t st ♦r ss♠ ①♣♦rt♦♥

r ♦♠♣rs♦♥ ♦ t ♥♦s ♥st② ♦ t ♥t t t ♦♥s ♦♥♦r t r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s t ♦ ♣♦t t ❩♦♦♠ ♦♥ ♥♦s♥st② ♦ mrad/s2/

√Hz

♣tr sr♠♥ts ♥ rtr③t♦♥ ♦ r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s

♠♠r② t

rs♦t♦♥ ♦r t rq♥② ♥ Hz Hz s ♣rs♥t ♥

t ♥ ♦♠♣r t t st s♥ ♦ r♦tt♦♥ s♥s♦rs

r♦♠trs

♥t

♦tt♦♥ s♥s♦r

s♦t♦♥

[mrad

s2

]

rs♦t♦♥ ♦ ♦tr r♦tt♦♥ s♥s♥ s②st♠s

♥ r② tt s♣t♦♥s ♦♥ ♣♦r ♦♥s♠♣t♦♥ ♦♠ s③ ♥ rs

♦t♦♥ t s ♥ ♥ ♣t r♦tt♦♥ s♥s♦r tt ♥

♥ t ♣r♦r♠♥s ♦ ♦tr r♦tt♦♥ s♥s♥ s②st♠s

♦♥s♦♥ ♦♥ ①♣r♠♥ts

t rtr③t♦♥ ♦ t r♦tt♦♥ s♥s♦r s ♣rs♥t ♥ ts ♣

tr tr ♣t♥ t ♦♠tr ♣r♠trs ♠♦ ② t t♥ ♣r♦ss t

s ♣♦ss t♦ ♦♠♣r t tr ♣r♦♣rts t t ♠♦s ♣rs♥t ♥ t

♣r♦s ♣tr t rst ♥ ♦♦ tt♥ ♦ s♠t ♣t♥ rt♦♥s

t t ♠sr♠♥ts ♣r♦r♠ ♥ s ♦♥r♠ ♠♣♦rt♥t ♣r♦♣rts ♦

t s♥s♦r s s t ♥♦♠♥ ♣t♥ ♥ t ♠♥ st♥ss ♥ ♥①t

st♣ rq♥② s♣ ♥②ss r ♣r♦r♠ t♦ t t tr♦♠♥

rs♦♥♥ rq♥② ♥ t qt② t♦r t s s♥ tt t ♥②t ♠♦s

♦rst♠t t qt② t♦r ♥② tr t rtr③t♦♥ ♦ t tr♦

stt s♣r♥ ♥ t♦ ♦♣t♠③ t s♥s♦r rs♣♦♥s t ♦r ♦ t

♥ ts ♦♥tr♦ ♦♦♣ s st ♥ t ♣r♦r♠♥s r t ♥♦s

♥st② ♣♦ts r tt t ②r s♥ s♥ ♦♠ tr♦s s t st r

ttr ♦r ♣r♦r♠♥ s♥s♦r t st t r♦tt♦♥ s♥s♦r ♣r♦r♠♥s

r ♦♠♣r t♦ ♦tr t♥♦♦s s s ♦♣ r♦♠trs ♦r ♥r

♠sr♠♥ts ♥ ♥ tr♦♠ s♦t♦♥ ♦♥s♦♥ s tt t r♦t

t♦♥ s♥s♦r ♦♣ ♥ ts ssrtt♦♥ s ♦♦ tr♦ t♥ ♣r♦r♠♥

♥ s③

♦♥s♦♥s ♥ ♣rs♣ts

♠♠r② ♦ t ♦r

♥ ss♠ ①♣♦rt♦♥ ♥ s♠♣♥ t♥q ♦ t ss♠ s

♣r♦♣♦s rqr♥ t ♣♦②♠♥t ♦ r♦tt♦♥ s♥s♥ s②st♠s t t r sr

♥ tr♠s ♦ rqr♠♥ts ts s②st♠s ♥ t♦ ♦r s♠s③ ②

s♥st ♥ t rs♦t♦♥ ♦ t ts ♥ ♣r♦r♠♥

♥r r♦♠tr s r③ rs♥ t tr♦♥ ♥tr ♥ t

♠♥tr♥ ♣r♦ss ♦ rs♦t♦♥ ♥r r♦♠trs

♦ ♥rst♥ t ② trs ♦ s♥♥ ♣r♦r♠♥ r♦tt♦♥

s♥s♦r t ♣t tt♦♥ ♥ t ♦r ♦♥tr♦r ♣r♦ ② t

r st t rs♣t t♦ t♦ s♥s♥ ♣r♥♣s t rst ♦♥ t

③♥ ♥ ♥ tr♦ r tr ♣t♦r ♥ t s♦♥ ♦♥ t③♥

♥ ♥ tr♦ ♣ ♣♦s♥ ♣t♦r s♣rt♦♥ ♦ t ♦r

t rs♣t t♦ t t♦ ♣t s♥s♥ ♣r♥♣s s ♦s♥ t♦ ♥②③ tr

rs♣t ♥ts ♥ s♦rt♦♠♥s t st sr s♥ ♣r♠trs r

tr③♥ t s♥s♦r ♦r r ♥t ♦r t t♦ ♦♥rt♦♥s st

rtr♠♦r t ♠♦♥ ♦ ♠♥ ♥ tr ♥♦s s♦rs ♦ s

t♦ tr♠♥ t ♥♥ ♦ s♥ ♣r♠trs ♦♥ t s♥s♦r rs♦t♦♥

♦♥sr♥ t t♥ ♦♥str♥ts ♠♣♦s ② t ♠♥tr♥ ♣r♦ss

t ♥ t s②st♠ ♣♥ t♦ strtrs r s♥ s ♦♥ t

t♦ s♥s♥ ♣r♥♣s sss t♦r♦ s♥ ♦ strtr strt

② ♦♠♣t t♦♥ ♦ ♠♥ st♥ss ♦♥ts ♦ s♣♣♦rt♥ ♠s

♥ ♠♣♥ ♠♦s ♦♣ ♥ t trtr r s t♦ ♣♣r♦①♠t t

qt② t♦r s rt t♦ ♠♥ ♥♦s st st♣ ♦ t s♥

s t tr♠♥t♦♥ ♦ t tr ♣r♠trs ♥② ♥ ♦♣t♠③t♦♥ ♦ t

s♥s♦r strtrs s ♣r♦r♠ t♦ ♥t② t st ♥ts ♦r ♣r♦t♦t②♣♥

♦♥s♦♥s ♥ ♣rs♣ts

s ♦♣t♠③t♦♥ r tt ♥♦♥♥r ♣t♦rs ♥tr♦ ♥ tr♦stt

s♣r♥ ♥ t ♠♥ s♣r♥ ♠t♥ ♦ ts tr♦stt

s♣r♥ t t ♠♥ ♦♥ ♦ s t♦ ♦t♥ ttr ♣r♦r♠♥ t♥ ♦r

♥r ♣t♦rs t st tr s♥s r st ♣r s♥ ♣t♦r

②r ♦♥rt♦♥ ♠①♥ tr ♣t♦rs ♥ ♣♦s♥ ♣t♦rs ♥

♣r ♣♦s♥ ♣t♦r

r♦tt♦♥ s♥s♦r ♣r♦t♦t②♣s r ♠r♦rt s♥ ♥ ♦♣t

♠③ ♣ rt ♦♥ t♥ ♣r♦ss ♦ rs r rtr

③t♦♥ st♣s r ♠♣♦② t♦ t t ♠♦ ♦♦ tt♥ ♦ ♠sr

♣t♥♦t rtrsts t ♠♦s s rr♥ ♦srt♦♥ ♠

r② t ♦♦ r♠♥t ♦ t tr♦♠♥ rs♦♥♥ rq♥② ♥ ♦

t tr♦stt s♣r♥ ♦♥ts ♣r♦ t rt② ♦ t ♥②t ♠♦s

s t ♠sr P s♣tr ♦ t r♦tt♦♥ ♣r♦t♦t②♣s ♦♣rt♥ ♥

♦s♦♦♣ ♦rrs♣♦♥ t♦ t ♦♥s s♠t r♥ t ♠♦♥ ♣s t

s♠r ♥♦s ♦♦r s st ♣r♦r♠♥s ♥ tr♠s ♦ ♥♦s ♦♦r r

♦t♥ t t ②r ♣r♦t♦t②♣ ♥ t ♠♥ rs♦♥♥ ♥t♦♥

② t tr♦stt s♣r♥ ♦♥ t ♦r s t♥ t ♣r ♣♦s♥

s♥ rst ♥ rs♦t♦♥ ♦ mrad.s−2 ♦r t rq♥② ♥

Hz Hz ♥ t♦♥ t♦ ♠t♥ t rqr♠♥ts ♦ ss♠ ①♣♦rt♦♥ ts

rs♦t♦♥ ♥ ♦tr r♦tt♦♥ s♥s♥ s②st♠s s ♥ ss♠♦♦②

♦♦♥

♥♥ s♣t ♦ ts tss s t♦ t rqr rs♦t♦♥ ♥

s♣t ♦ t sr t♥ ♦♥str♥ts s♠♠r③ ♥ t ♦r ♥st♥

t ① ♦♠ s③ t♦ s♥ t s♥st ♠♥t ♠t t ss♠

♠ss ♠♥s♦♥s ts ♠t♥ t s♥stt② ♥ rs♦t♦♥ ♥

♦r♥ t♦ qt♦♥s ♥ ts ♥ r s ♦ t strtr ♥rt

Jz rst ♥ ♦r ♠♥ ♥♦s Φmn ♥ ♦r ♥ Kfb ♥ ♦r

s ♦♥sq♥t② ♥ ♥trst♥ ♠♣r♦♠♥t t♦ ♠♣♠♥t t♦ ♥

rs t ss♠ ♠ss ♥rt

♦♦♥

♥ t tr♦s r s ♦r t tt♦♥ ♥ t tt♦♥ t ♠①

♠③t♦♥ ♦ t s♣♠♥tt♦♣t♥ ♥ Kθ−C s ♥ ♦r ttr

♣t tt♦♥ ♦r r s ♦ Kθ−C rst ♥ r

♥ Kfb ♥ ♠♣♦rt♥t s s ♦♥ s♦ s♣rt t tr♦s

s ♦r t tt♦♥ ♥ t ♦♥s s ♦r t tt♦♥ rst st ♦

s♥ t♦ ♠①♠③ t tt♦♥ t s♦♥ st ♦ s t♦ ♥

t ss♠ ♠ss r♦tt♦♥ t ♠t ♦r ts strt② ♦

♥ ♠♦r ♦♠♣①

♥② t t♠t st♣ ♥t♥s tst♥ ♦ t r♦tt♦♥

s♥s♦r t♦ ♦♥ ♦♥ ts ♣t② ♦ ♠sr♥ t r♥t ♦ sr s

r♥ ss♠ ①♣♦rt♦♥

s ♣ s ♥t♥t♦♥② t ♥

♣♣♥①

♣♣♥①

t♠t ♥♦t♦♥s ♦r rq♥②

♦♠♥ ♥②ss

s ♣♣♥① s r s♠♠r② ♦ ♠t♠t ♥♦t♦♥s ♦r rq♥② ♦

♠♥ ♥②ss ♦ rt♥ ♠♥ s②st♠ s ♥♦t♦♥s r s t♦ r

♠♥ ♥♦s ♥ st♦♥

t s ss♠ t♠ ♣♥♥t ♥t♦♥ f ♥tr ♥ t ♦♠♥ L1(R)

♦r r ♥♠r ω ♦♥ ♥ ♥ t ♦rr tr♥s♦r♠ ♦ f

F (f)(ω) =

∫ ∞

−∞e−jωtf(t)dt

t s ♥ ♠♣♦rt♥t ♥♦t♦♥ ♥ s♥ ♣r♦ss♥ r♠r ♥tt② s ♥ ②

t Prss t♦r♠ ∫

R

|f |2dt = 1

2π

∫

R

|F |2dw

ss♠♥ f ♥t♦♥ ♦ t ♦♠♥ L1(R) ∩ L2(R)

♥ ts ♠t♠t ♥♦t♦♥s ♦♥ ♥ sts s ② t♦ q♥t②

♥♦s ♣r♦ss ② s♥ t r s♣tr ♥st② ♦r ♠♥ sqr strt♦♥

♦ t ♥♦s ♥ ♥r rq♥② s♣ ♦r ♥st♥ t s ♦♥sr t t ♥♦s

♥t♦♥ Vn(t) r s♣tr ♥st② ♦ ts ♥♦s ♥t♦♥ s

Vn2 =

⟨|Vn|2

⟩

r t ♥ rts 〈. . .〉 ♥ t sttst r

♣♣♥①

♦♠tr ♣r♠tr s

♠♣♥ ♥②ss ♦ t s♥♦♠ s♥

♦♠tr ♣r♠trs s ♦r t t♦♥ ♦ t t♦r ♥ t ♠

♥ ♥♦s ♦ t s♥♦♠ s♥ ♥ st♦♥

Pr♠tr ❱ ❯♥t

♥ ♠♦♠♥t ♦ ♥rt Jz 8× 10−13 kg.m2

♥ ♥tr rq♥② f0 kHz

r ②♥♠ s♦st② η 1.85× 10−5 Pa.s

❲r t♥ss T µm

tr♦ t Wf µm

tr♦ ♦r♣ W0 µm

♦r♠ ♣ h0 µm

tr ♣ d µm

rst tr♦ ♣♦st♦♥ R1 µm

♠r ♦ ♥rs Nf

♠r ♦ ♣t♦rs Nc

♣♣♥① ♦♠tr ♣r♠tr s

♠♣♥ ♥②ss ♦ t ♣♦s♥ s♥

♦♠tr ♣r♠trs s ♦r t t♦♥ ♦ t t♦r ♥ t ♠

♥ ♥♦s ♦ t ♣♦s♥ s♥ ♥ st♦♥

Pr♠tr ❱ ❯♥t

♥ ♠♦♠♥t ♦ ♥rt Jz 8× 10−13 kg.m2

♥ ♥tr rq♥② f0 kHz

r ②♥♠ s♦st② η 1.85× 10−5 Pa.s

❲r t♥ss T µm

rst ①tr♠t② ♣♦st♦♥ R1 µm

♦♥ ①tr♠t② ♣♦st♦♥ R2 µm

♦r♠ ♣ h0 µm

♠r ♦ ♣t♦rs Nc

Pr♠trs ♦ s♥

Pr♠trs ♦ s♥

♦♠tr ♣r♠trs ♦♥ ♥ t ♦♣t♠③t♦♥ st② ♥ st♦♥ ♦r

♣rs♥ ♣t♦r s♥

Pr♠tr ❱ ❯♥t

❲r t♥ss T µm

♥tr ♥♦r rs Ra µm

♠ ♥t Lb µm

♠ t Wb µm

♥ ①tr♥ rs Re µm

tr♦ ♥t Lf µm

tr♦ t Wf µm

tr♦ ♦r♣ W0 µm

♦r♠ ♣ h µm

tr ♣ d µm

♠r ♦ ♥rs Nf

♠r ♦ ♣t♦rs Nc

♣♣♥① ♦♠tr ♣r♠tr s

Pr♠trs ♦ s♥

♦♠tr ♣r♠trs ♦♥ ♥ t ♦♣t♠③t♦♥ st② ♥ st♦♥ ♦r

②r ♣t♦r s♥

Pr♠tr ❱ ❯♥t

❲r t♥ss T µm

♥tr ♥♦r rs Ra µm

♠ ♥t Lb µm

♠ t Wb µm

♥ ①tr♥ rs Re µm

tr♦ ♥t Lf µm

tr♦ t Wf µm

tr♦ ♦r♣ W0 µm

♦r♠ ♣ h µm

tr ♣ d µm

♠r ♦ ♥rs Nf

♠r ♦ ♣t♦rs Nc

Pr♠trs ♦ s♥

Pr♠trs ♦ s♥

♦♠tr ♣r♠trs ♦♥ ♥ t ♦♣t♠③t♦♥ st② ♥ st♦♥ ♦r

♣r ♣♦s♥ ♣t♦r s♥

Pr♠tr ❱ ❯♥t

❲r t♥ss T µm

♥tr ♥♦r rs Ra µm

♠ ♥t Lb µm

♠ t Wb µm

♥ ①tr♥ rs Re µm

♦r♠ ♣ h µm

♠r ♦ ♣t♦rs Nc

r♥s

❬❪ r♠ s②st♠s ♥ rts ♦r sr ♣r ♦r ②r♦

s♦♣s P tss ♦r ♥sttt ♦ ♥♦♦②

❬❪ t♥ ❱ ♦♥ ♦♠ r ♥ rt♥

qst♦♥ ♥ Pr♦ss♥ ♦ P♦♥t r sr♠♥ts ♥ ♥ s♠

♥ ♥ ♦♥r♥ ①t♦♥ ②

❬❪ ♥ P rs ♥ttt ss♠♦♦② ❯♥rst② ♥ ♦♦s

❬❪ r ♥ P rt ①♣♦rt♦♥ s♠♦♦② ❱♦ st♦r② ♦r②

♥ t qst♦♥ ♠r ❯♥rst② Prss

❬❪ ②③rt s♥ r ♥ P ♠ ♥ s♠ t

qst♦♥ ❯s♥ ♦tt♦♥ ♥s♦rs ♥ t ♦♥r♥ ①t♦♥

♥

❬❪ P♣♦s ♥r③ s♠♣♥ ①♣♥s♦♥ r♥st♦♥s ♦♥ rts

♥ ②st♠s ♦♠r

❬❪ ss②r P ss②r ❲s③♥♦s ♥ P P♥♦

s♠ r♦tt♦♥ s s ♠♥ts ♦ t♦r② ♥ r♦r♥ ♥♥s ♦

♦♣②ss

❬❪ ♦s ③ss♥♦ ❲♦♥r ❲♥s ♥ ❲②sss♦♥

Pr♦r♠♥ rtrsts ♦ ♦tt♦♥ s♠♦♠tr ♦r r ♥

♥♥r♥ ♣♣t♦♥s t♥ ♦ t s♠♦♦ ♦t② ♦ ♠r

②

❬❪ ❯ rr t♠♥♥ ❱♦sts ❲ssr♠♥♥

tr♦ ❱r♥♦♥ ♥ P ❲s ♥ sr ♠sr♠♥ts ♦ r♦♥

r♥s

r♦tt♦♥s ♦r ss♠♦♦② t♥ ♦ t s♠♦♦ ♦t② ♦ ♠r

❬❪ r♦s③③ ♥ ❩ rs ♣♣t♦♥ ♦ r♦♣t r♦tt♦♥

ss♠♦♠tr ♥ ♥stt♦♥ ♦ ss♠ r♦tt♦♥ s ♣t♦tr♦♥s

♥

❬❪ ♦r ♥s ♥ tt ♦rt♦r② ♥ st♥ ♦

♦♠♠r ♦tt♦♥ s♠♦♠trs t♥ ♦ t s♠♦♦ ♦t②

♦ ♠r ②

❬❪ r♦s♦á ♥ á ♣♦rt s♥s♦r s②st♠ ♦r r♦tt♦♥ ss♠

♠♦t♦♥ ♠sr♠♥ts ♦ s♥t ♥str♠♥ts

st

❬❪ ♦ r♦♥ r♦tt♦♥ ♠♦t♦♥s r♦r ♥ ♥r s♦r r♦♥ ♦ rt

qs ♦♣②s sr ttrs

❬❪ ♦r ①r♦r♦♠ r♦♥♠♦t♦♥ ♠sr♠♥t t♥

s♠♦♦ ♦t② ♠r

❬❪ ♦ s s♥r Ps♦♥ r♦♥♦♥ ❯♥rtt ♥

sr♦tt♦ ♥tr ♦r s r♦tt♦♥ r♦♠tr ♦r

♣♣t♦♥s t rad/s2 rs♦t♦♥ ♥ t ♦t♣t ♥s♦rs

♦r♥ st

❬❪ Ps♦♥ ♠ss ♣t s♥s♦r ❯ Pt♥t

❬❪ ②③rt s♠ qst♦♥ s②st♠ ♥ t♥q ❯ Pt♥t ♣♣

❬❪ r♥st♥ r ❲ ② ♥ P ❲r ♦♥♦s r

t♦♥ s♥s♦r ♦r ♦♣②s ♣♣t♦♥s ♦r♥ r♦tr♦♠♥

②st♠s

❬❪ ♠♥ ♥ ♦sr ♠r♦♠♥ ② r♥t tr

r♦♠tr ♥ Pr♦♥s ♦ st♦♠ ♥trt rts ♦♥r♥ ♣s

r♥s

❬❪ P ♥ ♠♣♥ ♥ ❲♦♥tt rt②♠♣ ♥trt

♣t r♦♠tr s♥ ♦ ♣♦st♦♥ ♥ ♦t② ♥ ❬Pr♦

♥s❪ ♥tr♥t♦♥ ②♠♣♦s♠ ♦♥ rts ♥ ②st♠s ♦♠

♣s

❬❪ rs♦♥ ♥tr♠ ♥♦s ♥ ♠r♦♠♥ ♦st ♥

rt♦♥ s♥s♦rs r♥st♦♥s ♦♥ tr♦♥ s

❬❪ ♥ ♥ ♦s ♦s ♣r♦sss ♥ ♥♥♦♠♥ rs♦♥t♦rs

♦r♥ ♦ ♣♣ P②ss

❬❪ ②qst r♠ tt♦♥ ♦ tr r ♥ ♦♥t♦rs P②s

❬❪ ♦ r ♠♣♥ ♥ ♥②ss ♥ s♥ Pr♥♣s ♦ s

♣s sr

❬❪ ♦ tr♦stt tt♦♥ ♥ ♥②ss ♥ s♥ Pr♥♣s ♦

s ♣s sr

❬❪ ♠♠r ♥②t ♦ ♦r ♦♠♣t♥ r♥ s ♦r♥

♦ r♦tr♦♠♥ ②st♠s rr②

❬❪ ♦♠r ③r♦ ♥ ② ❲ ③♣s ♥

❩ ❩♥ ❲♠s② ♥ P rt tt ♣rs ss♠ r

r♦♠tr ♥ t ♥tr♥t♦♥ ♦♥r♥ ♦♥ r♦

tr♦ ♥ ②st♠s ♣s ♥r②

❬❪ ♥tr r♦s②st♠ s♥ r ♠ Psrs

❬❪ P ♥ ♠♣♥ ❱♦♦♣ P rr♦ ♥ ❲♦♥tt ♣

♣t♦♥ ♦ tr♦stt t♦ rt ♠♣♥ ♦ ♥ ♥trt s♦♥

♣t r♦♠tr ♥s♦rs ♥ tt♦rs P②s

❬❪ ♠♥ ♥ ♦sr tr①s ♠r♦♠♥ r♦♠tr t

♣♦st♦♥s♥s ♥tr ♥ t ♦sttr♠ tr♦♥s

♦r♥ ♦ ♦tt rts ♣r

❬❪ ❨♥t♦ ❳♦ ❲♣♥ ♥ ❲ ♥ s♥ ♥ ♥♦s ♥②ss

♦ s♠t ♣t ♠r♦♠♥ r♦♠tr ♦r♥ ♦ ♠

♦♥t♦rs ②

r♥s

❬❪ ❨③ ♥ ♦s ♥②ss ♥ r

tr③t♦♥ ♦ ♠t ♣t r♦r♦♠tr ♦r♥ ♦

♦tt rts rr②

❬❪ ❳ ♥ ❲♥ rt ♥ ♦sr ♥ ♥trt r r♦

♠♥ ♣t tr r♦♠tr t µg/√Hz rs♦t♦♥

❬❪ ♦sr ♥ ♦ r ♠r♦♠♥ r♦♠trs ♥ Pr♦

♥s ♦ t st♦♠ ♥trt rts ♦♥r♥ ♣s

❬❪ ❩♦ ♦♥♦s ♥tr ♦r ♣t ♠r♦r♦♠trs

P tss ♦r ♥sttt ♦ ♥♦♦②

❬❪ P ③③ ❱ ♦r♥s♥ ♥ ♥ r ♣ ♥ ♦r ♦ s♠t

♦♥rtrs ♥ Pr♦ss♥ ③♥

❬❪ Pr Pr♥♣s ♦ ♠t ♦t♦♥ ♦r ♥♦t♦t ♦♥rt

rs ♦t♦r♦

❬❪ rt P s ♥ st ♦s♦♦♣ s♦♥ r♦♠trs

Pr♦♥s rts s ♥ ②st♠s

❬❪ ♦sr ♥ ❲♦♦② s♥ ♦ s♠t ♠♦t♦♥ ♥♦

t♦t ♦♥rtrs ♦r♥ ♦ ♦tt rts

❬❪ ❨♥ ❳ ❲ ♥ ♥ ❩ ❩♦ rs♦t♦♥ ♥tr rt ♦r

♦s♦♦♣ r♦♠tr ♦r♥ ♦ ♠♦♥t♦rs ♣r

❬❪ ♠♦s♥♦ ♥ r ♥s ♦ ♠trs Psr s♦♥

t♦♥

❬❪ ♠♦s♥♦ ♥ ♦♦r ♦r② ♦ stt② ♦♠ ♦ ♦rs

♦ ♦rt P②ss ttr♦rt♥♠♥♥

❬❪ ❲ ♥♦s s♦tr♠ sq③ ♠s rtr② ♦ ♣♣ t♠ts

❳❳

❬❪ ♥ s♦tr♠ q③ ♠s ♦r♥ ♦ rt♦♥ ♥♦♦②

t♦r

r♥s

❬❪ ❱♦ ♦♠♣t ♠♦s ♦r sq③♠ ♠♣rs t ♥rt ♥

rr s ts ♦r♥ ♦ r♦♠♥s ♥ r♦♥♥r♥

❬❪ r♣♦ ♥ ❱ ③♥ t ♦♥ ♥tr♥ rr s ♦s ♦r♥ ♦

P②s ♥ ♠ r♥ t

❬❪ ❱♦ ♥ ts ♦ rr s ♦ ♥ s♦rt ♥♥s ♥ ♥ sq③♠

♠♣rs ♥ Pr♦♥s ♦ t ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♦♥

♥ ♠t♦♥ ♦ r♦s②st♠s ♣s

❬❪ ❱♠r ♦r ♦♥ ♥ ❱s♦s ♠♣♥ ♥ P tss

r♥ ♦♥

❬❪ ❨ ♦ P Ps♥♦ ♥ ♦ ❱s♦s ♠♣♥ ♠♦ tr② ♦s

t♥ ♠r♦strtrs ♦r♥ r♦tr♦♠♥ ②st♠s

❬❪ ❱♦ ♥ r♦s ♦♠♣t ♠♣♥ ♠♦s ♦r tr② ♠♦♥

♠r♦strtrs t srrt♦♥ ts ♦r♥ ♦ r♦tr♦♠♥

②st♠s ♥

❬❪ ♦ ♥ ❨♥ q③ ♠ r ♠♣♥ ♥ ♥s♦rs ♥

tt♦rs P②s

❬❪ ❱♦ ♠♣ t rt ♦s ♦r q③♠ ♠♣rs ♥

♥s♦rs ♣s

❬❪ ❱ r♥ ♥ rs♥ ♦♥♥r ②♥♠ ②st♠s ♥ ♥♥r♥

♣r♥r r♥ r r♥ r

strt és♠é

strt

♥ ss♠ ①♣♦rt♦♥ ♠♦st ♦ t s♥ qr ② ♣♦♥trr ♦♣♦♥s

s ♦♠♥t ② sr s ♦r r♦♥ r♦s s t② ♣r♦♣t ♥ t ♥r

sr r♦♥ r♦s ♦ ♥♦t ♦♥t♥ ♥② ♥♦r♠t♦♥ ♦♥ ♣r trts s

s♦rt s♣♥ t♥ rrs s rqr s♦ tt ts ♥♦s ♦♠♣♦♥♥t ♥

rt② rtr③ ♥ r♠♦ ② t tr♥ ♦r ♦♥sr♥

t ♦st ♦ ss♠ ①♣♦rt♦♥ ♥trs ♥ qst♦♥ t♥qs s♥ r

♣♦♥t rrs ♥ rr s♣♥ t♦ ♦♣ t♥q s r②

♥tr♦ ♥ ts ssrtt♦♥ rqr♥ rt ♠sr♠♥ts ♦ r♦♥ r♦t

t♦♥s t t r sr t ♠♥♠♠ ♦st t ♥ ♣♦r ♦♥s♠♣t♦♥

♦ rss ts ♥ t tss ♣r♦♣♦ss ♣r♦r♠♥ r♦tt♦♥ s♥s♦r

s ♦♥ t♥♦♦② ❯♥ rt♥ ②r♦s♦♣s s♥st t♦ r♦tt♦♥

rts tr♦ ♦r♦s t t s♦t♦♥ ♦♣ s ♥ ♥r r♦♠tr

s♥ ♦r r♥t ♣t♥ ♠sr♠♥ts ♦♥tr♦r s s♦

♠♣♠♥t t③♥ ♥ ♦rs♠♣ Σ∆♠♦t♦r t♦ ♥rs ②♥♠ ♣r♦r

♠♥s ♦ t s②st♠ ♦r♦ ♥②t s♥s ♦♥ t s♠t♦♥s r

♥ ② rt ♣r♦t♦t②♣s ♠sr♠♥ts t♦ s♥stt②

rs♦t♦♥ ♥ ①♣r♠♥t rs♦t♦♥ ♦ mrad.s−2 ♥ t r

q♥② ♥ Hz Hz s t♥ ♦t♥ s r ttr t♥ ♦tr ♠r♦

♠♥ ♥r r♦♠trs r♦♠ trtr ♦r♦r ♦♠♣rs♦♥ ♥②ss

r ♣r♦r♠ t s♣ ♥str♠♥ts s ♦r r♦tt♦♥ ss♠♦♦② t♦ ♦♥

♦♥ t st② ♦ s r♦tt♦♥ s♥s♦r ♦r ss♠ ①♣♦rt♦♥

②♦rs

s♠ ①♣♦rt♦♥ qst♦♥ t♥♦♦② ♥r r♦♠

tr ♣r♦r♠♥ r♥t ♣t♦r ♦r ♦♥tr♦ Σ∆♠♦t♦♥

strt és♠é

és♠é

♦rs ♣r♦s♣t♦♥ ss♠q ♥ rés ♣trs ts♥t ♣r♥♣

♠♥t s é♦♣♦♥s st é♣♦②é à sr r ♥ ♥rstrr s ♦♥s

ss♠qs ♣r♦♥♥t s♦ss♦ ♣♥♥t é♥r ♣té ♣r s é♦♣♦♥s

st r♠♥t ♦♠♥é ♣r s ♦♥s sr ♦ ♦♥s ② ♣r♦ts

♣r s♦r t♥t ♦♥♥é r ♥tr s ♦♥s sr ♥ ♦♥t♥♥♥t

♥ ♥♦r♠t♦♥ sr ♦♠♣♦st♦♥ s ♦s é♦♦qs ♣r♦♦♥s

t st ♥éssr ♠♣♦②r ♥ rés très ♥ ♣trs ♥s t

rtérsr ♣résé♠♥t s ♦♠♣♦s♥ts ♣s s trr ♣r s t♥qs

trt♠♥t s♥ ♦t♦s s ♦ûts ♥♥rés ♥ésst♥t ♥♦s ♠ét

♦s qst♦♥ s ♦♥s ss♠qs ♠♣♦②♥t ♠♦♥s ♣trs t ♣r♠tt♥t

érr ♣s rés ❯♥ t t♥q été ♠s ♥ é♥ ♠♦②♥♥♥t

♥ ♠sr ♣rés s r♦tt♦♥s sr r

♣st ①♣♦ré ♥s ♠♥srt st tst♦♥ ♥ ♣tr t

♣r♦r♠♥ ♣♦r ♠srr s r♦tt♦♥s sr r ♥ ♦ût ♥

♣♦s t ♥ ♦♥s♦♠♠t♦♥ étrq ♠♥♠① Ps ♣rtèr♠♥t ♦①

sst ♣♦rté sr rést♦♥ ♥ éér♦♠ètr ♥r ♠sr♥t r♦tt♦♥

♥tr♥♠♥t s♦♥ réér♥t ♦♥♣t♦♥ ♣tr ♣r♦♣♦sé ts

♥ t♥q ♠sr ér♥t ♣tés t ♥ ♦♥trô ♥ ♦ r

♠é r♣♦s♥t sr ♠♦t♦♥ Σ∆ ❯♥ ♠♣♦rt♥t tr ♠♦ést♦♥ t

s♠t♦♥ ♣r♠s rt♦♥ ♣srs ♣r♦t♦t②♣s q ♦♥t ♥st été

rtérsés ❯♥ rés♦t♦♥ ♦♥♠♥t mrad.s−2 ♥s ♥ ♥

réq♥s ♦♠♣rss ♥tr Hz t Hz ♥s été ♦t♥ s ♣r♦r♠♥s

♠srés sr♣ss♥t ♦♥ s trs éér♦♠ètrs ♥rs ttér

tr ♥♠♥t s ♥②ss ♦♠♣rts trs ♥str♠♥ts ♠sr

♦♥t ♣r♠s ♦♥r sr sté ♥♦tr s♦t♦♥ ♣♦r ♣r♦s♣t♦♥ ss

♠q

♦tsés

Pr♦s♣t♦♥ ss♠q ♠sr ♦♥s t♥♦♦ éér♦♠ètr ♥

r t ♣r♦r♠♥ ♠sr ér♥t ♣tés ♦♥trô ♥ ♦

r♠é ♠♦t♦♥ Σ∆