Upload
others
View
1
Download
0
Embed Size (px)
Citation preview
HAL Id: tel-01495449https://tel.archives-ouvertes.fr/tel-01495449
Submitted on 25 Mar 2017
HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.
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
♠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
♣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
♣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
♣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♦♥
♣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
♥
♣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 ♥
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♦♦♣ ♠♦
♣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♥
♣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
♦♠♣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♦♥
♣♣♥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∆