Poloha

Kapacitní senzor s proměnnou vzduchovou mezerou
C =
εS
,
d
⎛ 1
∆C
= εS⎜
−
⎝ d + ∆d
1 ⎞
⎟
d ⎠
⎛ 1
= Cd⎜
−
⎝ d + ∆d
1 ⎞
⎟
d ⎠
= C
∆d
−
d
∆d
1+
d
∆C
=
C
x =
∆d
−
d
∆d
1+
d
∆d
d
y =
f ( x)
=
⎡δf
⎤
f ( x0
) + x⎢
⎣δx⎥
⎦
Taylorova řada
x
f ( x)
= − 1 + x
x
δf
f (0) = 0, =
δx
0
+
1
2!
1
2
x
⎡
⎢
⎣
δ
,
δ
δ
2
2
f ⎤
⎥
⎦
2
x
f
= −
x
0
+
1
3!
3
x
δ
,
⎡δ
⎢
⎣ δ
3
f ⎤
⎥ ⎦
3
x
2 2
3
( 1+
x) δx
( 1+
x) δx
3
( 1+
x) 4
2
3
f
=
x
0
3⋅2
....
∆C
= −
C
∆d
+
d
2
⎛ ∆d
⎞
⎜ ⎟
⎝ d ⎠
3
⎛ ∆d
⎞
− ⎜ ⎟
⎝ d ⎠
+ ....