- Source: Force-sensing capacitor
A force-sensing capacitor is a material whose capacitance changes when a force, pressure or mechanical stress is applied. They are also known as "force-sensitive capacitors". They can provide improved sensitivity and repeatability compared to force-sensitive resistors but traditionally required more complicated electronics.
Operation principle
Typical force-sensitive capacitors are examples of parallel plate capacitors. For small deflections, there is a linear relationship between applied force and change in capacitance, which can be shown as follows:
The capacitance,
C
{\displaystyle C}
, equals
ε
A
/
d
{\displaystyle \varepsilon A/d}
, where
ε
{\displaystyle \varepsilon }
is permeability,
A
{\displaystyle A}
is the area of the sensor and
d
{\displaystyle d}
is the distance between parallel plates. If the material is linearly elastic (so follows Hooks Law), then the displacement, due to an applied force
F
{\displaystyle F}
, is
x
=
F
/
k
{\displaystyle x=F/k}
, where
k
{\displaystyle k}
is the spring constant. Combining these equations gives the capacitance after an applied force as:
C
=
ε
A
/
(
d
n
o
m
i
n
a
l
−
F
/
k
)
{\displaystyle C=\varepsilon A/(d_{nominal}-F/k)}
, where
d
n
o
m
i
n
a
l
{\displaystyle d_{nominal}}
is the separation between parallel plates when no force is applied.
This can be rearranged to:
C
=
(
ε
A
d
n
o
m
i
n
a
l
+
ε
A
F
/
k
)
/
(
d
n
o
m
i
n
a
l
2
−
F
2
/
k
2
)
{\displaystyle C=(\varepsilon Ad_{nominal}+\varepsilon AF/k)/(d_{nominal}^{2}-F^{2}/k^{2})}
Assuming that
d
n
o
m
i
n
a
l
2
>>
F
2
/
k
2
{\displaystyle d_{nominal}^{2}>>F^{2}/k^{2}}
, which is true for small deformations where
d
n
o
m
i
n
a
l
>>
x
{\displaystyle d_{nominal}>>x}
, we can simplify this to:
C
≃
(
ε
A
d
n
o
m
i
n
a
l
+
ε
A
F
/
k
)
/
(
d
n
o
m
i
n
a
l
2
)
{\displaystyle \simeq (\varepsilon Ad_{nominal}+\varepsilon AF/k)/(d_{nominal}^{2})}
It follows that:
C
≃
C
n
o
m
i
n
a
l
+
ε
A
F
/
k
d
n
o
m
i
n
a
l
2
{\displaystyle \simeq C_{nominal}+\varepsilon AF/kd_{nominal}^{2}}
C
≃
C
n
o
m
i
n
a
l
+
B
F
{\displaystyle \simeq C_{nominal}+BF}
where
B
=
ϵ
A
/
k
d
2
{\displaystyle B=\epsilon A/kd^{2}}
, which is constant for a given sensor.
We can express the change in capacitance
Δ
C
{\displaystyle \Delta C}
as:
Δ
C
=
B
F
{\displaystyle \Delta C=BF}
Production
SingleTact makes force-sensitive capacitors using moulded silicon between two layers of polyimide to construct a 0.35 mm thick sensor, with force ranges from 1 N to 450 N. The 8mm SingleTact has a nominal capacitance of 75 pF, which increases by 2.2 pF when the rated force is applied. It can be mounted on many surfaces for direct force measurement.
Uses
Force-sensing capacitors can be used to create low-profile force-sensitive buttons. They have been used in medical imaging to map pressures in the esophagus and to image breast and prostate cancer.
References
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