Principles of MEMS Transducers
Page 1 of 5
Prepared by D. Arnold
November 9, 2010
EEL5225 Principles of MEMS Transducers
HW7
Fall 2010 Semester
Assigned: Thursday, 11/4
Due:
Wednesday, 11/10
1.
Some details on general twoport theory…
a.
Prove that the
units
of
T
EM
and
T
ME
in the linear transducer model are the same.
b.
Derive the following relationship between the reciprocal impedance and admittance
transduction factors,
T
and
G
:
G
=
−
T
Z
EB
Z
MS
a.
T
EM
=
V
U
I
=
0
So,
T
EM
units
=
volts
m
/
s
Reducing V to base SI units:
V
=
W
A
=
J
/
s
A
=
J
A
⋅
s
=
N
⋅
m
A
⋅
s
=
kg
⋅
m
2
A
⋅
s
3
∴
T
EM
units
=
V
⋅
s
m
=
kg
⋅
m
A
⋅
s
2
 1
And
T
ME
=
F
I
U
=
0
So,
T
EM
units
=
N
Amps
Reducing
N
to base SI units: (use Force: F=ma)
N
=
kg
⋅
m
s
2
So,
T
EM
units
=
N
A
=
kg
⋅
m
A
⋅
s
2
 2
Thus, from equations 1 & 2, the units of
T
EM
and
T
ME
in the linear transducer model are the same.
b.
From L7, slide 17:
 1
 2
where
(reciprocal system)
From eq. 2,
Substitute in eq. 1,
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Principles of MEMS Transducers
Page 2 of 5
Prepared by D. Arnold
November 9, 2010
Solve for U,
∴
But, from slide 18
So, we get,
Now, from slide 21,
And, for reciprocal system,
G
ME
=
G
EM
=
G
∴
G
=
−
T
Z
EB
Z
MS
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 Fall '08
 Arnold
 Elementary algebra, SI base unit, International System of Units, Metre, Centimetre gram second system of units

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