NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p1
Lecture 2-5 Mechanical Transducers
-- Mechanical Circuit Components
 Mechanical resonators

Applications of precision frequency generation and filters.
1.
Cantilever resonators a.
Resonant frequency of singly clamped cantilever: f
R

1
2
 k m

1 .
03
2
 tv
L
2 v

E

Where k: beam spring constant, m=beam mass, L= length, t= beam thickness, v

E

: acoustic velocity. (for silicon: E=130 GPa,

=2.33 g/cm 3 , v=7470 m/s)
Note: beam width is not effective at all in the equation!!
The key parameter is the beam thickness to the length ratio. b.
Gravity effect
Deflection due to gravity:
 g

3
2
WL
3
(
Ewt
3
) g

3
2

L
4
(
Et
2
) g

0 .
38 f
R
2
W=cantilever weight, w=beam width, g=gravity=9.8 m/s 2
=> the frequency shift due to gravity

NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p2
 f f
R
 
1
6 Lf
R
2
Note: large effect in low frequency region. c.
Noise effect
Noise equivalent displacement:

N

2

3 k b
T f
0
3
MQ
M: effective mass of the cantilever
Note: reduce size (mass) of cantilever, noise going up!!
Thermal noise will be a major problem in micro scale cantilever device. Also drift may occur due to adsorption and desorption of contaminating molecules. d.
Viscous damping effect
For very low pressure: p<0.04/w (in Pa, w: width of beam)
Q

93 ( t
L
)
2
[
( E

)
1 / 2
P
]
=>Strong dependence of Q on the ambient gas pressure.
For larger pressure: p>0.04/w (in Pa, w: width of beam)
(1). Away from wall (no squeeze film effect)

NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p3
Q

( E

)
1 / 2
24

L
2 wt
2
=> Q is reduced
(2). close to wall (d/w<1/3, squeeze film effect)
Q

( E

)
1 /

L
2
2 wt
2
( d w
)
3
=> Q is further reduced
Resonant gate transistor (Westinghouse, 1967)
Using gold cantilever beam, V p
=20-70 V, L=500
 m, t=d=5
 m, Q=100 in air, f
R
=6.5 kHz (can be fabricated from 1-50 kHz)

NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p4
Project was abandoned, due to
(1). inadequate control over fabrication steps
(electroplating), which greatly affect Q and f
R.
(2). temp coefficient of material,
(3). resonant > 50 kHz is difficult (now is solvable),
(4). high polarization voltages
Others: double side clamped beam, using capacitance or piezoelectric method to sense.
2.
Lateral resonators
Fold-beam lateral comb-drive resonator (Nguyen and Howe,
1993):
Q can approach 10 5 in vacuum, for 2
 m polysilicon beam and gap, f
R
can approach 100 kHz, temp coefficient of frequency: -10 ppm/

C. Locally heating of the structures can reduce shifts in resonant frequency with temperature.
3.
Membrane resonators
Provide higher frequency (microwave) resonation. The

NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p5 frequency can go as high as 1.5-7.5 GHz, and Q can be 1300.
On chip heater for frequency control and stabilization.
 Mechanical relays and RF switches


Provide physical contact or separation on desired states.
Relays: optimized for high currents
 RF switches: optimized for impedance and parasitic parameters required for high frequencies.
1.
General purpose relays
 Applications: electronic switching where high resistance and low capacitance isolation is needed. Because
 solid-state switches do not have good off-state isolation and low cross talk properties.
Most are electrostatic drive for low power consumption, although electromagnetic and thermal drives have been demonstrated. a.
Electrostatically driven relays
Peterson (1978):

NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p6
Bulk micromachined silicon and plated thick gold as contact material, EDP bulk etch release relays.
Threshold voltage: 60 V, actuation time: ~40
 s, deflect angle: 4

, 10 billion cycles. Current density: 5*10 4
A/cm 2 . Contact resistance: 5

.
Drake (1995):
Bulk micromachined, metal sealing bound, actuation voltage: 50-100 V, on resistance~2.3

, 100 million cycles,
20
 s switch time.

NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p7
Saffer and Kim (1995):
MCNC process (300~500
 m)+mercury droplet (10
 m), drive voltage: 60 V, contact resistance between
1.9-3.2 k

, current capacity > 10 mA. Potential for high current applications. b.
Magnetically driven relays
Rogge (1995):
Two stage LIGA based magnetic relay with permalloy core and electroplated copper coils. Switch current at
1A for Ni and 45mA for NiFe. Switch current: 1 mA.

NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p8
2.
RF switches and switched circuits
Impedance matched to transmission lines and potentially capacitively coupled.
Applications: digitally controlled antenna matching circuits, transmit/receive switches, phase shifters, input filters, tuning circuits, etc.
Goldsmith, et al. (1996):

NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p9
Membrane-deflection-based capacitive RF switches for micro wave applications. Non-conductive anti-stiction coatings on the electrodes. Low power by electrostatic driven,
Important parameter--Off/on impedance:
Z off
Z on

C on
C off


R d air d ins
 d ins


R d air d ins
Impedance ratio, 100:1, enough for microwave application.
Pull down voltage: 50 V, insertion loss 0.3-0.5 dB at 10 GHz, off/on isolation 11 dB, switch time: 6
 s.
Zhou (1997):

NTHU ESS5841 The Principles and Applications of Micro Transducers
F. G. Tseng Spring/2001, 2-5, p10
Thermally driven bimorph, on-resistance 0.6-0.8

, power 8 mW (20 V), closure times 12
 s, 3.2*0.9 mm.