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B. Boser 1
Electrical On-Chip Resonators
Bernhard E. BoserBerkeley Sensor & Actuator Center
Dept. of Electrical Engineering and Computer Sciences
University of California, Berkeley
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Outline
Tunable Capacitors
3-Dimensional Inductors
Application:Voltage-Controlled Oscillator (VCO)
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Tunable Capacitors parallel plate Aluminum
200x200 m2, 1.5 m gap IC compatible processing
2pF + 15% for 3V tuning voltage
Q=60 at 1GHz
Comparison with junction capacitors:
+large signal operation (no forward biasing)
+excellent linearity- special packaging
- Brownian motion noise
Ref: D. Young et al, Hilton-Head 1996.
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Tuning Range Pull-in voltage
+50% max
Vp = 4V for fr=40kHz
Parasitics
CBP = C0 CTP < 0.1 C0
(larger in this design)
C0
CBP
CTP
Rtether
23
0
027
8r
AlP txV
=
X0=
t=
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Fabrication Process
1m sputtered Al Sacrificial photoresist
Tmax = 150oC
(plasma etch) Stiction / welding no
problem
(residual resist?)
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Coil Inductors Electroplated copper
50x5m2 traces 10-cm Silicon substrate Coil:
Increased L, Q Reduced substrate loss
Increased self-resonance
Reduced area
500 m
650 m
Ref: D. Young et al, IEDM 1997.
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Inductor Fabrication
Passivation oxide
Seed mask
5m electroplated Cu
for bottom traces(50m trace width)
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Fabrication (cont.)
Alumina core
Electroplated photoresist
Laser lithography
Electroplated Cu
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Inductor Performance
Turns Q (1GHz) L fself
1 30 5nH >10GHz
4 16 14nH >5GHz
low substrate losses
loss limited by bottom contact
(higher Q possible?)
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Voltage-Controlled Oscillator
VCO (136dBc, f=3MHz)
Meets GSM noise specs MOS Colpitts oscillator
Ref: Solid-State Sensor and ActuatorWorkshop, 1998.
Vbias
4pF
1pF
8.2nH
50pF Ctune
Rx
VDD
Vtune
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Power versus Q
Phase noise (relative to carrier):(Leesons Equation - simplified)
Increased Q Lower Power Psig
2
0
2
2
0
1
2
2
11
2)(
+=
f
f
QP
TFk
f
f
QP
TFkfN
sig
B
sig
B
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Power versus Q (cont.)
E.g. F=100,
fo=1GHz,
f=3MHz,N(f)=136dBc/Hz
Q=16 Psig= 5mW
Q= 4 Psig= 125mW
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Brownian Motion Noise
Inertial forces compensated by PLL
Brownian motion displacement noise:
( )2
2
22
2
11
14
+
=
rr
rBn
f
f
Qf
fmQ
Tkfx
0 2 4
20
0
10
30
x frel 1,( )
x frel 10,( )
50 frel
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FM Modulation
Resonant frequency shift
FM Modulation
( ) +=
+= 1
21
10
0
0x
x
LCr
|Vosc|
0 0+noise0-noise
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Ambient Pressure
Atmospheric pressure Vacuum (20mT)
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Oscillator Phase Noise
Brownian noise
insignificant beyond fr
Increasing Q concentratesnoise at fr
Increasing mass reducesnoise, but increases tuningvoltage
Large Cp reduces noisef
Selectrical
Smechanical
-20dB/dec
-60dB/dec
-30dB/dec
f1/f fr
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Results
-136-1943 MHz-105-105100 kHz
-85-6410 kHz
Sel
[dBc/Hz]Smech
[dBc/Hz]f
atmospheric pressure (low Qmech)
mechanical noise dominates close to carrier not significant problem in most applications
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Inductor / Resonator Applications
Stand-alone components Impedance Matching (e.g. LNA)
Noise-less loads
Transformers, Baluns
Filters
Voltage-Controlled Oscillators
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