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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