design and implementation of semi-passive tunable micro machined rf filters

8/3/2019 Design and Implementation of Semi-Passive Tunable Micro Machined RF Filters

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Design and Implementation of Semi-Passive

Tunable Micromachined RF Filters

Gabriel M. Desjardins <[email protected]>

Abstract – This paper presents design

techniques for integrated RF filters in the 2 GHzrange. These filters use quasi-passive LC

topologies. Bond wires serve as the inductive

elements, while both fixed parallel platecapacitors and tunable micromachined

capacitors are used. The tunable capacitors are

designed for fabrication in the MUMPS

polysilicon micromachining process. The effects

of finite quality factors and bond wire

inductance variation on the transfer

characteristic of 3-pole low-pass filters are

discussed. Filter simulation and optimization is

used to determine the desired value for the

tunable capacitance.

I. Introduction

Filters for cellular and PCS frequencies are

typically implemented as discrete circuits using

components with high quality factors. Thesedevices are mechanically tuned or trimmed during

the manufacturing process to achieve the desired

transfer characteristic. However, in many wireless

applications, it is desirable to have a tunable filter

that can allow a single radio to support multiple

architectures without duplication of hardware. This

requires that the filter characteristic be changeable.

It is not difficult to design tunable filters usingstandard integrated circuit processes, but it is

difficult to achieve the high quality (Q) factors

necessary for high-frequency operation.

We seek to develop a tunable low-passfilter for RF and wireless applications that uses low

Q components. Tunable MEMS capacitors with

relatively low Q factors have been developed for

use in oscillators at cellular frequencies [4][5].

Section II presents methods for filter design using

low- or finite-Q components. Sections III and IV

describe the properties of bond wire inductors andtunable MEMS capacitors, respectively. Section V

discusses filter optimization by tuning the capacitor

value. Section VI describes test structures, and

Section VII concludes the paper.

II. Filter TheoryFilters were long ago characterized

according to their passband attenuation and phase

characteristics. Component values for common

filter prototypes, such as Butterworth and

Chebyshev, are often simply read from tables for

simplicity and optimized in simulation.For finite Q circuit components, it is

convenient to specify filter prototypes using 3-dB

down k and q values [1], which relate the filter’sinsertion loss to the required Q factors of

components used in the circuit. A typical PCS filter

uses 3-pole Chebyshev design to filter a 60 MHzwide channel band around 1.88 GHz. This gives a

filter Q of 31; for 3 dB of insertion loss and 0.1 dB

ripple, the Q multiplier factor is approximately 10.

Thus the Q of the filter components must be 300 for

the filter to meet specifications. A plot of filter

insertion loss vs. Q multiplier is shown in Figure 1.

III. Bondwire InductorsHigh-Q inductors have been more difficult

to implement than capacitors in the same

technology. High-Q RF filters are implemented as

discrete packages using high dielectric constantceramics, Surface Acoustic Wave (SAW) devices

or cavities. These devices produce high-Q poles but

do not contain inductors or capacitors. Passive LC

filters are used extensively at low frequencies (<30

MHz) because of the availability of high-Q

inductors at these frequencies. Passive filters

contribute less noise and less distortion to a circuit

than comparable active filters, and occupy far lessarea than typical discrete packaged filters. We seek

100

101

102

103

-12

-10

-8

-6

-4

-2

0

Normalized Q

I L ( d B )

B u t t e r w o r t hC h e b y s h e v 0 . 0 1 d B R i p p l eC h e b y s h e v 0 . 1 d B R i p p l eC h e b y s h e v 0 . 5 d B R i p p l eG a u s s i a nL e g e n d r e

Figure 1: Normalized Filter Q vs. Insertion Loss



a high-frequency passive filter solution.CMOS-compatible passive inductors may

be implemented in several forms, including: 1)

circuit board spirals; 2) on-chip spirals; and 3) bond

wires. At GHz frequencies, on-board spirals can

have Q factors upwards of 200, but occupy

substantial area and require fabrication of circuit

boards [2]. Integrated on-chip spiral inductors are

smaller, but have Q factors on the order of 5 in the

frequency range of interest. Bond wire inductors

represent a trade-off: they have a Q an order of magnitude larger than on-chip spiral inductors at 1

GHz, and can be attached directly to an integratedcircuit. Unfortunately, the inductance of bond wires

is not well-controlled, so circuits that use bond

wires must allow for tuning other elements to

compensate for bond wire variation [3].

A. Bond Wire Quality Factor

Bond wires are frequently used to make

inductors because they have greater surface area perunit length than planar spiral inductors. This givesbond wires less resistive loss, and leads to a higher

quality factor. Bond wires also exhibit smallerparasitic capacitance to ground if they are placed

sufficiently far above any conducting planes. This

leads to a relatively simple physical model for bond

wires, since we may neglect the influence of other

conductors. The DC inductance of a bond wire is

given by:

Ll l

r =

−

µ

π0

2

20 75ln .

This gives an inductance of 2 nH for a standard 2

mm bond wire. The inductance value is weaklyfrequency-dependent, but varies on the order of 20-

25% depending on variations in length and themechanical quality of the bond.

For 1 mil Aluminum or Gold bond wires at

1 GHz, the skin depth is approximately 2.5 µm,which is small compared to the diameter of the wire

(25 µm). We assume that all of the current in thewire flows near its surface, giving an effective

resistance per unit length of 125 mΩ /mm at 1 GHz.

Rl

r

l

r

f = =

2 2

0

πδρ

µ

πρ

This does not take into account losses associated

with bond pads. The maximum inductor Q is:

Q L

Rr

l

r f = =

−

ωµ ρπ2

20 75 0ln .

The bond wire’s Q factor grows weakly with

increasing wire diameter, wire length, conductivityand operating frequency. Standard bond wires havea Q of approximately 50 at 1 GHz. The highest

achievable Q for 3 mil gold bond wires at 1.9 GHzis 284, though it is lower in practice.

IV. CapacitorsThe resonant frequency of an LC circuit is

inversely proportional to both L and C.If we are to

compensate for up to a 25% variation in the value

of our inductive element, we must be able to obtain

an equal variation in the capacitive element. We

0 2 4 6 8 1050

100

150

200

250

300

Length (mm)

Q

1 mil

3 mil

Figure 3: Bond wire Q vs. wire length at 1 GHz

0 2 4 6 8 100

2

4

6

8

10

12

Length (mm)

L ( n H )

3 mil1 mil

Figure 2: Bond wire inductance vs. length

1 1.5 2 2.5 3 3.5 4 4.5 550

100

150

200

250

300

350

400

450

Frequency (GHz)

Q

3 mil

1 mil

Figure 4: Bond wire Q vs. operating fr equency for 2

mm wire



propose to use a tunable parallel plate air -gap

capacitor. The top plate rests on springs attached tothe substrate, while the bottom plate is attached

directly to the substrate. A mechanical diagram of the capacitor is shown in Figure 5. The maximum

variation in capacitance is 50%.

In combination, the springs have an

effective spring constant k. A bias voltage isapplied to the upper plate, which creates an

electrostatic force that pulls it towards the bottom

plate. The top plate moves downwards until it

reaches an equilibrium displacement ∆D given by:

0

2

1)(2)( 2223 =−∆+∆+∆ bV

k

Ad d d d d ε

A is the area of the plates and d is the gap between

the plates. The pull -down voltage is the voltage

required to pull the top plate down to ∆D=d/3:

ε A

kd V b

3

27

8=

For RF applications, the pull -down voltage should

be less than 2V. If we use a standard 2 mm long

bond wire, we require a nominal capacitance of 3.5

pF in order to implement filters with 2 GHz cutoff

frequencies. A 500

µm square plate

provides sufficientcapacitance; for 2V

operation, we require

a suspension with a

spring constant of 80

N/m.

Suspendedparallel plate

capacitors have been

fabricated in several

processes using

similar structures

[4][5]. We may

construct asuspended plate

capacitor using the

three-layer Poly

MUMPS process.

Figure 6 shows a top view of the capacitorstructure. The fixed plate is fabricated in Poly1

instead of Poly0 to minimize the likelihood of

electrical contact between the suspension anchors

and the fixed plate. We model the suspended plate

as a cantilever fixed at both ends, which is

equivalent to two sets of series springs in parallel

with each other. The combined spring constant is:

3

3

3

2

)2 / (

3

L

EWt

L

EI k ==

Where E is the Young’s Modulus of Polysilicon,and W, t and L are the width, thickness and length

of the suspension. For a 36 µm wide by 77 µm longsuspension arm, the spring constant is 79.8 N/m

and the pull-down voltage is 2.12 V. Holes occupyapproximately 10% of the surface area of the

suspension arm; this allows for a wider arm while

simultaneously reducing its mass, but red ucing its

spring constant and resulting in a pull -down voltage

closer to 2V.

V. Filter Analysis and Expected Results

We implement a 3rd

-order LC filter using

two capacitors to eliminate the coupling betweeninductors. The circuit diagram is shown in Figu re 7.

One capacitor is implemented using the designdescribed in the previous section, while the other

capacitor can be a fixed parallel -plate design. The

bond wire Q is on the order of 50, while the tunable

capacitor Q is approximately 10; the Q of the fi xed

capacitor is sufficiently high that it may be ignored.

The relatively high sheet resistance of polysilicon

reduces the Q of the tunable capacitor compared to

Aluminum [5] or other metals. The inductor is

modeled as an LR series circuit; a two-dimensional

solver [6] gives a parallel resistance of

approximately 0.005 Ω to ground for a 500 µm

square poly-poly air-gap capacitor. This does notconsider the effects of etching holes in both plates.

Figure 8 shows the filter tuning process.

The top transfer characteristic is obtained for idealinductors and capacitors, nominally 2.9 nH and 3.5

pF. The inductor value is reduced by 20%, giving

the incorrect bottom transfer function. The

capacitor value is then tuned to produce the middle

characteristic, with less than 3 dB insertion loss and

a corrected cutoff frequency. Since the inductor and

capacitors vary substantially and their respective Q

factors are not predictable, this tuning process is

most easily performed by fabricating the circuit and

measuring each component. These measurementscan be back-substituted into a circuit simulator todetermine the optimal tuned capacitance value.

Figure 5: Tunable Capacitor

Figure 6: Tunable Capacitor

(top view)

Figure 7: Three -pole Low-pass Filter



VI. Test StructuresThere are numerous degrees of freedom in

designing the varactor structure. The capacitance

and pull-down voltage are functions of the

capacitor area, the size of the suspension andintrinsic material properties. The structure and

orientation of holes in the two plates greatly

influences the circuit parasitics. The size of the

capacitors limits the range of t est structures

(including bond pads, each capacitor measures at

least 800 µm by 600 µm). An entire wafer maycontain fewer than 16 capacitors.

Pull-down voltage is determined primarily

by the suspension spring constant, given in Section

IV, which is a function of suspension size. The

pull-down voltage for a capacitor with a 36 µmwide suspension as a function of the suspension

length is shown in Figure 9. Its thickness is fixed,and we fix its width and fabricate structures with

lengths of 80, 100 and 140 µm to obtain differentspring constants. The test structures consist of foursets of capacitors with the above suspension

lengths. Each set of capacitors uses different sized

etch holes (4, 6, 8 and 10 µm) in order to determinethe optimal hole size to release the structure. The

circuit layout is shown in Figure 10.

VII. ConclusionA tunable RF filter that uses bond wires,

and both a fixed parallel plate and a variable

MEMS capacitor was proposed. The design of the

variable capacitor was performed in the MUMPS

process. Circuit models for bond wires and tunablecapacitors were discussed and derived and their

variation with important pa rameters was

investigated. Compensation of circuit mismatch bytuning the filter was demonstrated using the derived

circuit models. The need for test structures for the

MEMS capacitor was discussed and appropriate

circuits were designed by varying structural

parameters.

VIII. References

1. A. Zverev, Handbook of Filter Synthesis, 1967

2. J.J. Ou, PhD Thesis, UC Berkeley, Dec. 2000

3. T.H. Lee, The Design of CMOS Radio-

Frequency Integrated Circuits, 19984. A. Dec, K. Suyama, A 1.9-GHz CMOS VCO

with Micromachined ElectromechanicallyTunable Capacitors, JSSC 8/2000, pp. 1231-1237.

5. D.J.Young, B.E. Boser, A micromachine-based

RF low-noise voltage-controlled oscillator, CICC1997, p.431-4, 606

6. Electro Student Edition, Integrated Engineering

Software, Winnipeg, Canada, 1996

Figure 8: Filter Optimization

Figure 10: Capacitor Layout

60 70 80 90 100 110 120 130 1400.5

1

1.5

2

2.5

3

3.5

Suspension Length (um)

V

p

Figure 9: Pull-down Voltage vs. Suspension

Length

design and implementation of semi-passive tunable micro machined rf filters

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