INF 5490 RF MEMS

LN10: Micromechanical filters

Spring 2011, Oddvar Søråsen Jan Erik Ramstad Department of Informatics, UoO

1 Today’s lecture

• Properties of mechanical filters • Visualization and working principle • Modeling • Examples • Design procedure • Mixer

2 Mechanical filters

• Well-known for several decades – Jmfr. book: ”Mechanical filters in electronics”, R.A. Johnson, 1983 • Miniaturization of mechanical filters makes it more interesting to use – Possible by using micromachining – Motivation  Fabrication of small integrated filters: ”system-on-chip” with good filter performance

3 Filter response

4 Several resonators used

• One silingle resonathtor has a narrow BP- response – Good for d e fini ng oscill a tor frequency – Not good for BP-filter • BP-filters are implemented by coupling resonators in cascade – Gives a wider pass band than using one single resonating structure – 2 or more micro resonators are used • Each of comb type or c-c beam type (or other types) – Connected by soft springs

5 Filter order

• NbNumber o f resonators, n, defines the filter order – Order = 2 * n

– Sharper ”roll-off” to stop band when several resonators are used •  ”sharper filter”

6 Micromachined filter properties

• + CtCompact ilimplemen ttitation – ”on-chip” filter bank possible • + High Q -ftfactor can bbidbe obtained

• + Low-loss BP-filters can be implemented – The individual resonators have low loss – Low total ”Insertion loss, IL” • IL: Degraded for small bandwidth  • IL: Improved for high Q-factor 

7 ”Insertion loss ”

IL: Degraded for small bandwidth

8 IL: Improved for high QQ--factorfactor

9 Mechanical model

• A coupled resonator system has several vibration modes • n independent resonators – RttthiResonates at their natlftural frequenci es determined by m, k – ”compliant” (soft) coupling springs • Determine the resulting resonance modes of the many-body system

10 Visualization of the working principle

• 2 osc illati on mo des – In phase: – No relative disp lacemen t be tween masses – No force from coupling spring – Oscillation frequency = natural frequency for a single resonator (both are equal, - “mass less” coupling spring*) •(* actual coupling spring mass can lower the frequency)

11 Visualization of the working principle

– OtOut of ph ase: – Displacement in opposite directions – Force from co upling spring (added force) – Gives a higher oscillation frequency (Newton’s 2.law, F=ma) –  the 2 overlappin g resonance frequencies are split into 2 distinct frequencies

12 3-resonator structure

• Each vibration mode corresponds to a distinct top in the frequency response – Lowest frequency: all in phase – Middle frequency: center not moving, ends out of phase – Highest frequency: each 180 degrees out of phase with neighbour

13 Illustrating principle: 3 * resonators

14 Mechanical or electrical design?

• MhiilitbtMuch similarity between description of mechanical and electrical systems • The dldual ciittircuit to a ”spring-mass-damper” system is a LC-ladder netktwork  – Electromechanical analogy used for conversion – Each resonator a LCR tank – Each coupling spring (idealized massless) corresponds to a shunt capacitance

15 Modeling

• Systems can be modeled and designed in electrical domain by using procedures from coupled resonator ”ladder filters” – All polynomial syntheses methods from electrical filter design can be used – A large number of syntheses methods and tables excist + electrical circu it simu lators • Butterworth, Chebyshev -filters • Possible procedure: Full synthesis in the electrical diddomain and conversion thildithto mechanical domain as the last step – LC-elements are mapped to lum ped mechanical elements • Possible, but generally not recommended –  knowledge from both electrical and mechanical domains should be used for optimal filter design

16 2-resonator HF -VHF micromechanical filter

• The coupl e d resona tor filter may be classified as a 2-port: – Two c-c beams –0.1 μm over substrate • Determined by thickness of ”sacrificial oxide” – Soft coupling spring – polySi stripes under each resonator  electrodes – Vibrations normal to substrate – DC voltage applied – polSitthlySi at the e dges function as tuning electrodes • (”beam-softening”)

17 Resistors

• AC-siliignal on input electrode through RQ1

–RQ1 reduces overall Q and makes the pass band more flat

• Matched impedance at

outttput, RQ2 – R’ s may be tailored to specific applications – e.g. may be adjusted for interfacing to a following LNA

18 ”Mechanical signal processing”

• This unit shows: Signal processing can be done in the mechanical domain

• Electrical input signal is converted to force – By capacitive input transducer

• Mechanical displacements (vibrations) are induced in x- direction due to the varying force

• The resulting mechanical signal is then “processed” in the mechanical domain – ”Reject” if outside pass band – ”Passed” if inside pass band

19 ”Mechanical signal processing”, contd.

• The mechanically processed signal manifests itself as movement of the output transducer

• The movement is converted to electrical energy

– Output current i0 = Vd * dC/dt

•  ”micr om ech ani cal si gn al pr ocessor”

• The electrical signal can be further processed by succeeding transceiver stages

20 BP-filter using 2 c-c beam resonators

21 22 Filter response

• Frequency separation depends on the stiffness of the coupling spring – Soft spring (”compliant”)  close frequencies = narrow pass band • Increased number of coupled resonators in a linear chain gives – Wider pass band – Increased number of passband ”ripples” –  the total number of oscillation modes are equal to the number of coupled resonators in the chain

23 24 Filter design

• Resona tors use d in m icromec han ica l filters are normally identical – Same dimension and resonance frequency – Filter centre frequency is f0 – (if ”massless coupling spring”) • Pass band determined by max distance btbetween nod e tops – Relative position of vibration tops is determined by

• Coupling spring stiffness ksij • Resonator properties (spring constant) kr at coupling points

25 Design, contd.

• At centre frequency f 0 and bandwidth B, spring constants must fulfill  f   k  B   0   sij       kij   kr  •kij = normalized coupling coefficient taken from filter cook books

 ksij  • RtiRatio   ittNOTbltlimportant, NOT absolute values  kr  • Theoretical design procedure A*

• (* can not be implemented in practice)

f – DtDetermi ne 0 an d k r Choose k sij for requ ire dBWd BW

– I real life this procedure is modified (procedure B )

26 Design procedures c-c beam filter

•A.Design resonators first – This will give constraints for selecting the stiffness of the coupling beam –  but bandwidth B can not be chosen freely! or •B.Design coupling beam spring constant first – Determine the spring constant the resonator must have for a given BW –  this determines the coupling points!

27 Design procedure A.

• A1. Determine resonator geometry for a given frequency and a specific material (ρ) – Calculate beam-length (Lr), thickness (h) and gap (d) using equations for f0 and terminating resistors (RQ)

• If filter is symmetric and Q_resonator >> Q_filter, a simplified model for the resistors may be used 

28 1/ 2 For a specific resonator frequency, geometry is E h  k  f  const   1 e  determined by: 0 2    Lr  km 

h, Lr : determined from f0  requirement

Wr , We : chosen as practical as possible

Added requirement : RQ  kre RQ  2 , Qres Q filter 0  q1 Q filter e

kre : given by resonator dimensions

0 : is given

q1 : from filter cook bkbook

Q filter : is given C V   V   P : only possible variation e P x d 2

VP : has limitations d : can be changed! (e, is centre position of beam) 29 Design-procedure A, contd.

• A2. Choose a realisti cwidth ofthf the coupli ng

beam W s12 • Length of cou pling beam shou ld be a qu arter wavelength of the filter centre frequency –  Coupling springs are in general transmission lines • The filter will not be very sensitive to dimensional variations of the coupling beam if a quarter wavelength

– Quarter wavelength requirement determines the length of the coupling beam Ls12

30 Design procedure A, contd.

• Constraints on width, thickness and length determines the coupling spring constant

ks12 – This limits the possibility to set the bandwidth independently (BW depends on the coupling spring constant)

 f0   ks12  B       k12   krc  – An alternative method for determining the filter- bandwidth is needed see design procedure B

31 Design procedure B

• B1. Use coupling points on the resonator to determine filter bandwidth

– BW determined by the ratio ks12

krc

• krc is the value of k at the coupling point! •krc position dependent, especially of the speed at the position

• krc can be selected by choosing a proper coupling point of resonator beam!

• The dynamic spring constant k rc for a c-c beam is largest nearby the anchors

– krc is larger for smaller speed of coupling point at resonance

32 Smaller speed Max. speed

keff 0  const  meff KE m  eff 1 v2 Smaller speed  effeff.. masshigher 2  effeff.. sppgring stiffnesshi gher

33 Positioning of coupling beam

• So: filter ban dw idth can be foun d by c hoos ing a value of fulfilling the equation kr  f   k  B   0   sij       kij   kr  – whihere k sij is given bhby the quarter wave lengt h requirement

• Choice of coupling point of resonator beam influences on the bandwidth of the mechanical filter 

34 Position of coupling beam

35 Design-procedure, contd.

• B2. GtGenerate a compl ltiltiitfete equivalent circuit for the whole filter structure and verify using a circuit simulator – Equivalent circuit for 2-resonator filter  – Each resonator is modeled as shown before – Coupling beam operates as an acoustic transmission line and is modeled as a T-network of energy storin g elements • Transformers are placed in-between resonator and coupling beam circuit to model velocity transformations that take place when coupling beam is connected at positions outside the resonator beam centre

36 37 HF micromechanical filter

• Coupling position • SEM of symmet ri c filt er : 7 .81 MHz l_c was adjusted to obtain the required • Resonators consist of phosphor doped poly bandwidth

• Torsion rotation of couppgling beam ma y also influence the mechanical coupling – Effecti ve val ue of l_c changes

38 HF micromechanical filter

Measured and simulated frequency response BW = 18 kHz, Insertion loss = 1.8 dB, Q_filter = 435

• Simulation and experimental results mat ch well in pass band • Large difference in the transition reggpion to the stop band – In a real filter poles that are not modeled, are introduced. Theyyp improve the filter sha pe factor, -due to the feed- through capacitance C_p between input and output electrodes (parasitic elt)Ffllittdlement). For fully integrated filters this capacitance can be controlled and the position of the poles can be chosen such that they contribute to a optimized filter performance 39 Comb structure

• Both series and parallel configurations can be used • In figure 5.11.b the output currents are added

40 Comb-structure, contd .

• Resona tors didesigne dfhid for having difftdifferent resonance frequencies f1 f2  f1  Q1

• Model taken from Varadan p. 262-263: – Model assumes a massless coupling beam. Possible to ignore the influence of the mass on the filter performance if the coupling beam length is a quarter wavelength of the centre frequency • Formulas inaccurate for high frequencies and small dimensions –  Better method: Use advanced simulation tools

41 Filter implemented using comb structure

42 43 44 Micromechanical mixer filters

• A 2 c-c beam structure can be modified to be a mixer – Suppose input signals on both on v_e (electrode) and v_b (beam)

• Fig 12.18 Itoh, shows schematic for a symmetric micromechanical mixer-filter-structure 

45 46 Mixer

Suppose vRF on electrode

Suppose local oscillator on beam, vb  vLO Force calculated: 1 C 1 C F  (v  v )2  (v 2  2v v  v 2 ) d 2 e b x 2 b b e e x Suppose : v  v  V cos t e RF RF RF vb  vLO  VLO cosLOt 1 C  F  ...   2V V cos t cos  t d 2 LO RF x LO RF  [where 2cos 1t cos 2t  cos( 1  2 )t  cos( 1  2 )t] 1 C  F  ...  V V cos(   )t d 2 RF LO x RF LO

Fd  ...... cosIF t

47 Micromechanical mixer filters, contd.

• SflltiSummary of calculations – Start with a non-linear relationship between voltage and force: voltage/force characteristic (square) – Linearization: Vp suppresses non-linearity – Voltage signals v_RF and v_LO are mixed down to itinterme ditdiate frequency (force) , ω_IF = difference between frequencies!

• Transducer no. 1 can couple the signal into the following resonator – If transducer no. 2 is designed as a micromechanical BP filter with centre frequency ω_IF,,g we will get an effective mixer-filter structure

48 Micromechanical mixer-filter, contd .

•  Mixer structure is a functional-block in a RF- system (future lecture) – This is a componen t tha t may rep lace presen t miIFixer + IF- filter (intermediate-filter) – Lower contact-loss between ppyarts and ideally zero DC power consumption •A non-conducting coupling beam is used for isolating the IF- port (e. g. 2. beam) from LO (local oscillator)

49 Mixer-filters using square -frame resonators

• MdMade us ing a pos t-CMOS process

• Laterally moving structures

• Examples from research at the Nanoelectronics group

50 FFSFR architecture

51 Free-free Square Frame Resonator

52 FFSFR w/self -assembly electrodes

VLO

A 4μm 181.8μm A’

VRF

AAA’A’

53 FFSFR filter design

45〫support beams Can be used as a 45〫couppgling beam

54 4th order FFSFR mechanical filter

55 SEM pictures - 6th order FFSFR

56 2 Mechanically coupled FFSFR

MODE 11MODEMODE 2

Bandwidth = 71.6 kHz fc = 9.978 MHz

57 3 Mechanically coupled FFSFR

MODE 1 MODE 22MODEMODE 3

Bandwidth = 117.8 kHz fc = 10.009 MHz

58 Simulation results

59