A Bidirectional Circuit for Actuation and Read-outof Resonating SensorsMehdi Azadmehr, Belal K. Khajeh, Yngvar Berg

Buskerud and Vestfold University CollegeInstitute of Technology

Horten, NorwayEmail: mehdi.azadmehr@hbv.no

Abstract— In this paper we have demonstrated a novel ap-proach for actuation and read-out of resonating sensors. In thisapproach, instead of reading the amplitude of the resonatingbeam in resonance, we use the frequency of the beam asa measure of the sensors response. By using a bidirectionalamplifier a pulse is sent to a resonating sensor in one directionand the frequency response of the sensor is measured using theopposite direction of the amplifier. This approach results in morecompact and more power conservative systems. This approachmimics the way radars operate where a pulse is sent out andthe reflection is measured. The circuit is very compact with lowcomponent spread and consumes an average power of 22µW anda maximum power of 100µW when actuating the sensor.

I. INTRODUCTION

Micro Electro Mechanical Systems (MEMS) for years havebeen employed in wide sensor applications to detect themagnitude environmental values in almost any energy domain.One of the most successful MEMS sensors are the resonating-beam sensors [1, 2] which can be made in various shapes andused for detecting various types of environmental signals suchas humidity [3], acceleration [4, 5], weight of small particles,gas sensors [6, 7, 8] and etc. Resonating sensors usually needto be activated, i.e. the sensor has to be actively forced intooscillation using electrical signal. There are three mechanismsfor exciting such a resonating sensor, electromagnetic, piezo-electric and electrostatic actuation. The traditional approachhas been that a circuit is used to keep the beam in resonanceand another circuit is used to read out the response of thecircuit. The amplitude of the oscillation in resonance is usedas a measure of the environmental signals. This approach mayhave some drawbacks such as high power consumption andcomplexity of the activation and read-out circuitry. Stemme[9] have reported resonant sensors with different excitationsand detection techniques in which each of them has its ownadvantages and disadvantages. In this paper a new approach foractivation and read-out is introduced. We use a bidirectionalamplifier [10, 11] as both the activation and read-out circuit.In such a case when the bidirectional interface circuit has adirection toward the sensor, a square pulse is sent to the sensor,and immediately after, the direction of the amplifier is swappedto read the sensor frequency response. Then the resonancefrequency of the sensor can be amplified by the circuit andmeasured by the following systems. As in many applications

where the continues sensing is not necessary, this approachmay result in less power consuming and faster systems.

II. ACTUATION AND READ-OUT USING A BI-DIRECTIONALCIRCUIT

Pulse in

Out

C1

CB

Cio

Cin

Φ

Φ

S1

VRLC

Fig. 1. Block diagram of the actuation and readout system.

The block diagram for the proposed sensor readout circuitryis illustrated in figure 1. In this figure CB is a resonatingsensor which is connected in series with capacitor C1 toV DD. These two capacitors form a voltage divider whichtranslates capacitive variations to voltage variations. The pointbetween the two capacitors, marked VRLC is connected to abidirectional amplifier through a capacitor Cio. The other sideof the bidirectional amplifier is connected to a switch thatconnects the amplifier to a pulse generator or the output ofthe system depending on the operation direction of the circuit.This switch and direction of the amplifier is controlled by acontrol signal connected to S1.

III. RESONATING SENSOR MODEL

The variable capacitive sensor CB in figure 1 can berealized using a polysilicon clamped-clamped cantilever beamwith a fixed plate placed under the beam with a distance dconnected ground as illustrated in Fig. 2. Capacitive sensinghas some advantages like as low cost, low power consumption,stability, compatibility with CMOS technology and mass pro-duction. To model this micro beam as an elastic continuum,following assumption should be considered. a) We assume thatthe amplitude vibration of the plate in resonance frequency islimited enough to consider linearity regime. b) The end plateis displaced out of plane in which two electrode plates create

978-1-4799-3773-8/14/$31.00 ©2014 IEEE

variable parallel plate capacitor. c) The mass of the beam isuniformly distributed. If an actuation voltage is applied onthe beam, it bends in the middle toward the ground platedue to electrostatic force between the beam and ground plateand when the voltage is removed, the beam vibrates towardits resting point. Maximum deflection of this beam occurs inmiddle of the beam and pressure, acceleration, temperature,force can cause a shift in natural frequency of the beam. Ifthe beam is actuated, then the resonating frequency is givenby [12]:

fbeam = 0, 615h

l2

√E

ρ(1− υ2)(1)

Where E is Young modulus,ρ is mass density, υ is poisonsratio of the material and h is the height, l is the length of thebeam. Table 4.3 shows the properties of polysilicon which thebeam is made from and dimensions of the beam.

Property l(m) w(m) h(m) υ(kg/m3) ρ E(Pa)Size 4m 200u 80u 120 2320 16E10

TABLE ISIZES AND MATERIAL PROPERTIES OF THE CLAMPED-CLAMPED BEAM

USED AS MODEL IN THIS PAPER.

l

w

VRLC

CB d

h

Fig. 2. The clamped-clamped cantilever used as resonating sensor and modelfor the RLC resonator in figure 3.

Figure 3 shows the simulation setup including the bidirec-tional amplifier where the beam is replaced by a equivalentelectrical model based on [13]. In this model the mass Mis represented by a inductor L and the spring constant k isreplaced by a capacitor C and the damping of the system bwith a resistor R. The R,L,C are connected in series whichforms a resonator with a resonant frequency equal given by:

fRLC =1

2π

√1

C(L+ δL)(2)

In our simulations the C = 300pF and L = 300uH andR = 10Ω. δL is the change in L that can be detected. Thebidirectional autozeroing amplifier for activation and readoutis based on digital inverter and consists four transistors:M1,M2,M3,M4. The power supplies V DD and GND ofthe autozeroing amplifier are excluded and instead named P1

and P2 and the input and the output are called IO1 and IO2.Because of the symmetry of the circuit, swapping the railes,P1 and P2 will change the direction of the circuit, i.e. theoutput becomes input and vice versa. This approach of makingcircuits bi-directional is explained in detail in [14]. The changeof the direction is controlled using a clock S1, where P1 andP2 are inverted compared to each other. When S1 is high, thenM6 is on and M5 off, IO1 is the input and IO2 is output andtransistors M1 and M2 work as amplifier. These transistorsare made large to be able to drive the resonator, see table 2.The input of this amplifier is made floating using an inputcapacitor, Cin. The floating gate is biased by transistors M3and M4 to V DD/2. These transistors form a non-invertingbuffer that operates in weak inversion and are used to initiatethe floating gate. The output of the amplifier is connected tothe input of the non-inverting buffer and the output of thenon-inverting buffer is connected to the input of the amplifierwhich forms a loop. This loop will force the floating-gate andthe output of the amplifier towards a weak and a continuousequilibrium state close to V DD/2. When S1 is high, we cansend a pulse to the RLC resonator from the input in throughthe amplifier which starts to resonate. Immediately after S1goes to ground which results in swap of P1 and P2 and theamplifier changes its direction. M6 is turned Off and M5 isturned On. In this direction the amplifier amplifies the responseof the RLC resonator to the output. This behavior is shownin figure 4 where an activation and readout are shown.

IO2

IO1

M2

M1M3

M4

P2

Cio

P1

C1

VRLC

R

C

L

Pulse in

Out

S1

M5

M6

Cin

Fig. 3. Schematic of bi-directional amplifier in the control circuitry. Thedirection of the circuit is controlled by swapping VDD and Ground.

Transistor M1 M2 M3 M4 M5 M6Width(nm) 3000 1000 120 120 900 900

TABLE IITRANSISTOR SIZES OF THE AMPLIFIER SHOWN IN FIGURE 1

IV. SIMULATIONS

The simulations presented in this paper are valid for the90nmCMOS transistor models from STM having a V DDequal to 1.2V and threshold voltage of 0.25V . Figure 4 showsthe simulation results of the circuit shown in figure 3 for 2actuation and readout cycles every 100µs. The period betweeneach activation and readout can be controlled depending onthe need for sensor measurement. Figure 5 is a close-up ofthe actuation and readout transition marked with a circle infigure 4 at the t = 100µs. Initially P1 (red line) is high and P2(black dashed line) is low and Io2 is the output and the circuitis in reading mode. At t = 100µs P1 goes low and P2 high.The amplifier is changing its direction and at t = 102µs anactivation pulse, the blue line in the plot, is sent to the RLCresonator and the resonator becomes activated. At t = 104µsP1 goes high and P2 goes low again and the amplifier goes toread-out mode and amplifies and inverts the response of theRLC circuit to the out node(the green line).

0. 8 1 1. 2 1. 4 1. 6 1. 8 2

x 10 −4

− 0. 2

0

0. 2

0. 4

0. 6

0. 8

1

1. 2

P1(S1)

P2

Out

Pulse in

VRLC

Time(S)

Vo

lt(V

)

Fig. 4. The response of the circuit shown in figure 2. P1 and P2 are powersupplies of the circuit.

One type of the resonating sensor could be a beam massdetector where the change of resonance frequency of the beamis a measure of the change in the mass on the beam. Wehave modeled this change of mass M as changes in L inthe equivalent RLC resonator as shown in figure 3. Figure6 shows the response of the system when L is swept from100µH to 500µH with an increase of 50µH . From the figurewe see that as the L increases the amplitude of the signal isdecreased, this can be seen by comparing the three markedcurves in figure 6. The increase of L in figure 7 shows thefrequency change as the value of the inductor is changed. Thefrequency is decaying as the size of the inductor is increasedwhich is described by equation 2.

0.92 0.94 0.96 0.98 1 1.02 1.04 1.06 1.08 1. 1 1.12

x 10 −4

− 0. 2

0

0. 2

0. 4

0. 6

0. 8

1

1. 2

Time(S)

Volt

(V )

P1

P2

Out

Pulse in

VRLC

Fig. 5. The actuation and read out area marked with black circle in figure4.

1.05 1.1 1.15 1.2 1.25 1.3

x10 −5

0.4

0.5

0.6

0.7

0.8

0.9

1

Time(S)

Vo

lt(V

)

L=100µH

L=500µH

L=300µH

Fig. 6. The response of the system to various values of the inductor L in theresonator varied from 100µH to 500µH with incremental step of 50µH .

A. Power Consumption

Figure 8 is the power consumption of the amplifier. Theblack dashed line is the total power consumption, the red lineis the power consumption of amplifier made of M3 and M4and the blue line is the power consumption of the amplifiermade of M1 and M2. From the simulation we can see thatonly 2 of transistors are consuming power , this is due tothe fact that only two transistors are working as amplifiers atany time and the other two transistors are operating in weakinversion and only act as biasing circuitry. The figure doesntinclude the power consumption of the clock signals becausethese are secondary circuitry and can vary depending on thesystem and application. We can clearly see that the circuit hasa continues power consumption of 22µW during read-out andreaches a peak of 100µW during a actuation of the RLC.The continues power consumption is due to the fact that theread-out amplifier is always active since the gates of transistors

1 1.5 2 2.5 3 3.5 4 4.5 5

x10−4

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.6x 10

6

L(H)

Fre

quen

cy(f

)

Fig. 7. The output frequency as the function of various values of the inductorL.

are always biased at V DD/2. The main drawback of this isa constant power consumption, even when no oscillation ispresent, but on the other hand we have an amplifier which iscontinuously on with fast response and smoother transition.The power consumption during the actuation is higher, this isdue to the large width of transistors driving the RLC resonator.The total power consumption is also dependent on how oftenand how long the actuation is needed.

0.96 0.98 1 1.02 1.04 1.06 1.08 1.1 1.12 1.14

x 10−4

0

10

20

30

40

50

60

70

80

90

100

110

Time(S)

Power(μW)

Fig. 8. The power consumption of the circuit, the dashed black line showsthe total consumption. The red line is the consumption of M1 and M2 andblue line is the consumption of the M3 and M4.

V. CONCLUSION

In this paper we have presented a novel approach foractuation and read-out of resonating sensors. By using a bidi-rectional circuit we are able to both actuate a resonating sensorand read out its response eliminating the need for two differentcircuits for actuation and read-out. The circuit presented isvery simple in its design and consists of only transistorsand capacitors. The circuit can be used with various typesof MEMS resonating sensors such as beams and discs. Thecircuit is also power conservative and the power consumptiondepends on how often and how long one needs to read-out theresponse. In our simulation as shown in figure 8 the actuationhas a duration of 4µs. This duration is chosen for presentationpropose and is much longer time than necessary and can bedecreased as actuation is a fast process. This will again furtherdecrease the power consumption.

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