A Fully Differential Amplifier with CMOSFeedback Biasing for sensing CMUT signals

Soumya Bose∗ and Pradip Mandal†∗India Design Center, Rambus Incorporated, Bangalore, India

†Department of Electronics & Electrical Communication Engineering, Indian Institute of Technology, Kharagpur

Abstract—The paper illustrates design of a fully differentialamplifier to sense current signals generated by CMUT forultrasound imaging. Detection of reflected ultrasonic waves frombody tissues requires low noise amplifier with wide input dynamicrange. The transducer, being capacitive, isolates dc voltage fromthe input of the amplifier necessitating additional biasing circuit.In this work, a differential amplifier topology is chosen for itsability to reject common mode interference. Biasing is done bylow frequency feedback using CMOS transistors which do notadd significant noise to the system. The amplifier is designed in0.18 μm CMOS process. Its input referred noise is 24.3 μV rmsin the band 1-15 MHz. At 10 MHz it provides a gain of 25.5 dBwith an input dynamic range of 62.5 dB. The amplifier consumes314 μW of power with 1.8V-GND supply.

I. INTRODUCTION

Capacitive Micromachined Ultrasonic Transducer (CMUT)has emerged as a captivating alternative to piezoelectric sensorfor sensing ultrasonic signals [1]. The transducer is adept insensing ultrasonic signals over a wide range of frequencieswith high sensitivity. Alongside its miniaturized geometry,ease of fabrication using MEMS technology unfolds a newdimension in the realm of ultrasonic receiver electronics.Integration of front-end circuits with the sensors is possiblebecause of CMUT’s compatibility to CMOS. This enhancesperformance of the signal acquisition system in terms of noisedue to reduced interconnects.The sensor comprises of thin parallel plates with a moving

plate facing the ultrasound waves as shown in Fig. 1(a) Itmaintains a static capacitance Cs with a DC bias. Incidence ofultrasonic wave deforms the moving plate and causes a smallchange in the capacitance value. Hence it transduces ultrasonicsignal to ac current [1]. The simplified equivalent model ofCMUT in Fig. 1(b) depicts it as a current source shunted withthe static capacitance Cs and a resistance Rs correspondingto the acoustic impedance [2]. A suitable amplifier is neededto sense the current signal and convert it into voltage forsubsequent signal processing.Transimpedance amplifier (TIA) with shunt-shunt feedback

is extensively used to sense capacitive signal current. However,high resistive feedback adds more noise to the output of theamplifier. To alleviate, capacitive feedback topology has beenused [3], [4], [5]. Being a capacitive sensor, CMUTs decouplesdc voltage from the input of the amplifier. So an externalbiasing circuit is required. But capacitive feedback imposesa challenge to provide dc bias to the amplifier. Switchingarchitecture has been adopted [3] to solve the problem. In this

A

+−CMUT

Iac coupC

Rs

Vdc

(a)

CsRsis

(b)

Fig. 1. (a) Operation of CMUT as receiver (b) Electrical equivalent modelof CMUT

scheme the TIA is configured as a unity gain buffer during thetransmit mode to store dc voltage in the input transistor’s gatecapacitance. Stored voltage supplies bias in the amplificationmode. But such a switching topology suffers from the effectslike charge leakage, clock feed-through, charge injection ofswitches. A charge adaptation circuit can also be used [4] tocontrol the dc voltage of the input floating node of a capacitivecharge amplifier. However, it entails complex tunneling andchannel hot electron injection mechanisms.In this work, we propose a simple differential amplifier with

CMOS feedback biasing to sense capacitive current signals.Single ended CMUT signal can be transformed into a differ-ential one by comparing its varying capacitance with respectto that of a static reference capacitor [6]. While single endedsignal sensing has been reported in most of the literatures, adifferential topology is explored here for its ability to cancelcommon mode interference. The dc biasing of the amplifier isdone using symmetrical CMOS feedback on either side of thedifferential input pair. Ultrasound imaging probe consists of acluster of CMUTs to scan the body tissue. Each of the sensorrequires its own front-end amplifier for sensing. For intra-vascular imaging it is difficult to manage cables connectingsuch a large number of sensors to their front-end circuit.[7].The simplicity of the proposed circuit can facilitate integrationof large number of sensors together with their amplifiers.The paper is organized into four sections. In Section II we

have discussed the feedback biasing scheme. Noise analysisof the amplifier has also been done in the second part ofthis section. Simulated performance of the designed amplifieris discussed in Section III. Finally, conclusion is drawn inSection IV.

II. THE PROPOSED AMPLIFIER CIRCUIT TOPOLOGYIn this section, we briefly describe the amplifier circuit

topology and analyze its operation. The schematic of the

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MF7

V

c

M3

Cc

C

MF8

MF6

M4

Vout− out+VMF5

MF3

MF1

M1

M5

MF4

MF2

I

M

M2CininC

dd

bias

bias

Vdd

Vin+ Vin−

Fig. 2. Schematic of the sensing amplifier

circuit is shown in Fig. 2. As it is the first stage of the receiverfront-end, considerable gain is required to suppress the noisecontribution of the system. At the same time, it must havehigh input dynamic range to accommodate reflected ultrasonicwaves from varying depths of body tissue. Voltage headroomlimitation under low supply rail poses a trade-off to theserequirements. A simple fully differential amplifier providesmore room to voltage swing at the output compared to highgain cascode structures.

A. CMOS Feedback Biasing

Feedback biasing using MOS transistors has the advantageof higher output voltage swing compared to resistive feedback[8]. The diode connected transistors MF3-MF6 in the circuitconstitute the feedback path for transistors M1-M4, respec-tively. A single feedback loop is shown in Fig. 3(a). Under dccondition, a decrease in the gate voltage of M1 increases itsdrain voltage. As a consequence, the feedback transistor MF3gets sufficient gate to source bias to conduct and charges thegate of M1. This negative feedback action enables a stable dcoperating point and the feedback transistors always remain insub-threshold region.The closed loop gain for a negative feedback system [9] is

ACL =A

1 +Aβ(1)

where A is the open loop gain and feedback factor is β. Theparameter Aβ is the loop-gain of the feedback loop.The loop-gain is analyzed in Fig. 3(b). It can be expressed

as

Aβ =gm1(Rout||1/sCL)1/sCi

1/(gmf3 + sCf ) + 1/sCi

=gm1

(Rout

1 + sRoutCL

)⎛⎝ 1 + s

(Cf

gmf3

)

1 + s(

Cf+Ci

gmf3

)⎞⎠ (2)

Here, gm1 and gmf3 are the transconductances of M1 andMF3, respectively. Cf comprises of gate to drain capacitanceof M1 and gate to source capacitance of MF3. The outputimpedance Rout is mainly the parallel combination of drain

resistances of M1 and M3. CL is the capacitive load. The loopis terminated with Ci which is equal to Cin in parallel to thegate to source capacitance of M1.Transistor MF3 being in sub-threshold region, gmf3 is very

low. Also Cin is higher to isolate the sensor from the frontend. Thus Cf , Ci and gmf3 forms the dominant pole of theloop gain at very low frequency by Eq. 2. So, for frequenciesmuch higher than this,

Aβ � 1 (3)

Thus the closed loop-gain by Eq. 1 becomes

ACL ≈ A (4)

It implies that the amplifier operates in open loop condition athigher frequencies. But for very low frequency the loop-gainby Eq. 2 is

Aβ = gm1Rout (5)

which is high. Hence the feedback provides dc bias to theinput transistor. The zero formed by Cf & gmf3 and the poledue to Rout & CL are at much higher frequencies compare tothe unity gain bandwidth of the loop-gain. It ensures stabilityof the feedback with higher phase margin. Transistor MF1 isadded to provide a weak discharge path for the gate of M1that improves the linearity of the feedback. The circuit sizing

VdM3

V

V

V

C

dM5

out−

in+ in M1

MF3

(a)

+

−

C

V

M1VV

out−

L

outloop

1/g Routmf3C

C

f

i in

(b)

Fig. 3. (a) The negative feedback loop (b) Simplified circuit to calculateloop gain

is done accordingly to keep the dominant pole of the loop-gainwell below the operating frequency of the amplifier. It catershigh open loop gain at the frequency of interest.The active load transistors M3 and M4 have also been

provided similar feedback to ensure low impedance at theoutput nodes, Vout+ and Vout− under dc condition. Thetransistor ladder comprising of MF7-MF5-MF3-MF1 are sizedin such a way so that the source voltage of MF7 or MF5 isprecisedly equal to the voltage required to be supplied at thegate of M3 to maintain the dc current through M3 exactly halfof the tail current through M5. Thus a common mode feedbackis provided with Vdd as the reference voltage and Vout+ orVout− as the sampled voltage. However, such a feedback tothe load transistors brings a pole-zero pair at the gate of M3and M4. To nullify that, larger compensation capacitors Cc

have been used. They are connected between the gates of theactive loads to provide less dc voltage across its plates whichwill reduce the leakage current.Mismatch of the transistors on either side of the differential

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M1

Vout− Vout+

i n,M3 i n,M4

i n,M1 i n,M2

2 2

2 2

I

Vdd

d,M5

M2

M4M3

(a)

rO3

rO1

Vdd

n,i 2MF1

n,MF32i

/1 gm2

MF3

MF1

M1

(b)

Fig. 4. (a) Noise sources of differential pair (b) Noise calculation of theCMOS feedback

pair will produce a small dc offset at the output of theamplifier. Using suitable offset cancellation technique this hasto be nullified in the subsequent stage.

B. Noise Contribution of the AmplifierThe sensing amplifier is the interface between the CMUT

and the receiver front end. So its input referred noise mustbe minimized to limit the total noise contribution of thesystem. Moreover, low noise floor ameliorates sensitivity ofthe amplifier.In this section, we have analyzed the noise performance

of the amplifier considering all potential noise sources. Thenoise model of the amplifier circuit is shown in Fig. 4. Asthe frequency of operation is in the megahertz, flicker noise isnot significant here. So we have considered only the thermalnoise sources generated by the MOS transistors.Thermal noise in MOS transistors manifests itself in the

form of channel noise current. For long channel MOS devicesthe noise current is expressed as

in2 =4kT.

2

3gm (6)

This current generates output noise voltage on loading atthe output resistance. Considering identical operating pointparameters for either side of the differential pair the totaloutput noise voltage due the four transistors M1-M4 [Fig.4(a)]is

vn1,out2 =2(in,M12 + in,M3

2)Rout2

=8KT.2

3(gm1 + gm3)Rout

2(7)

The gain of the amplifier is gm1Rout. Thus the input referrednoise due to these four transistors is

vn1,in2 =8KT.2

3

(1

gm1

+gm3

gm12

)(8)

The width of the input transistors M1 and M2 are kept highto increase the transconductance, gm1 and gm2. It helps inreducing the noise as evident from the Eq. 8.

Noise analysis of the feedback transistors MF1 and MF3 isdone using Fig. 4(b). The noise current source of MF1 has noeffect at the output node as the gate of M1 is shorted to acground. Channel noise current of transistor MF3 flows throughthe output node creating an output noise voltage of

vn2,out2 =in,MF32Rout

2

=4kT.2

3gmf3.(Rout)

2(9)

Output noise voltage due to other feedback loops can becalculated in similar way. Hence, the total input referred noisedue to the feedback transistors is given by

vn2,in2 =4kT.2

3gm12(gmf3 + gmf4 + gmf5 + gmf6) (10)

However, the feedback transistors MF3-MF6 remain in sub-threshold region. So their transconductance is very smallcompare to that of input transistors M1 and M2. It impliesthat the feedback transistors contribute negligible noise.For resistive feedback based transimpedance amplifier, the

noise sources are shown in Fig. 5. The thermal noise, vn,RF2

due to the feedback resistance RF equals to 4kTRF . It is

+ −+ −

+ −RF

RF

+ −

v n,RF

2

FRn,v 2

out+

out−

in−v 2

v 2

n1,

n2,A

A

in+

Fig. 5. Noise sources in a transimpedance amplifier with resistive feedback

directly referred to the input. As RF needs to be higher forhigh gain, the input noise of the amplifier is dominated bythe feedback resistor. Thus, compare to resistive feedback theCMOS feedback used in this work does not add significantnoise.

III. SIMULATION RESULTS AND DISCUSSIONSThe amplifier is designed in 180nm UMC technology

and simulated using Cadence Spectra. Capacitors of 100fFare considered as load at the output of the amplifier. Thedifferential gain and loop gain response are shown in Fig.6. Gain of the amplifier at 10 MHz frequency is 25.47 dB.The figure depicts the band-pass response of the amplifier.The high pass response is due to the input capacitor Cin

that isolates the front end amplifier from the sensor dc bias.The dominant pole formed at the high impedance output nodelimits the bandwidth of the amplifier. The sizes of the feedbacktransistors are kept low to reduce effect of their parasiticcapacitance at the output of the amplifier. Along with that,lower length increases the threshold voltage and ensures theirsubthreshold operation. The measured 3 dB cut off frequencyis 56.86 MHz.

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Fig. 6. Differential and loop-gain of the amplifier

The ultrasonic signals reflected from the body tissues varyin amplitude depending upon the depths of penetration. Thetransient response of the designed amplifier is captured using asinusoidal input whose amplitude varies after regular intervalof time. It is shown in Fig. 7.

Fig. 7. Transient response of the amplifier

Summary of noise analysis of the amplifier is in Fig. 8. Itshows that thermal noise of M1 and M2 is the main source ofnoise as derived in section II-B. Input referred noise voltage

Fig. 8. Noise summary of the amplifier

for the band 1 MHz to 15 MHz is 24.3 μV rms.Ultrasound imaging requires detection of wide range of

input signals reflecting from varying depths of body tissues.At the same time detection should be noise optimized whichdemands higher gain. But more the gain, less the inputmaximum voltage due to voltage headroom constraint. Thesizing of the amplifier is done in such a way that the outputcommon mode voltage remains closer to half of the supplyrail that allows undistorted output swing for much higher inputvoltage at significant gain. A 62.5 dB of input dynamic rangeis obtained considering the noise floor as the lowest input. Fig.

Fig. 9. Third harmonic distortion for maximum input signal

9 shows that the third harmonic distortion for the maximuminput signal is below -30 dB.The tail current source together with the biasing current

draws 174.5 μA current from a supply voltage of 1.8 V toground. It implies that the power consumed by the amplifieris about 314 μW.

IV. CONCLUSIONThe proposed amplifier uses a simple differential amplifier

to sense the CMUT signals. It can be used for sensing othercapacitive sensor based signals as well. Unlike conventionalresistive feedback, the CMOS feedback biasing adopted heregives noise optimized performance. Moreover, it does notinvolve any floating node as in capacitive feedback based tran-simpedance amplifier. The simpler structure of the amplifieraids in integrating large number of sensors together with thefront end amplifiers. Such a compact ultrasonic receiver probewill be useful for intra-vascular imaging. Nevertheless, higherresolution ultrasound imaging requires sensing of signals withvery wide dynamic range. The input dynamic range of thedesigned amplifier can be improved by using suitable lineariz-ing technique at the cost of gain. The physical design of theamplifier is to be done with proper common centroid matchingto provide identical biasing condition on either side of thedifferential pair.

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[6] T. Singh, T. Saether, and T. Ytterdal, “Current-mode capacitive sensorinterface circuit with single-ended to differential output capability,” In-strumentation and Measurement, IEEE Transactions on, vol. 58, no. 11,pp. 3914–3920, 2009.

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