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CHAPTER 5

A LOW POWER CMOS ANALOG FRONT END FOR

BIOMEDICAL ACQUISITION

5.1 INTRODUCTION

The demand for low power and small size biopotential acquisition

system is increasing now more than ever. Highly integrated application

specific circuits (ASICs) in bioelectric data acquisition systems poses new

insights into the origin of light-weight, low-power, low-cost medical

measurement devices that allow long-term studies. There is significant cost

reduction in medical care, as patients need not be hospitalized for observation

and can become mobile as pointed by Refet et al (2009). Thus, the

development and successful implementation of a universal ASIC, which

meets the specifications like long term power autonomy and high signal

quality of broad variety of biopotential signals continues to pose a challenge.

A cost-effective approach uses state of the art microelectronics in medical

measurement equipment, replacing the presently available discrete, single

application devices (Fuchs et al 2002).

In biomedical instrumentation, the crucial and power consuming

block is the analog front end which consists of low noise pre amplifiers and

low pass filters. Low frequency filters are the major building blocks in any

biomedical system. Most commonly used biomedical signals like ECG, EEG,

EMG are low amplitude signals with frequencies ranging within 10KHz. ECG

is the graphical recording of the bioelectric signals representing the electrical

155

activity of the heart. In heart rate measurements, the weak signal (amplitude

less than a few millivolts) has to be amplified first and filtered for further

processing. Low voltage operation is critical design issue for achieving low

power consumption. Low power and low voltage are the two important

attributes that is addressed in circuits used for ECG, to achieve a long battery

life. Since the average power consumption of CMOS digital circuits is

proportional to the square of the supply voltage, digital circuit benefits from

the scaling and reduced supply voltage of the analog circuits helps to achieve

increased speed and reduced power consumption as described in Lasanen and

Kostamovaara (2005). In this case, the analog front-end circuit acts as the

interface between physical signals and digital processor and helps in

bioelectrical signal acquisition.

As it is briefly described above, this study aims at designing analog

front end to perform preprocessing for heart activity detection. The analog

front end employs a fully differential OTA and single ended folded cascode

OTA as preamplifiers and a second order filter built using these OTA’s as low

pass filter, for signal processing. The amplifier designed concentrates on the

ECG signal extraction with high gain, CMRR and low noise. The filters

realized using these OTA’s help in sensing and continuous time filtering of

the bioelectric signals.

The architecture and design procedure of various fully differential

and single ended OTA’s are detailed in Chapter 2. The OTA’s discussed in

this work are applied with biomedical signals and present a linearity approach

to implement the OTA-C filter system (Ng and Chan 2005).

5.2 FULLY DIFFERENTIAL (FD) OTA

The preamplifier is designed using an operational transconductance

amplifier (OTA) for the acquisition of cardiac signals which, typically are in

156

the range of 50 V to 8 mV while the frequencies are below 250 Hz. In

analog integrated circuits, differential circuits are preferred to single ended

structure because it improves noise and reduces distortion. The other

advantage is that any amount of noise or power supply ripple tends to appear

as common mode signal and gets cancelled in differential processing. Also,

the non linearity of the active device is doubled when used in a differential

fashion. For example, the MOS transistor is a square law device, whose

second order nonlinearity for a voltage v can be given as

I = g v + g v (5.1)

g1 and g2 are coefficients expressing non linearity and I is the current of the

square law device. However, applying the differential signal v+ as +v and v- as

–v, the current equation is obtained as

i = g (+v) + g (+v) and i = g ( v) + g v) (5.2)

The output is obtained by taking its difference,

i = i i = 2g v (5.3)

Thus, this mode not only cancels the nonlinearity, but also doubles

the linear part of the signal. In this OTA, small transconductance value is

maintained using current division and current cancellation techniques. (gm,

typically of the order of a few nano amperes per volt). A fully differential

circuit is chosen to provide a good dynamic range rather than single ended

structure since dynamic range is related to the power consumption. The

common mode rejection is high and so, the noise is reduced in the differential

circuit. Common mode feedback circuits are used suitably for continuous data

applications to regulate the common mode output of the OTA and to provide

good tuning capability to the filter.

157

5.2.1 Structure of OTA

OTA’s are voltage to current converters that generate huge

harmonic distortion components. Hence it is necessary to linearise the OTA

circuits. A transistor with large saturation voltages, with very low distortion,

is one choice to design linearised voltage to current converters. Since, the

OTA is being used in for low frequency applications. OTA also requires low

transconductance value for its design. The devices in the OTA are operated in

subthreshold region to obtain low transconductance. Various OTA based

continuous time filtering circuits stated in Solis et al (2000), Veeravalli et al

(2002), Salthouse Sarpeshkar (2003), Rodriguez et al (2004), use open loop

OTA-C integrators operating in subthreshold region to achieve low

transconductance and power. Also, current division and current cancellation

techniques are employed to lower the transconductance of the OTA circuit as

shown in Figure 5.1. Thus the OTA yield a low transconductance with good

linearity as proposed by Shuenn-Yuh and Chih-Jen (2009).

Figure 5.1 Fully differential OTA for Low Frequency Applications

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In the OTA, transistors MM, M1 ,MN and MM,’ M1

’, MN’ act as

source followers where the differential input voltage is converted to current

by transistors MR and MR’ that are biased in edge of moderate inversion

region and triode region respectively. The conductance in the MOSFET in the

sub threshold region increases linearly with ID, while in the strong inversion

region the conductance increases as the root of ID, which can be understood

from Figure 5.2 (Jacob et al 1997).

Figure 5.2 Drain Current plotted from Weak inversion to Strong inversion

The drain current of MR transistor is split into transistors MM, M1

and MN where MM transistor is responsible for current division and MN for

current cancellation. The transconductance ratio between MM, M1, and MN is

M: N: 1.The transistors MM, M1, and MN are biased near the weak inversion

region. The remaining transistors work in sub threshold region and help in

attaining low transconductance with very good linearity. The channel current

equation for these transistors is given by the following equation

I = I e e (5.4)

Most of the current in the circuit flows to ground through MM

transistors because the transconductance of MM transistor is greater than that

159

of M1 and MN transistor. (gmMM>> gmM1, gmMN) . Thus the small signal

transconductance is given as

G =i

(v v )=

NM + N + 1

g (5.5)

Where g0MR is the small signal drain–source conductance of transistor MR,

given by

g = CWL

(v V V ) (5.6)

Here M can be defined as the ratio of transconductance between

MM and M1; N is the ratio of transconductance between MN and M1, p is the

mobility of the carriers in the channel and Vt is the threshold voltage of the

transistor, respectively. VgsMR is the source to gate voltage of MR, and WMR

and LMR are the gate width and the gate length of MR, respectively. The small

signal model of the differential circuit is shown in Figure 5.3.

Figure 5.3 Small Signal Model of the Fully Differential OTA

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In case of low frequency applications, it is desirable that ac small

signal transconductance is low. So, the M and N ratios are adjusted to lower

the ac small signal transconductance g0MR. It is desirable to keep gmMM

>>5g0MR to reduce harmonic distortion components in the circuit. Due to

current division effect, noise contributions by transistors MBP, MM, and MR

are very small and so, noise performance gets improved. But still the effect of

noise from M1, MN, and MBN transistors would be present, and thus can be

reduced by increasing the length of the transistors. Also in the case of low

frequency applications, p-channel transistors are used as input transistor to

keep low the flicker noise. The design values are given in Table 5.1.

Table 5.1 Design Parameters of the Fully Differential OTA

Transistor numbers W/LMM, MM’ 5 m/0.18 mMN, MN’ 2.5 m/0.18 m

M1, M1’, MR, MR’,MC 0.18 m/0.18 mMBP,MBP’ 100 m/0.18 m

MCP 20 m/0.18 mMBN,MBN’ 0.67 m/0.6 m

MCN 1 m/0.18 mVbp 0.4V

5.2.2 Common Mode Feed Back Circuit

The common mode feedback circuit used for the fully differential

OTA is shown in Figure 5.4. The MOS transistors MF1, MF6, MF4, and MF5

form two different structures to sense the common mode level. The outputs

from the OTA are given as inputs cm1 and cm2 to the transistors MF1 and

MF4. The common mode voltage VC is given as inputs to the common mode

gate terminal of transistors MF6 and MF5.

161

Figure 5.4 CMFB Circuit with N-MOS Diode Connected Transistor load

Then differential structures compare the output voltages of OTA

with common mode voltage VC. If output common mode voltage is not equal

to the reference voltage, a corrected current would be set by transistor MF3 to

the load transconductor. Then, the output common mode voltage is adjusted

to desired output voltage. The output from the Vfb terminal is given as

feedback to the N-MOS current sink transistors of the OTA circuit. The

design parameters of the circuit are shown in Table 5.2. The main advantage

of continuous time CMFB is that they do not require a circuit for generation

of non overlapping clock and work in continuous domain. So, the continuous

time CMFB circuits would be suitable for high performance applications and

for continuous data circuits (Behzad Razavi 2002).

Table 5.2 Design Parameters of CMFB Circuit

Transistor numbers W/L

MF1,MF4,MF5,MF6 0.5 m/0.18 m

MF2,MF3,MF7,MF8 0.18 m/0.18 m

Vc 0.4V

vbp MF8

vfb

cm1cm2

MF7

MF6

MF1

MF5

MF2 MF3

MF4

vc

162

Behind the amplifier, an ultra-low power filter with low cut-off

frequency is chosen to avoid the out-of-band noise (typically above the

frequency of 250 Hz). In low frequency Electrocardiogram (ECG)

applications, large time constant ( =RC) are to be used in low pass filter

design which necessarily uses an acceptable capacitor’s value (typically 10

pF) that requires greater resistance. Switched capacitor (SC) technique is a

good option to implement long term ECG monitor system. However, the

leakage problem in the switch based topologies makes in unsuitable for

applications requiring large time constant (of the order of millisecond or

more). In order to overcome this problem, additional leakage reducing

mechanism is required in the switched capacitor circuits. Alternatively, a low-

power continuous time OTA-based filter is opted for the realization of the

filter that comprises of the open-loop OTA-C integrators. The

transconductance of the OTA dominates to determine the time constant of

OTA-C integrators. For a differential input of 1mV, the differential output is

30.446 mV. Hence approximately 30 dB gain is obtained. The other simulated

parameters are tabulated in Table 5.3.

Table 5.3 Simulated Parameters of the Fully Differential OTA

Parameter Fully Differential OTATechnology (µm) 0.18

Supply Voltage (V) 1Gain (dB) 30

CMRR (dB) 93PSRR (dB) 62.5

Transconductance (nS) 500THD (dB) -101.22HD3 (dB) -69.05

Slewrate (V/µS) 13.37Load capacitance (pF) 10

Power consumption ( W) 2.919

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5.3 LOW PASS FILTER

The biomedical signals with very low amplitude and frequency are

inherently presented with external disturbance or noise like signals due to

interference. Voltages or currents that tend to corrupt the main signal, such as

switching noise in the system power supply ripple, tend to affect the data

present in the signal. Hence, low pass filters are used to remove the unwanted

frequency components. In practice, there are a number of situations in which

analog continuous time filters are a necessity. Analog filter circuits provide

band limiting of the signals before the signals can be sampled for further

processing. A transconductance based low pass filter circuit is built for this

purpose.

5.3.1 Second Order Butterworth Low Pass Filter using FD OTA

A biquad filter is a type of linear filter that implements a transfer

function that is the ratio of two quadratic functions. Biquad filters are

typically active and implemented with a single amplifier biquad (SAB) or

two-integrator-loop topology as stated in Solis-Bustos et al (2000).

• The SAB topology uses feedback to generate complex poles

and possibly complex zeros. In particular, the feedback moves

the real poles of an RC circuit in order to generate the proper

filter characteristics.

The two integrator loop topology is derived by rearranging a

biquadratic transfer function. The rearrangement will equate

one signal with the sum of another signal, its integral, and the

integral's integral. In other words, the rearrangement reveals a

state variable filter structure. By using different states as

outputs, any kind of second-order filter can be implemented.

164

The SAB topology is sensitive to component choice and can be

more difficult to be adjusted. Hence, usually the term biquad refers to the two

integrator loop state variable filter topology. A complete second order Gm-C

filter built using fully differential OTA is shown in Figure 5.5, where gm1

converts the input voltage into a current, gm2 represents the resistors R, the

capacitors C1 remains unchanged, and gm3 and gm4 form a gyrator with the

inductor L = . This filter is build using the fully differential OTA.

Fully differential circuits provide a higher common-mode rejection and an

increment of 3 dB in dynamic range when compared to single end structures

(Schaumann et al 2003).

Figure 5.5 Second order Gm-C filter structure

The low pass filter designed using Gm-C (transconductance and

capacitor) topology operates at low supply voltage, provides wide tuning

range and good controllability. Continuous time filtering has signals that are

continuous in time and require no sampling, making them suitable to be used

in high speed circuits. Fully differential Second order Gm-C lowpass filter

structure is implemented and simulated in the Synopsys tool. From the Figure

5.6, it can be observed that the open loop gain is found to be -10 dB and

cutoff frequency is nearly 250 Hz as designed in Shuenn-Yuh and Chih-Jen

165

(2009). Table 5.4 gives the various simulated parameters of the Second order

Gm-C low pass filter.

Figure 5.6 AC Analysis of Second order Gm-C Low Pass Filter

Table 5.4 Parameter of the Second Order Gm-C Low Pass Filter

Parameter Second order Gm-C LPFTechnology (µm) 0.18Supply Voltage (µm) 1Gain (dB) -10Power consumption ( W) 14.65THD (dB) 6.98Load capacitance C1,C2 ( F) 2, 0.6

The operational transconductance amplifier has been designed and

simulated using standard CMOS 0.18 m technology with a supply voltage of

1V in Synopsys tool. The simulated results shows that fully differential OTA

attains 30 dB gain, power of 2.919 W, transconductance value of 500 nS and

THD of -101.22 dB. The second order OTA based Butterworth low pass filter

operates at 250 Hz with a power consumption of 14.65 W. Thus, this

structure is suited to be an analog front end for cardiac signal processing.

166

5.4 SINGLE ENDED FOLDED CASCODE (SEFC) OTA

Various types of OTA are available as amplifiers for amplifying the

weak biomedical signals, such as telescopic OTA, Folded Cascode OTA

using Wilson Current Mirror, Folded Cascode OTA using Cascode Current

mirror and gain boosted OTA. The telescopic topology has low power

consumption and low noise, but is inhibited in its input and output swings.The

folded cascode OTA with Wilson mirror has a limited output swing and to

overcome this limitation, the cascode current mirror is used. The Folded

cascode OTA with cascode current mirror provides higher gain, good slew

rate and an increased output swing. Thus, this OTA is used in the analog front

end processing of cardiac signals. The architectures of these OTA’s are

already discussed in Chapter 2. The Single ended folded cascode OTA with

cascode current mirror (Figure 5.7) is applied with biomedical signals.

Figure 5.7 Folded Cascode OTA based on Cascode Current Mirror

M3

Vout

M4

M6M5

M1 M2

VDD

V- V+

CL

M7 M8

M11

M12

M9 M10Ibias

VSS

Ibias

167

The input differential stage consist of PMOS transistors M9 and M10 which

intends to charge the cascode current mirror M1-M4. MOSFETS M11 and

M12 provide the DC bias voltages to M5, M6, M7 and M8 transistors. The

circuit has high gain and transition frequency. The degradation of the

bandwidth is due to the first pole weakening of the OTA without increasing

the DC gain as indicated by Houda et al (2006). Further, the circuit has an

output and input common mode range near of ±Vdd with an offset voltage.

Thus the OTA is designed with the specification given in Table 5.5.

Table 5.5 Specifications of OTA

Specifications ValuesAv(dB) 82.15

fT(Hz) 250

CL(pf) 0.1

ID(nA) 4.8

±Vdd(V) ± 2

Channel length(µm) 1

A top down synthesis methodology for CMOS OTA architectures

illustrated by Silveira et al 1996 is used for design of the OTA. The design

plan is based on gm /ID methodology. In the gm/ID method, the relationship

between the ratio of the transconductance gm over dc drain current ID and the

normalized drain current IO= ID / (W/L) as a fundamental design tool is

considered. The gm/ID methodology is strongly recommended because it

indicates the device operating regions and helps in determining device sizes.

The gm/ID indicates that the greater the gm/I D value, greater is the

transconductance value resulting in higher gain. Thus, this is an efficient

method to design an OTA. The design parameters are provided in Table 5.6.

168

Table 5.6 Design Parameters of the Folded Cascode OTA

Parameters ValuesW9,10(µm) 35

W1,2,3,4(µm) 18

W5,6,7,8,11,12(µm) 6

The performance of the folded cascode OTA for the biomedical

signal is analyzed here. A differential input voltage of 20 µV is applied to the

OTA to obtain the differential output of 0.5V, as shown in Figure 5.8.

Figure 5.8 Differential Response of Folded Cascode OTA

The frequency response of the implemented folded cascode OTA

(based on cascode current mirror) is shown in Figure 5.9. From the figure, it

is clear that the OTA obtains a gain of 82.18 dB.

169

Figure 5.9 Frequency Response of Folded Cascode OTA

Figure 5.10 shows the frequency response for the calculation of

CMRR of the folded cascode OTA. The CMRR obtained is about 131.41dB.

Figure 5.10 Frequency Response for Measuring CMRR

The slew rate and PSRR is measured as 148.66 µV/s and 82.5 dB

and is shown in Figure 5.11 and 5.12 respectively.

170

Figure 5.11 Differential Response for measuring Slew Rate

Figure 5.12 Frequency Response for measuring PSRR

The measured transconductance is 121 µS of the folded Cascode

OTA. The HD3 and THD of the OTA is calculated as -56.13dB and -44.16dB

171

respectively. The folded cascode OTA is simulated using CMOS 0.35µm

technology in H-Spice Synopsys tool and the results are tabulated as in

Table 5.7.

Table 5.7 Simulated Results of Folded Cascode OTA

Parameters ValueSupply Voltage(V) 2DC gain(dB) 82.15Common Mode Rejection Ratio(dB) 131.77Power Supply Rejection Ratio(dB) 82.503Slew Rate(V/µs) 149.09Transconductance(µS) 121THD (dB) -44.16HD3 (dB) -56.134Power(µW) 158.5

Low-voltage operation is an important design issue when aiming

for low power consumption. The folded cascode OTA designed is able to

obtain high gain and CMRR with low power consumption. It also achieves

good PSRR, HD3 and THD. So, the OTA can be used in second order filter

structure to perform filtering of biomedical signals.

5.5 CANONICAL SECOND ORDER FILTER STRUCTURES

Second-order filter structures find widespread applications in the

design of higher-order filters. Canonical second order filter circuits have

constant-Q pole adjustment, constant bandwidth 0 adjustment, and

independent pole and zero adjustment. Four such 2nd order Gm-C low pass

filter structures are build using single ended folded cascode OTA’s and their

designs are given here. The first structure employs constant bandwidth 0

172

adjustment where as second, third and fourth structure involves independent

pole and zero adjustment. In all the four filter structures, the input voltage is

applied to Va and inputs Vb and Vc are connected to ground to make the filter

to act as a low pass filter as indicated by Geiger and Sanchez-Sinencio

(1985).

5.5.1 First Structure of 2nd Order Gm-C Low Pass Filter

The First structure of second-order low-pass filter is shown in

Figure 5.13.

Figure 5.13 First structure of 2nd order Low Pass Filter

The output voltage, Vo1, is given by the expression

Vs C C V + sC g V + g g V

s C C + sC g + g g (5.7)

This circuit is with Constant 0 adjustment by setting = g =

g . Thus the transfer function of the above filter structure becomes

( ) =g g

s C C + sC g + g g(5.8)

173

The common transfer function of a 2nd order low-pass filter as in equation

( ) =s + Q s +

(5.9)

Comparing 5.8 and 5.9, the frequency is calculated from the Equation (5.10)

=g

c1c2 (5.10)

The Quality Factor of the filter designed is calculated from the Equation (5.11)

(5.11)

Where = g = g and , then

g =I IV V

(5.12)

The cutoff frequency of the filter is 224 Hz. and is shown in Figure 5.14.

Figure 5.14 Frequency Response of the First structure of Low Pass Filter

174

5.5.2 Second Structure of 2nd Order Gm-C Low Pass Filter

The Second structure of second-order low-pass filter is shown in

Figure 5.15.

Figure 5.15 Second structure of 2nd order Low Pass Filter

The output voltage, Vo2, is given by the expression

=s C C V + sC g V + g g Vs C C + sC g g R + g g

(5.13)

This is a circuit where both 0 and Q can be independently

adjusted. Thus the transfer function of the above filter structure becomes

=g g V

s C C + sC g g R + g g (5.14)

Comparing 5.13 and 5.14, the frequency bandwidth w0 and Quality

Factor Q are given by the expressions 5.15 and 5.16.

175

=g g

C C (5.15)

Q =1

g Rg CC g

(5.16)

Here poles can be moved in a constant Q manner by adjusting gm1 =gm2=gm

and keeping gm3 constant. Similarly, constant 0 movement is obtained by

adjusting gm3 and maintaining gm1 =gm2=gm constant. The cutoff frequency of

the filter is 255Hz. Figure 5.16 shows the frequency response of the filter.

Figure 5.16 Frequency Response of the Second structure of Low Pass

Filter

5.5.3 Third Structure of 2nd Order Gm-C Low Pass Filter

The Third structure of second-order low-pass filter is shown in

Figure 5.17.

176

Figure 5.17 Third structure of 2nd order Low Pass Filter

The output voltage, Vo3, is given by the expression

V = (5.17)

This circuit is also with independent 0 and Q adjustment. Thus the

transfer function of the above filter structure becomes

V = g g V

s C C + sC g + g g (5.18)

Comparing with the common transfer function of a 2nd order low-

pass filter, the frequency bandwidth 0 and Quality Factor Q are given by the

expressions 5.19 and 5.20.

= (5.19)

Q =CC

g gg

(5.20)

177

Here 0 can be adjusted linearly by setting gm1 =gm2=gm and gm3 constant.

This is called as constant bandwidth movement. By adjusting gm1, gm2, and gm3

simultaneously, constant Q movement is possible.The cutoff frequency of the

filter is 251 Hz. Figure 5.18 shows the frequency response of the filter.

Figure 5.18 Frequency Response of the Third structure of Low Pass Filter

5.5.4 Fourth Structure of 2nd Order Gm-C Low Pass Filter

The fourth structure of second-order low-pass filter is shown in

Figure 5.19.

Figure 5.19 Fourth structure of 2nd order Low Pass Filter

178

The output voltage, Vo4, is given by the expression

V (5.21)

This is also a circuit where both 0 and Q can be independently

adjusted. Thus, the transfer function of the above filter structure becomes

Vg g V

s C C + sC g + g g (5.22)

Comparing with the common transfer function of a 2nd order low-

pass filter, the frequency bandwidth 0 and Quality Factor Q are given by theexpressions 5.23 and 5.24.

= (5.23)

Q = (5.24)

The constant Q and 0 movement is made similar as in third structure.

The cutoff frequency is found to be 255 Hz from the frequency

response of the filter and is shown in Figure 5.20.

Figure 5.20 Frequency Response of the Fourth structure of Low Pass Filter

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5.6 SECOND ORDER BUTTERWORTH LOW PASS FILTER

USING SEFC OTA

The single ended representation of the second order Gm-C

Butterworth Low Pass Filter provided by Schaumann et al (2003) is shown in

Figure 5.21. The filter is realized using the single ended folded cascode

structure to compare its performance with the canonical structures.

Figure 5.21 Single ended Second order Gm-C Filter Structure

The frequency response of the filter is shown in Figure 5.22 and the

cutoff frequency of the filter is 258 Hz. The power consumption of the

Butterworth filter is measured to be 380.1µW and the THD is -50.610 dB.

Figure 5.22 Frequency Response of the Butterworth Filter

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The performance comparison of the four canonical and Butterworth low pass

filter structures are tabulated in Table 5.8.

Table 5.8 Comparison of the Low Pass Filter Structures

Low Pass Filter Power(µW) THD (dB) CutoffFrequency(Hz)

1st Canonical LPF 316.9 -37.80 2242nd Canonical LPF 475.4 -37.79 2553rd Canonical LPF 475.4 -37.80 2514th Canonical LPF 475.4 -37.80 255Butterworth LPF 380.1 -50.610 258.5

Out of the four canonical structures designed the 2nd, 3rd, and 4th

structures gives more accurate results compared to the first structure as they

have independent pole and zero adjustments. They can be also used as low

pass filters in the analog front end processing. The second order Butterworth

low pass filter designed using the folded cascode OTA shows a better

response when compared to canonical structures in terms of power and total

harmonic distortion. There is about 20.06 % reduction in power and 12.8 dB

improvement in total harmonic distortion when compared to 2nd, 3rd, and 4th

canonical structures.

5.7 SIMULINK MODEL OF FIRST ORDER LOW PASS FILTER

A first order passive RC filter is transformed into active filter using

OTA. The series combination of resistor with voltage source is realized with a

Norton’s circuit using shunt resistor together with a current source. The active

filter realized from passive components is replaced with real OTA’s, as

181

illustrated in Figure 5.23 which includes an input voltage to current transducer

and an equivalent grounded resistor of OTA based on the close loop

configuration. Its transfer function is depicted as

+(5.25)

Figure 5.23 First Order Filter using OTA

The performance analysis of the first order filter is assisted by

including non ideal parameters like nonlinearity, intrinsic noise and finite gain

(Shuenn-Yuh and Chih-Jen 2009). The details are described below.

5.7.1 OTA Nonlinearity

The performance of OTA is evaluated with the nonlinear effects

present in the circuits. In general, a nonlinear transconductance is expressed

as

= (1 + + ) (5.26)

Where is the transconductance of the OTA with the zero input

differential voltage and i represents the coefficient with respect to the

Gm2Gm1

+

-+

-

VinVout

182

higher order expansion term of nonlinearity. The Simulink model of OTA

using nonlinear transconductance is shown in Figure 5.24, where af1 and af2

refer to the coefficient in (5.26), respectively.

Figure 5.24 Simulink Model using nonlinear Transconductance

5.7.2 OTA Noise

Flicker and thermal noise are the two main noise sources that

influence the performance of OTA. The flicker noise influences the

performance of OTA in low-frequency band and thermal noise is influenced

by temperature. The flicker noise is also known as 1/f noise, because its noise

power spectral density is inversely proportional to frequency. The simulink

model of the first order filter including the non-idealities is shown in

Figure 5.25.

1

af1

af2

1

1

gm0

X

X

X

constant

alpha1

alpha2

Vd

Gm

Gm0

+

+

+

183

Figure 5.25 Simulink Model of First Order Low Pass Filter including

non linearities

The noise power spectrum density (PSD) of input referred 1/f noise

is given as

S , =KF

C W L f(5.27)

Where the parameters KF and AF represents the coefficient and exponent

constant of flicker noise, respectively, Cox is the oxide capacitance per unit

area, and Weff and Leff are the effective channel width and length of

transistors, respectively. The PSD equation of input-referred thermal noise is

expressed as

S , = . . . (5.28)

1

noin

OTA noise

Vd Gm

++

X 1

Iout

Gm curve

1/(sCL + 2g0)-1

+-

11 Vd

Vd

Iout

Iout

Gm1

Gm2

VinVOUTGain

TF1OTA

OTA

184

Where K is Boltzmann’s constant, T is the absolute temperature. The value of

is chosen as 1/ (2k) to operate the transistor in sub threshold region for low-

power and low-frequency requirements.

The total input referred noise is obtained for the spectrum of the

sum of N sine waves with random phase i, along with the amplitude of 1/f

noise af, and the amplitude of thermal noise ath.

, ( ) = , + . sin(2 + ) (5.29)

The coefficient af,i is given as in Equation (5.30) considering 1/f noise.

, = 2 ( ) (5.30)

Here in ECG application, f is chosen as 1 Hz to make N as 250. When

thermal noise is considered as white noise, its magnitude is given as

= 2 f (5.31)

Referring to (5.29), the total input referred noise is then

superimposed on the nonlinear model of Figure 5.25 and simulated in the time

domain to find the circuit performance.

5.7.3 OTA Finite Gain

Ideally, the OTA has infinite output resistance. But in practice, a

finite resistance is present always due to channel length modulation. This

results in larger integrator loss and also influences the performance of the

filter response. The transfer function can be represented as

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VV

GsC + G + 2g

(5.32)

where 1/ is the finite resistance.

5.8 FIRST ORDER FILTER USING SIMULINK MODEL

The non-idealities present in the OTA simulink model of the first

order low pass filter is designed using the transfer function and is shown in

Figure 5.26.

Figure 5.26 Simulink implementation of First Order Filter

The subsystem in the first order filter is shown in Figure 5.27

which includes the noise block with the specifications of flicker noise and

thermal noise.

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Figure 5.27 Simulink implementation of noise added to the signal

The non linearity in transconductance is implemented using

simulink as in Figure 5.28 with the values 1 and 2 taken as -0.291 and

-2.246 respectively and gm0 is 126 µS for folded cascode OTA.

Figure 5.28 Simulink implementation of the non linear transconductance

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The spectrum analyzer displays the frequency response of the

system analyzing both the input and output of the system. It gives better

results when inputs with high harmonic distortion contents are provided.

The frequency response of the output of the low pass filter with folded

cascode OTA is shown in Figure 5.29. The cut off frequency is 1595 rads/s

(253.98 Hz).

Figure 5.29 Spectrum Response of the First Order Filter

The power spectral density block displays the frequency content of

the signal. The power spectral density of the filter output is shown in

Figure 5.30. The output indicates that there is no data available after the cut

off frequency which indicates that efficiency of the filter.

The noise Voltage density is shown in the Figure 5.31. The

maximum amplitude of the noise is 4.2*10(-6) V.

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Figure 5.30 Power Spectral Density of the First Order Filter

Figure 5.31 Noise Voltage Density applied in the First Order Filter

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.5

1

1.5

2

2.5

3

3.5

4

4.5x 10-6 NOISE

Time (ms)

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The noise Power spectral density is shown in Figure 5.32. The

noise Power Spectral density shows that the noise is very less in amplitude at

all frequencies below 250Hz.

Figure 5.32 Noise Power Spectral Density

All signal components are delayed when passing through a device

such as an amplifier, filter etc. The delay is different for different frequencies.

The group delay response of the first order filter output is shown in

Figure 5.33. In this filter it is in the order of milliseconds for frequencies

within the desird bandwidth of 250Hz.

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Figure 5.33 Group Delay Response of First Order Filter Output

Thus all the results of the filter structure using folded cascode OTA

in simulink model indicates that the filter can be used for ECG applications.

5.9 CONCLUSION

In real world, signals are in continuous time format. Also the

process of band-limiting, anti aliasing, and reconstruction is done to interface

the signals with real world. Even internal to a digital transmission system,

analog filters are used for band-limiting to achieve noise reduction, and to

equalize gain or delay to compensate for losses in the transmission channel.

The basic OTA desired for the filter implementation is based on the following

criteria such as gain, CMRR, power consumption, operating frequency range

and noise. The designed folded cascode OTA achieves high gain of 82.15 dB,

CMRR of 131.77dB, PSRR of 82.5 dB with -44.16 dB THD and 158.5 µW of

power. Thus, the Second order Gm-C filter designed using folded cascode

OTA meets most of the factors required to filter the low frequency cardiac

signal. The Butterworth low pass filter achieves THD of -50.6 dB, power

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consumption of 380.1µW at a cutoff frequency of 258.5Hz and the results are

validated using CMOS 0.35µm technology in Synopsys tool. This shows that

Butterworth filter performs better than the canonical filter structures and can

be utilized as an analog front end for bio acquisition system.