M OTIVATIONS

The electrophysiological signals of human body are very small and the frequency is low. The common voltage range is from 50 micro volts for the brain wave (EEG) to 5 mV for some heart voltage (ECG). This rarely goes down to 0.5 micro volts for evoked potential like retina voltage (ENG) or hearing hair cell to the brain steam audio nerve voltage. Besides, the frequency range is usually low, no more than 2 KHz for most cases and seldom extended to 40 KHz.

Besides, there are a lot of low frequency noises in the human body. The frequency of these noises overlaps the frequency range of human body signals. Therefore, the most important part of the front-end portable system is the instrumentation amplifier (INA).

We use the INA to compress the noises and amplify the electrophysiological signals we need. So we have to design a high common-mode rejection ratio (CMRR) instrumentation amplifier which is the first stage of the portable system. Another point is that once our signal is very small, input offsets voltage and input noise play an important role in our instrumentation amplifier. Once the input offset voltage or input-referred noises become higher than the signals, we will not get any output signals.

Behind the instrumentation amplifier is the low-frequency bandpass filter to filter the signals we want. Human body signals are very low frequency (about 50Hz to 2 kHz), and the bandpass filter needs very large capacitors or resistors. It will increase the difficulty for put the large devices on chip or increase the size of the chip and the costs.

To overcome this problem, we use some method in the thesis without using large devices.

Another problem is about the power of the circuits. Like most of the mobile systems, we need a low power design to make it more convenient to be portable. So the low power is another design consideration.

1.4 THESIS ORGANIZATION

This thesis contains four chapters. Chapter1 introduces the background of nursing system and remote medical care. Besides, the structure and function of the front-end circuit of the electrophysiological signals measurement system are also mentioned. At the end of Chapter1, some architectures of instrumentation amplifier which are already proposed to archive high CMRR will be described. Also the new architecture design of INA and low frequency filter of this thesis are presented. In Chapter2, we’ll describe the circuits to construct the INA and the low frequency bandpass filter.Chapter3 shows the

simulation results of the front-end circuit of the electrophysiological signals measurement system. Finally, chapter4 describes the conclusion and future work.

CHAPTER 2

ARCHITECTURE AND CIRCUITS DESIGN

2.1 ARCHITECTURE DESIGN OF THE INSTRUMENTATION AMPLIFIER

2.1.1 Differential Difference operational amplifier (DDA)

Differential difference operational amplifier (DDA) is the extension concept of the differential operational amplifier. Its expression is showed in Fig. 2.1 and the difference between opamp and DDA is that instead of two single-ended inputs as in the case of op-amps, it has two differential input ports

(

V₂ −V₁

)

and

(

V₄ −V₃

)

.The output voltage of the DDA can be written as:

( ) ( )

[

V₄ V₃ V₂ V₁

]

A

V_O = _O − − − (2-1) A is the open-loop gain of the DDA. When a negative feedback is introduced to O

V1 or V4, the basic equation that characterizes the operation of the DDA is obtained as :

3 4 1

2 V V V

V − = − (2-2) when A_O →∞

The DDA is a widely used block in many circuit applications because it has four inputs to have more function changing.

V

1

V

2

V

3

V

4 ^+_

V

^O

+ + + _ _ __ +

Fig. 2.1 The symbol for Differential Difference Operational Amplifier

2.1.2 Differential Difference operational transconductance amplifier (DDGm)

Like the differential difference operational amplifier which is extended from operational amplifier, differential difference operational transconductance amplifier (DDGm) is extended from operational transconductance amplifier. Fig. 2.2 is the expression of DDGm and its function is:

( ) ( )

[

V₄ V₃ V₂ V₁

]

G

I_O = _m − − − (2-3) G is the transconductance m

V

1

V

2

V

4

V

3

I

o

Fig. 2.2 The symbol for Differential Difference Operational Transconductance Amplifier

When the output has a resistor loading, we can obtain the same function (2-2).

The differential difference operational transconductance amplifier also has multiple functions and we’ll use the DDGm in our new structure of instrumentation amplifier.

2.1.3 New structure design of the instrumentation amplifier

We have introduced some structures of instrumentation amplifiers in chapter1;

most of the structures transfer the voltages of input signals into current in the first stage.

Then they amplify the current and subtract the current in the second stage. If we can do

the action of current transformation and the subtraction of the input signals simultaneously at the first stage then amplify the signals at the second stage, the common mode signals will be compressed twice. Fig. 2.3 shows the structure of this idea.

Fig. 2.3 Expression for the new approach of instrumentation amplifier

As showed in Fig. 2.3, we subtract input signals in the first stage and the noises (common-mode signals) will almost equals to zero with differential signals become double. As a result, before entering the gain stage, the noises have been eliminated and the gain stage also has the ability to compress common-mode signals. Under this structure, common mode rejection ratio would be high.

The function of the idea for first stage can be realized by our new circuit – differential difference operational transconductance amplifier. Once we connect the differential difference operational transconductance amplifier like Fig. 2.4, we can get the output signal as:

( ) ^{( )}

( )

And we can get a voltage subtraction function using this method to cancel the common-mode signals.

Fig. 2.4 Subtraction of input signals using two DDGm

After using the function showed in equation (2.3), we can design a new structure of high CMRR instrumentation amplifier. Fig. 2.5 is the structure of the new high CMRR INA using DDGm. The main function of the first stage is to cancel the common-mode and doubles the differential signal like Fig. 2.6 showed. Briefly speaking, we can say that the first stage constructed with two DDGm is to enhance the differential signal and to compress the common-mode signals (noises). Then the second stage with Gm amplifier and is to provide the gain for signals. Equation (2.4) derives the node voltage of Vx1 and Vx2.

RG

X1

1st stage 2nd stage

Fig. 2.5 The new structure of high CMRR instrumentation amplifier

Differential Input

2.2 CIRCUIT DESIGN OF THE DIFFERENTIAL DIFFERENCE OPERATIONAL TRANSCONDUCTANCE AMPLIFIER

2.2.1 The Flipped Voltage Follower (FVF)

The most commonly used voltage follower is shown as Fig. 1.13. It is widely used in many operational amplifiers for voltage buffer and input stage for operational transconductance amplifier like Fig. 1.12. This voltage follower is also used in many analog circuits. However, it has a drawback that would influent the performance of the analog circuits.

To solve this problem, the paper [14] claimed a new voltage follower circuit called flipped voltage follower (FVF) shown in Fig. 2.7. In Fig. 2.7 the current through M1 is held constant and independent on the output current. It could be described as a voltage follower with shunt feedback. Neglecting body effect and the short-channel effect,

is held constant, and voltage gain is unity. Unlike the conventional voltage follower, FVF is able to source a large amount of current, but its sinking capability is limited by the biasing current . The large sourcing capability is due to the low impedance at the output node, which is approximately

1

VSGM

Ib

1 2 1

1

o m m

o g g r

r = , where and

are the transconductance and output resistance of transistor, respectively. This value is in the order of 20-100 .

gmi

roi

Ω

And we will use this circuit to construct our differential difference operational transconductance amplifier.

V^o Vⁱ

I

^b

M1 M2

Fig. 2.7 Flipped Voltage Follower

2.2.2 The differential difference operational transconductance amplifier

Using the flipped voltage follower (FVF), we can design a DDGm circuit shown in Fig. 3.8. The magnitude of Gm can be derived as follow:

Fig. 2.8 The DDGm amplifier using FVF method

In Fig. 2.8, are the cascode current mirror. The stacked MOS can decrease the channel length effect of and enhance the accuracy of the mirrored current

16

~ 13 M M

ratio. On the other hand, the output resistance of an ideal transconductance amplifier is infinite, so the stacked MOS M9 M~ 16 can increase of the DDGm circuit. r_o

MOS size m

M1、M2 (0.5/10) 10

M3、M4、M5、 M6 (0.5/10) 1

M7、M8 (0.7/10) 1

M9、M10 (0.4/9) 1

M11、M12 (0.4/4) 1

M13、M14 (1/4.2) 3

M15、M16 (1/4) 5

Table 2.1 The size of the DDGm amplifier in Fig. 2.10

2.3 STRUCTURE DESIGN OF THE LOW-FREQUENCY BANDPASS FILTER 2.3.1 Specification of the low-frequency bandpass filter

For the electrophysiological measurement system, we can set the spec of the low-frequency bandpass filter as Table 2.2.

From the Table 2.2, we can find the frequency range is from 50 Hz to 2 kHz, the stopband attenuation is about 35 to 40 dB, and the passband ripple is from 3 to 8dB.

From the spec we set, we can use the Inverse Chebyshev or the Elliptic filter to realize it.

By the comparison of the two LC networks of Inverse Chebyshev and the Elliptic filter we derived, we can find that the element values of Elliptic filter is much more realizable than the f Inverse Chebyshev filter. So finally, we choose the 5th-order Elliptic filter structure to design our desired low-frequency bandpass filter.

Filter Spec

Low corner frequency 50 Hz High corner frequency 2 kHz

Stop band ratio 1.98

Stop band attenuation 35~40 dB

Pass Band Ripple 3~10 dB

Gain >0dB Type of the Filter 5th order Elliptic

Table 2.2 The specification of the low-frequency bandpass filter

2.3.2 LC network and the leapfrog structure

From the spec of Table 2.1, we can derive the transfer function of the low-frequency bandpass filter showed in equation (2.5). And from equation (2.5),we can derive the LC network in Fig. 2.9. In Fig. 2.9, we can find that the element values of the capacitors won’t be able to be realized on the integrated circuits. So we have to scale the element values of Fig. 2.9 into the values that can be made on chip reasonable. Fig.

2.9(b) is the circuit after normalizing the element values from Fig. 2.9 (a); we make all the capacitor values from 0.1pF to 10pF using the normalization method of equation (2.6) and (2.7). As we mentioned before, we’ll use the leapfrog structure to decrease the effects of

variations for element values. Leapfrog structure uses the feedback topology, so the performance of the filter will be less sensitive to the variation of the element values. For leapfrog structure, we change the position of the elements in Fig. 2.9(b) into the Fig.

2.9(a) to make more blocks showed in Fig. 2.10(b).

~

change for leapfrog

structure

Fig. 2.9 (a) The prototype LC network of the 5th-order Elliptic bandpass filter (b) The LC network after element value normalization.

(c) The LC network after element position change for leapfrog structure

~

^Rs _{L1 L4} ^RL

Fig. 2.10 (a) The LC network of the 5th-order BP Elliptic filter

(b) The block diagram of leapfrog structure for the 5th-order BP Elliptic filter (c) The block diagram of leapfrog structure for the 5th-order BP Elliptic filter

The Fig. 2.10 (a) (b) (c) shows the procedure of how to transfer LC network into leapfrog structure. It is obvious to see that in each block diagram that the loops consists of an inverting and a noninverting block so that the gain around each loop is negative as required for stability. Also from the Fig. 2.10 (a) (b) (c), we can now understand that why we have to change the element position in Fig. 2.9(b) into Fig. 2.9(c). This action not only increases the block diagram but decentralize the elements so we can gain more stability of the filter.

Fig. 2.11 The simulation result of 5^th –order Elliptic LC ladder

Fig. 2.11 shows the simulation result of the 5^th –order bandpass Elliptic filter by the LC ladder in Fig. 2.9(c). We can find the ripple in both the passband and stopband as we discussed in chapter 1.2. In the next section, we’ll transfer the LC ladder into leapfrog structure and Gm-C filter.

2.3.3 Gm-C filter

After deciding the block diagram of the leapfrog structure, it’s time to decide the actual implementation of the circuit. Fig. 2.12 shows how to realize the blocks in Fig.

2.10(b).

Fig. 2.12 Circuits implementations for functions of the functions in Fig. 2.10

In Fig. 2.12, is the normalize factor and is the in Fig. 2.10(c); therefore we can realize the different function shown in Fig. 2.10(c). Back to Fig. 2.10, we can find the value of the inductors is hard to implement on an integrated circuit. To solve this problem, we have to replace the passive inductors with some active circuits. A two-port network is shown in Fig. 2.13, we call this kind of structure “Gyrator” which is composed of transconductance amplifiers and impedance loading. So we can realize the passive inductor into an “active” inductor by transconductance amplifiers and capacitors.

Fig. 2.13 The two port network of Gyrator

+

Fig. 2.14 (a) The realization of a grounded inductor (b) The realization of a floating inductor

+ _ + _

Gm2

Gm1

+ _ +

_

Gm2 Gm1

V¹ V²

+ _ +

_

Gm2 G^m1

V1

(a)

(b)

Fig. 2.15 (a) The realization of a grounded inductor composed of Gm and capacitor (b) The realization of a floating inductor composed of Gm and capacitor

2

1 m

m G

G L C

= ⋅ (2.8) Fig. 2.14(a) and Fig. 2.14(b) are the Gyrator of grounded and floating inductors shown in two-port networks. Fig. 2.15(a) and Fig. 2.15(b) are the Gyrator composed of Gm amplifier and capacitors. Equation (2.8) is the relation of the inductor、the Gm amplifier and the capacitor. Finally, from Fig. 2.10(c)、Fig. 2.12 and Fig. 2.15 (a), we can derive the leapfrog Gm-C filter for low-frequency and bandpass Elliptic type.

Table 2.3 is the Gm values of the Gm-C filter. We can find the Gm value is very small, and the very small transconductance value is a little bit hard to realize because we need a huge resistor value to make a small transconductance. On the other hand, small Gm causes small current, so we have to eliminate the offset current of the Gm amplifier.

In the following sections, we’ll discuss some nonideal effects of the Gm amplifier when used in leapfrog filters.

+_

Fig. 2.16 The low-frequency bandpass Gm-C filter with leapfrog structure

Gm1、Gm4、Gm6、Gm8、Gm9、Gm10 1nA/V

Gm2、Gm3、Gm7、Gm11~Gm16 10nA/V

Gm5 100nA/V

Table 2.3 Gm values of the Gm amplifier in Fig. 2.17

2.4CORE CIRCUIT DESIGN OF THE FILTER

2.4.1 The Gm amplifier using the mos resistor

As the shown in Fig. 2.16, the Gm value is from 1nA/V to 100nA/V which needs almost GΩ scale resistor to have such Gm value. However, it’s impossible to have passive resistors to GΩ scale on integrated circuits. As a result, we need to have a mos resistor operated in the subthreshold region to get a GΩ scale resistor. Fig. 2.17 shows the core circuit of the Gm amplifier and Table 2.3 shows its size. Fig. 2.18 is the Gm amplifier with mos resistor operated in subthreshold region. We use Vctrl in Fig. 2.18 to control the mos resistor value. Equation (2.10) is the equation of the mos current operated in subthreshold region and equation (2.11) is the slope of Vctrl versus Ids. The equation (2.9) is the Gm value derived and this equation includes the channel length modulation of M7 & M8

Vbias1

Vbias2 Vbias2

M1 M2

M3 M6

M7 M8

M9 M13

M12

M10 M11

M15

M14 M16

Vout

Vx1 Vx2

Rm

Io

V- V+

Vdd

Fig. 2.17 The circuit of the Gm amplifier

MOS size m

Table 2.4 The size of the DDGm amplifier in Fig. 2.10

⎥⎥

Fig. 2.18 The circuit of the Gm amplifier connected with MOS resistor

( )

^{q(V V) mkT}

(

^{qV kT}

2.4.2THE NONIDEAL EFFECTS OF THE GM AMPLIFIERS

When we simulate the low-frequency bandpass Elliptic filter with ideal Gm amplifiers with high output impedance and infinite bandwidth, we’ll have a perfect simulation result of the filter. However, once we put the realistic Gm amplifier into the Elliptic filter, some nonideal effects of the Gm amplifier appears. These nonideal effects will affect the performance of the filter a lot. We’ll discuss these effects in the following sections.

(a) Background current

The Gm amplifier we use is the circuit in Fig. 2.17 with a mos resistor connected at nodes Vx1 and Vx2 and we use Vctrl in Fig. 2.18 to control the Gm value. Although we can get small Gm value through the mos resistor operated in subthreshold region, what if the “gm” of the circuit in Fig. 2.16 itself larger than the Gm we want? Once this happen, we will never get the small Gm no matter how large the resistor value is. This current we don’t want is called the “background current “of our Gm amplifier.

Fortunately, we find a way to eliminate this background current. If we connect our Gm amplifier like Fig. 2.19, the background current won’t flow forward to output. In Fig. 2.19, we connect the Gm amplifier’s inputs in opposite way and connect the output together, then the background current will flow from the upper Gm amplifier with mos

resistor into the Gm amplifier below without mos resistor. After using this method, we can get the Gm value we want no matter how small it is.

However, the advantage of the way to eliminate background current will also increase our power of the Gm amplifier. For our electrophysiological signal measurement system, this would be a problem.

+ _

+ _

Vctrl

Isignal+Ibackgroud

Ibackground

Fig. 2.19 The method to eliminate the background current of the Gm amplifier

(b) Finite Ro effect in the Gyrator

We have introduced Gyrator in chapter 2.3, the ideal floating inductor for Gyrator is like 2.15(a). When we consider the finite output resistance of the Gm amplifier, we’ll have a nonideal term compared to the equation (2.8). It is shown in Fig. 2.20 and derived as below:

sL

From equation (2.9) we can find that besides the imagine part term “sL” we want, there will be a real part term Rs. Like the Q value of passive inductors, once we don’t have enough output resistance of Gm amplifier, the frequency response of the LC tank at the resonant frequency will not be sharp enough.

+ _

+ _

Ro

Ro Vi

C

Paralleled Gm

Paralleled Gm

Fig. 2.20 The finite Ro of Gm amplifier in the Gyrator

(c) Finite Ro and bandwidth limit of Gm amplifier in low-frequency filter design We have discussed the nonideal effect of Gyrator caused by the finite output resistance of Gm amplifier. Besides the Gyrator, output resistance not high enough will also bring serious problem in a low-frequency filter.

As showed in Fig. 2.21, if the output load of the Gm amplifier is a capacitor, the impedance of the capacitor is

C jω

1 . When the Gm amplifier is operated in

low-frequency, the effect of finite output resistance appears. Suppose the input frequency is 1 kHz with a 1pF capacitor load at the output, the impedance of the capacitor is 0.16GΩ. Therefore, if we don’t have enough output resistance, the current we want (the Gm we designed) will not totally flow into the capacitor. So we have to design a Gm amplifier with 5~10GΩ output impedance.

However, another question arises when we design a large output resistance of the Gm amplifier. That is when we have a large Ro, the dominant pole located at the output will be very small. For a filter whose passband is between 50~2 kHz, the bandwidth of the Gm amplifier should be at least 3kHz or above.

V+

V-Isignal Vctrl

R=1/Gm

+ _

C j Z 1

= ω

Gm ^Ro C

Fig. 2.21 The Gm amplifier with a capacitor load

Fig. 2.22 shows the ideal filter and the filter adding the nonldeal effects of finite output resistance and too small bandwidth. The upper wave is the filter with infinite output resistance and bandwidth, and the below one is the filter with 3GΩ output resistance and 2.5 kHz bandwidth. In Fig. 2.22, the double-side narrow represents the gain decay caused by the infinite output resistance, and the circle represents the result with too small bandwidth.

Fig. 2.22 The transfer function of the filter with ideal and nonideal Gm

Fig. 2.22 The transfer function of the filter with ideal and nonideal Gm

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