The nonideal effects of the Gm amplifiers

Chapter 2 ARCHITECTURE AND CIRCUITS DESIGN

2.4 C ORE C IRCUIT DESIGN OF THE F ILTER

2.4.2 The 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:

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 Vi

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

Because of the tradeoff between Gm amplifier’s output resistance and bandwidth, we have to do some optimize of the MOS sizes of the Gm amplifier in Fig. 2.17.And the output stage is showed in Fig. 2.23. Equation (2.13) derives the relation between Rout and the size of the output stage MOS and equation (2.14) shows the relation between 3dB frequency and the size of the output stage MOS.

From equation (2.13) and (2.14), we can find that under the situation that the dc level of the Gm amplifier has been decided and the size of the MOS are scaled together, the Gm amplifier’s Rout is proportional to

W L³

and f₃_dB is proportional to 1₄

L . From the conclusion we derived, we can find that when the W of the MOS are scaled, Rout would be scaled the same multiple and won’t change. As a result, we can design the W as minimum size. As regards to L, we can find that we can increase or decrease L neither because we won’t gain both benefit in Rout or . So we can just design our length to a middle value to ensure Rout and are archiving the enough value.

f₃dB

Fig. 2.23 The output stage of the Gm amplifier

CHAPTER 3 SIMULATION RESULTS

3.1 SIMULATION RESULTS OF THE FLIPPED VOLTAGE FOLLOWER (FVF) In chapter1 and chapter2, we have introduced the flipped voltage follower (FVF) which has the unity gain insensitive to output loads compared to the conventional voltage follower. And we have proved it in Fig. 3.1. We put different from1kΩ to100MΩ at both the output of the FVF and conventional voltage follower. From Fig.

3.1, we can find that when goes down from 100MΩ to 5MΩ, its gain degrades.

And from 5MΩ to 100kΩ, the gain degrades more seriously. On the other side, the FVF will not degrade its gain until goes down to 500kΩ. From the comparison in Fig.

3.1, the conclusion that FVF’s gain is much more insensitive is proved.

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

100M 10M 5M 1M 500k 100k 50k 1k RG(Ω)

Gain(Vout/Vin)

Conventional one

FVF

Fig. 3.1 The gain comparison of the conventional voltage follower and FVF versus R_G

3.2 SIMULATION RESULTS OF THE GM AMPLIFIER

Fig. 3.2 shows the frequency response of Gm amplifier with different Gm values.

Gm=3.2uA/V

Gm=1.6uA/V

Fig. 3.2 The frequency response of the Gm amplifier with different Gm values

Fig. 3.3 shows the small Gm value that can achieve to 1.6nA/V and 3.2nA/V. It proves that we can successful eliminate the background current we discussed in chapter2.

Fig. 3.3 The frequency response of the Gm amplifier with nA/V Gm values

In chapter2, we know the Gm value equals Rm

2 . Now, we can prove that our

output current after simulation almost equals to the current we calculate in theory in Fig.

3.4. We use different from 100kΩ to 1GΩ and observe the output current. From Fig. 3.4, the HPICE simulated current and the theoretical current are almost perfect matched.

0.00E+00 1.00E+00 2.00E+00 3.00E+00 4.00E+00 5.00E+00 6.00E+00 7.00E+00 8.00E+00 9.00E+00

1G 500M 100M 10M 5M 1M 500k 100k

theoretical simulated Iout(uA)

RG(Ω)

Fig. 3.4 The calculated and HSPICE simulated Iout versus R_G

3.3 SIMULATION RESULTS OF THE INSTRUMENTATION AMPLIFIER

First, we have to test if the function of (2.3) and Fig. 2.4 works. If we input a differential signal whose amplitude is 0.1mV, then we can find the amplitudes of node and (in Fig. 2.4) show in Fig. 3.5. From Fig. 3.5 we can find the amplitude is doubled.

VX V_X₂

Fig. 3.5 The differential-mode signal of node V_X₁ and V_X₂

Next we have to check if the common-mode signals are successfully subtracted.

We input two 0.1mV common-mode signals whose phases are the same and we can get the transient response shown in Fig.3.6, we can find that the common-mode signals are perfectly compressed to almost zero volt.

As a result, we have confirm that the method in (2.3) works. The noises (common-mode signals) have been canceled enormously. Next we will check the CMRR performance of the circuit.

Fig. 3.6 The common-mode signal of node V_X₁ and V_X₂

Fig. 3.7 shows the frequency response of our new instrumentation amplifier. We can find that the CMRR can archive to the magnitude of 215 dB. It is a very high magnitude.

Fig. 3.7 The frequency response of the proposed INA structure

Fig. 3.8 The frequency response of the proposed INA structure with four corners

CMRR

Vdm

Vcm

Fig. 3.9 The HSPICE Monte-Carlo simulation of the frequency response of the proposed INA structure

Fig. 3.8 shows the simulation results of frequency response of INA with four corners and we can find that the CMRR range can still maintain from 197.1dB to 231.5dB. Fig. 3.9 is the Monte-Carlo simulation results of the frequency response of the proposed INA. We put 5% device mismatch in the HSPICE Monte-Carlo simulation and from Fig. 3.9 we can find that the CMRR degrades seriously from 40 to 103dB.

This serious degradation is caused by the first stage of the subtraction function. Table 3.1 shows the simulation results of the proposed INA with the comparison of perfect and 5% device mismatch. We can find the most obvious different between the simulation result is the CMRR which degrades from 200~250dB to 40~100dB. As a result, we have to solve this problem in the future work.

Perfect Matching Mismatch situation (5% device mismatch)

Vdd 3.3V Vdd 3.3V

Tuning gain 10~60dB Tuning gain 10~60dB

CMRR 200~250dB CMRR 40~103dB

f_3dB 2~16 kHz f _3dB 2~16kHz

Output swing +0.4V~-0.4V Output swing +0.38~ -0.35

Power 0.1mW Power 0.1mW

Table 3.1 Simulation results of the INA

3.4 SIMULATION RESULTS OF LOW-FREQUENCY BANDPASS FILTER

We have simulated the ideal case of the bandpass LC ladder shown in Fig. 2.12(a) and filter with ideal Gm in Fig. 2.18.

Fig. 3.10 shows the simulation result of the bandpass Gm-C Elliptic filter with leapfrog structure using the Gm amplifier we design in chapter 2.3. Due to the tradeoff of the output resistance and the bandwidth of the Gm amplifier, we can’t design a very high output resistance with high bandwidth we want. As a result, the simulation result have some different with the ideal case.

Fig. 3.10 Simulation results with the comparison of the ideal and the realistic filter

. From Fig. 3.10’s comparison, we can find the attenuation decreases to 38.5 dB, and the passband ripple increase to 7dB. And we design a 30dB gain in the passband.

Fig. 3.11 shows the simulation results with four corners, we can find the frequency range of the filter drifts when fs and ff. However, we can use the tunable Gm amplifier to change the frequency range that drifts back to the frequency range we want.

Fig. 3.11 Simulation results of the low-frequency BP filter with four corners

Filter Spec Simulation

Low corner frequency 50 Hz 50Hz High corner frequency 2 kHz 2kHz

Stop band ratio 1.98 2.0

Stop band attenuation 40 dB 38.5dB

Pass Band Ripple 3 dB 7dB

Gain >0dB 30dB

Power Dissipation NA 130uW (39.28uA)

Type of the Filter Elliptic

Table 3.2 Simulation results of the low-frequency BP filter

3.5 WHOLE SIMULATION OF THE FRONT-END ELECTROPHYSIOLOGICAL

SIGNAL MEASUREMENT SYSTEM

Fig. 3.12 shows the simulation result of the whole front-end of the electrophysiological measurement system which is compose of instrumentation amplifier and low-frequency bandpass filter. The upper curve is the differential mode and the below one is the common-mode.

Fig. 3.12 The differential and common mode simulation results front-end circuit of the electrophysiological measurement system

Table 3.3 shows the simulation results of the front-end circuit of the electrophysiological signal measurement system. The CMRR can achieve 200~250dB and tunable gain from 10 to 120dB. The frequency range is from 50Hz to 2kHz. The total power consumption is 230uW.

Simulation results of INA+Filter

CMRR 200-250dB

Voltage Gain 10-120dB

Frequency range 50Hz~2kHz Stop band ratio 2.0

Stop band attenuation 38.5dB Pass Band Ripple 7dB Power dissipation 230uW

Table 3.3 Simulation results of the front-end circuit of the electrophysiological signal measurement system

CHAPTER 4 CONCLUSIONS AND FUTURE WORKS

4.1 CONCLUSIONS

With combination with wireless network, home nursing and remote medical care will be indispensable in the future. In this thesis, we have designed the front-end circuit of the electrophysiological measurement system. We announced a new structure of instrumentation amplifier and designed a low-frequency bandpass filter using 5^th-order Elliptic type and leapfrog structure.

For achieve high CMRR INA, we design a new analog block called differential difference operational transconductance amplifier (DDGm) with the similar operation principle as differential difference amplifier (DDA). Our new structure of INA proposed in the thesis is constructed with two differential difference Gm amplifiers and one Gm amplifier. The new INA can achieve high common-mode rejection ratio with tunable gain

After the INA, there is the bandpass filter with very low frequency between 50 Hz to 2 kHz. We use leapfrog structure to minimize the sensitivity of the filter to element value variations. The process of how to transfer a LC network to a leapfrog Gm-C filter is describe in detail. Due to the high Rs of the LC network that after normalized, we have to design the Gm amplifiers with small Gm value. So we have to use MOS in subthreshold region to obtain the small Gm value. Although small Gm value will encounter the problem of subthreshold current, we propose a method to solve it in this thesis. For the tunable Gm amplifier, we use a flipped voltage follower (FVF) to solve the problem of voltage follower which change its gain by output loads in most of the

tunable Gm amplifier.

For very low frequency filters, there are some critical design issues. We need very high output resistance to reduce the equivalent parasitic resistance. However, the corner frequency of the Gm amplifier is inverse proportional to output resistance. As a result, the bandwidth and the output resistance is a tradeoff design parameter. So we have to do the MOS size optimum to achieve the best performance of the Gm amplifier.

For the whole front-end circuit of the electrophysiological signal measurement system, we designed with TSMC 0.35um technology and the whole chip has a 230 micro-watt power consumption. With the very small power dissipation and high CMRR value with insensitive filter, we’ve successful designed a high performance front-end circuit of the electrophysiological signal measurement system.

4.2 FUTURE WORKS

Although we have proposed a instrumentation amplifier with high CMRR, the CMRR value is still affected by the process variation. The CMRR degrades when we run Monte-Carlo simulation, and we have to think some solution to solve it. It can also called the input offset problem. Many papers [15] announced the method of chopper amplifier to eliminate input offset problem. It maybe a good idea to combine our INA with switches to solve the problem. Another problem of the INA is the input referred noise that would also be a problem of the INA. We have to model the noise and find the way to optimize the input referred noise.

For very low-frequency using leapfrog structure, we will encounter the problems we have discussed in the chapter2. The tradeoff between output resistance and the bandwidth of the Gm amplifier need to be solved by new Gm amplifier circuit. If the tradeoff is limited by technology, we can also use 0.18um technology to simulate the

filter and we will have much more margin to design the Gm amplifier.

For the front-end circuit of the electrophysiological signal measurement system, low power and high CMRR is the most critical part of it. We have designed a low power and high CMRR circuit. In the our future work, we will also integrate the analog to digital converter (ADC), wireless part, and digital process circuits to a single chip.

Once the single chip is realized, it will be a memorable achievement of the combination of IC technology and medical. Also our live will be changed when that day comes. The layout, fabrication, and measurement of the front-end circuits of the electrophysiological signal measurement system will go through after the simulation.

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