research article a novel differential log-companding...
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Research ArticleA Novel Differential Log-Companding Amplifier forBiosignal Sensing
Zigang Dong,1,2 Xiaolin Zhou,1,2 and Yuanting Zhang1,2,3
1Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, 1068 Xueyuan Road, Xili, Nanshan, Shenzhen,Guangdong 518055, China2Key Laboratory for Health Informatics of the Chinese Academy of Sciences (HICAS), 1068 Xueyuan Road, Xili, Nanshan,Shenzhen, Guangdong 518055, China3Department of Electronic Engineering, The Chinese University of Hong Kong, Shatin, Hong Kong
Correspondence should be addressed to Xiaolin Zhou; [email protected]
Received 23 May 2016; Accepted 31 July 2016
Academic Editor: Stephane Evoy
Copyright ยฉ 2016 Zigang Dong et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We proposed a new method for designing the CMOS differential log-companding amplifier which achieves significantimprovements in linearity, common-mode rejection ratio (CMRR), and output range. With the new nonlinear function used inthe log-companding technology, this proposed amplifier has a very small total harmonic distortion (THD) and simultaneously awide output current range. Furthermore, a differential structure with conventionally symmetrical configuration has been adoptedin this novel method in order to obtain a high CMRR. Because all transistors in this amplifier operate in the weak inversion, thesupply voltage and the total power consumption are significantly reduced.The novel log-companding amplifier was designed usinga 0.18 ๐m CMOS technology. Improvements in THD, output current range, noise, and CMRR are verified using simulation data.The proposed amplifier operates from a 0.8V supply voltage, shows a 6.3๐A maximum output current range, and has a 6๐Wpower consumption. The THD is less than 0.03%, the CMRR of this circuit is 74 dB, and the input referred current noise density is166.1 fA/โHz. This new method is suitable for biomedical applications such as electrocardiogram (ECG) signal acquisition.
1. Introduction
In recent years, portable and wearable personal healthcaredevices have become more and more popular in the world.For these kinds of devices, the biomedical signal acquisitionis an important part. The analog amplifier is one of the keybuilding blocks to the signal acquisition unit. Therefore, sev-eral requirements such as low power, low noise, low voltage,high total harmonic distortion (THD), and high common-mode rejection ratio (CMRR) are imposed on the amplifier inthe biomedical applications. The log-companding technique[1, 2] is a new tool to reduce the amplifierโs supply voltage,the internal voltage dynamic range (DR), and the powerconsumptions. It is also a good method to solve the trade-offbetween increasing the signal dynamic range and decreasingthe supply voltage [3]. This technique, indeed, provides apractical solution for biomedical applications for its property
of low power consumption, especially for the portable andwearable medical devices.
For the log-companding technique, the input signal firstlyneeds to be compressed from the current domain to thevoltage domain by logarithmic (log) law. Then, a nonlinearsignal processing can be done in the voltage domain. Finally,the processed signal is expanded back to the linear currentdomain from voltage domain to realize an external linearamplification. The log-companding technique is realizedwith MOS transistors biased in the subthreshold region fortheir exponential current versus voltage characteristics whichconsume very low power.
However, this technique has its limitations. For example,the output current range and the signal linearity are difficultto improve because of the property of MOS transistoroperating in the weak inversion. To reduce the distortion,the transistors are biased with low currents which will limit
Hindawi Publishing CorporationJournal of SensorsVolume 2016, Article ID 5358963, 7 pageshttp://dx.doi.org/10.1155/2016/5358963
2 Journal of Sensors
Nonlinearfunction
ExpanderF
Externally linear signal processing
IinIout
Vin Vout
CompressorFโ1
Figure 1: Diagram of log-companding technique.
the input and output current swings and reduce the signal-to-noise ratio (SNR). Although the biased currents can beimproved by enhancing the widths of the transistors, itwill increase the power consumption and induce a largeparasitic capacitance. Because the differential operation ofthe conventional differential log-companding amplifier isoperating in the current domain [4โ7], it is not very effectivein improving CMRR and THD for the log-compandingtechnique.
In this paper, a novel method is proposed to improve theperformance in linearity, CMRR, and low power of the log-companding amplifier by exploiting a nonlinear function andintroducing a new differential stage.This method realizes thedifferential operation between the input signals in the logand linear domains, which is more effective in eliminatingthe common-mode input signal. A novel nonlinear functionis employed to improve the system linearity and extendthe output linear range. This paper is organized as follows:the log-companding design technique will be introduced inSection 2. In Section 3, the novel log-companding amplifierwill be presented. The simulation results will be listed inSection 4, and Section 5 includes the conclusion.
2. Log-Companding Design Techniques
2.1. Basics of Log-Companding Techniques. For the expandingtechnique, the input signal in current domain is firstlycompressed to voltage domain. Then, a nonlinear processis performed in the voltage domain. Finally, the processedsignal is expanded back to the current domain to ensurean external linear function with the input signal. The blockdiagram of log-companding technique is shown in Figure 1[8].
As shown in Figure 1, the log-companding techniqueincludes three basic building blocks: I-V compressor ๐นโ1,nonlinear function, and V-I expander ๐น. Compressor ๐นโ1and expander ๐น are used to perform log-compression andlog-expansion, respectively, by using aMOS transistor biasedin weak inversion region which exactly gives the logarithmicfunction.
According to the EKV model [9], I-V function of aNMOS transistor can be expressed as follows:
๐ผ๐ท
= ๐ผ๐
(๐
๐ฟ) ln2 (1 + ๐(๐GBโ๐TONโ๐๐SB)/2๐๐๐ก)
โ ๐ผ๐
(๐
๐ฟ) ln2 (1 + ๐(๐GBโ๐TONโ๐๐DB)/2๐๐๐ก)
๐ผ๐
= 2๐๐ฝ๐2
๐ก
,
(1)
where ๐ผ๐
, ๐, ๐ฝ, ๐TON, and ๐๐ก stand for the specific current,subthreshold slope, current factor, threshold voltage, andthermal potential, respectively.๐GB,๐DB, and๐SB are the gate-bulk, drain-bulk, and source-bulk voltage difference, respec-tively. MOS transistors can operate in three main operatingregions which are called weak inversion, moderate inversion,and strong inversion, respectively. Each operating region canbe further categorized into three saturation regions whichcan be called conduction, forward, and reverse saturation,respectively. Under these conditions, I-V (1) can be simplifiedas follows:
๐ผ๐ท
= ๐ผ๐
(๐
๐ฟ) ๐(๐GBโ๐TON)/๐๐๐ก๐
โ๐SB/๐๐ก (2)
(in weak inversion and forward saturation) and
๐ผ๐ท
= ๐ผ๐
(๐
๐ฟ) ๐(๐GBโ๐TON)/๐๐๐ก (๐
โ๐SB/๐๐ก โ ๐โ๐DB/๐๐ก) (3)
(in moderate inversion and conduction saturation).
In the conventional log-companding amplifier, all MOStransistors are biased inweak forward inversion such as in theblocks of compressor ๐นโ1 and expander ๐น shown in Figure 1,since it exactly gives the logarithmic function. Moreover,the compressor and expander functions are two reciprocalfunctions to ensure external linear amplification.
For the PMOS operating in moderate conduction andweak forward inversion, I-V functions are depicted as fol-lows:
๐ผ๐ท
= ๐ผ๐
(๐
๐ฟ) ๐(โ๐GBโ๐TOP)/๐๐๐ก (๐
๐SB/๐๐ก โ ๐๐DB/๐๐ก) (4)
(in moderate inversion and conduction saturation)and
๐ผ๐ท
= ๐ผ๐
(๐
๐ฟ) ๐(โ๐GBโ๐TOP)/๐๐๐ก๐
๐SB/๐๐ก (5)
(in weak inversion and forward saturation).
2.2. Conventional Log-Companding Amplifiers. The mainpurpose of every amplifier is to obtain a linearly scaled copyof the input signal at the output port. In other words, theinput signal is multiplied by a gain factor to yield the outputsignal. For the log-companding amplifier, however, this stepis accomplished by adding a gain factor to the compressionsignal in the log region that is translated from the input signalby the log law, which corresponds to the part of nonlinearfunction in Figure 1. The general CMOS implementation ofthe log-companding amplifier topology is shown in Figure 2[3].
3. Novel Log-Companding Amplifier
The proposed differential log-companding amplifier consistsof four main parts including a compressor, a differentiator, a
Journal of Sensors 3
Iin Iout
Vin Vout
Vgaini Vgaino
VgainGC
+โ
+โ
+ โ
Figure 2:Thegeneral log-companding amplifier topology (auxiliarycircuitry in dashed line).
N1 N2
X Y
N3
Vb1
Vb
i1 i2
I1 I2
Ib
Figure 3: The diagram of compressor.
processor, and an expander [10].The compressor is employedto logarithmically compress the input current signal intovoltage signal. The differentiator is used to compare thedifference between the two input current signals in voltagedomain; the processer will process the nonlinear signal toimprove the CMRR and THD. The expander will convertthe voltage signal back to the current signal using log law tomaintain external linear amplification.
3.1. Compressor. The compressor is shown in Figure 3, where๐1
and ๐2
are the input current. All of the MOS transistors inthis schematic are biased in weak forward saturation. From(2) and Figure 4, we can get the following:
๐ผ1
โ ๐ผ2
= ๐1
โ ๐2
๐ผ1
+ ๐ผ2
= ๐ผ๐
= ๐ผ๐
(๐
๐ฟ)๐3
๐(๐
๐โ๐TON)/๐๐๐ก
N3 N4
N5
N6 N7
P1 P2
P3
X Y
VdmVref
Figure 4: The diagram of differentiator.
๐ผ1
= ๐ผ๐
(๐
๐ฟ)๐1
๐(๐
๐๐ตโ๐TON)/๐๐๐ก๐
โ๐SB/๐๐๐ก
๐ผ2
= ๐ผ๐
(๐
๐ฟ)๐2
๐(๐
๐๐ตโ๐TON)/๐๐๐ก๐
โ๐SB/๐๐๐ก
๐ผ1
โ ๐ผ2
๐ผ1
+ ๐ผ2
=๐1
โ ๐2
๐ผ๐
=๐ผ1
/๐ผ2
โ 1
๐ผ1
/๐ผ2
+ 1=๐๐
๐๐/๐๐
๐ก โ 1
๐๐๐๐/๐๐๐ก + 1
= tanh( ๐๐๐
2๐๐๐ก
) .
(6)
Therefore,
๐1
โ ๐2
= ๐ผ๐
tanh( ๐๐๐
2๐๐๐ก
) , (7)
where ๐ผ๐
is the quiescent operating current which will fix theinput circuit operating point and control the amplifierโs gainby tuning its value.
3.2. Differentiator. As shown in Figure 4, ๐ref is a biasedvoltage that is provided by the biased circuit (it is not shown inthis paper) to bias theMOS๐1,๐7 in weak forward inversion.๐dm is the output of differentiator.
Suppose that the MOS transistors are biased in weakforward inversion; recalling (2) and (5), we can get
๐๐๐
= ๐dm โ ๐ref (8)
๐1
โ ๐2
= ๐ผ๐
tanh(๐dm โ ๐ref2๐๐๐ก
) . (9)
Thedifferentiator plays an important role in getting a highCMRR since the differential operation in the voltage domain.
4 Journal of Sensors
P7 P8
P9N10 N11
N12 N13
N17
Vdm
Vo
Io
Ibias
Figure 5: The diagram convertor and expander.
Ibias
Vref
Figure 6: The current bias.
3.3. Nonlinear Convertor and Expander. The basic nonlinearprocessor is shown in Figure 6.The circuit converts the inputsignal ๐dm from voltage domain to current domain by MOS๐7 for conveniently tuning the signal. The current mirrorinvolves two pairs of composite MOS transistors ๐12 and๐13, respectively. MOS transistors ๐8, ๐9, and ๐16 expandthe current signal back to voltage domain and complete signal๐dm nonlinear conversion to ensure linear amplification.
Suppose that ๐8 operates in weak forward saturation andthe others in Figure 5 operate in weak inversion; according to(5), the drain current of ๐7 can be written as
๐ผ = ๐ผ๐
(๐
๐ฟ)๐7
๐(โ๐dB+๐TOP)/๐๐๐ก , (10)
where
๐๐ต
= ๐DD. (11)
According to (4) and (5) and assuming that the supplyvoltage is enough to saturate transistor ๐9, the current andvoltage expressions of ๐8 and ๐9 can be given by
๐ผbias = ๐ผ๐ (๐
๐ฟ)๐9
๐(โ๐OB+๐TOP)/๐๐๐ก๐
๐SB/๐๐๐ก (12)
๐ผbias + ๐ผ = ๐ผ๐ (๐
๐ฟ)๐8
๐(โ๐OB+๐TOP)/๐๐๐ก [1 โ ๐
๐SB/๐๐๐ก] . (13)
From (10)โ(13), we can get
(1 +(๐/๐ฟ)
๐8
(๐/๐ฟ)๐9
) ๐ผbias + ๐ผ๐ (๐
๐ฟ)๐7
๐(โ๐dB+๐TOP)/๐๐๐ก
= ๐ผ๐
(๐
๐ฟ)๐8
๐(โ๐OB+๐TOP)/๐๐๐ก .
(14)
Multiply ๐๐ref/๐๐๐ก by both sides of (14), rearranged to give
๐ผ๐
(๐
๐ฟ)๐8
๐(๐refโ๐๐)/๐๐๐ก โ ๐ผ
๐
(๐
๐ฟ)๐7
๐(๐refโ๐dm)/๐๐๐ก
= (1 +(๐/๐ฟ)
๐8
(๐/๐ฟ)๐9
) ๐ผbias๐โ(๐DD+๐TOPโ๐ref)/๐๐๐ก .
(15)
Let
๐
=(1 + (๐/๐ฟ)
๐8
/ (๐/๐ฟ)๐9
) ๐ผbias
๐ผ๐
๐โ(๐DD+๐TOPโ๐ref)/๐๐๐ก .
(16)
Equation (15) can be written as
๐(๐dmโ๐ref)/๐๐๐ก =
((๐/๐ฟ)๐7
/ (๐/๐ฟ)๐8
) ๐(๐
๐โ๐ref)/๐๐๐ก
1 โ (๐/ (๐/๐ฟ)๐8
) ๐(๐๐โ๐ref)/๐๐๐ก. (17)
Then, let us take a look at the following function:
๐2๐ฅ
=๐
1 โ ๐. (18)
Solving (18) for ๐, this yields
๐ = tanh (๐ฅ) + 1
๐2๐ฅ + 1. (19)
In most practical cases, the second term of the right handof (19) is much less than the first. For example, if ๐ = 1.2,๐๐ก
= 26mv, ๐dm = 0, ๐ref = 400mv, calculated to give
ฮ =1
๐(๐refโ๐dm)/๐๐๐ก + 1โ 2.7 ร 10
โ6
. (20)
For this reason, assuming that
๐ = (๐
๐ฟ)๐7
(21)
and combining (9), (17), (18), and (19), we find
๐1
โ ๐2
= ๐ผ๐
(๐/๐ฟ)๐7
(๐/๐ฟ)๐8
๐(๐
๐โ๐ref)/๐๐๐ก . (22)
Journal of Sensors 5
โ30 โ20 โ10 0 10 20 300
2
4
6
8
10
12
14
Out
put c
urre
nt(๐
A)
Input current (nA)
Figure 7: The output current curve with a varied input current.
0 0.1 0.2 0.3 0.4 0.54
5
6
7
8
9
10
11
Time (ms)
Out
put c
urre
ntI o
(๐A)
Figure 8: Transient response of output current of the amplifier.
From (2) and (22), the output current is given by
๐๐
=(๐/๐ฟ)
๐8
(๐/๐ฟ)๐17
(๐/๐ฟ)๐7
(๐/๐ฟ)๐3
๐(๐refโ๐๐)/๐๐๐ก (๐
1
โ ๐2
) . (23)
Recalling (16) and (21), the biasing current can beexpressed as
๐ผbias = ๐ผ๐ (๐/๐ฟ)
๐7
(๐/๐ฟ)๐9
(๐/๐ฟ)๐8
+ (๐/๐ฟ)๐9
๐(๐DD+๐TOPโ๐ref)/๐๐๐ก , (24)
where ๐ผbias is implemented as shown in Figure 6.Although the derivation of (23) is based on the assump-
tion that all MOS transistors operate in weak forwardinversion, it can also keep the performance of the proposedamplifier when๐7,๐8, and๐9 operate inmoderate inversion.
4. Simulation Results
The differential log-companding amplifier is designed ina standard 0.18 ๐m CMOS technology. The supply voltageis 0.8 V and the bias voltage ๐
๐
is 320mv. Note that theamplifierโs gain can be controlled by voltage ๐
๐
. Because allthe aforementioned deductions are based on the EKVmodel,
1 10 1000
10
20
30
40
50
60
Frequency (Hz)
Curr
ent g
ain
(dB)
501kHz3dB frequency:
100M10M1M100 k10k1k
Figure 9: Frequency response of the amplifier.
โ160
โ140
โ120
โ100
โ80
โ60
โ40
Frequency (Hz)
Out
put c
urre
nt sp
ectr
um (d
B)
70.83 dB
1M100 k10k1k
Figure 10:The distribution of THDwith respect to the gain current.
Table 1: The corner simulation results.
Typical Worst case Best caseMOS model Typical Fast SlowTemperature (โC) 27 0 80Voltage supply (V) 0.8 0.8 0.8Open loop gain (dB) 50 51.7 46.83 dB frequency (kHz) 510 340 850Maximum input range (nApp) 20 10 46Maximum output swing (๐App) 6.3 2.58 10THD@maximum output swing (%) 0.028 0.056 0.03CMRR (dB) 73 77.8 64.2
the design adopts the EKV model from the foundry in thefollowing simulations to verify the analytical conclusions.
The output current changes from 0.23 ๐A to 13.6 ๐Awhenthe input current varies from โ20 nA to 20 nA as shownin Figure 7. The transient response of the output current isshown in Figure 8 with a sinusoidal input signal of 10 kHzfrequency and 20 nApp peak-to-peak amplitude. Figure 9shows the frequency response of the amplifier. The CMRR oflog-companding amplifier is up to 73 dB using two stages ofthe differential structures shown in Figures 3 and 4.The THDof the proposed circuit is less than 0.03% at the maximumoutput as illustrated in Figure 10.
Considering that THD and CMRR are influenced by thedevice mismatch, the result of Monte Carlo simulation isprovided as shown in Figure 11. THD is more than 80 dB and
6 Journal of Sensors
Table 2: Performance comparison with other works.
This work [11] [4] [8]Technology 0.18 ๐m CMOS 0.18๐m CMOS 0.25 ๐m CMOS โTopology Current mode Current mode Current mode Current modeSupply voltage (V) 0.8 1 0.6 1Open gain (dB) 50 dB 44.5/50/55.9 โ40 to 38 โ40 to +40Bandwidth (Hz) 510 k 0.3โผ1 kโผ10 k 200 k โInput referred noise density (fA/sqrt (Hz)) 166.1 fA (@10 kHz) 153 fA (@10 kHz) โ โMaximum input current (nApp) 20 20 โ โInput dynamic range (dB) 92.9 53.29 โ โPower consumption (๐W) 6 13 3.16 25CMRR (dB) 74 โ 35.76 โTHD@maximum input (%) 0.0287@50 dB 1.03 0.55 0.6
0 5 10 15 20 25 306065707580859095
100
Monte Carlo
(dB)
THDCMRR
Figure 11: The Monte Carlo simulation.
0.2 0.25 0.350.3
Gai
n (lo
g)
Vb (V)
104
103
102
SimulatedPredicted
Figure 12: The amplifier gain curve with a varied ๐๐
.
has a satisfactory result, CMRR is almost more than 72 dBand a very few points degrade. Figure 12 gives the comparisonbetween the simulated gains and the predicted gain accordingto (24). The figure shows a good estimation.
The corner simulation results are shown in Table 1, whichexhibit a good capability of operating in the real circum-stance. Three corner simulations are different in temperature
and same in voltage supply. Open loop gains vary only 5 dB inthe range of different corners. 3 dB frequency has poor valuein the worst case but it is acceptable for biosignal sensingapplication. They all have a good performance in THD andCMRR.
Table 2 displays the performance comparison with otherdesign methods. They employed the same current-modetopology andwork below the voltage supply 1 V.Thiswork hasthe least power consumption only 6 ๐W and the best inputdynamic range 92.9 dB. The proposed amplifier in this papershows the lowest THD and the highest CMRR. Furthermore,it also shows excellent performance in low supply voltage andlow power consumption.
5. Conclusions
A novel high linearity, low power, and high CMRR differ-ential log-companding amplifier is introduced in this work.The amplifier is designed in a standard 0.18 ๐m CMOStechnology with excellent linearity, high CMRR, and lowpower consumption. With the new nonlinear function usedin the log-companding technology, the proposed amplifierhas a very small THD and simultaneously a wide outputcurrent range. Furthermore, a differential structure withconventionally symmetrical configuration has been adoptedin the novel method in order to obtain a high CMRR. Thevoltage supply is 0.8 V, the power consumption is 6 ๐W, andthe THD is less than 0.03% at the maximum input. TheCMRR of this circuit is 74 dB and the input referred currentnoise density is 166.1 fA/โHz. It can be used in biomedicalsignal processing to decrease total power consumption, toensure the signal linearity, and to eliminate common-modenoise. In conclusion, this technique can be used to designlog-companding amplifier for many portable and wearablepersonal healthcare applications.
Competing Interests
The authors declare that there is no conflict of interestsregarding the publication of this article.
Journal of Sensors 7
Acknowledgments
This study was funded by the National Basic ResearchProgram 973 (no. 2010CB732606), National High-Tech R&DProgram of China (863 Program, no. SS2015AA020109),the National Natural Science Foundation of China (no.61401453), the STS Key Health Program of Chinese Acad-emy of Sciences (nos. KFJEW-STS-097 and KFJ-EW-STS-095), the Guangdong Innovation Research TeamFund for Low-Cost Healthcare Technologies in China, theExternal Cooperation Program of Chinese Academy ofSciences (no. GJHZ1212), Guangdong Science and Technol-ogy Project for Application Research and Development (no.2015B010129012), the Key Lab for Health Informaticsof Chinese Academy of Sciences, the PeacockProgram to Attract Overseas High-Caliber Talentsto Shenzhen, and Shenzhen Municipal Government(nos. CXZZ20150504145109589, JCYJ20150630114942270,JCYJ20140417113430655, and JCYJ20140417113430619).
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SensorsJournal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
Navigation and Observation
International Journal of
Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014
DistributedSensor Networks
International Journal of