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Low Power Current Mode True RMS-to-OC Converter for Biomedical Applications
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*Pantre Kompitaya Khanittha Kaewdang
Faculty of Engineering, UbonratchathaniUniversity,Warinchamrap,Ubonratchathani34190
TEL: 0-4535-3354 E-mail: [email protected]
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Abstract
This paper presents a low power current mode
true RMS-to-DC converter for biomedical
applications. The proposed circuit suitable for both
positive and negative input current signal. Its main
proposed circuit consists of two quadrant current
squaring circuit, low-pass filter and square root
circuit. This circuit is based on the characteristic of
CMOS operating in subthreshold region. Simulation
results are demonstratedby HSPICE. They find that
the circuit gives good results, the power
consumptionare less than 3.4 nW, low relative error
less than 1.5% and concomitantly to the theory.
Keywords: true RMS-to-DC converter, current
squaring circuit, subthreshoid region, biomedical,
translinear
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ot.:lHm:bbG1"bbt'l:bb1.:1'ilU,fl ElU,il.:1 G1",'j~,'j t:-I t'l1~m1u111l fI'II
nli.:lG1".:I ~.:Il1ib'VI:lJ1:G1":IJ~';):'Ill:IJlvr~u,1'V11m.h:£Jn~1i'II '...
nuirurulru,.lJi1 bb'l"l'Yl£f 'VI1ElElUnm4bb 'I"I'Yl£fbbU1JU~n~.:IQI'II It qJ
~1 tJb'VI~ t:-It'l'il.:lmh1'Yl1,'j t:-I11l£J~.:I'l~ ElEln bbU1Jd.:l,;)1• 'II
bbUt'l.:lirurulru, RMS bUu,irurulrn.'lvJ..:Jlm:bbG1"~1,'j ~(L/ CII IU Q,/
'Y11.:11U,1u,1'VI:lJlilm:bbG1"bbUuoii:IJElG1"llil £J'l~'IllbG1"U,El1.:1,;)1
m: bbG1"!.Jnnl i.:l G1"El.:l~'Y11.:11U,1U,cil u,~lnl1 bb1.:1'ilu,ii Iil b~:IJ
(Cardiac sense amplifier) [11]
,;)lmu~ 1 bbG1"Iil.:lU~ElnlIilEl:bbm:IJ1.:1,;)1'lJ£Jl!.J'II
i'f!j'f!jlru,fI~u,l vJ..:Jli'l h ot.:l1U,U'Ylfl11:IJ11ltJd';):'Il1 bffU,El
b'YlflUfi n11El an bbUU1.:1,;)1bu'1"1,"):1U,~lU'lJ El.:l1.:1,;)1bbUt'l.:l
irunnrn. RMS bUu,'lvJ..:Jlm:bbG1"tlm b~flu1:!.Jn<n1inu~~ .irurulrn..lJi1bb 'I"I'YltJbUd.:l,;)1'lJ£J1tJirurulru,fI~U, 'l vJ..:Jli'l h
IU IU !U IU
bbUUUt'ln~~.:I llil!.J'il: lib 'YlflUfln11El ElnbbUU~l !.Jl1fn11'IJ
bbUU~1.:1 (direct or explicit computation method) [12]
.t.:l lm.:lG1"11.:1'lJEl.:l1.:1,;)1'il:U1:nElU~l!.J1.:1'il1'V1in 'l~bbri
l.:1,;)1m:bbG1"!.Jnnli.:lG1"El.:l(squarer/divider circuit) 1.:1';)1
mEl.:li'f!j'f!jlru,fI11:IJiitlh~1U, (low-pass filter) bbt'l:l.:1,;)1d 0 Q..o A
{lElIil11n'YlG1"El.:l(square root circuit) G1"1-.11Ub'Ylflu,flm1
ElElnLbUU1.:1,;)1 RMS ~'IllbG1"U,Eld 'il:;:'Y111~l.:1,;)1'lJ!.Jl£J
irurulrn.fI~U,'ll~..:Jli'lh lu,1u~ 1 'l1i~El.:lii~lU,'lJEl.:l~ ~ 'IJ
l.:1,;)1flli:IJmrn ~.:It:-It'l1~l.:1'il1ii'lJu,1Iilb~nt'l,'j .t,'j1.:1'il1~'IJ
'IllbG1"u,fll~ElElnLbUUlliltJElli!.J'VIinm1mlw~f~hittJf'lJEl.:l
'Yl11U,oUG1"b<nElfLLuuoii:IJElG1"~'Y11.:11u,tv.:lJlilm:bbG1" 1u., Q..<O d ..d. Q..O Q..oO fi'
ff1l11:n ElU,bb1.:11ilU,'lJ1ilb1:IJ ffl:IJ11mbG1"Iil.:lfl11:IJ G1":IJ'I"Iu,ll
'lJEl.:lbm'ilu,bbt'l:m:bbffl U,ff1l11:'il.:ln~11'il,'jff:IJm1~ (1)
(1)
U1: tJn ~1inm:uu.lJi1 n11bb 'I"I'Yl£f b'liU,1u.~lU,'lJ El.:l•l.:1,;)1'lJ£J1!.Jirurul ru,fI ~u, i'1 h (cardiac sense amplifier)
[7,11] bUU,~U,
(2)
b~fl IDo=2n.ucox(:) V/ ,2n fiEl 'il1bbU1~bbU1~1:IJ
, '" Q..I ~ 4 IVT bbt'l:mfl11:IJb'lJ:IJ'lJU,'lJEl,'j"1!U,~1U,1El.:l, J.l flEl mfl11:IJ
fI~El.:l'il1'lJEl.:l'l"l1'V1:U~b1ru,bb"1!U,bbU,t'l, Cox fiEl fI11:IJbnU
'l6', .:t .cd a d".d
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108
VDDI I = IDJD5m D3 4
(4)
ISQ +lin (5)1m =2
ID3 =ISQ -lin (6)
2
ID4 = ISQ - 18 (7)
IDS =ISQ (8)
M11brl flf11V\'\-l,Cfl1i'lJU1Cfl'lJ fl.JmlWil~bCfl flfbb'll i.'l:;';1 fj~1
~IsQ(W/L)l = (W/Lh use (W/L)4 = (W/L)5 = 2(W/L)1 b')"T;):
~1lJ11f11bml:vfm:bb~ ID 'lJfl.Jmluo]l~bCflflf M1, M3,
M4 bbi.'l:M5 1~';.J~3Jm1~ (5)-(8)~M~H M2
M52X
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'L' -. 6' dd:nfl1JmUYl11Wi5~bCjJfld M1, M3, M4 bbi.'l:M5 'l!.J
11"';lnu1 U~n'l!l'rn:l.Jdfl1JmluGf~ bu'uf (translinearbrlmbYlU~3Jmd~ (5), (6), (7) bbi.'l:(8) i.'l.J1U~3Jm1~ (4)
~:IJ1dm']UU~3Jmd1V1:lJ1~ fifl""" Q.,oO Q..O 6' Q..oO
!oop) 'iJ:\illJ1dflV-l'iJldrnlml3J~3JV-lW!l'lJfl.J bb1.JCflUbbi.'l:
m:bb~'iJlm.J'iJd';.Jdtl~ 2 M';.J~3Jmd~ (3)'IJ (9)
(3)bi:lflISQ ~fl m:bb~bfll~Y'lCjJ'lJfln.J'iJdUnnl~.J~fl.J bbi.'l:lin
IE ~fl m:bb~aUV-lCjJbbi.'l:m:bb~11Jel~CjJl3J~1';1J,'iJln~3Jmd~ (9) nlnlV1UCfl1i IE bUU~l~.J~ 'iJ:
V-l1J_'hm:bb~ ISQ 'iJ:Yil.J1UbUU'V'r~rfiuunnl~.J~fl.J'lJfl.J
m:bb~a'l.tV-lCjJlin,
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d. 1'i.<1 a..-.::.. A Ii' I (1.,1
b3JflmVlUCfl VI~rn~3J1JCjJ'lJfl.JYldlU'l!~bo/lfldbYllnU bbi.'l:,lb~11:vf~3Jm11CfluHVI~nm1i.'lflm1Yi3J 'iJ:1~
2.2 ";
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M12
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(4)
, M3,
(5)
(6)
(7)
(8)
.dl'YI (4)
(9)
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1~'i)1LLUi.'h'liIlJIlJlrnRMS dhl.iIlJIlJlrn'l.wvh
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m:::LLb1'tJm'i1t~b1'£l~(1U~ 2) 1~'i)1m£l~ml;J~~1~,hu'U
d(M12 LL"':::CAY)LL"':::1~'i)1n£l~11mlb1'£l~(M16 - M19)
[13] 'fil;J~liU 'i)lm~'i)1'V'1U'"hLil£lm:::LLb1'ISQ L'Jil~
1~'i)1m£l~iIlJIlJlrnml;J~~1~lU l~tJ:iJ'mlu.nm'fi£lf
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IAv 'lJ£l~1~'i)1'1.~i~b1';Jm1~(10)
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Ld£l T=CAV / gm12 fi£l fllfl~ilLl"'l (time constant)
gm12 fifl fllmlm'h (transconductance) 'Yl11U.nb1'L'fiflf
M12
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'fil;J~liu .t~L~fl;J~£lnU1U1Ul~1£lU'mlu~"i~LittJf 1~tJ'U
Ldf)fi1v\u'fil",,~u~ (W/L) 'lJfl~'mlU.nb1'L'fi£lfLL~",:::il
L'Yhnu'YlnU1:::m1'i):::b1'1;Jl1n1Lf111:::'\{b1';Jn11m:::LLb1'lu,.d 'I. "'..1~'i)1n£l'fi11n'Ylb1'£l~'fifl£l 1016=IAv, ID17=IB LL"':::
6'0:=. Q 6' ~ 6''lJfl~1~1£lU'Yl11Ub1''''LUtJ1 L11'i):::b1'l:1J11n,Lf111:::v\b1';Jm1
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.. dV\1£lb1';Jnl1'Yl(13)
(13)
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m1fllUlrnv\lfllLU£lfLofiu';1udJ", (percent ripple) [14]
'lJ£l~1~'i)1i~1U~3 b1'1;J11nfllmrnM'i)ln~:lJm1~ (14)'U
percent ripple = 1 x 100% (14)2,]1+4W1T2
. .til£l w=27rj LL"':::f fi£l filml;Jii'lJ£l~iIlJIlJlrn€iu'I1'fi
(10)
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(15)
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nrr B
'mlU.nb1'L'fi£lfM12 LL"':::icMIN) fi£l filml:IJii€iu'I1'firjll~'fi
l'U,'Jil~ml;J~~b1'uh
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RMS Luu'l.wvhm:::LL~'fi1~fflWrUU1:::tJn'fi1']j1uirurulrn, ~~;;lLL'V'I'Y1!r~'I1.1L~U£li~1U~3 M'ill"'£l~m1'111~lu.ji'ltJ
"lU1LLm;J HSPICE l'fitJH'[;JL'fi"''mlU.n~L'fi£lf BSIM4
Level 49 'lJfl~L'Ylfllul",~ CMOS TSMC 0.18 'I.:lJf11£lU
LrimilV\u~l""fil~U~ W/L 'lJf)~'mlU.n~L'fi£lfM4 LL"':::
M5 :iJfil 1.8 iJm I 0.18 iJm fflWrU'mlU.nb1'L'fi£lfil
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~fl'fifl~€J~'fil;J'Yl'1~fi.yh1.1L~U£l(12)
110
2n "" .. i\-'" ..._"" ..,+.-"""",-.+" ...,,,,,.,,,,,';,,,,,,.,,,,,,.,,.;,,,,-,,,,._.+-,,,,,,,,-""+.""""".,,.+_..."-+""-"".,,.+"" ."-/".;._,,,i\
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; I -----j-..- ... -
-In :tiOOp' '4)op 600p 800p In-400p .200p 200p 400p
lin (A)
97m 97.2m 97.4m 97.6m 9i.8m 98m 98.2m 98.4m 98_6m 98.8m 99m 99.2m 99.4m 99.6m 99.8m 100m
Time(S)
~Iu
Time(S)
~lmll~ 4 LL"'il'l1~anTl-;jlalhlmnh"lU"lJEhl-hl~1'II
[Jmhf""a" l'V1lJ'ilm::LL"LLUU2 "'il1l1fl~,.t1L","a i'l111l• 'II
.. .4 .1" !'I •112 1JI'''~lJl'l4(n) LlJU~am111'il"aU"lJTICm::m1m'l11U., ., '1••1 ,d"lJa'l11"~1111'11'illUflcu,an1fcu,::bTim'l1 ViU11LlJarneue•
~UViIillin = 1 nA LLa::18 = 0.5 nA ViU11m::LL"Lal~ViIil• •, (L.o ,c:I( , .. ...
ISQ rmnu 2.01 nA lJfl1mllJflal'ilLflaaU1a[Ja:: 0.5 LLa:::
LrlfIfll'V1U'ill~ irunn cu,~UVililLuuirurul cu,"llJ L'VI ~ [JlJ., ILl " Vol QI
(I.; S",c:I( I ,Q.oO dL.a:::"tytylcu,lJI'l[JU3Jfl1LmnU1 nA fl113JCl1 kHz LLa:::
m:::LL"18 iifilfl"~L'r'hnu 0.5 nA ViU11 1'11~1.y;
aanuuu iifilfl113Jflal'ilLfl~Em fa [Ja:::2.18 LLa:::fa!Ja:::
0.4 t'ilmL"'il'l1~am1-;11aa"m1'r'l1'111Ulu11l~4("lJ)LLa:::'II
4(fl) Iill:IJthilu
11li'II
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t'il!Jl'1ft,
dH'VIIHJ:JJ
d1-\1i)"i'l1
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1'·lf·"····~-··"··;····'~··-···i············!··-·~'·-··i···-·····-··;·-·~··-··~··-···········t··..~·····+·-····-··+·-·~······t
l,-··-·*··-··-·.. ···t·······_··_··· . ......................_ _.... .......•.•... . _.... ..._.. .- ,-_.....•........
2. 95 2.9 55 2. 96 2.9 65 2.997 2.9 75 2.998 2.9 85 2. 99 2.9 95Time(S)
I,
soopiIRMS f!...
600p 1\ 1\ !i\/ LI\ 1\400p I \ I \ I \ / \ / \
/ \ / i \ J \ lin J \ I \200p
/ \ I \ I V I \ { \0
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2.195 2.9 i55 2.196 2.9i65 2.ln 2.9 i75 2.998 2.9i85 2.S99 2.9 i95 j
Time(S)
I,Jt=+===r===r===r===r=::;=:;==t==t==t==t====t<,..._-_ .._-_ .._-- .._-_.._-------_. ---------_._-- _._-_._----- -----------800p f-------
IRMS
lin$ 200p . - - -... . -..- -.. ;/.:...... ..-..- r--········+-·····-····-·f···········_·+I 0 1-····..............•. -. -..-.- -. -.. ..- -.- _.- ..- •........_- - -.._..,, ., _+., .; _ _ +U -200p ------ --- --------- ----------- ----.--.------ -------_. __ ------------.- ---.------ .-.--------- .-------_. I
·6GOp 1········ - ..- ..- ..- _ ................•...... - _...... . - ·..··_·······f···..·· ······f·..·· ·······+·800p il······+-············ __ .._ _.. . - _.. ········-·····+··..···--··-1···-·········;··1, i c •• r--,_ _ r---,.--- ,-: ..--_ r---' .'.'..'-."'.'r--
2.995 2.955 2.996 2.9965 2.997 2.9975 2.998 2.9 85 2.999 2.9995Time(S)
"itJ~ 5 bt~~hl~G1!ilfllJ~Ufl-\lm.JnG11'lJfl.J1.J~"iLLtJG1\l'IJ
inmnru. RMS LUULyJ~lm::LL~!il'J-\I~l1.1L~Ufllw:itJ~ 3~ ~ 'IJ
Lrl flnl'V1U~ 1vi'irunnru.awV'l!il lin bUUirurulru.'l51 EJ'I!QI QI" QI QI
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t~Ellv\ t; = 1 nA ml:JJ~ 1 kHz bLG1::';1LnlJtJ"i::~ CAV ii,
TilL'YhnlJ 250 pF 'I'-IlJl1 iryrylru.Lfll~~!il IRMs ~l~iiI II.-' d ,
'lJU1~bmnlJ 0.708 nA 0.583 nA LLG1::0.99 nA 'l5-\1m
ml:JJI'IG11~ LI'I~ flWlJ fl\l rmuilG1-\1iryrylru.iiTil L'Yl1nlJ
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lin~ 0 •••- --_.- -.--- •••.•-- ••.--•••..--.. •.• .•..-••-..•.••..v-:- .8 -2p,1l-.--!-------·!\---·- .f\--.-- -- -!l..-.-.- j~..-- -_i'
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-ep
!-Sp
-lOp
2.5 2.5 2.6 2.65 2.7 2.75 2.8 2.5 2.9 2.5 j
Time(S)
lOp ,A ~ A , A A
8pf'\
" n 1'\ /KM' Ii\ r\6p
1 \ i f \ I \ I'\ I i \
2p I \ !' \)in / \ J \ I \I \ I , \ / \ I \ I \
0 I \ 7 ! \ I \ I \ I i \-2p
/ \ J ' \ / \ / \ I \ i-4p
I \ I ! \ I \ I \ I \.6p
if \I i W U -U \-Sp
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2. 2,55 ., 2.65 , 275 ,:8 2F 2.95Time(S)
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