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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: khanittha.k@ubu.ac.th

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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)

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[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

U1:'ilbb~.:I'lJEl.:lbn<nElEln 'l11il<nEl'l"lU,'Yl, W / L flEl 'I"Iu,'Yl•fI11:IJn11M ~U,~fI11:IJ!.J11 U1:~'Ylnt:-lt'l'lJEl.:lbb"1!u,bmt'l

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

l.J'iJdUnnl~.J~fl.J~'ltlb~Ufl';.Jdtl~ 2 1~flflmb1J1J

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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,

( I 1 (I 1 (I 1 (I 'InV In _____QL_ +n V In ____f2]__ = n V In _IM_ +n V In ___I2'l_T WI LIDO T WI LIDO T WI LIDO T WI LIDO,

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 ";

(M12

[13] ,

M12

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lew-pi

IAV'lJE

M12

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(M14

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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

m:::LLI;Hl1~~'I1.1Lb1'UmLb1'~~i~1U~3 U1:::n£lu.ji'ltJl~'i)1'U

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

M12 ~£l'lJU1UnU CAY .t~LuuilLnUU1:::'i)~~£l1,rnuunn 'I1TV\,xl~LUU1~'i)1m£l~iIlJIlJlrnl'I'I:IJ'fim:::LLb1'

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IAv 'lJ£l~1~'i)1'1.~i~b1';Jm1~(10)

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'i):::b1'1;J11mJ'filu1Utime-domain 'I.'fi1'V\:1Ji~b1';Jm1(11)"

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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U1:::nflU~ltJ'mlU.nb1'L~£lfM16, M17, M18 LL"':::M19

'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"':::

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.. dV\1£lb1';Jnl1'Yl(13)

(13)

'i)lnb1';Jm1~(13) 'V'Iu'"hm:::LLb1'L£ll';Vl'fiIRMs mJlu, "1Uuuusi in £l~11n~ b1'£l~'lJ£l~fll LU~tJiru nn rum:::LLb1''U ~ ~

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

3.~~nl1~1~€l\lnl1nl\11"~€l\ll\l~11um1'ill '"fl~m1'111~lU'lJ£l~1~'i)1LLU"'~iIlJIlJl ru

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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f11~V\U~'lJfl~'lJU1'fi~IlJIlJlrn£lU'I1'filin LL"':::LL1~'fiUl"iL"'tJ~.d ..d 0

Voo ;Jm 0.9 V 'll'~~"'m1'Yl'fi~£lUm1'Y11~lU'lJfl~1~'i)1

LL~'fi~'I..ji'i~1U~4 n~1U~ 7 'fil;J~liU .t~'i):::L~uM'"h'U "

1~'i)1~1;J11n'l11~lULUU1~'i)1tJmilt~ ~£l~1V\:IJ'fim:::LL~

~fl'fifl~€J~'fil;J'Yl'1~fi.yh1.1L~U£l(12)

110

2n "" .. i\-'" ..._"" ..,+.-"""",-.+" ...,,,,,.,,,,,';,,,,,,.,,,,,,.,,.;,,,,-,,,,._.+-,,,,,,,,-""+.""""".,,.+_..."-+""-"".,,.+"" ."-/".;._,,,i\

L8n ·-t \ /L6n f---.t,----'I,\c-.r;.."·-"-+"·""""""+-'·""-"·+·-"--+-··"""""+"-""+-""""+"-""'Vf"/' """'~~'''-i

~ :: 3~~-·~·-"f\f,-'~:_sc".'"'+'"''''''''''+''''''''''''-1---''''''''+'''''''''"--i-"-",_._.!""".""."/"+"/".y/,,,,,,+.,,,,,,-,--r---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

.. .ummwityqjlcu,

t'il!Jl'1ft,

dH'VIIHJ:JJ

d1-\1i)"i'l1

1'1f-+-~-·.·+·,~·i·'·7'+-·····-+·-~··-+.··'..A ..j .. -.+800pj~... J;::;~!\4==:::J;+!:+\ t==::t;~!.\\t}RM~S(:+\. +===+=t=r:\\:::t==:;,::'1\ c -\ ,f \ 1mr-\I+ Hr:·\i ~.~::..

~8 ·200p1f···-··+············;1H············!I·······_··/;·············it-·_····· , _._ ···_······,,············;I··-··_···Ii·

::: ::~~: ..~ ::. ::I\I·\'_·····:+/·/r++·::.-~·_·iti+\+\._tiff \ /++············-+1-\2.soOPjf_+··· ...v: V V V J ..

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

-200p I \ I \ I \ I \ I \-400p / \ / \ / \ I \ / \-600p I \ I \ I \ I \ I \-SOOp i I \ I \ I \ I \ I \·1,

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

q,.. .cd Q,..; d.cd 0 Q..<o

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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

fflElG1:: 0.14 0.52 LLG1::1 !ill:JJ~lilJ

lOp i f\ (\ [\ IRMS!\ (\,'._._..._+8p 1--.---++: ! -r-r-r-

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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

! I-lOp _..

2. 2,55 ., 2.65 , 275 ,:8 2F 2.95Time(S)

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