Design Considerations of Time Constant Mismatch Problem for Inductor DCR Current Sensing Method

Transcription

1 Design onsideraions of ime onsan Mismach Problem for Inducor D urren ensing Mehod ei Hua emech orporaion 00 Flynn oad amarillo, A 900 Absrac - his paper idenifies adanages and disadanages of seeral commonly used curren sensing mehods such as dedicaed sense resisor sensing, MOFE D(ON curren sensing, and inducor D resisance (D curren sensing. Among hese curren sense mehods, inducor D curren sense will become dominan one in he fuure. he mismaching issue beween he ime consan made by he curren sensing nework and he one formed wih oupu inducor and is D resisance is addressed. A small signal model of a buck conerer using inducor D curren sensing wih mismached ime consans is presened, and he modeling has been erified experimenally. I. INODUION Wih he deelopmen of modern echnologies, here is an eer-increasing demand for high efficiency and high power densiy power supplies. In all he power supply and conerer designs, one of key echniques is how o accuraely and imely acquire curren signal ha will be used for curren conrol and monioring purpose. Alhough a radiional curren sensing mehod using a dedicaed sense resisor afer he oupu inducor can achiee high accuracy in curren sensing, his mehod would inroduce quie a bi of exra power loss, especially for high oupu curren applicaions. o minimize unnecessary power loss on curren sensing, a MOFE D(ON curren sensing mehod has been used in producs. Howeer, he accuracy of his approach srongly relies on he olerance of he MOFE on-sae resisance ( D(ON. Unforunaely, hough emiconducor manufacurers hae pu so much effor on improing MOFE D(ON olerance, lile progress has been made. he MOFE D(ON olerance usually falls in 0%~40% under he curren indusrial gauge. For a muliphase conerer which has been widely used in oday s powerful PU olage regulaor applicaions, poor curren sensing accuracy using MOFE D(ON may cause significan phase o phase curren sharing unbalance. Inducor D urren ensing uses he olage drop on he oupu inducor D esisance (D o derie he oupu curren informaion. ince D olerance can be conrolled a 5% wih curren process, is curren sensing accuracy is much beer han ha from MOFE D(ON curren sensing. Addiionally, i can be implemened by jus adding a couple of resisors and capaciors, which is almos a free and lossless curren sensing mehod. his curren sensing echnique becomes more and more popular due o higuo uo Dell ompuer orporaion One Dell Way ound ock, X 7868 he good radeoff beween he accuracy and is lossless characerisics. Howeer, wih his curren sense scheme, he sensed curren signal may be disored if he ime consans mismach beween he one formed by sensing nework and one made by he oupu inducor plus is D happens. Wha is more, een if he wo ime consans is prey close a he iniial operaing poin, he mismach is sill ineiable since acual inducance and is D always ary wih he operaing poin (emperaure, curren, e.. his paper analyzes he side effecs of he ime consan mismach problem. And suggesions were made o minimize he errors inroduced. Finally a small signal model wih mismached ime consans is presened and erified experimenally. II. IUI OPEAION HAAEIZAION AND IMUAION EU A buck conerer using inducor D curren sensing is drawn o illusrae he circui operaion. As shown in Fig., W and W represen he conrol and freewheeling swiches in a ypical synchronous buck conerer, respeciely. is he oupu filering inducor and is he D resisance of. OU and E represen he oupu capacior and is parasiic resisance, respeciely. he nework formed by and is he curren sensing circui. is drawn in doed line since i is no always necessary. is added only under he circumsance in which scaling down of he deeced curren signal or/and emperaure compensaion funcion are needed. W W V V I E OU Fig. : Buck onerer wih Inducor D urren ensing OAD /06/$ IEEE. 68

2 o analyze he olage signal on, he circui as shown in Fig. is inesigaed under four differen cases. he ime consan formed by he oupu inducor is defined as. And he ime consan composed of is defined as when is no used and ( ( when is adoped. he case ha we call i ime consan mach is when equals. And he case ha we call i ime consan mismach is he one when does no equal. A. wo ime onsans Mach ( wihou his siuaion is he mos common approach for applicaions using inducor D curren sensing. As shown in Fig., when he ime consan equals he ime consan, he olage ( across in doed line, oerlaps he olage ( across he inducor D drawn wih solid line. And he relaionship beween ( and ( can be described as in (. i m D m 0 0 (-D Fig. : Illusraion of olage signal ( ( ( i i wihou under he condiion in which and olage drop ( Wih mached ime consan, he olage across can 00% represens he olage across generaed by he inducor curren i so ha lossless curren sensing can be achieed by using he olage signal across. B. wo ime onsans Mach ( wih is ofen used o scale down he olage signal across when eiher ( is oo high or a emperaure compensaion funcion is needed. Wih he presence of, he ime consan formed by is changed and can be ( expressed as ( (. he olage signals across and are illusraed in Fig.. i m m 0 i i 0 (-D D Fig. : Illusraion of olage signal ( and ( wih under he condiion in which As shown in Fig., he olage signal ( is no 00% of ( bu scaled down by he facor of (. he relaionship beween ( and ( can be wrien as in ( and (. i ( ( ( (. ime onsans Mismach ( wihou Howeer, in real applicaions, i is ery hard o mach he ime consan wih due o arious limiaions such as he olerance of he used passie componens and he emperaure dependence of. Addiionally, he inducance also changes wih is D curren bias, which deerioraes he exising mismached siuaion. All hese realisic circumsance raises up he quesion on why he sensed curren signal ges disored and how his is going o affec he conerer s normal operaion. he basic operaion of he curren sensing nework is a process of charging and discharging on capacior. As shown in Fig., when he conrol swich W closes, he inpu olage, ogeher wih, will be applied o he inducor plus and he curren sensing nework wih. ince he is ery small, he olage across is ery weak. o he curren flowing hrough, I, can be considered o increase linearly wih he slew rae of ( VIN VO. And a he same ime, he olage across he ges charged up wih he ime consan. When he conrol swich W is urned off and he freewheeling ( ( 69

3 swich W is urned on, only he oupu olage is applied o he inducor plus. I sars o decline wih he slew rae of. And a he same ime, ges discharged wih he same ime consan. he whole charging and discharging process is illusraed in Fig. 4. i 0 m D m 0 (-D i Fig. 4: urren ignal i and Volage Waeform ( ae in eady When he ime consan is much bigger han he swiching cycle, which is rue for mos of he applicaions in which he swiching frequency is aboe 00kHz. During he D and (-D ime, he exponenial charging and discharging processes can be simplified wih linearizaion. We can use he slew rae of he charging process a 0 o approximae he olage slope of ( during D ime. And use he slew rae of he discharging process a o approximae he olage slope of ( during (-D ime. Assume he iniial olage across a 0 and is ( 0 and ( respeciely. he olage (, across during D and (-D ime, can be described as in (4 and ( ( ( ( [ ( 0, VIN e 0 e ( ( ( [ (, e e A he ime and 0 he charging slew rae and he discharging slew rae are addressed in (6 and (7 respeciely: HAGE ( 0 ( VIN ( 0 (6 (7 DIHAGE ( ( ( ince he olage on is ery small, he iniial olage across, ( 0 and ( in (6 and (7, can be omied in he following analysis. If he ime consan, (4 (5 hen he equaion (6 and (7 can be rewrien as in (8 and (9: HAGE ( 0 ( VIN (8 (9 DIHAGE ( ( From (8 and (9, we can see ha he peak-o-peak olage ripple across is he same as he peak-o-peak olage ripple across he inducor D resisance, which can be characerized in (0. ~ V PKPK ( VIN VO D (0 Howeer, in real applicaions, i is ery hard o make. o he slew raes of he charging and discharging process need o be adjused wih a correcion facor. e firs define he capaciance needed o mach he ime consan as in (. DEAM ( Assume is he real alue seleced in real applicaions. he slew raes of charging and discharging processes on can be modified as shown in ( and (. DEAM ( HAGE ( 0 ( VIN DEAM DIHAGE ( ( V O ( Now we can see ha, a 0 and, if he in a real applicaion is less han DEAM, he peak-o-peak olage ripple across is acually bigger han he peak-o-peak olage ripple across generaed by I ~. is he A componen of he oupu curren flowing hrough. his means ha he slew rae of ( is acually amplified by he coefficien of DEAM. And if is bigger han DEAM, hen he peak-o-peak olage ripple across will be acually smaller han he peak-o-peak olage ripple across generaed by I ~, which means ha he slew rae of ( is acually scaled down by he facor of DEAM. D. ime onsans Mismach ( wih In some oher applicaions, because he olage drop across is oo high or emperaure compensaion funcion is needed, anoher resisor, as shown in Fig., is adoped o leel shif he D olage on or o proide emperaure compensaion. he appearance of changes he ime consan preiously defined by and. Will his exra resisor change he slew rae of he charging and discharging? o analyze he charging and discharging processes on I ~ 70

4 , Fig. 5 and Fig. 6 are drawn o illusrae he circui operaion during D ime and (-D ime. And relaie waeforms are shown in Fig. 7. Wih he assumpion ha he ime consan is much bigger ha he swiching cycle of he conerer, he exponenial charging process can be simplified wih linearizaion as addressed before. he olage across, (, can be described as he funcion of ime as shown in (4 and (5 during D ime and (-D ime wih he assumpion ha ( 0 and ( are so low ha hey can be omied in he following analysis. ( [ 0, (4 ( [ ( (, e (5 A he ime and 0 he charging slew rae and he discharging slew rae are addressed as in (6 and (7 respeciely: HAGE ( 0 ( VIN (6 (7 DIHAGE ( ( Based on (6 and (7, we can derie ha, a he ime 0 and, he slew raes of charging and discharging are no affeced by he presence of. he direc influence of is ha he D olage on is leel shifed by he facor of. his ineresing phenomenon implies ha he slew rae of he olage ripple on is only affeced by and. Wih he DEAM as predefined in (, he slew raes of he charging and discharging process on, een wih he presence of, can be characerized as in (8 and (9: DEAM ( (8 HAGE 0 ( VIN ( V IN VO DIHAGE( ( ( e DEAM 0 (9 i 0 V Fig. 6: Discharging process on during (-D ime m D m (-D 0 I i Fig. 7: urren ignal i and Volage ( wih in eady ae A swiching mode simulaion circui was buil in spice as shown in Fig. 8. he simulaion resuls under differen ime consan mismach condiions are gien in Fig.9, Fig.0 and Fig.. V I Fig. 5: harging process on during D ime Fig. 8: imulaion ircui In Fig.9, Fig.0 and Fig., he cure on he op is he olage drop across. he cure a he boom is he olage across. he simulaion resuls, as lised in Fig.0 and Fig., clearly show ha, under he condiions in which, he slope of he olage across is eiher scaled down or scaled up by he facor of DEAM een wih 7

5 . he usage of. And he D olage on is scaled down by he facor of from I and i remains he same under hose condiions as shown in Fig.9, Fig.0 and Fig.. he modeling mehod in his paper for peak curren mode conrol is described in chaper in he book Fundamenals of Power Elecronics. Fig. illusraes he ariables used in he modeling. he reference designaors are based on he parameers defined in Fig.. As shown in Fig., he relaionships of he conrol ariables can be expressed in (0, ( and (. i ( D m ' D m ic ( M a d (0 IN OU DEAM m ( m OU m a d DEAM i c ( V Fig. 9: Waeforms under he ondiion--- (μh; mω; 0KΩ; 50nF; 0KΩ m m d ' m d -m a - m i c a i i( d i( ' d 0 D (-D Fig. urren ignal I and Volage Waeform V wih in Operaion he simplified conrol flow char is shown in Fig.. V g d : D Fig. 0: Waeforms under he ondiion < (μh; mω; 0KΩ; 00nF; 0KΩ g I d (s Z i d - Z o (s F m g F g - - F i - F i i i c Fig. onrol Flow har And F g, F m, F and F i can be expressed as: Fig. : Waeforms under he ondiion > (μh; mω; 0KΩ; 5nF; 0KΩ F D Fg ( D DEAM DEAM ( (4 III. MA IGNA MODE FO BUK ONVEE UING INDUO D UEN ENING WIH MIMAHED IME ONAN F m M F i a (5 (6 7

6 Z i s ( // s Z o // s VOU D Fm Zo F D Z Fi i Z F o he conrol o oupu ransfer funcion G c (s is o i (7 (8 (9 (0 slope of he olage drop on is 4.66V/m. By plugging in he correcion coefficien DEAM. calculaed from he parameers lised aboe, he slope of V (9.8V/m is close o he scaled up alue. 4.66V/m 9.7V/m calculaed from he olage slope on ogeher wih he correcion facor. G c Z o i ( F Zoom In i IV. EXPEIMENA VEIFIAION i A buck conerer was buil o erify he analysis of he slew rae of he olage ripple on and is sabiliy issue under he ime consans mismach siuaion. he buck conerer plus is conrol flow char is shown in Fig. 4. In he Fig. 4, a and b, ogeher wih EA se he oupu olage. he curren signal is sensed hrough he nework made wih, and. V is amplified by EA and hen compared wih he oupu of EA o generae he PWM signals o drie he W and W, he parameers of he esed circui are described as follows: μh,.mω, 0KΩ, 0nF, 0KΩ, OU 00μF, E mω, 5V,U.8V, F W 750KHz. Fig.5: urren waeform in oupu inducor and olage across he gain plo and phase plo of he calculaed model under 0A load condiion are shown in Fig.6 and 7 respeciely. And he bode plo of he esed module a 0A load condiion is in Fig.8 (he Blue cure is he gain plo and he red cure is he phase plo. W I W d' V E OU OAD EA d OMP V EA a b Fig.6: alculaed Gain Plo of G V V ref Fig.4: he Buck onerer under es ess were done wih A load o check he curren signal in and he olage across. As shown in Fig. 5, he red cure in he middle is V. he ligh blue cure on he op is he zoom in of he red cure for illusraion due o he limied ampliude of V. And he dark blue cure a he boom is he curren signal I. he cure reading shown in Fig. 5 indicaes ha he olage slope on is 9.8V/m. he slope of he curren signal in is.64a/μ. o he Fig.7: alculaed Phase Plo of G V 7

7 Fig.8: Bode Plo of G V of he esed Module V. EMPEAUE OMPENAION NEWOK o minimize he error inroduced by he emperaure dependency of he, a widely used hree resisors nework including an N resisor is inroduced as shown in Fig e g V N Fig.9: Inducor D urren ensing ircui wih emperaure ompensaion Nework As shown in Fig.9, he resisor nework made of e, g and N is he emperaure compensaion nework ha can proide almos complee compensaion for copper hermal ariaions. Based on he required oer curren proecion hreshold and he formed by he inducor and, and plus he equialen of he resisor nework ( e, g and N can be compued. I is preferable o make /( around hen we pick up an N resisor whose alue is close (wihin 5% o he calculaed a 5. If no be able o find one N resisor, calculae anoher se of, and equialen unil you can find one N resisor. Based on he characerisics of he seleced N resisor, coefficiens A and B are calculaed as in ( and ( a 50 and 90 : A ( N ( 50 / N (5 B N ( 90 / N (5 ( r and r are calculaed a 50 and 90 as defined in (4, (5, (6 and (7. w ( ( /( /( ( 5 (4 j( w( /( w( (5 r j(50 / j(5 (6 r j(90 / j(5 (7 Parameers such as r e, r g and r N can be compued as characerized in (8, (9 and (40. r e ( A B r r A( B r B ( A r A ( B r B ( A r ( A B A rg ( A /( re r re rn /( r r (8 (9 (40 hen calculae N as shown in (4 based on he calculaed. elec he closes alue of one N hermisor aailable. Also compue a scaling facor k based on he raio of he acual hermisor alue used relaie o he compued one as in (4. N rn (4 k N ( Acual / N ( alculaed (4 Based on he compued parameers as shown aboe, e and g can be calculaed as shown in (4 and (44 based on he calculaed. g (4 (44 e (( k ( k re Finally, e and g are seleced from resisor bank wih he resisances closes o he calculaed resuls from (4 and (44. VI. UMMAY Inducor D curren sensing is a common pracice in high curren applicaions. o achiee imely and accurae curren sensing effec, he ime consan of he curren sensing nework has o mach he one formed by he inducor and is D. his paper analyzes, in deails, he charging and discharging process of he curren sensing nework and clarifies ha he slew raes of he olage ripples on he curren sensing capacior is deermined by he relaionship beween and no maer wheher, as in Fig., is used or no. he consequences inroduced by he ime consan mismach are summarized, simulaed and esed. A small signal model for a buck conerer using inducor D curren sensing wih mismached ime consans is deried and experimenally erified. And as shown in he analysis, a lile bigger alue of compared wih he one formed by / is recommended if a wider bandwidh and faser dynamic response is preferred. Howeer, noise issue should be aken ino accoun while adjusing he produc of. And a hree resisors emperaure compensaion nework as shown in Fig.9 can be used o calibrae oer curren proecion riggering poin caused by he hermal dependency of he inducor D. EFEENE [. ober W. Erickson. Fundamenals of Power Elecronics [. idley,. B. A New oninuous-ime Model for urren-mode onrol g e k r g 74