Proceedngs of the World ongress on Engneerng and omputer cence 0 ol WE 0, October 9-, 0, an Francsco, UA esgn-orented Analyss and Modelng of a ngle-nductor ontnuous nput-urrent Buck-Boost - onverter J.. osas-aro, J.. Mayo-Maldonado, J. E. aldez-esendz,. alas-abrera, H. sneros-llegas,. astllo-barra, J. G. Gonzalez-Hernandez Abstract Ths paper presents an analyss of a buck-boost converter wth contnuous nput current that s useful for wde converson range applcatons. ome of these applcatons nclude () power supply for portable devces where the battery s dschargng, () voltage regulated rectfers wth wdely varyng voltage, () P panels, n partcular for obtanng the - curve, and (v) burn-n test for power supples. Ths paper analyzes the converter. Ths s the a dc-dc converter wth only one swtch and one nductor wth that s able of of buckng or boostng the nput voltage and provdng a contnuous nput current. A detaled analyss along wth smulaton and expermental results are provded. ndex Terms - power converson, Power converson, Pulse wh modulated power converters, boost converter. F. NTOUTON O voltage regulators n portable applcatons fed wth a battery s hghly desrable to work wth a wde voltage range to optmze the battery charge. n some cases, t s also desrable to provde ether a hgher or a lower output voltage wth respect to the voltage supply. For example to produce a fxed 3.3 output as the battery voltage vares between.5 and 5.5 [-5]. n other applcatons, for example a voltage-regulated rectfer wth unty power factor (PF) and unnterruptble power supply (UP), one source s wdely varyng ts voltage whle the other s a constant dc battery or bus. Thus, a converter wth buck and boost capablty can be used for ths purpose as well [0-8]. Ths feature can be performed by a traonal buck-boost converter. On the other hand, for mnmzng EM problems t s desrable for the converter to have contnuous nput current [6-9] whch also optmzes the battery lfe. However, t s well-known that the traonal buck-boost converter has dscontnuous nput current. nce a converter wth buck and boost capablty and contnuous nput current s hghly desrable [8-9], the uk and EP converters were developed. These converters can acheve those features wth the draw-back of the use of an Ths work was developed under the project nvestgacón de topologas de electronca de potenca regstered n GET 0. J.. osas-aro, J.. Mayo-Maldonado, J. E. aldez-esendz,. alas-abrera, H. sneros- llegas and. astllo-barra are wth the Madero ty Technologcal nsttute (e-mal rosascarojc@tcm.edu.mx). J. G. Gonzalez-Hernandez s wth Unversdad Tecnologca de Altamra, epartamento de Mecatronca, Altamra, Mexco. BN: 978-988-80-9-6 N: 078-0958 (Prnt); N: 078-0966 (Onlne) extra-nductor n comparson wth traonal - converters topologes whch use only one nductor. n adon, several solutons such as cascadng converters have been employed [3-5]. An emergng but also mportant applcaton for converters wth buck-boost capablty s the measurng of the the - curve of P panels [6] for ths purpose, the contnuous nput current s requred along wth the capablty of buckng and boostng the nput voltage. After a deep revew of the topologcal lterature [6, 8-9, 6-4], only one topology wth buck-boost voltage capablty and contnuous nput current that employs only the basc components such as one voltage source, one nductor, one capactor, one transstor and one dode (two transstor and dodes f bdrectonal power flow s requred) was found. However, t has been apparently hdden n lterature for more than 0 years [5] even n modern lterature where the topology appears [8]. n other words, ther benefts, applcatons, desgn-orented analyss and modelng have not been fully explored and reported. The purpose of ths paper s to analyze and model ths converter that s called converter. Ths converter has the advantage of provdng a contnuous nput current and a smple structure whch has the basc components of the traonal buck-boost converter components. A detaled analyss along wth smulaton and expermental results are provded.. THE ONETE The converter s shown n Fg. along wth the traonal buck-boost converter. As mentoned before, after a deep revew of the lterature authors has found the topology n Fg. (b) n [5], [8]. However a deep analyss of ths converter s stll mssng. n ths paper, some of the features such as waveforms, modelng and desgn analyss for ths converter are explored. Fg.. (a) Traonal buck-boost converter, (b) converter. WE 0
Proceedngs of the World ongress on Engneerng and omputer cence 0 ol WE 0, October 9-, 0, an Francsco, UA As seen n Fg., the topology s smlar to the traonal buck-boost converter, the topologcal dfference s the capactor s connecton whch s connected from the dode to the postve sde of nput voltage nstead of been connected from the dode to the negatve sde f the nput voltage. A. teady state operaton n M Fg. shows the equvalent crcut accordng wth the swtchng state, and some mportant waveforms n contnuous conducton mode M. efnng d as the duty cycle, the tme when the swtch s on over the total swtchng perod Ts and by usng the small rpple approxmaton [6], the average voltage across the nductor n steady state can be expressed as: v ( t) ( )( ) () Note than the -component of varables d, v and v are wrtten as, and and respectvely, durng the steady state, ths average voltage as the average current n the capactor are equal zero, and then the voltage n the capactor can be expressed as: ( )( ) 0 n () Fg. and Fg., the output voltage can be expressed as: o (3) The converter has the same converson rato than the traonal buck-boost converter. The man advantage of the proposed converter can be seen n Fg. and Fg., the nput voltage s connected to the reference node wth the nductor and the load, both the nductor and the load dran a contnuous current and then the nput voltage becomes contnuous. Now lets to derve the -current n the nductor. By usng the small rpple approxmaton, the average current n the capactor can be expressed as: ( t) ( ) ( t) ( ) (4) urng the steady state, ths average current s equal zero, and then the current n the nductor can be expressed as: (5) ( ) By substtutng () n (5) the -current n the nductor s expressed as: ( ) ( ) (6) ( ) The swtch and dode voltage and current stress can be calculated wth a smlar procedure. When the swtch s open t blocks the capactors voltage gven by () ths s actually the same voltage ratng for a swtch n a traonal buck-boost converter and n the uk converter, the current n the swtch can be averaged from the swtchng states (Fg. ) and expressed as: Fg.. Equvalent crcuts for the swtchng states n M when (a) the swtch s on (b) the swtch s off (c) some mportant waveforms. The voltage n the capactor s the same as n a traonal boost converter, but n ths case the output voltage s not gven only by the capactors voltage but also by the nput voltage, because the nput voltage s n seres wth the capactor voltage, and then, consderng the polarty sgns defned n BN: 978-988-80-9-6 N: 078-0958 (Prnt); N: 078-0966 (Onlne) ( t) As the nductor current n the nput-seres buck-boost converter s the same as n the traonal buck-boost converter for converters rated to the same voltage and output power, the current n the swtch s the same and we can say the swtch s dentcal n the proposed topology than n the traonal buckboost converter. When the dode s open t blocks the voltage n the capactor expressed n () and the same as n the traonal buck-boost converter, the average current can be expressed as: ( t) ( ) ( ) ( ) (7) (8) WE 0
Proceedngs of the World ongress on Engneerng and omputer cence 0 ol WE 0, October 9-, 0, an Francsco, UA Ths s also the same as n the traonal buck-boost converter. The steady state analyss s then resumed n equatons (), (3), (6), (7) and (8), t can be seen the proposed converter has the same nductor, transstor and dode than the traonal buck-boost converter. From those equatons, the man dsadvantage of the proposed topology can be seen; the capactor has the same voltage as the traonal boost converter, whch s hgher than n the traonal buck-boost converter, so far n the authors understandng ths s the only dsadvantage of the dscussed topology, ths dsadvantage s also presented n one of the capactors of the uk and n the EP converter whch are the other buck-boost converters wth contnuous nput current. nce the nput voltage may vary from 50-to-00 the converters gan would vary from.5-to-0.75 and the duty cycle wll vary from 0.6-to-0.4. Two extreme operatng ponts wll be defned, A s when the nput voltage s 50, and B s when the nput voltage s 00, see Fg. 3.. EGN OENTE ANAY For selectng the nductance and capactance, the equatons for the voltage-rpple n the capactor and current rpple n the nductor can be derved by usng the small rpple approxmaton [6]. From Fg., the nductor current can be expressed durng the tme when the swtch s on as: T (9) The nput current s the sum of the nductor current plus the load current o, the output current s decreasng durng the on-tme when the nput current s ncreasng because the capactor s dschargng durng ths tme, that means the output current rpple Δ o cancels part of the nductor current rpple Δ and then the nput current rpple Δ s smaller than the nductor current rpple Δ, but snce the load current rpple s expected to be pretty small by selectng a correct capactor value, the load current rpple may be neglected for calculatng the nput current rpple and the nput current rpple can be approxmated to the nductor current rpple. urng the same tme (when the swtch s off) the capactor voltage rpple (see Fg. ) can be expressed as: v ot (0) mlar to the nput current-tpple, neglectng an nput voltage rpple, the output voltage rpple s the same as the capactors voltage rpple. A. esgn example A converter wll be feed wth a voltage between 50 to 00 t s desred to have a constant output voltage of 75, the load s a 0Ω resstor, the desred nput current rpple s 0% of the nput current (whch ensures operaton n M) and the output voltage rpple % of the rated output voltage, the swtchng frequency s 5 khz. Note: snce the oversze-percentage of all components s up to the desgner, the components varables wll be provded from the descrbed equatons (wthout oversze), securty consderatons for operatng the converter under dfferent conons and losses won t be consdered n ths desgn example. The soluton s shown n Fg. 3. Fg. 3. esgn example wth both extreme operaton ponts. B. apactor selecton The mnmum voltage stress would be when the nput s 50; the capactor would have 5 accordng wth (), the maxmum one would be when the nput s 00 and the capactor would have 75. The maxmum output voltage rpple needs to be 0.75 (% of 75), from (0) t can be seen that the rpple wll vary wth the duty cycle, and the maxmum would be when the duty cycle s the hgher (0.6) and then: v T 0.75 7.5 0.6 40 () o And from () and the above explanaton, a capactor of 40μF s selected wth a voltage ratng of 75.. nductor selecton The mnmum current stress would be when the nput s 00; accordng wth (6) the nductor-current would be 6.568A n pont B (00 nput), the maxmum nductor current would be 9.375A n pont A. The nput current rpple s the same as the nductor current rpple whch s gven by (9). n pont B the nput current s hgher and then the nput current would be set to 0% of.88a. T 0.565 00 0.4 40 () And from () and the above explanaton, an nductor of 3mH s selected wth a current ratng of 9.57A (9.37A + 00mA), ths s because accordng wth (6) the current rpple n pont A s equal to (3): 50 0.6 40 400mA (3) 3m BN: 978-988-80-9-6 N: 078-0958 (Prnt); N: 078-0966 (Onlne) WE 0
Proceedngs of the World ongress on Engneerng and omputer cence 0 ol WE 0, October 9-, 0, an Francsco, UA And the maxmum current n the nductor would be the current n pont A plus a half of ts current-rpple at that pont.. MA GNA MOENG AN EQUAENT UT Ths secton presents the small sgnal model along ther equvalent crcut models. Frst of all the average dynamc equatons should be wrthen from the equvalent crcuts accordng wth the swtchng state. From Fg. the state equaton for the nductor can be wrtten as: d v ( d) v (4) All varables are wrthen n lower case for ndcated they are not constant. n an analog way, the state equaton for the capactor can be wrtten as (5). dv v v ( d) (5) The next step s to consder that all varables: the duty cycle d, the nput voltage v, the capactor voltage v and the nductor current are composed by a large constant value plus a small ac component: v vˆ ˆ ; d dˆ : v vˆ (6) d dvˆ ˆ ˆ d ˆ d ˆˆ vˆ vˆ (0) From (0) the dervatve of s zero snce that s the dc component, from (5), the constant components n (0) cancel each other; and then (0) becomes: dvˆ ˆ vˆ vˆ ˆˆ ( d d () )ˆ By neglectng the multplcaton of two ac sgnals, as explaned because of the small sgnal lnearzaton () becomes: dvˆ v v d ˆ ˆ ˆ ( )ˆ () Ths may be represented by a crcut model, see Fg. 4(b). Both crcut model combned are shown n Fg. 4(c) and a full crcut model wth an deal transformer s shown n Fg. 4(d). By substtutng (6) n (4) one gets: d d vˆ ˆ vˆ dˆ dˆ vˆ vˆ vˆ d ˆ dˆ vˆ (7) From (7) the dervatve of s zero snce that s the dc component of the nductance current, and snce s equal to (-) the constant components of (7) cancel each other, and then (7) becomes: dˆ vˆ ( )ˆ v d ˆ dv ˆˆ (8) The lnearzaton of small sgnal modelng s based on consderng the multplcaton of ac components s neglgble small snce they are small sgnals and the product of two small sgnal s a sgnal too small, and then from (8) the small sgnal equaton becomes: dˆ vˆ ( )ˆ v d ˆ (9) Ths may be represented by a crcut model, see Fg. 4(a). n the other hand, by substtutng (6) n (5) and followng the same procedure one gets: Fg. 4. mall sgnal ac crcut models (a) equvalent to equaton (9) (b) equvalent to equaton (7) (c) equvalent crcut model (d) equvalent crcut model wth the deal transformer.. ONTNUOU ONUTON MOE The converter can be desgned wth parameters to ensure the current n the nductor s contnuous as n the desgn example, but t can be desgned for operate n dscontnuous conducton mode. The current rpple durng the tme nterval T s stll expressed as (9), the current n the nductor would be contnuous f the component (6) s hgher than a half of the current rpple expressed n (9) and then: ( ) T (3) BN: 978-988-80-9-6 N: 078-0958 (Prnt); N: 078-0966 (Onlne) WE 0
Proceedngs of the World ongress on Engneerng and omputer cence 0 ol WE 0, October 9-, 0, an Francsco, UA From (8) t can be seen that: T ( ) (4) Equaton (4) express the relaton between constant parameters and the duty cycle whch may change durng the operaton, traonally /T s defned as and the functon of as a T the converter would operate n contnuous conducton mode M f > T. Otherwse the converter operates n M. Ths conon s the same for the traonal buck-boost converter. For calculatng the boost-factor durng the M equatons for the volts-per-second for the nductor and amps-per-second n the capactor should be analyzed, snce the output capactor should be calculated to mantan a constant voltage, the small rpple approach can be consdered for the capactor voltage but not for the nductor current whch would seems such as shown n Fg. 5. n the M there are three swtchng states, nstead of two, an extra swtchng state s when both dode and transstors are open, remember the dode s closed by nductor current when the swtch s off, and then when the nductor current reaches zero, the dode opens, before the swtch closes, the equvalent crcuts and mportant waveforms are shown n Fg. 5, nstead of dvdng the swtchng perod n two tme-perods ths would be dvded nto three tme perods, T, T and 3 T, see Fg. 5, the nductor voltage can be expressed as: d ) (0) (5) ( 3 ( 3 ) (0) 0 (6) From Fg. 5 the capactor s dscharge by the load current whle s charged wth the nductor current durng, see gray areas n the capactors current n Fg. 5, n steady state, the sum of both should be zero, the amps-per-second that charges the capactor can be calculated as the area of durng shown n gray color n Fg. 5, and ths should be equal to the load current whch dscharges the capactor all the tme: The current rpple s stll expressed as (9) and then: T Where =/T, by substtutng (6) n (8): (7) (8) (9) And then, the output voltage can be derved as (30): o o (30) Ths s the same gan as the traonal buck-boost converter n M. And By substtutng (9) n (6) the tme-perod can be expressed as: (3). EXPEMENTA EUT Fg. 5. Equvalent crcuts for the swtchng states n M when (a) the swtch s on and the dode s off (b) the swtch s off and the dode s on (c) both dode and swtch are off (d) mportant waveforms. n steady state ths voltage along wth the capactor current should be zero and then: A prototype was developed to provde expermental results, the schematc s the same as Fg. (b) wth =0µF, =3µH, =55Ω, duty cycled=0.6, swtchng frequency 0 Hz, the prototype s shown n Fg. 6 along wth expermental results. Fgure 4 show the steady state expermental traces of the nput current and the output voltage. BN: 978-988-80-9-6 N: 078-0958 (Prnt); N: 078-0966 (Onlne) WE 0
Proceedngs of the World ongress on Engneerng and omputer cence 0 ol WE 0, October 9-, 0, an Francsco, UA. ONUON Ths paper dscusses an outstandng buck-boost dc-dc converter topology wth the advantage of provdng a contnuous nput current and a smple structure; t has the basc components of the traonal buck-boost converter. The converter may be used for voltage regulaton n portable devces where the battery s dschargng and the voltage regulator need to work wth a wde voltage range. Another possble applcaton are voltage-regulated rectfers wth unty power factor PF and unnterruptble power supply UP where one of the source, or load, s a wdely varyng voltage whle the other s a constant dc battery or bus. And fnally an emergng applcaton for converter wth buck-boost capablty s the measurng the - curve of P panels where the contnuous nput current along wth the capablty of buckng and boostng the nput voltage s requred. More nformaton wll be publshed n future work for space reasons. 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[6] Hebertt ra-amírez and amón lva-ortgoza. ontrol esgn Technques n Power Electroncs evces. prnger. 006. WE 0