= f 8 f 2 L C. i C. 8 f C. Q1 open Q2 close (1+D)T DT 2. i C = i L. Figure 2: Typical Waveforms of a Step-Down Converter.

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1 Inroducion Oupu Volage ipple in Sep-Down and Sep-Up Swiching egulaors Oupu volage ripple is always an imporan performance parameer wih DC-DC converers. For inducor-based swiching regulaors, several key facors can affec his imporan parameer, including swiching frequency, duy cycle, and oupu capacior value. Sep-down and sep-up swiching regulaors have differen circui opologies, so some facors ha affec he oupu volage ripple for sep-down DC-DC converers will no affec oupu volage ripple for sep-up DC-DC converers. This applicaion noe analyzes facors affecing oupu volage ripple based on he derived oupu volage ripple equaions for sep-down and sep-up DC-DC converer opologies in CCM. This documen can help provide insigh in undersanding oupu volage ripple. Sep-Down Converer Oupu ipple IN Sep-Down IC Q PMOS Conrol Circui Q NMOS SW FB L I L C + GND - Figure : Sep-Down DC-DC Converer. To derive he sep-down DC-DC converer oupu volage ripple equaion, coninuous conducion mode (CCM) operaion is assumed. The oupu volage includes he DC componen and AC componen. is produced by he inducor curren I L flowing hrough he load ( in Figure ) and oupu capacior (C in Figure ). In a well designed converer, he oupu capacior will provide a very low impedance o ground wih respec o he load a he sep-down DC-DC regulaor swiching frequency in order o filer he inducor AC ripple curren (ΔI L ). Hence almos all of he inducor AC ripple curren will flow hrough he oupu capacior, C in Figure. Inducor curren: il = IL + il Oupu volage: v O = + v O Using he circui in Figure, where he Q and Q ransisors are alernaively urned on/off, he following inducor curren componens (DC and AC) can be derived: Inducor curren DC componen: I L = I O = Inducor curren AC componen: i = - L L = L ( - ) Where D = duy cycle D = and T = swiching period. Skyworks Soluions, Inc. Phone [78] 76- Fax [78] A Skyworks Proprieary Informaion Producs and Produc Informaion are Subjec o Change Wihou Noice. Sepember,

2 Oupu Volage ipple in Sep-Down and Sep-Up Swiching egulaors The oupu capacior charging and discharging curren is equal o he inducor AC ripple curren. Figure illusraes he ypical oupu capacior volage ripple waveform resuling from he inducor AC ripple curren flowing hrough he oupu capacior. Using he blue secion, or area under he waveform, of he oupu capacior curren (i C ) waveform in Figure, he oupu volage ripple equaion can be derived: v = i C 8 f C = f 8 f L C ( - D) W Q close Q open Q open Q close T i L IO i L (+D)T T i C (+D)T T i C = i L v O v O (+D)T T Figure : Typical Waveforms of a Sep-Down Converer. From he oupu volage ripple equaion, swiching frequency (f), duy cycle (D), inducor value (L) and oupu capacior value (C) can all affec oupu volage ripple. The daa curves in Figure illusrae he effec of hese parameers on oupu volage ripple. Skyworks Soluions, Inc. Phone [78] 76- Fax [78] A Skyworks Proprieary Informaion Producs and Produc Informaion are Subjec o Change Wihou Noice. Sepember,

3 Oupu Volage ipple in Sep-Down and Sep-Up Swiching egulaors Sep-Down Oupu ipple vs. Frequency and C (L =.µh; D =.5) Sep-Down Oupu ipple vs. Frequency and L (C = µf; D =.5) Oupu Volage ipple (mv) C = 4.7µF C = µf C = µf Oupu Volage ipple (mv) L =.4µH L =.µh L = 4.7µH L = 6.8µH.5 (a) (b) Buck Oupu ipple vs. Frequency and Duy (L =.µh, C = µf) Oupu Volage ipple (mv) D =.7 D =.5 D =. (c) Figure : The Effec of Four Parameers [f, D, L, C] on Sep-Down Converer Oupu Volage ipple. From Figure, he following is observed: Swiching frequencies beween MHz ~ MHz resul in mv or less oupu volage ripple for oupu capacior values of 4.7µF ~ µf and inducor values of.4μh ~ 6.8µH wihou high swiching losses. As he duy cycle is increased, oupu volage ripple is decreased. In oher words, duy cycle is inversely proporional o oupu volage ripple. As he inducor value is increased, oupu volage ripple is decreased. In oher words, inducor value is inversely proporional o oupu volage ripple. The oupu curren has no effec on he oupu volage ripple of a sep-down DC-DC converer. Skyworks Soluions, Inc. Phone [78] 76- Fax [78] A Skyworks Proprieary Informaion Producs and Produc Informaion are Subjec o Change Wihou Noice. Sepember,

4 Oupu Volage ipple in Sep-Down and Sep-Up Swiching egulaors Sep-Up Converer Oupu ipple L I L IN Sep-Up IC SW D I D + Conrol Circui Q NMOS FB C GND - Figure 4: Sep-Up DC-DC Converer. As wih he sep-down DC-DC converer, he sep-up DC-DC converer oupu volage ripple can be derived from he oupu capacior charging and discharging curren (i C ) for CCM operaion. Figure 5 illusraes he oupu volage ripple waveform resuling from he capacior curren (i C ). Time: (-D)T Capacior curren: i c = - Using small ripple approximaion v o vo Vo i c = i L - v o il IL, vo V o V o Capacior curren: ic = - ic = IL - Inegrae he capacior curren V o Oupu volage ripple: vo = D T V o C = I L - V o C (-D)T Where D = duy cycle ( D = - ) and T = swiching period. 4 Skyworks Soluions, Inc. Phone [78] 76- Fax [78] A Skyworks Proprieary Informaion Producs and Produc Informaion are Subjec o Change Wihou Noice. Sepember,

5 Oupu Volage ipple in Sep-Down and Sep-Up Swiching egulaors VSW VO - VD Q close Q open T i C IL - VO T vo v O (+D)T T Figure 5: Typical Waveforms of a Sep-Up DC-DC Converer. Using he v O = i c d equaion, he sep-up DC-DC converer oupu volage ripple is derived: C Where D = duy cycle ( D = - D T v O = = C ) and f = swiching frequency = /T. The daa curves in Figure 6 illusrae he effec of duy cycle (D), oupu curren (I O ), oupu capacior value (C), and swiching frequency (f) on sep-up DC-DC converer oupu volage ripple ( v O ). From hose daa curves, he following can be observed: As he duy cycle is increased, oupu volage ripple is increased. In oher words, he duy cycle is proporional o oupu volage ripple. As he oupu capacior value is decreased, oupu volage ripple is increased. In oher words, oupu capacior value is inversely proporional o oupu volage ripple. As he oupu curren is increased, oupu volage ripple is increased. In oher words, oupu curren is proporional o oupu volage ripple. The inducor value has no effec on he oupu volage ripple of a sep-up DC-DC converer. D I O C f Skyworks Soluions, Inc. Phone [78] 76- Fax [78] A Skyworks Proprieary Informaion Producs and Produc Informaion are Subjec o Change Wihou Noice. Sepember, 5

6 Oupu Volage ipple in Sep-Down and Sep-Up Swiching egulaors Sep-Up Oupu ipple vs. Frequency and D (C = µf; I O = A) Sep-Up Oupu ipple vs. Frequency and C (L =.µh; D =.5) Oupu Volage ipple (mv) D =.76 D =.5 D =.8 Oupu Volage ipple (mv) C = 4.7µF C = µf C = µf (a) (b) Sep-Up Oupu ipple vs. Frequency and I O (D =.5; C = µf) Oupu Volage ipple (mv) I O =.A I O =.5A I O =.A (c) Figure 6: The Effec of Four Parameers [f, D, I O, C] on Sep-Up Converer Oupu Volage ipple. 6 Skyworks Soluions, Inc. Phone [78] 76- Fax [78] A Skyworks Proprieary Informaion Producs and Produc Informaion are Subjec o Change Wihou Noice. Sepember,

7 Oupu Volage ipple in Sep-Down and Sep-Up Swiching egulaors Conclusion For sep-up and sep-down inducor based DC-DC converers, facors affecing oupu volage ripple overlap for boh converer opologies. The common facors for boh DC-DC converer opologies are swiching frequency, oupu capacior value, and duy cycle. For he sep-up DC-DC converer, inducor value is no a facor in influencing he oupu volage ripple, while for he sep-down DC-DC converer i is. This is also rue for oupu curren; Table provides a brief comparison of he wo differen opologies regarding facors/parameers which influence oupu volage ripple. Type Oupu Volage ipple Formula Duy Facors Affecing Oupu Volage ipple Swich Frequency L C D I O Sep-Up v O = D I O C f V D = - S V O Sep-Down V v O O = ( - D) D = 8 f L C Table : Facors and Parameers ha Affec Oupu Volage ipple in Sep-Down and Sep-Up DC-DC Converer Topologies. Copyrigh Skyworks Soluions, Inc. All ighs eserved. Informaion in his documen is provided in connecion wih Skyworks Soluions, Inc. ( Skyworks ) producs or services. These maerials, including he informaion conained herein, are provided by Skyworks as a service o is cusomers and may be used for informaional purposes only by he cusomer. Skyworks assumes no responsibiliy for errors or omissions in hese maerials or he informaion conained herein. Skyworks may change is documenaion, producs, services, specificaions or produc descripions a any ime, wihou noice. Skyworks makes no commimen o updae he maerials or informaion and shall have no responsibiliy whasoever for conflics, incompaibiliies, or oher difficulies arising from any fuure changes. No license, wheher express, implied, by esoppel or oherwise, is graned o any inellecual propery righs by his documen. Skyworks assumes no liabiliy for any maerials, producs or informaion provided hereunder, including he sale, disribuion, reproducion or use of Skyworks producs, informaion or maerials, excep as may be provided in Skyworks Terms and Condiions of Sale. THE MATEIALS, PODUCTS AND INFOMATION AE POVIDED AS IS WITHOUT WAANTY OF ANY KIND, WHETHE EXPESS, IMPLIED, STATUTOY, O OTHEWISE, INCLUDING FITNESS FO A PATICULA PUPOSE O USE, MECHANTABILITY, PEFOMANCE, QUALITY O NON-INFINGEMENT OF ANY INTELLECTUAL POPETY IGHT; ALL SUCH WAANTIES AE HEEBY EXPESSLY DISCLAIMED. SKYWOKS DOES NOT WAANT THE ACCUACY O COMPLETENESS OF THE INFOMATION, TEXT, GAPHICS O OTHE ITEMS CONTAINED WITHIN THESE MATEIALS. SKYWOKS SHALL NOT BE LIABLE FO ANY DAMAGES, IN- CLUDING BUT NOT LIMITED TO ANY SPECIAL, INDIECT, INCIDENTAL, STATUTOY, O CONSEQUENTIAL DAMAGES, INCLUDING WITHOUT LIMITATION, LOST EVENUES O LOST POFITS THAT MAY ESULT FOM THE USE OF THE MATEIALS O INFOMATION, WHETHE O NOT THE ECIPIENT OF MATEIALS HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. Skyworks producs are no inended for use in medical, lifesaving or life-susaining applicaions, or oher equipmen in which he failure of he Skyworks producs could lead o personal injury, deah, physical or environmenal damage. Skyworks cusomers using or selling Skyworks producs for use in such applicaions do so a heir own risk and agree o fully indemnify Skyworks for any damages resuling from such improper use or sale. Cusomers are responsible for heir producs and applicaions using Skyworks producs, which may deviae from published specificaions as a resul of design defecs, errors, or operaion of producs ouside of published parameers or design specificaions. Cusomers should include design and operaing safeguards o minimize hese and oher risks. Skyworks assumes no liabiliy for applicaions assisance, cusomer produc design, or damage o any equipmen resuling from he use of Skyworks producs ouside of saed published specificaions or parameers. Skyworks, he Skyworks symbol, and Breakhrough Simpliciy are rademarks or regisered rademarks of Skyworks Soluions, Inc., in he Unied Saes and oher counries. Third-pary brands and names are for idenificaion purposes only, and are he propery of heir respecive owners. Addiional informaion, including relevan erms and condiions, posed a are incorporaed by reference. Skyworks Soluions, Inc. Phone [78] 76- Fax [78] A Skyworks Proprieary Informaion Producs and Produc Informaion are Subjec o Change Wihou Noice. Sepember, 7

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