# Switching Regulator IC series Capacitor Calculation for Buck converter IC

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1 Swiching Regulaor IC series Capacior Calculaion for Buck converer IC No.14027ECY02 This applicaion noe explains he calculaion of exernal capacior value for buck converer IC circui. Buck converer IIN IDD Figure 1 is he basic circui of buck converer. When swiching elemen Q1 is ON, curren flows from VIN hrough he coil L and charges he oupu smoohing capacior Co, and he oupu curren Io is supplied. The curren which flows ino he coil L a his ime induces a magneic field, and elecric energy is ransformed ino magneic energy and accumulaed for sorage. When swiching elemen Q1 is OFF, free-wheeling diode D urns ON and energy sored in L is hen released o he oupu side. VIN ICIN ON OFF CIN ID Q1 D IL Curren which flows a ON L ICO CO Figure 1 Basic buck converer circui RL Curren which flows a OFF VOUT Calculaion of Inpu capacior Raed volage of inpu capacior mus be higher han he maximum inpu volage. Also raed ripple-curren of he capacior mus be higher han he maximum inpu ripple-curren of he IC. Alhough he average value of an inpu curren becomes smaller in proporion o he ransformaion raio, momenarily he same curren equal o oupu curren flows hrough he buck converer as shown as IDD in Figure 2. This will be averaged by he inpu capacior, bu as i is clearly shown as ICIN of Figure 2, he alernaing ripple-curren flowing in he inpu capacior, is higher han ICO of he oupu. Effecive value of ICIN can be calculaed by following equaion: Q1 IDD ID OFF ON OFF ON OFF ON IIN ΔIL IL 1 [ARMS] (1) Figure 3 shows he ripple hea generaion characerisics of a ceramic capacior (by Muraa Manufacuring Co.). Wheher i can be used as inpu capacior or no is decided by his graph and he absolue maximum raing of ripple-curren. Be well aware of he emperaure and DC bias impressed o he capacior when using ceramic capacior. ICO ICIN 1 of 6 Figure 2 Curren waveform of each par

2 Capacior Calculaion for Buck converer Applicaion Noe Change of capaciance value due o emperaure can obain sable emperaure characerisic by using high permiiviy ceramic capacior wih he characerisics of X5R and X7R. Capaciance value reduces when DC bias a boh sides of ceramic capacior increases. Figure 4 shows he DC bias characerisics (by Muraa Manufacuring Co.). TEMPERATURE RISE ( ) 0 Example: Characerisic of Ceramic Capacior (make: Muraa Manufacuring Co.) fsw = 1MHz 0.5 Raed volage GRM32ER7YA6KA12 µf±%, 35V, X7R CAP. CHANGE (%) CURRENT (A) DC BIAS (V) Figure 3 Ripple hea generaion characerisic Figure 4 DC bias characerisic Inpu ripple volage of regulaor is decided by he value of inpu capaciance. Inpu ripple volage ΔVIN can be calculaed by he following equaion. [V P-P ] (2) : Inpu volage [V] : Oupu volage [V] : Maximum load curren [A] : Inpu capacior [F] : Swiching frequency [Hz] : Maximum equivalen series resisance ESR [Ω] of inpu capacior 2 of 6

3 Capacior Calculaion for Buck converer Applicaion Noe Calculaion example of inpu capacior For his design example, parameers lised in Table1 will be used. As for he inpu capacior, Muraa Manufacuring Co. makeµf / 35V ceramic capacior is considered for reference. Parameer Value Inpu volage range VIN 7V o 28V Oupu volage VOUT 3.3V Inpu ripple volage ΔVIN 300mV Oupu ripple volage ΔVO 33mV (1% of oupu volage) Oupu raing curren 3A Inducor ripple curren ΔIL 0.9A (30% of oupu raing curren) Operaion frequency fsw 1MHz Table1 Design parameer Calculae inpu ripple curren by subsiuing each parameer o he equaion (1) [ARMS] (3) From Figure 3 ripple curren capaciance obains enough margins. Nex, calculae inpu ripple volage by subsiuing each parameer o equaion (2). A his poin consideraion for DC bias characerisic of ceramic capacior is necessary. In his example, since he maximum volage impressed o capacior is 28V, 48% will be reduced from raing capaciance value as from Figure 4. Also, ESR of ceramic capacior is 2mΩ [mvp-p] (4) Ripple volage of minimum inpu volage can be shown as below mehod [mvp-p] (5) The design requiremen for inpu ripple volage below 300mV can be confirmed. Maximum volage a boh ends of inpu capacior is VIN(MAX) + ΔVIN/2. To obain more volage margins, give consideraion of using wo 4.7µF / 50V capaciors in parallel. Also, be cauious for acual inpu ripple volage ha may ge higher han he calculaed value, due o oupu impedance of he volage source (preceding circui) and parasiic componen resuling from he PCB layou. 3 of 6

4 Capacior Calculaion for Buck converer Applicaion Noe Calculaion of oupu capacior Imporan elemens in designing oupu capacior are raing volage, ripple raing curren, and ESR (equivalen series resisance). Ripple curren and volage impressed o he capacior mus be less han he maximum raing. ESR is an imporan elemen o decide he oupu ripple volage wih he inducor curren. The effecive value of ripple curren, he alernaing componen included in he oupu curren, can be calculaed by he following equaion as i is a riangular waveform like ICO of Figure 2. [ARMS] (6) : Maximum inpu volage [V] : Oupu volage [V] : Inducor value [H] : Swiching frequency [Hz] Oupu ripple volage is he composie waveform creaed by he ripple curren of he inducor flowing hrough he oupu capacior depending on elecrosaic capaciance, ESR, and ESL. I can be calculaed by he following equaion. [V P-P ] (7) : Maximum inpu volage [V] : Inducor ripple curren [A] : Oupu capacior [F] : Inducor value [H] : Swiching frequency [Hz] ESR: Equivalen series resisor of oupu capacior [Ω] ESL: Equivalen series inducor of oupu capacior [H] When using leaded ype aluminum elecrolyic capacior wih high ESR and ESL as an oupu capacior, noice ha ripple by ESR and ESL may ge bigger han he ripple by capaciance. 4 of 6

5 Capacior Calculaion for Buck converer Applicaion Noe Calculaion example of oupu capacior For his design example, parameers lised in Table 1 will be used. As for he inpu capacior, Muraa Manufacuring Co. make 22µF / 25V ceramic capacior is considered as reference. Calculae ripple curren by subsiuing each parameer o equaion (6). Use 4.7µH value for coil L [A RMS] (8) From Figure 5 ripple curren capaciance obains enough margin. Nex, calculae oupu ripple volage by subsiuing each parameer o equaion (7). A his poin consideraion for DC bias characerisic of ceramic capacior is necessary. In his example, because he volage impressed o capacior is 3.3V, 2% will be reduced from raing capaciance value as in Figure 6. Also, ESR of ceramic capacior is 2mΩ and ESL is 0.4nH [mv P-P] (9) Oupu ripple volage requiremen is 33mV, meaning ha he above value saisfies. Bu, he acual oupu ripple volage can be influenced by ESR, ESL elemens of capacior and by parasiic elemen originaed in PCB layou, causing difference from he calculaed value. TEMPERATURE RISE ( ) 0 1 Example: Characerisic of Ceramic Capacior (make: Muraa Manufacuring Co.) GRM32ER71E226ME15 22µF±20%, 25V, X7R fsw = 1MHz Raed volage CURRENT (A) DC BIAS (V) CAP. CHANGE (%) Figure 5 Ripple hea generaion characerisic Figure 6 DC bias characerisic 5 of 6

6 Capacior Calculaion for Buck converer Applicaion Noe Equaion of buck converer Effecive value of ripple curren flowing in inpu capacior 1 [A RMS ] Inpu ripple volage [V P-P ] : Inpu volage [V] : Minimum inpu volage [V] : Oupu volage [V] : Oupu raing curren [A] : Inducor ripple curren [A] (Usually se beween 20% and 50% of ) : Maximum load curren [A] : Inpu capacior [F] : Swiching frequency [Hz] : Maximum equivalen series resisance (ESR) of Inpu capacior [Ω] IIN IDD ICIN ON OFF Q1 IL L VIN CIN ID D ICO CO RL VOUT Buck converer Effecive value of ripple curren flowing in oupu capacior [A RMS ] Oupu ripple volage [V P-P ] : Maximum inpu volage [V] : Oupu volage [V] L: Inducor value [H] : Swiching frequency [Hz] : Inducor ripple curren [A] (Usually se beween 20% and 50% of ) : Oupu capacior [F] ESR: Equivalen series resisance of oupu capacior [Ω] ESL: Equivalen series inducance of oupu capacior [H] 6 of 6

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