Download, print and study this document offline |
Page 1 Buck Converter When CH is ON ? ? o t DT ?? Voltage across inductor ? ? L S O V V V ?? When CH is OFF (DT < t < T) Voltage across inductor LO VV ? Applying volt-sec balance across inductor ? ? ? ? ? ? S O O V V DT V T DT 0 ? ? ? ? ? ? ? ? ? ? S O O V V D V 1 D 0 ? ? ? ? OS V DV ? D = duty cycle = ON T T Where T = switching period = 1 f f = switching frequency Page 2 Buck Converter When CH is ON ? ? o t DT ?? Voltage across inductor ? ? L S O V V V ?? When CH is OFF (DT < t < T) Voltage across inductor LO VV ? Applying volt-sec balance across inductor ? ? ? ? ? ? S O O V V DT V T DT 0 ? ? ? ? ? ? ? ? ? ? S O O V V D V 1 D 0 ? ? ? ? OS V DV ? D = duty cycle = ON T T Where T = switching period = 1 f f = switching frequency ? Average output voltage = S DV ? rms output voltage = S DV ? Average source current = O DI ? Average current of FD = ? ? O 1 D I ? Ripple in output current When CH is ON ? ? 0 t DT ?? ? ? L S O S V V V 1 D V ? ? ? ? During this period, since voltage is positive current increase from minimum value to maximum value. max min i I I ? ? ? t DT 0 DT ? ? ? ? ? ? ? ? ? ? ? ? S i L 1 D V DT ? ? S D 1 D V i fL ? ?? ? This formula gives approximate value of output ripple current for maximum ripple, D = 0.5 ? ? S max V i 4fL ?? ? L max O I II 2 ? ?? ? L min O I II 2 ? ?? Critical Inductance (L C) Value of inductance at which inductor voltage waveform is just discontinuous. ? ? ? ? c 1 D R L 2f Page 3 Buck Converter When CH is ON ? ? o t DT ?? Voltage across inductor ? ? L S O V V V ?? When CH is OFF (DT < t < T) Voltage across inductor LO VV ? Applying volt-sec balance across inductor ? ? ? ? ? ? S O O V V DT V T DT 0 ? ? ? ? ? ? ? ? ? ? S O O V V D V 1 D 0 ? ? ? ? OS V DV ? D = duty cycle = ON T T Where T = switching period = 1 f f = switching frequency ? Average output voltage = S DV ? rms output voltage = S DV ? Average source current = O DI ? Average current of FD = ? ? O 1 D I ? Ripple in output current When CH is ON ? ? 0 t DT ?? ? ? L S O S V V V 1 D V ? ? ? ? During this period, since voltage is positive current increase from minimum value to maximum value. max min i I I ? ? ? t DT 0 DT ? ? ? ? ? ? ? ? ? ? ? ? S i L 1 D V DT ? ? S D 1 D V i fL ? ?? ? This formula gives approximate value of output ripple current for maximum ripple, D = 0.5 ? ? S max V i 4fL ?? ? L max O I II 2 ? ?? ? L min O I II 2 ? ?? Critical Inductance (L C) Value of inductance at which inductor voltage waveform is just discontinuous. ? ? ? ? c 1 D R L 2f Critical Capacitance (C C) Value of capacitance at which capacitor voltage waveform is just discontinuous. C 1 C 8fR ? Step-up chopper (Boost converter) ? ? ? ? ? LS when CHis ON 0 t DT , V V ? ? ? ? ? ? ? ? L S O when CHis OFF DT t T , V V V Applying volt-sec balance across inductor ? ? ? ? ? ? S S O V DT V V 1 D T 0 ? ? ? ? ? ? S O V V 1D ? ? ? Since D < 1, OS VV ? ? ? ? ? ? ? ? CO when CHis ON 0 t DT , I I ? ? ? ? ? ? ? C L O when CHis OFF DT t T , I I I ? ? ? ? ? ? ? ? ? ? ? ? O L O Applying Ampere sec balance across capacitor I DT I I 1 D T 0 ? ? ? ? O L I I 1D Ripple in inductor current ? ? ?? min max When CHis ON 0 t DT , current increase from I to I ? ? ? ? ? ? ? ? S S L SL V DT DV i L V i DT L fL Page 4 Buck Converter When CH is ON ? ? o t DT ?? Voltage across inductor ? ? L S O V V V ?? When CH is OFF (DT < t < T) Voltage across inductor LO VV ? Applying volt-sec balance across inductor ? ? ? ? ? ? S O O V V DT V T DT 0 ? ? ? ? ? ? ? ? ? ? S O O V V D V 1 D 0 ? ? ? ? OS V DV ? D = duty cycle = ON T T Where T = switching period = 1 f f = switching frequency ? Average output voltage = S DV ? rms output voltage = S DV ? Average source current = O DI ? Average current of FD = ? ? O 1 D I ? Ripple in output current When CH is ON ? ? 0 t DT ?? ? ? L S O S V V V 1 D V ? ? ? ? During this period, since voltage is positive current increase from minimum value to maximum value. max min i I I ? ? ? t DT 0 DT ? ? ? ? ? ? ? ? ? ? ? ? S i L 1 D V DT ? ? S D 1 D V i fL ? ?? ? This formula gives approximate value of output ripple current for maximum ripple, D = 0.5 ? ? S max V i 4fL ?? ? L max O I II 2 ? ?? ? L min O I II 2 ? ?? Critical Inductance (L C) Value of inductance at which inductor voltage waveform is just discontinuous. ? ? ? ? c 1 D R L 2f Critical Capacitance (C C) Value of capacitance at which capacitor voltage waveform is just discontinuous. C 1 C 8fR ? Step-up chopper (Boost converter) ? ? ? ? ? LS when CHis ON 0 t DT , V V ? ? ? ? ? ? ? ? L S O when CHis OFF DT t T , V V V Applying volt-sec balance across inductor ? ? ? ? ? ? S S O V DT V V 1 D T 0 ? ? ? ? ? ? S O V V 1D ? ? ? Since D < 1, OS VV ? ? ? ? ? ? ? ? CO when CHis ON 0 t DT , I I ? ? ? ? ? ? ? C L O when CHis OFF DT t T , I I I ? ? ? ? ? ? ? ? ? ? ? ? O L O Applying Ampere sec balance across capacitor I DT I I 1 D T 0 ? ? ? ? O L I I 1D Ripple in inductor current ? ? ?? min max When CHis ON 0 t DT , current increase from I to I ? ? ? ? ? ? ? ? S S L SL V DT DV i L V i DT L fL Ripple in output voltage ?? CO when CHis ON , I I C O V C. I DT ? ?? ? ? O OC I DT VV C ? ? ? ? ? -ve sign indicates voltage decrease ? ? O O I DT V C ? ? ? Critical Inductance (Lc) L L I I 2 ? ? ? ? ? ? C D 1 D R L 2f Critical Capacitance (C c) O O V V 2 ? ? ? C D C 2fR If inductor also has an internal resistance, then ? ? ? ? OS 2 1D VV r 1D R ?? ? ?? ? ?? ?? ?? r = internal resistance of inductor R = load resistance Page 5 Buck Converter When CH is ON ? ? o t DT ?? Voltage across inductor ? ? L S O V V V ?? When CH is OFF (DT < t < T) Voltage across inductor LO VV ? Applying volt-sec balance across inductor ? ? ? ? ? ? S O O V V DT V T DT 0 ? ? ? ? ? ? ? ? ? ? S O O V V D V 1 D 0 ? ? ? ? OS V DV ? D = duty cycle = ON T T Where T = switching period = 1 f f = switching frequency ? Average output voltage = S DV ? rms output voltage = S DV ? Average source current = O DI ? Average current of FD = ? ? O 1 D I ? Ripple in output current When CH is ON ? ? 0 t DT ?? ? ? L S O S V V V 1 D V ? ? ? ? During this period, since voltage is positive current increase from minimum value to maximum value. max min i I I ? ? ? t DT 0 DT ? ? ? ? ? ? ? ? ? ? ? ? S i L 1 D V DT ? ? S D 1 D V i fL ? ?? ? This formula gives approximate value of output ripple current for maximum ripple, D = 0.5 ? ? S max V i 4fL ?? ? L max O I II 2 ? ?? ? L min O I II 2 ? ?? Critical Inductance (L C) Value of inductance at which inductor voltage waveform is just discontinuous. ? ? ? ? c 1 D R L 2f Critical Capacitance (C C) Value of capacitance at which capacitor voltage waveform is just discontinuous. C 1 C 8fR ? Step-up chopper (Boost converter) ? ? ? ? ? LS when CHis ON 0 t DT , V V ? ? ? ? ? ? ? ? L S O when CHis OFF DT t T , V V V Applying volt-sec balance across inductor ? ? ? ? ? ? S S O V DT V V 1 D T 0 ? ? ? ? ? ? S O V V 1D ? ? ? Since D < 1, OS VV ? ? ? ? ? ? ? ? CO when CHis ON 0 t DT , I I ? ? ? ? ? ? ? C L O when CHis OFF DT t T , I I I ? ? ? ? ? ? ? ? ? ? ? ? O L O Applying Ampere sec balance across capacitor I DT I I 1 D T 0 ? ? ? ? O L I I 1D Ripple in inductor current ? ? ?? min max When CHis ON 0 t DT , current increase from I to I ? ? ? ? ? ? ? ? S S L SL V DT DV i L V i DT L fL Ripple in output voltage ?? CO when CHis ON , I I C O V C. I DT ? ?? ? ? O OC I DT VV C ? ? ? ? ? -ve sign indicates voltage decrease ? ? O O I DT V C ? ? ? Critical Inductance (Lc) L L I I 2 ? ? ? ? ? ? C D 1 D R L 2f Critical Capacitance (C c) O O V V 2 ? ? ? C D C 2fR If inductor also has an internal resistance, then ? ? ? ? OS 2 1D VV r 1D R ?? ? ?? ? ?? ?? ?? r = internal resistance of inductor R = load resistance Buck-Boost Converter When CH is ON (O < t < DT) LS VV ? CO II ?? When CH is OFF (DT < t < T) LO VV ? ? ? C L O I I I ? ? ? Applying volt-sec balance across inductor ? ? ? ? ? ? ? SO V DT V 1 D T 0 ? ? S O DV V 1D ? ? ? Applying Ampere-sec balance across inductor ? ? ? ? ? ? O L O I DT I I 1 D T 0 ? ? ? ? ? ? ? O L I I 1D ? ? ? ? ? ? ? ? ?? ? ? 2 OS L V DV I R 1 D R 1 D Ripple in inductor current When CH is ON (O < t < DT) Inductor current increase from min max I to I ? ?? L S I LV DT S L DV I fL ??Read More
|
Explore Courses for Electrical Engineering (EE) exam
|