80679_FC.qxd 12/11/09 6:23 PM Page ii har80679_FC.

qxd 12/11/09 6:23 PM Page iii

Vm
Commonly used Power rms voltage for a half-wave rectified sine wave: Vrms ⫽
2

and Converter Equations Power factor: pf ⫽

P
⫽
P
S Vrms Irms

I 2n
Aa
Instantaneous power: p(t) ⫽ v(t)i(t) Total harmonic distortion: THD ⫽ n⫽2
I1
t2
1
Energy: W ⫽ p(t)dt Distortion factor: DF ⫽
3 A 1 ⫹ (THD)2
t1
Irms
t0 ⫹T t0 ⫹T Form factor ⫽
Iavg
W 1 1
Average power: P ⫽ ⫽ p(t) dt ⫽ v(t)i(t) dt
T T3 T3 Ipeak
t0 t0 Crest factor ⫽
Irms
Average power for a dc voltage source: Pdc ⫽ Vdc Iavg
Buck converter: Vo ⫽ Vs D
1 T 2
rms voltage: Vrms ⫽ v (t)dt Vs
BT3 Boost converter: Vo ⫽
0 1⫺D

Buck-boost and Ćuk converters: Vo ⫽ ⫺ Vs a

D
rms for v ⫽ v1 ⫹ v2 ⫹ v3 ⫹ . . . : Vrms ⫽ 2V 1,2 rms ⫹ V 2,2 rms ⫹ V 3,2 rms ⫹ Á b
1⫺D

SEPIC: Vo ⫽ Vs a
D
b
Im
rms current for a triangular wave: Irms ⫽
13 1⫺D

Flyback converter: Vo ⫽ Vs a
D
b a 2b
Im 2 N
rms current for an offset triangular wave: Irms ⫽ a b ⫹ I dc
2
1 ⫺ D N1
B 13

Forward converter: Vo ⫽ Vs D a
N2
rms voltage for a sine wave or a full-wave rectified sine wave: Vrms ⫽
Vm b
12 N1