power electronics

,Commonly used Power
and Converter Equations

Instantaneous power: p(t) ⫽ v(t)i(t)
t2

Energy: W ⫽ p(t)dt
3
t1

t0 ⫹T t0 ⫹T
W 1 1
Average power: P ⫽ ⫽ p(t) dt ⫽ v(t)i(t) dt
T T3 T3
t0 t0


Average power for a dc voltage source: Pdc ⫽ Vdc Iavg

1 T 2
rms voltage: Vrms ⫽ v (t)dt
BT3
0


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

Im
rms current for a triangular wave: Irms ⫽
13

Im 2
rms current for an offset triangular wave: Irms ⫽ a b ⫹ I dc
2
B 13

Vm
rms voltage for a sine wave or a full-wave rectified sine wave: Vrms ⫽
12

, Vm
rms voltage for a half-wave rectified sine wave: Vrms ⫽
2

P P
Power factor: pf ⫽ ⫽
S Vrms Irms

q
2
In
Aa
n⫽2
Total harmonic distortion: THD ⫽
I1

1
Distortion factor: DF ⫽
A 1 ⫹ (THD)2
Irms
Form factor ⫽
Iavg

Ipeak
Crest factor ⫽
Irms


Buck converter: Vo ⫽ Vs D

Vs
Boost converter: Vo ⫽
1⫺D

D
Buck-boost and Ćuk converters: Vo ⫽ ⫺ Vs a b
1⫺D
D
SEPIC: Vo ⫽ Vs a b
1⫺D

D N
Flyback converter: Vo ⫽ Vs a b a 2b
1 ⫺ D N1

N2
Forward converter: Vo ⫽ Vs D a b
N1

, Power Electronics
Daniel W. Hart
Valparaiso University
Valparaiso, Indiana