SEMICONDUCTOR DEVICE PHYSICS AND DESIGN

192 CHAPTER 4. JUNCTIONS IN SEMICONDUCTORS:P-NDIODES

Vin VO

Input Output

C

Vx IL L

Time

Vx

Inductor

current

T

ton toff

(a)

(b)

Figure 4.28: (a)Buck converter schematic (b) Voltage and current changes

OFF timeVx=0. Thus in steady state

if−ii=0=

∫tON

0

(Vin−Vo)dt+

∫tON+tOFF

tON

(−Vo)dt (4.8.17)

which gives
(Vin−Vo)tON−VotOFF=0 (4.8.18)
or
Vo
Vin

=

tON

T

(4.8.19)

Using D as the “duty cycle” gives

D=

tON

T

(4.8.20)

the voltage relationship becomesVo=DVin. Since the circuit is ’lossless’ and the input
and output powers must match on the averageVoIo=VinIin. This requires the diode to