Tools

Performance measurement and analysis of DC-DC buck regulator

Theory

The circuit configuration of buck converter is given in Fig. 1.

Fig.1 Circuit configuration of Buck Converter.


Based on the operation of switch (Sw: ON/OFF-state) the operating principle of the converter is explained below briefly.

Mode – I : Switch (Sw): ON and Diode (Db): OFF


Fig. 2(a). Equivalent circuit in mode-I.

Mode – II : Switch (Sw): OFF and Diode (Db): ON


Fig. 2(b). Equivalent circuit in mode-II.


a) Voltage conversion ratio or voltage gain (M)

Voltage across inductor L:

Mode – I :

..(1)


Mode – II :

..(2)


Applying volt-sec balance on inductor (eqn. 1 and 2)

..(3)



On solving eqn. 3

..(4)


b) Average current through inductor (IL):
Current through capacitor

Mode – I :



..(5)



Mode – II :

..(6)



Applying charge-sec balance on capacitor (eqn. 5 and 6)

..(7)


On solving

..(8)



Therefore, average inductor current is load current.

c) Power balance under ideal condition (neglecting losses):

Under ideal condition, input power must be equal to output power, hence


..(9)
 
..(10)


Substituting eqns. 4 and 10

..(11)


d) Inductor current ripple:

From eqn. 1,



..(12)


 

..(13)


Therefore, the inductor ripple current is

..(14)




e) Current through various components:

The current through various components is given in Fig. 3.

Fig. 3 Current through various components.


  Mode-I
(DT) 		Mode-II
(1-D)T 		Average Current
imin imax imin imax Iavg
iL
iC 0
iSw 0 0
iDb 0 0


f) Voltage and current stress on various components:


Component Voltage stress Current Stress
Inductor (L)
Capacitor (C) V0
Switch (Sw) Vin
Diode (Db) Vin


g) Efficiency analysis:


..(15)


..(16)


The power loss occurring in various components are given below.

Power loss in inductor:


..(17)


Power loss in capacitor:

..(18)

Power loss in switch:


..(19)


Power loss in Diode:

..(20)

Total power loss:


..(21)




h) Effect of non-idealities on voltage gain expression:



Fig. 4 Circuit configuration of conventional buck converter with non-idealities






Voltage across inductor L

Mode – I :



..(22)


Mode – II :



..(23)


Applying volt-sec balance on inductor (eqn. 22 and 23)

..(24)

Simplifying eqn. (24) results in


..(25)



(Effect of rc is not considered for simplification of equation)

("For more Information on mathematical analysis, see references")