Question
Conversion ratio analysis of the SEPIC of Fig. 4 a) Suppose that the converter operates at...
Answers
Given data for SEPIC Converter is,
D = 0.225
Vg = 120V
L1=50*10^-6H
C1=47*10^-6F
f=100KHZ
R=10 Ohmss
L2= 75*10^-6H
C2= 200*10^-6F
The Out put voltage is determined by equation given below.
V0=Vg (D/(1-D)) = 120*(0.225/(1-0.225)) = 34.838V
Average current in L1, IL1 =(V0^2)/(Vs*R) = (34.838*34.838)/(120*10) = 1.0114 Amps
The variation in iL1 when the switch is closed is found from
change in IL1 = (Vs*D)/L1*f = (120*0.225)/(50*10^-6* 100*10^3) = 5.4Amps
Maximum current in L1 , IL1 Max = IL1 + (change in IL1/2)= 1.0114+(5.4/2) = 3.7114Amps
Minimum current in L1, IL1 Min = IL1 - (chang ein IL1/2) = 1.0114 - (5.4/2) = -1.6886 Amps
the average current in L2 is IL2 = I0 = V0/R = 34.838/10 = 3.484 Amps
cahnge in IL2 = (Vs*D)/L2*f = (120*0.225)/(75*10^-6* 100*10^3) = 3.6 Amps
Maximum current in L2 , IL2 Max = IL2 + (change in IL2/2)= 3.484+(3.6/2) = 5.284Amps
Minimum current in L1, IL1 Min = IL1 - (chang ein IL1/2) = 3.484 -(3.6/2) = 1.684 Amps
Diode current is expressed as ID = zero, when switch is closed.
= IC1+IL2 , when switch is open
The graphical representation is as shown below.
c). discontinuous mode of operation graphs are shown below.
b).
, a discontinuous conduction mode (DCM) means that the third time interval of operation cycle is nonzero, not that either inductor current is discontinuous.
Three distinct time intervals appears there, namely D1Ts , D2Ts and D3Ts with D1 + D2 + D3 = 1
for a constant switching frequency. For DCM, besides of expressions of average inductor currents, average input and output currents, average voltage across the energy storage capacitor C1 and average currents transistor and diode, we have to determine the parameter D2 that fixes the decay interval of inductor currents and the dc voltage conversion ratio implicitly.
Concerning the waveforms of inductor currents, it can see that the shapes of the currents are similar to those CCM.
IL01= - IL02 = IL0
The currents through inductors can be expressed as
IL1=i1+IL0
IL2=i2-IL0
For the first two time intervals D1Ts and D2Ts , change in IL1 and change in IL2 keep their validity. For the third time interval ( D3Ts ), the voltages across inductors are zero:
vL1 = vL2 = 0V. Taking into account that the average voltages across the inductors over a switching period are zero, the following relationships result
VC1= V1 = (D2/D1)*V0
The above relationships yield the dc voltage conversion ratio
M = V0/Vi = D1/D2 and VC1= V1
The remark regarding the relationship VC1= V1 that is the same as change in IL2 = (Vs*D)/L2*f for the converter with CCM keeps its validity for the converter with DCM. The determination of the conversion ratio M needs the value of parameter D2 too. It is obvious that the conditions of ripple cancellation from the inductor current found for CCM remain unchanged for DCM. Also, the two effective inductances and two parameters of conduction through the inductors hold their expressions.
Similar way D2= sqrt( Kem);
Kem = 2 Lem*f/R
Lem = L1e//L2e
