Modeling And Analysis Of Buck-Boost DC/DC Pulse Converter XII ...
Modeling And Analysis Of Buck-Boost DC/DC Pulse Converter XII ...
Modeling And Analysis Of Buck-Boost DC/DC Pulse Converter XII ...
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Fig.4. Voltage and current waveforms for the case<br />
of continuous (point a) and discontinuous (point b)<br />
inductance current at the mode of the voltage increase.<br />
Below are the basic formulas which characterize<br />
mathematical relationship describing the discussed<br />
converter working in continuous and discontinuous<br />
mode with inductance current which directly results<br />
from the analysis of individual states of its work. The<br />
parameters are set in a mode of a fixed work of the<br />
converter. At the mode of the set work the average<br />
inductance voltage value and the average value of the<br />
capacitor current is zero.<br />
The filling factor of PWM wave:<br />
ton<br />
k = = ton<br />
f<br />
(1)<br />
T<br />
where: f - means the PWM wave frequency.<br />
The relative diode conduction time:<br />
- in the mode of operation with continuous<br />
inductance current (CCM)<br />
1 − k , (2)<br />
- in the mode of operation with discontinuous<br />
inductance current (<strong>DC</strong>M)<br />
2Lf<br />
k1<br />
= . (3)<br />
R<br />
The average value of voltage at the load:<br />
- in the mode of operation with continuous<br />
inductance current<br />
d U<br />
k<br />
U 0 = , (4)<br />
1−<br />
k<br />
- in the mode of operation with discontinuous<br />
inductance current<br />
U<br />
0<br />
d U<br />
k<br />
= . (5)<br />
k<br />
1<br />
139<br />
The average value of the load current:<br />
- in the mode of operation with continuous<br />
inductance current<br />
− k<br />
I = I<br />
1<br />
, (6)<br />
R<br />
- in the mode of operation with discontinuous<br />
inductance current<br />
k1<br />
I R = I d . (7)<br />
k<br />
The average value of the inductance current:<br />
- in the mode of operation with continuous<br />
inductance current<br />
k<br />
I L = U d<br />
(8)<br />
2 ( 1− k)<br />
R<br />
- in the mode of operation with discontinuous<br />
inductance current<br />
k<br />
( k + k )<br />
1 k<br />
I L = U d . (9)<br />
2Lf<br />
The average value of the source current<br />
calculated assuming that there are no energy losses in<br />
the converter system:<br />
P =<br />
- in the mode of operation with continuous<br />
inductance current<br />
d<br />
0 = I RU<br />
0 ≈ I dU<br />
d Pd<br />
, (10)<br />
⎛ k ⎞ 1<br />
I d = ⎜ ⎟ U d , (11)<br />
⎝1<br />
− k ⎠ R<br />
- in the mode of operation with discontinuous<br />
inductance current<br />
⎛ k ⎞ 1<br />
I d = ⎜ U d<br />
k ⎟ . (12)<br />
⎝ 1 ⎠ R<br />
The maximum value of the inductance current:<br />
- in the mode of operation with continuous<br />
inductance current<br />
⎛ 1 1 ⎞<br />
I ⎜<br />
⎟<br />
L max =<br />
⎜<br />
+ kU d<br />
( k)<br />
R Lf ⎟<br />
, (13)<br />
2<br />
⎝ 1−<br />
2 ⎠<br />
- in the mode of operation with discontinuous<br />
inductance current<br />
U d<br />
I L max = ∆iL<br />
= k . (14)<br />
Lf<br />
The minimum value of the inductance current:<br />
- in the mode of operation with continuous<br />
inductance current<br />
2<br />
2
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