1st part but when the polarity of voltage is reversed to a negative –U2, which in accordance with zero averaged voltage rule is applied in time interval U1t1 , U2 the current of inductor linearly decreases for the same value (Fig.1.2). In such way at the periodically changing of polarity of the applied voltage the current of inductor is deviating around an average meaning of current but the range of deviations (current ripple range) depends in reverse proportion on the inductance of inductor — if the inductance is higher than at constant other parameters ripple range is lower, i.e., a current is better smoothed. t2 =
uL
iL uL
0
L
t2
U1 t1
U2
t
iL Iav
DI
t
Fig.1.2. Variations in periodic process instantaneous meanings of inductor voltage and current
If the ideal inductor (resistance-less) is introduced in AC circuit with the ideal diode (Fig. 1.3), then switched to the sinus shape voltage at its initial zero point the changes of current in cycle time can be calculated from the expression U m sin ωt = L
di . (1-19) dt
Accounting an initial value i = 0 A at ωt = 0, the expression for the current changes is i=
Um (1− cos ωt ) . (1-20) ωL
The peak value of this current will be at ωt = π, when I m = 2U m / ωL, but the current decreases to zero value only at the end of full cycle, i.e. the diode conducts current continuously. The average value of the current is I av =
1 2π
2π
∫ 0
Um U (1− cos ωt )dωt = m ; (1-21) ωL ωL
but its rms value
16
EnergoelektronikaEN BOOK.indb 16
07.05.2018 17:53:18