Question

POWER ELECTRONICS

Q3. CL0-03: Explain DC-DC converters and use them in applications. The figure below depicts the instantaneous inductor current (iu) in a DC-DC converter. a. ALL i. DT T Derive the expression for the average value of this current (IL) in terms of the maximum value (max) and the ripple (A1). [12] Derive the expression of the instantaneous voltage across the inductor L through which this current is flowing and sketch it for one time-period. Also calculate the average value of the inductor voltage. [8] ii.

Answer 1

Imax I. Tmin o DT T here o į = Imax Imin. Let the Average current be Io and it IS Given by Area Under 1 time period T Io Time period (T) Area of triangle Irody ABC A Imin А SABC - 1 & SIXT DT T آراد DABC 2 Area of AC TO rectangle 0 Imin x T Imin T

so, Area Under 1 time Period DABC t Rectangle Area ACTO I siet + Imin T so I ALT + Imint Io = T Isi & Imin Io - -id I sin + (Imax - Dů) { Imax -Imin sų } Io Įsiu max that know Inductor voltage is (2) we given by V L die dt here L is the Inductor voltage the change an Inductor Current di is in dt time.

so, in time for ott a DT di = Δί, So, Was Ai L DT in time for DT < t <t di -oil so, Jw L Ai (1-D) T here shows that current negative sign decreasing } is V (Anductor Voltage) an DT t Viz