cameroon gce advanced level 2025 power electronics 2

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3. Chopper

 

(Image of Figure 4, a chopper circuit with a DC source, switch K, diode D, inductor L, and motor M.)

In the circuit of Figure 4, the supply voltage of the series chopper is constant with a value of Vs​=210V.

D is an ideal diode and K is a perfect switch.

The duty cycle ratio is α and the period is T which is equal to 0.1ms.

For t∈[0;αT], K is closed.

For t∈[αT;T], K is opened.

It is considered that the voltage at the terminals of the motor is equal to its emf E and E is proportional to the rotational speed of the motor: E=kn with k=5.25×10−2 V/(rev/min).

It is assumed that the current i varies linearly between the minimum and maximum values Imin​ and Imax​.

a) Give the expression of i(t) for the interval

i. t∈[0;αT] (2 marks)

ii. i(t)∈[αT;T]. (2 marks)

b) Draw in synchronism the waveform of Vo​(t), iD​(t), iK​(t) and $i(t)$ for two periods. (7 marks)

c) Give the expression of the average load voltage in function of $\alpha$ and Vs​. Deduce the relation between E, $\alpha$ and Vs​. (4 marks)

d) Express the ripple current Δi=Imax​−Imin​ in function of $\alpha$, Vs​, L and T. (4 marks)

e) What value of $\alpha$ that $\Delta i$ is maximum? Calculate the value of (Δi)max​. (4 marks)

f) Calculate the value of $\alpha$ to regulate the rotational speed to $N=1000\text{ rev/min}$. (3 marks)

g) Express the average values of iD​ and iK​. (4 marks)