Question 1 |

In the dc-dc converter circuit shown, switch Q is switched at a frequency of 10 kHz
with a duty ratio of 0.6. All components of the circuit are ideal, and the initial current
in the inductor is zero. Energy stored in the inductor in mJ (rounded off to 2 decimal
places) at the end of 10 complete switching cycles is ________.

10 | |

5 | |

15 | |

20 |

Question 1 Explanation:

Buck boost converter,

D=0.6\rightarrow \text{store energy}

D=\frac{T_{ON}}{T}=0.6

T_{ON}=0.6\: T\rightarrow \text{store energy}

T_{OFF}=0.4\: T\rightarrow \text{releasing energy}

For one cycle: Rise in current for 0.2T

For 10 cycles: Find rise in current (0.2T) \times 10 = 2T

i=\frac{50}{L}t

i=\frac{50}{L}(2T)=\frac{50\times 2}{LP}=\frac{100}{10\cdot 10^{-3}\times 10\cdot 10^{3}}=1\, A

\therefore \, \text{Energy stored}=\frac{1}{2}Li^{2}=\frac{1}{2}\times (10\cdot 10^{-3})(1)^{2}=5\: mJ

D=0.6\rightarrow \text{store energy}

D=\frac{T_{ON}}{T}=0.6

T_{ON}=0.6\: T\rightarrow \text{store energy}

T_{OFF}=0.4\: T\rightarrow \text{releasing energy}

For one cycle: Rise in current for 0.2T

For 10 cycles: Find rise in current (0.2T) \times 10 = 2T

i=\frac{50}{L}t

i=\frac{50}{L}(2T)=\frac{50\times 2}{LP}=\frac{100}{10\cdot 10^{-3}\times 10\cdot 10^{3}}=1\, A

\therefore \, \text{Energy stored}=\frac{1}{2}Li^{2}=\frac{1}{2}\times (10\cdot 10^{-3})(1)^{2}=5\: mJ

Question 2 |

In a DC-DC boost converter, the duty ratio is controlled to regulate the output voltage at 48 V. The input DC voltage is 24 V. The output power is 120 W. The switching frequency is 50 kHz. Assume ideal components and a very large output filter capacitor. The converter operates at the boundary between continuous and discontinuous conduction modes. The value of the boost inductor (in \mu H) is _______.

12 | |

24 | |

28 | |

14 |

Question 2 Explanation:

\begin{aligned} P_0&=120W,\\ V_s&=24V\\ V_0&=48V\\ V_0&=\frac{V_s}{(1-D)}\\ 1-D&=\frac{24}{48}\\ D&=0.5\\ P_0&=V_0I_0=120\\ I_0&=\frac{120}{48}=2.54A\\ V_sI_s&=V_0I_0\\ I_s&=\frac{120}{24}=5A \end{aligned}

At boundary of continuous and discontinuous,

\begin{aligned} I_L&=I_s=\frac{\Delta I_{L}}{2}\\ \Delta I_L&=\frac{DV_s}{fL_c}=2 \times 5\\ L_c&=\frac{0.5 \times 24}{50 \times 10^3 \times 10}=24\mu H \end{aligned}

At boundary of continuous and discontinuous,

\begin{aligned} I_L&=I_s=\frac{\Delta I_{L}}{2}\\ \Delta I_L&=\frac{DV_s}{fL_c}=2 \times 5\\ L_c&=\frac{0.5 \times 24}{50 \times 10^3 \times 10}=24\mu H \end{aligned}

Question 3 |

A DC-DC buck converter operates in continuous conduction mode. It has 48 V input voltage, and it feeds a resistive load of 24 \Omega. The switching frequency of the converter is 250 Hz. If switch-on duration is 1 ms, the load power is

6 W | |

12 W | |

24 W | |

48 W |

Question 3 Explanation:

Geven that,

\begin{aligned} & \text{Supply voltage, } V_s=48V\\ & \text{Load resistance, }R_L=24\Omega \\ & \text{Switch frequency, }f_s=250Hz\\ &\text{on time of switch } (T_{ON})=1ms\\ & \text{Time period, } T=\frac{1}{f_s}=\frac{1}{250}=4ms\\ & \text{Duty cycle, } \alpha =\frac{T_{ON}}{T}=\frac{1ms}{4ms}=0.25\\ & \text{Load power }=\frac{(V_0)^2}{R}=\frac{(\alpha V_s)^2}{24}\\ &=\frac{(0.25 \times 48)^2}{24}=6 \text{ Watt} \end{aligned}

\begin{aligned} & \text{Supply voltage, } V_s=48V\\ & \text{Load resistance, }R_L=24\Omega \\ & \text{Switch frequency, }f_s=250Hz\\ &\text{on time of switch } (T_{ON})=1ms\\ & \text{Time period, } T=\frac{1}{f_s}=\frac{1}{250}=4ms\\ & \text{Duty cycle, } \alpha =\frac{T_{ON}}{T}=\frac{1ms}{4ms}=0.25\\ & \text{Load power }=\frac{(V_0)^2}{R}=\frac{(\alpha V_s)^2}{24}\\ &=\frac{(0.25 \times 48)^2}{24}=6 \text{ Watt} \end{aligned}

Question 4 |

A dc to dc converter shown in the figure is charging a battery bank, B2 whose voltage is
constant at 150 V. B1 is another battery bank whose voltage is constant at 50 V. The value
of the inductor, L is 5 mH and the ideal switch, S is operated with a switching frequency of
5 kHz with a duty ratio of 0.4. Once the circuit has attained steady state and assuming the
diode D to be ideal, the power transferred from B1 to B2 (in Watt) is ___________ (up to 2
decimal places). .

8 | |

10 | |

12 | |

16 |

Question 4 Explanation:

During T_{on} the circuit behaves as,

\begin{aligned} V_s&=L\frac{di}{dt} \\ di&=\frac{V_s}{L}dt \end{aligned}

Integrating on both sides,

\begin{aligned} I_P&=\frac{V_s}{L}T_{on}\\ T_{on}&=\alpha T=\frac{\alpha }{f}=80 \times 10^{-6}s\\ I_P&=\frac{50}{5 \times 10^{-3}}\times (80 \times 10^{-6})\\ &=0.8A \end{aligned}

During T_{off}, it is T_{on}\leq t\leq \beta T

\begin{aligned} \text{KVL, } V_L&=V_s-V_0 \\ (V_L)_{avg}&=0 \\ V_sT_{on}+&(V_s-V_0)(\beta T-T_{on}) =0 \\ V_s\beta T &=V_0(\beta T-T_{on}) \\ \frac{V_0}{V_s}&=\frac{\beta }{\beta -\alpha } \\ \beta &=0.6\\ &\text{Fromt the graph of } i_L, \\ I_{L(avg)}&=\frac{\frac{1}{2} \times b \times h}{T}\\ &=\frac{\frac{1}{2} \times \beta T \times I_P}{T}\\ &=\frac{1}{2} \times 0.6 \times 0.8=0.24A\\ &\text{Power transferred to } B_2 \text{ is,}\\ P&=V_s \times (I_L)_{avg}\\ \text{ where } I_s&=I_L\\ P&=50 \times 0.24\\ &=12W \end{aligned}

Question 5 |

The figure shows two buck converters connected in parallel. The common input dc voltage
for the converters has a value of 100 V. The converters have inductors of identical value.
The load resistance is 1 \Omega. The capacitor voltage has negligible ripple. Both converters operate in the continuous conduction mode. The switching frequency is 1 kHz, and the switch control signals are as shown. The circuit operates in the steady state. Assuming that the converters share the load equally, the average value of i_{S1}, the current of switch S1 (in Ampere), is _____ (up to 2 decimal places).

5.55 | |

6.85 | |

7.25 | |

12.50 |

Question 5 Explanation:

Hence it is buck converter,

\begin{aligned} V_0&=\alpha V_s\\ V_0&=0.5 \times 100=50V\\ I_0&=\frac{V_0}{R}=\frac{50}{1}=50A\\ V_sI_s&=V_0I_0\\ I_s&=\frac{V_0I_0}{V_s}=\frac{50\times 50}{100}=25A\\ I_{s1}&=I_{s2}=\frac{I_s}{2}=12.5A \end{aligned}

\begin{aligned} V_0&=\alpha V_s\\ V_0&=0.5 \times 100=50V\\ I_0&=\frac{V_0}{R}=\frac{50}{1}=50A\\ V_sI_s&=V_0I_0\\ I_s&=\frac{V_0I_0}{V_s}=\frac{50\times 50}{100}=25A\\ I_{s1}&=I_{s2}=\frac{I_s}{2}=12.5A \end{aligned}

Question 6 |

In the circuit shown all elements are ideal and the switch S is operated at 10 kHz and 60% duty
ratio. The capacitor is large enough so that the ripple across it is negligible and at steady state
acquires a voltage as shown. The peak current in amperes drawn from the 50 V DC source is
________. (Give the answer up to one decimal place.)

37 | |

40 | |

22 | |

56 |

Question 6 Explanation:

Buckboost converter,

\begin{aligned} V_0&=\frac{\alpha V_s}{1-\alpha }\\ V_s&=50V\\ \alpha &=0.6\\ V_0&=75V\\ \frac{V_0}{V_s}&=\frac{I_s}{I_0}=\frac{\alpha }{1-\alpha }\\ &=\frac{0.6}{1-0.6}=\frac{3}{2}\\ I_0&=\frac{V_0}{R}=\frac{75}{5}=15A\\ I_s&=\frac{\alpha }{1-\alpha }I_0=\frac{3}{2} \times 15=22.5A \end{aligned}

Since capacitor is very large i_c=0 at steady state

\begin{aligned} (i_L)_{avg}&=(I_s)_{avg}+(i_0)_{avg}\\ I_L&=I_s+I_0\\ I_L&=22.5+15=37.5A\\ \Delta I_L&=\frac{\alpha V_s}{fL}\\ &=\frac{0.6\times 50}{10 \times 10^3 \times (0.6 \times 10^{-3})}\\ &=5A\\ (i_L)_{peak}&=I_L+\frac{\Delta I_L}{2}\\ &=37.5+\frac{5}{2}=40A \end{aligned}

Peak value of current drawn from source =(i_L)_{peak}=40A

\begin{aligned} V_0&=\frac{\alpha V_s}{1-\alpha }\\ V_s&=50V\\ \alpha &=0.6\\ V_0&=75V\\ \frac{V_0}{V_s}&=\frac{I_s}{I_0}=\frac{\alpha }{1-\alpha }\\ &=\frac{0.6}{1-0.6}=\frac{3}{2}\\ I_0&=\frac{V_0}{R}=\frac{75}{5}=15A\\ I_s&=\frac{\alpha }{1-\alpha }I_0=\frac{3}{2} \times 15=22.5A \end{aligned}

Since capacitor is very large i_c=0 at steady state

\begin{aligned} (i_L)_{avg}&=(I_s)_{avg}+(i_0)_{avg}\\ I_L&=I_s+I_0\\ I_L&=22.5+15=37.5A\\ \Delta I_L&=\frac{\alpha V_s}{fL}\\ &=\frac{0.6\times 50}{10 \times 10^3 \times (0.6 \times 10^{-3})}\\ &=5A\\ (i_L)_{peak}&=I_L+\frac{\Delta I_L}{2}\\ &=37.5+\frac{5}{2}=40A \end{aligned}

Peak value of current drawn from source =(i_L)_{peak}=40A

Question 7 |

The input voltage V_{DC} of the buck-boost converter shown below varies from 32 V to 72 V. Assume that all components are ideal, inductor current is continuous, and output voltage is ripple free. The
range of duty ratio D of the converter for which the magnitude of the steady state output voltage remains constant at 48 V is

\frac{2}{5}\leq D \leq \frac{3}{5} | |

\frac{2}{3}\leq D \leq \frac{3}{4} | |

0 \leq D \leq 1 | |

\frac{1}{3}\leq D \leq \frac{2}{3} |

Question 7 Explanation:

\begin{aligned} V_0&=\frac{\alpha V_s}{1-\alpha }\\ \text{when, } V_s&=32V \text{ and }V_0=48V\\ \alpha &=\frac{3}{5}\\ \text{when, }V_s&=72V \text{ and }V_0=48V\\ \alpha &=\frac{2}{5}\\ \frac{2}{5}\leq &\alpha \leq \frac{3}{5}\\ \therefore \; \text{This answer is }& \frac{2}{5}\leq D \leq \frac{3}{5} \end{aligned}

Question 8 |

A DC-DC boost converter, as shown in the figure below, is used to boost 360V to 400 V, at a power of 4 kW. All devices are ideal. Considering continuous inductor current, the rms current in
the solid state switch (S), in ampere, is _________.

2.5 | |

3.5 | |

6.5 | |

8.5 |

Question 8 Explanation:

\begin{aligned} \frac{V_0}{V_s}&=\frac{1}{1-\alpha } \\ \frac{400}{360}&= \frac{1}{1-\alpha }\\ \alpha &= 0.1\\ V_sI_s&= \text{Power}\\ 360I_s &=4000\\ I_s&=11.1A \end{aligned}

Neglecting ripple in i_s

\begin{aligned} I_{\text{switch (rms)}}&=I_s\left ( \frac{T_{on}}{T} \right )^{1/2}\\ &=I_s\sqrt{\alpha }\\ &=11.1\sqrt{0.1}=3.5A \end{aligned}

Question 9 |

A buck-boost DC-DC converter, shown in the figure below, is used to convert 24 V battery voltage to 36 V DC voltage to feed a load of 72 W. It is operated at 20 kHz with an inductor of 2 mH and output capacitor of 1000 \muF. All devices are considered to be ideal. The peak voltage across the solid-state switch (S), in volt, is ____________.

24 | |

36 | |

60 | |

72 |

Question 9 Explanation:

When switch 'S' is off, diode D is on then

Therefore, Peak voltage across switch =24+36=60V

Therefore, Peak voltage across switch =24+36=60V

Question 10 |

A buck converter, as shown in Figure (a) below, is working in steady state. The output voltage and the inductor current can be assumed to be ripple free. Figure (b) shows the inductor voltage V_L during a complete switching interval. Assuming all devices are ideal, the duty cycle of the buck converter is ________.

0.2 | |

0.4 | |

0.8 | |

1 |

Question 10 Explanation:

Average voltage across inductor is zero.

\begin{aligned} V_{L(avg)} &=0 \\ 30(T_{on})-20(T_{off})&=0 \\ 30(\alpha T)&=20(1-a)T \\ 30a+2\alpha &= 20\\ 50\alpha &=20 \\ \alpha &=\frac{2}{5}=0.4 \end{aligned}

\begin{aligned} V_{L(avg)} &=0 \\ 30(T_{on})-20(T_{off})&=0 \\ 30(\alpha T)&=20(1-a)T \\ 30a+2\alpha &= 20\\ 50\alpha &=20 \\ \alpha &=\frac{2}{5}=0.4 \end{aligned}

There are 10 questions to complete.