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Question B1 [20 pts] Underneath shows a basic pulse-width-modulated (PWM) boost regulator, operating in continuous conduction mode. The input voltage, output voltage and the output load vary over the range of 4.8-7.2Vdc, 13.5Vdc and 10-30 ?, respectively. The switching frequency of the converter is 50kHz. The output capacitor is 220uF. a) The gate voltage waveform of the power MOSFET is shown on page 13. According to the voltage polarity and current direction (as shown in Fig. B3), draw the steady state voltage and current waveforms of the switch, inductor, diode and capacitor. (8 marks) b) Derive from the first principle, show that the minimum inductance of the converter operating in continuous conduction current mode (CCM) is: $L = \frac{R(1 - D)^2 DT_s}{2}$ $L = 39.8 \mu H$ $D_{min}, R_{max}$ $I_L = \frac{1}{2} \frac{\Delta I_L}{\Delta t}$ $V_{out} = \frac{L}{\Delta t} \frac{\Delta I_c}{\Delta t}$ $V_{out} = \frac{L \frac{\Delta I_L}{\Delta T}}{(1 - D) \Delta T}$ (5 marks) c) Determine the minimum value of the inductor L. $V_{out} = \frac{L(1 - D) \Delta T}{\Delta t}$ (2 marks) d) Determine the maximum peak current of the inductor L $L = \frac{V_{out} (1 - D) \Delta T}{2 I_L}$ (2 marks) A e) Determine the maximum output ripple voltage $V_{out} = \frac{V_{out} (1 - D) \Delta T}{2 I_{out}}$ (3 marks) $13.5$ $4.8$ $13.5$ $7.2$ $I_L = 1.35A$ Input voltage 0.644 797 57 A $ \frac{dV}{dt} = \frac{I}{C} $ $ \Delta Q = C \Delta V $ $I_{out} \Delta T$ Fig. B1

          Question B1 [20 pts]
Underneath shows a basic pulse-width-modulated (PWM) boost regulator,
operating in continuous conduction mode. The input voltage, output voltage and
the output load vary over the range of 4.8-7.2Vdc, 13.5Vdc and 10-30 ?,
respectively. The switching frequency of the converter is 50kHz. The output
capacitor is 220uF.
a) The gate voltage waveform of the power MOSFET is shown on page 13.
According to the voltage polarity and current direction (as shown in Fig. B3),
draw the steady state voltage and current waveforms of the switch, inductor,
diode and capacitor.
(8 marks)
b) Derive from the first principle, show that the minimum inductance of the
converter operating in continuous conduction current mode (CCM) is:
$L = \frac{R(1 - D)^2 DT_s}{2}$
$L = 39.8 \mu H$
$D_{min}, R_{max}$
$I_L = \frac{1}{2} \frac{\Delta I_L}{\Delta t}$
$V_{out} = \frac{L}{\Delta t} \frac{\Delta I_c}{\Delta t}$
$V_{out} = \frac{L \frac{\Delta I_L}{\Delta T}}{(1 - D) \Delta T}$
(5 marks)
c) Determine the minimum value of the inductor L.
$V_{out} = \frac{L(1 - D) \Delta T}{\Delta t}$
(2 marks)
d) Determine the maximum peak current of the inductor L
$L = \frac{V_{out} (1 - D) \Delta T}{2 I_L}$
(2 marks)
A e) Determine the maximum output ripple voltage
$V_{out} = \frac{V_{out} (1 - D) \Delta T}{2 I_{out}}$
(3 marks)
$13.5$
$4.8$
$13.5$
$7.2$
$I_L = 1.35A$
Input
voltage
0.644
797
57 A
$ \frac{dV}{dt} = \frac{I}{C} $
$ \Delta Q = C \Delta V $
$I_{out} \Delta T$
Fig. B1

Question B1 [20 pts]
Underneath shows a basic pulse-width-modulated (PWM) boost regulator,
operating in continuous conduction mode. The input voltage, output voltage and
the output load vary over the range of 4.8-7.2Vdc, 13.5Vdc and 10-30 ?,
respectively. The switching frequency of the converter is 50kHz. The output
capacitor is 220uF.
a) The gate voltage waveform of the power MOSFET is shown on page 13.
According to the voltage polarity and current direction (as shown in Fig. B3),
draw the steady state voltage and current waveforms of the switch, inductor,
diode and capacitor.
(8 marks)
b) Derive from the first principle, show that the minimum inductance of the
converter operating in continuous conduction current mode (CCM) is:
L = (R(1 - D)^2 DTs)/(2)
L = 39.8 μ H
Dmin, Rmax
IL = (1)/(2)(Δ IL)/(Δ t)
Vout = (L)/(Δ t)(Δ Ic)/(Δ t)
Vout = (L (Δ IL)/(Δ T))/((1 - D) Δ T)
(5 marks)
c) Determine the minimum value of the inductor L.
Vout = (L(1 - D) Δ T)/(Δ t)
(2 marks)
d) Determine the maximum peak current of the inductor L
L = (Vout (1 - D) Δ T)/(2 IL)
(2 marks)
A e) Determine the maximum output ripple voltage
Vout = (Vout (1 - D) Δ T)/(2 Iout)
(3 marks)
13.5
4.8
13.5
7.2
IL = 1.35A
Input
voltage
0.644
797
57 A
(dV)/(dt) = (I)/(C)
Δ Q = C Δ V
IoutΔ T
Fig. B1

Added by Ivan A.

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