Figure 1 shows one application employing a dc-dc converter to deliver 5 V output voltage to a 5 Ω load
resistor. The input voltage of this circuit is coming from a photovoltaic panel which has a minimum input
voltage of 2.5 V and maximum output voltage of 3.5 V. If the average load current is 1 A and the switching
frequency is based on Table 1, determine:
i)
The duty ratio, D for a continuous current operation
ii)
The average inductor current, 𝐼𝐿
iii) The value of the inductor, 𝐿 if the inductor current variation must be less than 30 % of the
average
iv) The value of the output capacitor, 𝐶 out if the output voltage ripple is less than 4 %
v)
Compare your calculated values with simulations result in Matlab/Simulink (please clearly show
your simulation circuit, the output voltage, the average inductor current, and the minimum and
maximum inductor current).
Basic rubric:
Design parameter (5 marks)
Calculation (10 marks)
Matlab design (10 marks)
Result (Voltage/current waveform) (10 marks)
Figure 1
5Ω load resistor
2.5V minimum input voltage,Vin
3.5V maximum output voltage, Vout
1A average load current
130kHz Switching frequency, Fsw
vi)
The duty ratio, D for a continuous current operation
𝑉𝑠
𝑉𝑜
2.5
𝐷 = 1−
= 0.2857
3.5
𝐷 = 1−
= 0.2857 × 100%
𝐷 = 28.57%
vii)
The average inductor current, 𝐼𝐿 and the value of the inductor, 𝐿 if the inductor
current variation must be less than 30 % of the average.
𝐷(1 − 𝐷)2 𝑅
2𝐹
0.2857 × (1 − 0.2857)2 × 5
=
2 × 130𝑘
𝐿𝑚𝑖𝑛 =
= 2.8033𝜇𝐻
𝐿 = 𝐿𝑚𝑖𝑛 + 30%𝐿𝑚𝑖𝑛
30
= 2.8033𝜇 + [(
) × 2.8033𝜇]
100
𝐿 = 3.6443𝜇𝐻
∆𝑖𝐿 =
=
𝑉𝑠𝐷𝑇
𝐿
1
)
130𝑘
3.6443𝜇
2.5 𝑥0.2857 (
∆𝑖𝐿 = 1.5076𝐴
𝑖𝐿 =
𝑉𝑠
2.5
=
(1 − 𝐷)2 𝑅 (1 − 0.2857)2 𝑥5
𝑖𝐿 = 0.98𝐴
𝐼𝑚𝑎𝑥 =
𝑉𝑠
𝑉𝑠𝐷𝑇
+
2
(1 − 𝐷) 𝑅
2𝐿
= 0.98 +
1
)
130𝑘
2 𝑥 3.6443𝜇
2.5 𝑥 0.2857 (
𝐼𝑚𝑎𝑥 = 1.7338𝐴
𝐼𝑚𝑖𝑛 =
𝑉𝑠
𝑉𝑠𝐷𝑇
−
2
(1 − 𝐷) 𝑅
2𝐿
= 0.98 −
1
)
130𝑘
2 𝑥 3.6443𝜇
2.5 𝑥 0.2857 (
𝐼𝑚𝑖𝑛 = 0.2262𝐴
viii)
The value of the output capacitor, out if the output voltage ripple is less than 4 %
𝑟=
𝐷
𝑅𝐶𝐹
0.04 =
0.2857
5 𝑥 𝐶 𝑥 130𝑘
𝐶 = 10.9885𝜇𝐹
DESIGN PARAMETERS
From our circuit design, we set our parameters as follows:



Input Voltage, Vin = 2.5V
Output Voltage, Vout = 3.5V
Voltage Ripple Factor, r = 0.04

Switching Frequency, fsw = 130kHz


Inductance, L = 3.6443𝜇𝐻
Resistance, R = 5Ω


Capacitance, C = 10.9885𝜇𝐹
Duty Ratio, D = 28.57%