Answer :
i. The Buck-Boost converter circuit diagram is as follows:
```
+--------------+
| |
Vin+ ------->| |
| Switch |------> Vout+
Vin- ------->| |
| |
+------+------+
|
|
|
----- GND
```
ii. The duty cycle (d) is calculated using the formula:
d = Vout / Vin = 24 V / 48 V = 0.5
iii. The value of the inductor (L) can be calculated using the formula:
L = (Vin - Vout) * (1 - d) / (fs * Vout)
L = (48 V - 24 V) * (1 - 0.5) / (60 kHz * 24 V)
L = 24 V * 0.5 / (60 kHz * 24 V)
L = 0.5 / (60 kHz)
L ≈ 8.33 μH
iv. The maximum and minimum values of the inductor can be determined using the inductor ripple current (ΔI_L) and the maximum load current (I_Lmax) as follows:
ΔI_L = AV * (Vout / L)
ΔI_L = 0.2 V * (24 V / 8.33 μH)
ΔI_L ≈ 0.576 A
Lmax = (Vin - Vout) * (1 - d) / (fs * ΔI_L)
Lmax = (48 V - 24 V) * (1 - 0.5) / (60 kHz * 0.576 A)
Lmax ≈ 16.67 μH
Lmin = (Vin - Vout) * (1 - d) / (fs * I_Lmax)
Lmin = (48 V - 24 V) * (1 - 0.5) / (60 kHz * 12 A)
Lmin ≈ 0.167 μH
v. The maximum energy stored in the inductor (Emax) can be calculated using the formula:
Emax = 0.5 * Lmax * (ΔI_L^2)
Emax = 0.5 * 16.67 μH * (0.576 A)^2
Emax ≈ 2.364 μJ
vi. The waveform of the inductor current (i_L) during the switching on and switching off modes can be represented as follows:
During switching on:
i_L rises linearly with a slope of Vin / L
During switching off:
i_L decreases linearly with a slope of -Vout / L
The non-isolated Buck-Boost converter circuit designed can provide 24 V at 12 A from a 48 V battery. The calculated values for the duty cycle, inductor, maximum and minimum inductor values, maximum energy stored in the inductor, and the waveform of the inductor current during the switching on and switching off modes have been provided.
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