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Answer :
Here's a comprehensive approach incorporating step-by-step calculations and derivations:
1. Converter Selection and Mode Analysis:
Since the desired output voltage (-28V) is negative and has a larger magnitude than the input voltage (100V), a non-inverting buck-boost converter is the most suitable topology.
2. Key Design Parameters:
- Input voltage (Vin) = 100 V
- Output voltage (Vo) = -28 V (negative due to non-inverting buck-boost)
- Load resistance (R) = 10 Ω
- Output voltage ripple (ΔVo) ≤ 0.5% of Vo (0.005 * -28 V) = 0.14 V
3. Duty Cycle (D) Calculation:
In a non-inverting buck-boost converter, the output voltage relates to the input voltage and duty cycle (D) through the following equation:
Vo = - Vin * D / (1 - D)
We need to solve for D:
D = (Vo + Vin) / (Vo - Vin) = (-28 V + 100 V) / (-28 V - 100 V) ≈ 0.778
4. Inductance (L) Calculation:
To minimize output voltage ripple, we can use the following equation for the minimum inductance:
L ≥ (Vin * D * (1 - D)) / (ΔVo * f)
where f is the switching frequency. We'll choose a common switching frequency (f) of 50 kHz for this design.
L ≥ (100 V * 0.778 * (1 - 0.778)) / (0.14 V * 50 kHz) ≈ 1.1 mH
5. Capacitor (C) Selection:
The output capacitor (C) value is selected based on the allowable ripple current (ΔIL). A larger capacitance reduces ripple. We can estimate ΔIL using the following equation:
ΔIL ≈ (Vin * D) / (f * L) ≈ (100 V * 0.778) / (50 kHz * 1.1 mH) ≈ 14.1 A
Assuming a desired ripple current ratio (ΔIL / Iout) of 10% (typical value), where Iout is the output current:
ΔIL / Iout = 0.1
Iout = Vin / R = 100 V / 10 Ω = 10 A
Therefore, ΔIL ≈ 1 A
Using the formula for capacitor ripple voltage (ΔVc) and assuming a desired ΔVc of 10 mV (a small value relative to ΔVo):
ΔVc = (ΔIL * L) / (f * C) = 10 mV
C ≥ (ΔIL * L) / (f * ΔVc) ≈ (1 A * 1.1 mH) / (50 kHz * 10 mV) ≈ 22 µF
We can choose a standard value slightly higher, such as C = 33 µF.
6. Component Selection:
- Inductor (L): Use a 1.2 mH or higher inductor with a current rating exceeding the maximum load current (Iout = 10 A). Consider core material, size, and temperature limitations.
- Capacitor (C): Use a 33 µF or higher electrolytic capacitor with a voltage rating exceeding the output voltage magnitude (|Vo| = 28 V). Consider voltage ripple and temperature specifications.
- Switch (MOSFET): Select an N-channel MOSFET with a voltage rating exceeding the input voltage (Vin = 100 V) and a current rating exceeding the maximum load current (Iout = 10 A). Choose a MOSFET with low on-resistance (RDS(on)) for better efficiency. Consider switching speed and gate drive requirements.
- Diode (Schottky): Use a Schottky diode with a voltage rating exceeding the output voltage magnitude (|Vo| = 28 V) and a current rating exceeding the maximum load current (Iout = 10 A). Consider forward voltage drop and switching speed.
7. Additional Considerations:
- Feedback Loop: Implement a feedback loop using a controller IC (e.g., TL431) and optocoupler to regulate the output voltage and maintain stability. This ensures the output voltage stays at -28V even with input voltage variations.
- Heat Dissipation: Calculate power dissipation in each component (MOSFET, diode) and choose appropriate heat sinks to prevent overheating.
- Layout:
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