Final answer:
To design the boost converter, you need to calculate the values of the inductance, capacitance, and switching frequency. The inductance should be 0.9H, the switching frequency should be approximately 46kHz, and the capacitance should be 34μF.
Step-by-step explanation:
To design the boost converter, we need to determine the values of the inductance, capacitance, and switching frequency. Here are the steps:
- Calculate the duty cycle (D) using the formula: D = Vout / (Vout + Vin), where Vin is the input voltage (12V) and Vout is the desired output voltage (20V). In this case, the duty cycle is 20 / (20 + 12) = 0.625.
- Calculate the value of the inductor (L) using the formula: L = (Vin * (1 - D)) / (Iout * fs), where fs is the switching frequency. Given that the load current (Iout) is 0.5A, and the inductor current variation is no more than 25% (0.25 * Iout = 0.125A), the minimum value of the inductance is 0.9H.
- Choose the switching frequency (fs) based on the desired output voltage ripple. The output voltage ripple (ΔVout) is calculated using the formula: ΔVout = (L * Iout * fs) / (Vin - Vout), which should not exceed 2% of the output voltage. Let's assume a value of 1% for simplicity. Solving the equation, we find that fs is approximately 46kHz.
- Choose the value of the output capacitor (C) based on the desired output voltage ripple and the switching frequency. The capacitor should be able to supply the necessary charge during the on-time of the switch. The formula to determine the value of the capacitance is: C = (Iout * D) / (ΔVout * fs). Plugging in the values, we get C ≈ 34μF.
Therefore, to design the boost converter with an output voltage of 20V from a 12V source, a switching frequency of approximately 46kHz, an inductance of 0.9H, and a capacitance of 34μF is required.