Question

In a step-up converter, consider all the components to be ideal, Let Vd be 8−16 V, Vo =24 V (regulated), fs =20kHZ,P₀ ≥6 W.

Calculate the minimum inductance L required to keep the converter operation in continuous-conduction mode under all conditions.

Answer 1

The minimum inductance required for a step-up converter in continuous-conduction mode is 0.8mH.

Step-by-step explanation:

In a step-up converter, the input voltage Vd is usually lower than the output voltage Vo. To keep the converter operating in continuous-conduction mode, we need to ensure that the inductor current doesn't reach zero during each switching cycle.

The minimum inductance L required can be calculated using the formula:

L >= (Vo - Vd)/(fs * P₀)

Where Vd is the input voltage range, Vo is the output voltage, fs is the switching frequency, and P₀ is the minimum power requirement. Plugging in the given values, we get:

L >= (24 - 8)/(20kHz * 6W) = 0.8mH

Therefore, the minimum inductance required to keep the converter operation in continuous-conduction mode under all conditions is 0.8mH.

Answer 2

To calculate the minimum inductance required for a step-up converter to remain in continuous-conduction mode, one must use the relation involving output power, inductor current ripple, switching frequency, and inductance. While the exact numerical answer cannot be given without the current ripple value, the formula reveals the dependence of minimum inductance on these parameters.

Step-by-step explanation:

To calculate the minimum inductance L required to keep a step-up converter operating in continuous-conduction mode under all conditions, we need to apply the principles of power electronics. The relation between the output power, inductor current ripple, and other converter parameters is given by Po = (DeltaI)^2 * L * fs / 2, where Po is the output power, DeltaI is the ripple current, L is the inductance, and fs is the switching frequency. Knowing the minimum output power Po, the switching frequency fs, and assuming Vo is the output voltage, we use this formula to find the minimum inductance required to support this operation.

For continuous-conduction mode, the current ripple DeltaI can be estimated by DeltaI = Vd / (2 * L * fs), where Vd is the input voltage range. By substituting the given values into this formula and solving for L, we achieve the answer. Without the exact value of DeltaI, we cannot provide a numerical answer, but the process to determine L remains consistent.