Known Parameters:
Input voltage: 12V Vin
Duty cycle: don
Output voltage: 36V Vout
Output power rating: 150W Pmon
Maximum output power: 200W Pmax
Minimum output power: 50W Pmin
Boost diode voltage drop: 1V Vd
Operating frequency: 100kHz f
Efficiency set to: 88% η
1. Duty Cycle CalculationDuring steady-state operation, the increase in inductor current during the on-time is equal to the decrease during the off-time. This relationship can be expressed as:
(Vi * don) / (f * L) = [(Vout + Vd - Vi) * (1 - don)] / (f * L) (1)
Simplifying this equation gives:
Don = (Vout + Vd - Vi) / (Vout + Vd) (2)
Substituting the known values, we get:
Don ≈ 0.6756756757
We round it to Don = 0.68 for practical purposes.
2. Inductor Value CalculationTo ensure that the inductor current rises to the output current level during each switching cycle, the inductance value is calculated using:
L = (Vin² * don * Vout * η) / [2 * f * Pout * (Vout - Vin * η)] (3)
Where L is in henries (H). When the output power is at its minimum (Pout = 50W), the calculation yields:
L ≈ 12.1938μH
We choose L = 12μH for the design.
The ripple current (dIL) is calculated as:
dIL = Vi * Ton / L
This ripple is set to 20% of the average inductor current (Iin), where:
Iin = Vo * Io / Vi
IL_avg = Iin
IL_peak = 1.1 * Iin
IL_rms = IL_avg * sqrt(1 + (0.22 / 12))
The inductor is chosen such that the ripple current is 20% of the average, which helps in minimizing losses and improving efficiency.
3. Schottky Diode SelectionThe peak current through the diode is:
Id_peak = 1.1 * Iin
The reverse voltage rating of the diode must be at least equal to the output voltage:
Vrd = Vout
This ensures the diode can handle the voltage when the switch is off.
4. Switching Transistor SelectionThe peak current through the switch is:
Isw_peak = 1.1 * Iin
The voltage across the switch during turn-off is:
Vsw = Vout
The transistor must be able to withstand this voltage and handle the peak current.
5. Capacitor SelectionThe RMS ripple current for the input capacitor is:
Icin_rms = dIL / 120.5
The RMS ripple current for the output capacitor is:
Ico_rms = sqrt(Io² * D + (Iin - Io)² * (1 - D))
Capacitors are selected based on their voltage rating, ripple current capability, and capacitance value to ensure stable output performance.
6. Core, Turns, and Air Gap Design1) Using a magnetic core PQ3230 with an effective area (Ae) of 161 mm² and a maximum flux density (Bmax) of 0.23 T,
2) The number of turns (N) is calculated as:
N = (L * Ipmax) / (Bmax * Ae) (4)
Where L is in microhenries, Ae in mm², Bmax in tesla, and Ipmax is the peak current at maximum output power.
3) At maximum power (Pmax), the peak current (Ipmax) is:
Ipmax = (2 * Pout * L * f + Vin² * don * η) / (2 * Vin * f * L * η) (5)
Substituting the values, we find:
Ipmax ≈ 22.34A
4) The inductor current during the on-time (Ion) is given by:
Ion = (2 * Pout - Ip * Vin * η) / (Vin * η) (6)
At Pmin, the calculation confirms that the inductor current matches the output current, validating the previous equations.
5) Using N = 7.5 turns and L = 12μH, the saturation current (Is) of the core is:
Is = (N * Bs * Ae) / L (7)
With Bs = 0.36T at 100°C, we get:
Is ≈ 36.225A
6) The air gap (lg) is calculated using:
lg = 4π * Ae * [(N² / (Lp * 1000)) - 1 / AL] (8)
With AL = 5140 nH/N², the result is:
lg ≈ 0.9mm
7. Wire Diameter Selection1) The maximum RMS inductor current under full load is:
Imax-rms = (Pmax * don) / (Vin * η) + Pmax / Vout (9)
Substituting the values, we get:
Imax-rms ≈ 18.43A
We round it to 18A for practical use.
2) For a current of 18A, the wire diameter is determined using a rule of thumb of 300 mils per ampere, resulting in a cross-sectional area of 3.48 mm².
3) A choice of 110 copper wires with a diameter of 0.2mm is suitable for this application.
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