The formulas to calculate the minimum output capacitance are:
Calculate \( T_{on} \):
\[ T_{on} = \frac{1}{f} \times D_{max} \]
Calculate \( I_{pk} \):
\[ I_{pk} = 2 \times \frac{I_o}{1 - D_{max}} \]
Calculate Minimum Output Capacitance \( C_{min} \):
\[ C_{min} = \frac{I_{pk} \times T_{on}}{V_{ripple}} \times 10^6 \, (\mu F) \]
Calculate ESR:
\[ ESR = \frac{65}{C_{min} \times 10^6} \, (\Omega) \]
Switching Frequency (f): The frequency at which the switch operates, measured in kHz.
Output Current (Io): The current delivered to the load, measured in amperes (A).
Maximum Duty Cycle (Dmax): The maximum duty cycle of the switch.
Output Ripple Voltage (Vripple): The acceptable peak-to-peak ripple voltage at the output, measured in millivolts (mV).
Ton: The on-time of the switch, measured in microseconds (µs).
Ipk: The peak current, measured in amperes (A).
Cmin: The minimum output capacitance, measured in microfarads (µF).
ESR: Equivalent series resistance, measured in milliohms (mΩ).
Example: Calculate the minimum output capacitance
Step 1: Calculate \( T_{on} \):
\[ T_{on} = \frac{1}{60,000} \times 0.457 = 7.62 \, \mu s \]
Step 2: Calculate \( I_{pk} \):
\[ I_{pk} = 2 \times \frac{1}{1 - 0.457} = 3.68 \, A \]
Step 3: Calculate \( C_{min} \):
\[ C_{min} = \frac{3.68 \times 7.62 \times 10^{-6}}{0.12} \times 10^6 = 233.68 \, \mu F \]
Step 4: Calculate ESR:
\[ ESR = \frac{65}{233.68 \times 10^6} \times 10^3 = 0.00028 \ = 0.28 \, \Omega \]