3.1 Design Steps

Select C_FF: In the simplified approach, the DC blocking capacitor C_INJ is first selected as a standard practical value that satisfies most operating conditions. For this design example: C_INJ = 100 nF.

Select C_FF: Next, the feed-forward capacitor C_FF is selected in the typical range of 1 nF to 10 nF. This value generally provides adequate ripple integration and helps maintain proper loop behavior. For this example: C_FF = 4.7 nF.

Select ΔV_FB: The feedback ripple amplitude is chosen within the recommended range of 40 mV to 200 mV, unless otherwise specified in the datasheet. Here, a practical target is selected: ΔV_FB = 100 mV.

Calculate R_INJ: Using the selected values of C_FF and ΔV_FB, the ripple injection resistor is calculated using:

Equation 3-1.

R_{INJ} = \frac{V_{O} \cdot (1 - D)}{∆ V_{FB} \cdot C_{FF} \cdot F_{SW}}

For this design: R_INJ = 36 kΩ

Calculate F_C: The crossover frequency is then estimated using:

Equation 3-2.

F_{C} = \frac{V_{O} \cdot (1 - D)}{2 πLC ∆ V_{FB} F_{SW}}

The calculated crossover frequency is: F_C = 26 kHz.

Select R1 and Calculate R2: R1 is typically selected in the kΩ range to minimize the feedback divider current while maintaining good noise immunity. If R1 is too large, it may allow noise to be introduced into the voltage feedback loop. If R1 is too small, it will decrease the efficiency of the power supply, especially at light loads. Once R1 is selected, R2 can be calculated using equation . So, considering R1 = 10k, the result is R2 = 1.36k for V_OUT = 5V.

Verify Stability Criteria: Finally, the selected components are checked against the required stability criteria. First, the impedance of C_FF at the switching frequency must be much lower than R1‖R2:

$\frac{1}{2 {πC}_{FF} F_{SW}} < R 1 ∥ R 2 129 Ω ≪ 1.15 kΩ$

Next, the time-constant criterion must be satisfied. The ripple injection time constants should be significantly greater than the total switching period to ensure that the injected feedback ripple remains approximately linear over each switching cycle.

R_INJC_INJ > R1C_FF > T_SW

3.6 ms > 47 μs > 3.8 μs

Finally, the crossover frequency must remain below one-fifth of the switching frequency:

$F_{C} < \frac{F_{SW}}{5}$

26 kHz < 53 kHz

Since all three conditions are satisfied, the simplified ACOT control-loop design is complete. This approach provides a quick and practical method for selecting ripple injection components, while still ensuring that the loop meets the basic stability requirements.