Gain and Output Impedance are two important parameters that are considered for designing the input filter. The maximum impedance of the whole circuit needs to remain under the target impedance limit of the converter. This target impedance Z_target for the DC/DC converter can be calculated Equation 1.

In this equation, V_dd is the supply voltage of the power rail, I_max is the worst case maximum current from the chip and ΔV is the maximum allowed variation in the voltage level of power rail. In the target impedance calculation, transient current is used because the slope of this current can trigger the high resonant frequencies of PDN impedance, resulting in significant output voltage variations.

The design steps to select the inductor and capacitor values for the input filter are discussed further. Gain value is calculated as the first step in designing the input filter. The maximum input current amplitude I_{in_max} without a filter and the desired amplitude of input current I_req are important to calculate the gain of the filter. The maximum input ripple current is calculated with Equation 2. The operating conditions are input voltage V_in of 5-V, output voltage V_o of 3.3-V, switching frequency f_sw of 2.25 MHz and maximum load current I_o of 1-A.

In Equation 2, I_o is the maximum load current, D is the duty cycle, V_o is the output voltage and L is the inductor value. Then gain can be calculated with Equation 3 with desired amplitude of input current I of 1 mA and calculated maximum input ripple current value I_{in_max}.

In next step, cut-off frequency f_c/o can be determined based on the gain and switching frequency f_sw with Equation 4.

Further, the third step involves calculating the input impedance of the converter. All of these values are derived from the efficiency vs. output current graphs plotted in the TPS6281x-Q1 2.75-V to 6-V Adjustable-Frequency Step-Down Converter data sheet for the operating conditions of the device.

The output impedance Z_out,f of the filter needs to be less than the input impedance Z_in,c of the converter for stability of an overall system. One-eighth of input impedance of converter seems reasonable limit for output impedance of filter.

After computing all the data in above equations, it gives gain value of 0.030, crossover frequency of 69.5 kHz and output impedance of filter is 1.2 Ω. Keeping these values as base parameters, the values of L_f,in and C_f,in are chosen. The AC impedance equations can help to give the minimum filter capacitance and maximum filter inductor value to maintain the calculated impedance limit.

After inserting the maximum impedance value and cut-off frequency of the filter in Equation 7, it gives maximum filter inductance of 2.7 µH and minimum filter capacitance of 1.9 µF. The filter components used for further analysis from the available range are inductor L_f,in value of 530 nH and a capacitor C_f,in value of 10 µF to check its impact on the stability of the overall step-down converter.