Switching regulators exhibit negative input impedance, which is lowest at the minimum input voltage. An underdamped LC filter exhibits a high output impedance at the resonant frequency of the filter. For stability, the filter output impedance must be less than the absolute value of the converter input impedance.

Equation 20.

The passive EMI filter design steps are as follows:

• Calculate the required attenuation of the EMI filter at the switching frequency, where C_IN represents the existing capacitance at the input of the switching converter.
• Input filter inductor L_IN is usually selected between 1 μH and 10 μH, but it can be lower to reduce losses in a high-current design.
• Calculate input filter capacitor C_F.

Figure 9-2 Passive π-Stage EMI Filter for Buck Regulator

By calculating the first harmonic current from the Fourier series of the input current waveform and multiplying it by the input impedance (the impedance is defined by the existing input capacitor C_IN), a formula is derived to obtain the required attenuation as shown by Equation 21.

Equation 21.

where

• V_MAX is the allowed dBμV noise level for the applicable conducted EMI specification, for example CISPR 25 Class 5.
• C_IN is the existing input capacitance of the buck regulator.
• D_MAX is the maximum duty cycle.
• I_PEAK is the peak inductor current.

For filter design purposes, the current at the input can be modeled as a square-wave. Determine the passive EMI filter capacitance C_F from Equation 22.

Equation 22.

Adding an input filter to a switching regulator modifies the control-to-output transfer function. The output impedance of the filter must be sufficiently small so that the input filter does not significantly affect the loop gain of the buck converter. The impedance peaks at the filter resonant frequency. The resonant frequency of the passive filter is given by Equation 23.

Equation 23.

The purpose of R_D is to reduce the peak output impedance of the filter at the resonant frequency. Capacitor C_D blocks the DC component of the input voltage to avoid excessive power dissipation in R_D. Capacitor C_D must have lower impedance than R_D at the resonant frequency with a capacitance value greater than that of the input capacitor C_IN. This prevents C_IN from interfering with the cutoff frequency of the main filter. Added input damping is needed when the output impedance of the filter is high at the resonant frequency (Q of filter formed by L_IN and C_IN is too high). An electrolytic capacitor C_D can be used for input damping with a value given by Equation 24.

Equation 24.

Select the input damping resistor R_D using Equation 25.

Equation 25.