Switching regulators exhibit a negative input impedance characteristic, which is lowest at the minimum input voltage and full load. An underdamped LC filter exhibits a high output impedance at the resonant frequency of the filter. For stability, the filter output impedance, approximated by the characteristic impedance of the LC components, must be less than the absolute value of the regulator input impedance.

Equation 18.

The 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 regulator.
• The input filter inductor L_IN is usually selected between 1μH and 6.8μH, but can be lower to reduce losses in a high-current design.
• Calculate input filter capacitor C_F.

Figure 8-2 Buck Regulator With π-Stage EMI Filter

By calculating the first harmonic current from the Fourier series of the input current waveform and multiplying by the input impedance (the impedance is defined by the existing input capacitor C_IN), Equation 19 presents an expression to obtain the required attenuation.

Equation 19.

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 operating duty cycle (at minimum input voltage)
• I_L(PEAK) is the peak inductor current

For filter design purposes, the current at the input can be modeled as a square-wave. Determine the EMI filter capacitance C_F from Equation 20.

Equation 20.

Adding an input filter to a switching regulator as shown in Figure 8-2 modifies the control-to-output transfer function. The output impedance of the filter must be sufficiently low such that the input filter does not significantly affect the loop gain of the buck regulator. The impedance peaks at the filter resonant frequency. Use Equation 21 to calculate the resonant frequency of the filter.

Equation 21.

The purpose of R_D in Figure 8-2 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 requirement prevents C_IN from interfering with the cutoff frequency of the main filter. Added damping is needed when the output impedance of the filter is high at the resonant frequency (Q of the filter formed by L_IN and C_IN is too high). Use an electrolytic capacitor C_D for parallel damping with a value given by Equation 22.

Equation 22.

Use Equation 23 to select the damping resistor R_D.

Equation 23.