Input Filter Design for Switching Power Supplies: Written by Michele Sclocchi Michele.Sclocchinsc.com Application Engineer, National SemiconductorThe design of a switching power supply has always been considered a kind of magic and art, for all the engineers that design one for the first time. Fortunately, today the market offers different tools that help the designers. National Semiconductor was the first company to offer the “Simple Switcher” software, and an on-line simulation tool that allows the design and simulation of a switching power supply. New ultra-fast MOSFETs and synchronous high switching frequency PWM controllers allow the realization of high efficient and smaller switching power supply. All these advantages can be lost if the input filter is not properly designed. An oversized input filter can unnecessarily add cost, volume and compromise the final performance of the system. This document explains how to choose and design the optimal input filter for a switching power supply application.The input filter on a switching power supply has two primary functions. One is to prevent electromagnetic interference, generated by the switching source from reaching the power line and affecting other equipment. The second purpose of the input filter is to prevent high frequency voltage on the power line from passing through the output of the power supply. A passive L-C filter solution has the characteristic to achieve both filtering requirements. The goal for the input filter design should be to achieve the best compromise between total performance of the filter with size and cost. UNDAMPED L-C FILTER:The first simple passive filter solution is the undamped L-C passive filter shown in figure (1). Ideally a second order filter provides 12dB per octave of attenuation after the cutoff frequency f0, it has no gain before f0, and presents a peaking at the resonant frequency f0.Figure 1: Undamped LC filterOne of the critical factors involved in designing a second order filter is the attenuation characteristics at the corner frequency f0. The gain near the cutoff frequency could be very large, and amplify the noise at that frequency.To have a better understanding of the nature of the problem it is necessary to analyze the transfer function of the filter:The transfer function can be rewritten with the frequency expressed in radians:Ffilter1s ( )Voutfilters ( )Vinfilters ( )=11sL RloadL Cs2f012 L CCutoff frequency Hz (resonance frequency)1001103110411054030201001020Second Order Input filterFrequency, HzMagnitude, dB30.11120.707Figure 2 : Transfer Function of L-C Filter for differents damping factorsThe damping factor describes the gain at the corner frequency. For the two poles are complex, and the imaginary part gives the peak behavior at the resonant frequency. As the damping factor becomes smaller, the gain at the corner frequency becomes larger, the ideal limit for zero damping would be infinite gain, but the internal resistance of the real components limits the maximum gain. With a damping factor equal to one the imaginary component is null and there is no peaking. A poor damping factor on the input filter design could have other side effects on the final performance of the system. It can influence the transfer function of the feedback control loop, and cause some oscillations at the output of the power supply. The Middlebrooks extra element theorem (paper 2), explains that the input filter does not significantly modify the converter loop gain if the output impedance curve of the input filter is far below the input impedance curve of the converter. In other words to avoid oscillations it is important to keep the peak output impedance of the filter below the input impedance of the converter. (See figure 3) On the design point of view, a good compromise between size of the filter and performance is obtained with a minimum damping factor of 1/, which provides a 3 dB attenuation at the corner frequency, and a favorable control over the stability of the final control system.The transfer function presents two negative poles at: 01Ffilter1 11L C2j LRload=11j 2 0202sj 01L CCutoff frequency in radiantL2 RL CDamping factor (zeta)1001103110411050.010.1110100ImpedanceFrequency, HzOhmPower supply input impedanceFilter output impedanceFigure 3 : Output impedance of the input filter, and input impedance of the switching power supply: the two curves should be well separated. PARALLEL DAMPED FILTER:In most of the cases an undamped second order filter like that shown in fig. 1 does not easily meet the damping requirements, thus, a damped version is preferred:Figure 4 : Parallel damped filterFigure 4 shows a damped filter made with a resistor Rd in series with a capacitor Cd, all connected in parallel with the filters capacitor Cf. The purpose of resistor Rd is to reduce the output peak impedance of the f