Input Filter Design for Switching Power Supplies1

hjp · 发表于 2007-9-27 13:33:27

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Input Filter Design for Switching Power Supplies:<h1 style="MARGIN: 0cm 0cm 0pt">Written by Michele Sclocchi</h1>Michele.Sclocchi@nsc.comApplication Engineer, National Semiconductor The 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.<h2 style="MARGIN: 0cm 0cm 0pt; LINE-HEIGHT: 12pt"><wrapblock><shapetype id="_x0000_t75" stroked="f" filled="f" path="m@4@5l@4@11@9@11@9@5xe" o:preferrelative="t" o:spt="75" coordsize="21600,21600"><stroke joinstyle="miter" /><formulas><f eqn="if lineDrawn pixelLineWidth 0" /><f eqn="sum @0 1 0" /><f eqn="sum 0 0 @1" /><f eqn="prod @2 1 2" /><f eqn="prod @3 21600 pixelWidth" /><f eqn="prod @3 21600 pixelHeight" /><f eqn="sum @0 0 1" /><f eqn="prod @6 1 2" /><f eqn="prod @7 21600 pixelWidth" /><f eqn="sum @8 21600 0" /><f eqn="prod @7 21600 pixelHeight" /><f eqn="sum @10 21600 0" /></formulas><path o:connecttype="rect" gradientshapeok="t" o:extrusionok="f" /><lock aspectratio="t" v:ext="edit" /></shapetype><shape id="_x0000_s1028" style="MARGIN-TOP: 8.35pt; Z-INDEX: 3; LEFT: 0px; MARGIN-LEFT: 3.6pt; WIDTH: 301.2pt; POSITION: absolute; HEIGHT: 36pt; TEXT-ALIGN: left" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C

OCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image001.wmz" /><wrap type="topAndBottom" /></shape><shape id="_x0000_s1037" style="MARGIN-TOP: 50.15pt; Z-INDEX: 12; LEFT: 0px; MARGIN-LEFT: 3.6pt; WIDTH: 402.75pt; POSITION: absolute; HEIGHT: 131.55pt; TEXT-ALIGN: left" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C

OCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image002.png" /><wrap type="topAndBottom" side="right" /></shape></wrapblock> Figure 1: Undamped LC filter</h2><wrapblock><shape id="_x0000_s1035" style="MARGIN-TOP: 6.6pt; Z-INDEX: 10; MARGIN-LEFT: -3.6pt; WIDTH: 397.8pt; POSITION: absolute; HEIGHT: 216.6pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C

OCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image004.wmz" /><wrap type="topAndBottom" side="right" /></shape></wrapblock>  One of the critical factors involved in designing a second order filter is the attenuation<s> </s>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:<wrapblock><shape id="_x0000_s1027" style="MARGIN-TOP: 13.8pt; Z-INDEX: 2; MARGIN-LEFT: 4.8pt; WIDTH: 202.2pt; POSITION: absolute; HEIGHT: 49.2pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image006.wmz" /><wrap type="topAndBottom" /></shape></wrapblock> The transfer function can be rewritten with the frequency expressed in radians:<wrapblock><shape id="_x0000_s1029" style="MARGIN-TOP: 139.8pt; Z-INDEX: 4; MARGIN-LEFT: 1.2pt; WIDTH: 331.8pt; POSITION: absolute; HEIGHT: 19.8pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image008.wmz" /><wrap type="topAndBottom" side="right" /></shape><shape id="_x0000_s1030" style="MARGIN-TOP: 0px; Z-INDEX: 5; MARGIN-LEFT: 0px; WIDTH: 253.8pt; POSITION: absolute; HEIGHT: 135pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image009.wmz" /><wrap type="topAndBottom" side="right" /></shape></wrapblock> The damping factor <span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">z describes the gain at the corner frequency.For <span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">z<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">><span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">1 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 Middlebrook’s 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/<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">Ö<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">2, which provides a 3 dB attenuation at the corner frequency, and a favorable control over the stability of the final control system. <wrapblock><shape id="_x0000_s1036" style="MARGIN-TOP: 0px; Z-INDEX: 11; MARGIN-LEFT: 0px; WIDTH: 409.8pt; POSITION: absolute; HEIGHT: 232.2pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image011.wmz" /><wrap type="topAndBottom" side="right" /></shape></wrapblock>

ARALLEL 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: <h2 style="MARGIN: 0cm 0cm 0pt"><wrapblock><shape id="_x0000_s1038" style="MARGIN-TOP: 0px; Z-INDEX: 13; LEFT: 0px; MARGIN-LEFT: 0px; WIDTH: 348.75pt; POSITION: absolute; HEIGHT: 120.75pt; TEXT-ALIGN: left" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image013.png" /><wrap type="topAndBottom" side="right" /></shape></wrapblock> Figure 4 : Parallel damped filter</h2> Figure 4 shows a damped filter made with a resistor Rd in series with a capacitor Cd, all connected in parallel with the filter’s capacitor Cf. The purpose of resistor Rd is to reduce the output peak impedance of the filter at the cutoff frequency. The capacitor Cd blocks the dc component of the input voltage, and  avoids the power dissipation on Rd.The capacitor Cd should have lower impedance than Rd at the resonant frequency, and be a bigger value than the filter capacitor, to not effect the cutoff point of the main R-L filter.The output impedance of the filter can be calculated from the parallel of the three block impedancesZ1, Z2, and Z3: <wrapblock><shape id="_x0000_s1026" style="MARGIN-TOP: 0px; Z-INDEX: 1; MARGIN-LEFT: 0px; WIDTH: 355.8pt; POSITION: absolute; HEIGHT: 50.4pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image015.wmz" /><wrap type="topAndBottom" /></shape></wrapblock> The transfer function is:<wrapblock><shape id="_x0000_s1033" style="MARGIN-TOP: 0px; Z-INDEX: 8; MARGIN-LEFT: 0px; WIDTH: 301.8pt; POSITION: absolute; HEIGHT: 38.4pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image017.wmz" /><wrap type="topAndBottom" side="right" /></shape></wrapblock> Where Zeq2.3 is Z2 parallel with Z3. The transfer function presents a zero and three poles, where the zero and the first pole fall close to each other at frequency <span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">w<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">»1/RdCd. The other two dominant poles fall at the cutoff frequency, <span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">w<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">o=<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">1<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">/<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">ÖLC. Without compromising the results, the first pole and the zero can be ignored, and the formula can be approximated to a second order one: <wrapblock><shape id="_x0000_s1034" style="MARGIN-TOP: 0px; Z-INDEX: 9; MARGIN-LEFT: 0px; WIDTH: 5in; POSITION: absolute; HEIGHT: 113.4pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image019.wmz" /><wrap type="topAndBottom" side="right" /></shape></wrapblock> (for frequencies higher than <span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">w<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">»1/RdCd, the term  (1+RdCd s)<span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">» RdCd s )The approximated formula for the parallel damped filter is identical to the transfer function of the undamped filter; the only difference being the damping factor <span lang="EN-US" style="FONT-SIZE: 12pt; FONT-FAMILY: Symbol; mso-bidi-font-size: 10.0pt; mso-ascii-font-family: "Times New Roman"; mso-hansi-font-family: "Times New Roman"; mso-char-type: symbol; mso-symbol-font-family: Symbol">z is calculated with the Rd resistance.<wrapblock><shape id="_x0000_s1031" style="MARGIN-TOP: 0px; Z-INDEX: 6; MARGIN-LEFT: 0px; WIDTH: 100.5pt; POSITION: absolute; HEIGHT: 33pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image021.wmz" /><wrap type="topAndBottom" side="right" /></shape></wrapblock> It is demonstrated that for a parallel damped filter the peaking is minimized with a damping factor equal to:<wrapblock><shape id="_x0000_s1032" style="MARGIN-TOP: 22.2pt; Z-INDEX: 7; MARGIN-LEFT: 3.6pt; WIDTH: 114.75pt; POSITION: absolute; HEIGHT: 34.5pt" o:allowincell="f" type="#_x0000_t75"><imagedata src="file:///C:DOCUME~1HEJUNP~1LOCALS~1Tempmsohtml1clip_image023.wmz" /><wrap type="topAndBottom" side="right" /></shape></wrapblock>

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Input Filter Design for Switching Power Supplies1

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