[YU71A] Yu, Y., and J. J. Biess, *Some Design Aspects Concerning Input Filters For DC-DC
Converters*, IEEE Power Conditioning Conference - 1971 Record, pp.
66-76.

Various DC-DC converter input filter requirements as applied in spacecraft power processing equipment, are reviewed with respect to the spacecraft, its power source and filter loads. The conflicting implications arising from the requirements are noted. A filter configuration capable of providing a satisfactory overall compromise is presented. Various design aspects for converter input filters are analyzed. These include minimum weight toroid inductor design, the possibility non-linear oscillation developing through the interaction of an input filter and a negative impedance regulator and problems in using paralleled capacitors to supply switching regulator loads. (AUTHOR ABSTRACT) Electric Power Processing Department, TRW Systems, Redondo Beach, CA. 11 pages, 7 figures, 28 equations, 7 references.

[BIES71A] Biess, J. J., and Y. Yu, *A Two-Stage Filter with Nondissipatively Controlled Damping*,
presented at International Magnetics Conference in Denver, Colorado, April
1971. Digest in IEEE Transactions on Magnetics, September 1971, pp.
584-585.

Proposes a two-stage LC input filter for switching-mode regulators with a damping resistor in series with the first capacitor to control resonant peaking. Compares the advantages with two commonly used filters, an LC filter with no damping and an LC filter with resistive damping in series with the capacitors. The digest does not contain the guidelines for filter selection, the transfer function, the numerical example, or the computer simulation verifying the performance. (JF) Electrical Power Processing Department, TRW Systems, Inc., Redondo Beach, CA. The digest contains 2 pages, 2 figures, no equations, and no references.

[SOKA73A] Sokal, N. O., *System Oscillations From Negative Input Resistance at Power Input
Port of Switching-Mode Regulator, Amplifier, DC/DC Converter, or DC/AC
Inverter*, IEEE Power Electronics Specialists Conference - 1973 Record, pp.
138-140. PESC

A switching regulator or a switching-mode amplifier, dc/dc converter, or dc/ac inverter can have a negative dynamic input resistance at the dc power input port. Frequently an LC decoupling filter is inserted in the dc power line between this equipment and the prime dc power source, to keep switching transients off the dc power buss. The negative input resistance of the equipment can exceed the positive output resistance of the LC filter and the power source. Then the system as a whole can oscillate. This oscillation can cause malfunction of the negative-resistance equipment or of other types of equipment which may also be operated from the prime source. The conditions required for oscillation to take place are defined, and ways are shown to prevent the oscillation. The predicted oscillations have been observed experimentally. (AUTHOR ABSTRACT) Design Automation, Inc., 809 Massachusetts Avenue, Lexington, MA 02173. 3 pages, 2 figures, 8 equations, 1 reference.

[MIDD75A] Middlebrook, R. D., *A Continuous Model For the Tapped-Inductor Boost Converter*,
IEEE Power Electronics Specialists Conference - 1975 Record, pp. 63-79. PESC
Republished in Advances in Switch-Mode Power
Conversion, Volumes I and II, 2nd edition, TESLAco, 1983, paper 5, pp.
55-71.

A continuous, low-frequency, small-signal averaged model for the tapped-inductor boost converter with input filter is developed and experimentally verified, from which the dc transfer function and the small-signal line input and duty ratio input describing functions can easily be derived. A new effect due to storage-time modulation in the transistor switch is shown to explain observed excess filter damping resistance without associated loss in conversion efficiency. The presence of an input filter can cause a severe disturbance, even a null, in the control duty ratio describing function, with consequent potential performance difficulties in a converter regulator. (AUTHOR ABSTRACT) California Institute of Technology, Pasadena, CA 91125. 17 pages, 28 figures, 51 equations, 3 references.

[MIDD76C] Middlebrook, R. D., *Input Filter Considerations in Design and Application of
Switching Regulators*, IEEE Industry Applications Society Annual Meeting,
October 11-14, 1976, Chicago, IL. IAS Republished in Advances in Switch-Mode Power Conversion,
Volumes I and II, 2nd edition, TESLAco, 1983, paper 7, pp. 91-107.

Switching-mode regulators have a negative input resistance at low frequencies, and can become unstable by addition of post facto line input filters. This problem is treated in a general manner based on a small-signal linear model that accommodates all forms of switching converter, and which predicts the proper change of input impedance from negative at low frequencies to positive at frequencies beyond regulator loop gain crossover. Preferably, a suitable input filter should be incorporated in original regulator design; criteria are developed for input filter resonant frequency and Q that ensure not only system stability but also specified perturbations of the important regulator properties, loop gain, output impedance, and line rejection. If, on the other hand, a line filter is to be added to an existing regulator "black box," measurements of input impedance lead to criteria for an input filter that will ensure stability, but for which only incomplete prediction can be made of the resulting regulator properties. 17 pages, 29 figures, 1 table, 32 equations, and 10 references. (AUTHOR ABSTRACT) California Institute of Technology, Pasadena, CA.

[MIDD78C] Middlebrook, R. D., *Design Techniques for Preventing Input-Filter Oscillations in
Switched-Mode Regulators*, Proceedings of PowerCon 5, the Fifth National
Solid State Power Conversion Conference, May 4-6, 1978, San Francisco, CA.
Republished in Advances in Switch-Mode Power
Conversion, Volumes I and II, 2nd edition, TESLAco, 1983, paper 10, pp.
153-168.

The development of a canonical model of a switching-mode dc-to-dc converter is reviewed. The model permits design criteria to be developed for stability and performance degradation analysis of a switching-mode converter with a line filter. New results are introduced to show how optimal damping of the input filter and of the converter effective filter can be achieved with the smallest value of capacitance used to couple the shunt damping resistance. California Institute of Technology, Pasadena, CA.16 pages, 16 figures, 1 table, and 38 equations.

[PHEL79A] Phelps, T. K., and W. S. Tate,
*Optimizing Passive Input Filter Design*, Proceedings of
the Sixth National Solid-State Power Conversion Conference, (PowerCon 6), Miami
Beach, FL, May 1979.

Nine commonly used one and two section LC filters are examined with various popular damping arrangements. Parameters considered for optimization include peaking, output impedance, weight, volume, and cost. Energy storage and EMI requirements are considered as the given requirements. Hughes Aircraft Company, Torrance, CA. 10 pages, 14 figures, 3 tables, 1 reference.

[KELK82A] Kelkar, S. S., and F. C. Lee,
*A Novel Input Filter Compensation Scheme for Switching
Regulators*, IEEE Power Electronics Specialists Conference - 1982 Record,
pp. 260-271. PESC

The interaction between the input filter and the control loop of switching regulators often results in detrimental effects, such as loop instability, degradation of transient response and audio-susceptibility, etc. The concept of pole-zero cancellation is employed to mitigate some of these detrimental effects and is implemented using a novel feedforward loop, in addition to existing feedback loops of a buck regulator. Experimental results are presented which show excellent correlation with theory. (AUTHOR ABSTRACT) Department of Electrical Engineering Virginia Polytechnic Institute and State University. 12 pages, 17 figures, 49 equations, 8 references.

MIL-HDBK-241B,*Military Handbook, Design Guide For Electromagnetic Interference (EMI) Reduction in Power Supplies*, 30 September 1983.

**SCOPE**. This handbook offers guidance to
power supply designers in techniques which have been found effective in
reducing conducted and radiated interference generated by power supplies. It is
a compilation of information from library sources, pertinent military
laboratory programs including contracts to universities and industry, and
practical fixes derived from the experience of engineers. Topics related to
power supplies include selection criteria, power conversion approaches,
off-line switching-mode power supplies, potential problems, and dc-to-dc
converter topologies.

**TOPICS**. Topics related to EMI associated
with ac to dc rectification include basic rectifier action, rise/fall time
effects, problems with excessive harmonics, and standard solutions. Topics
related to EMI from switching-mode conversion include powerline conducted
differential-mode noise, ripple on output leads, suppression of internally
radiated noise, and future low-noise designs. Topics related to components and
circuit design include semiconductor switching devices, capacitors, inductors,
transformers, ferrites and ferrite beads, conductors, resistors, mechanical
contact protection, additional filter considerations, shielding, and
reliability and EMI. Appendix B discusses the "Middlebrook Criteria"
for preventing input-filter oscillations in switching regulators. 174
pages.

[MIDD85B] Middlebrook, R. D., *Power Filter Damping*, Proceedings of the Power Electronics
Design Conference, 1985, pp. 96-105. PEDC

Every switched-mode converter incorporates a low-pass LC filter whose design involves an inherent conflict between the requirement for a nonpeaked response (high damping) and the requirement for high efficiency (low damping). The desired lossless damping can be achieved by a parallel dc-blocked resistance. It is shown that an infinite blocking capacitance is not desirable even ideally, but that there is a range of values that give optimum performance. Criteria for choice of the damping resistance and blocking capacitance values are given, and a buck regulator is used as a design example. (AUTHOR ABSTRACT) California Institute of Technology. 10 pages, 16 figures, no tables, 23 equations, 7 references.

[ERIC90A] Erich, Sandra Y., and William
M. Polivka, *Input Filter Design Criteria for
Current-Programmed Regulators*, IEEE Applied Power Electronics Conference,
1990, pp. 781-791. (Republished in IEEE Transactions on Power Electronics, Vol.
7, No. 1, January 1992. pp. 143-151 with some clarifications.) APEC

The design of input filters for switched-mode regulators is discussed, and it is shown that the filter's effect on the power system depends on the control method used in the regulator's dc-dc converter. Design inequalities are reviewed for duty-ratio programmed converters, and specific expressions are presented for current-programmed converters. Application examples to practical regulator circuits are given where current-programmed criteria, computer-driven measurement tools, and numerical evaluations of analytic expressions are used to design input filters from laboratory data or from specified "black box" parameters. (AUTHOR ABSTRACT)

An example of a current-programmed buck converter shows analytically and experimentally that the onset of instability caused by violating the design criteria for adding an input filter is not reflected in the normal Bode plot of voltage gain, which appears to have adequate gain and phase margin at the onset of instability as measured by nearly sustained oscillation of the input current due to a transient load change. The onset of instability is also not reflected in the regulator output impedance measurements. The onset of stability would be reflected in the Bode plot of total gain, but this requires special digital modulation techniques (not usually used by most designers). The authors recommend making a Nyquist plot as part of the filter design process by measuring the regulator input impedance Zi and the filter output impedance Zs and plotting the minor loop gain T1=Zs/Zi on a Nyquist plot, which will indicate the instability risk. This paper contains all the equations necessary for analysis of both duty-ratio and current programmed control. Note that figures 1 and 2 are reversed in the paper. (JF ABSTRACT)IBM Federal Sector Division, Owego, NY. 11 pages, 12 figures, 1 table, 22 equations, 8 references. [KP]

[KOHU90A] Kohut, Charles R., *Input Filter Design Criteria for Switching Regulators Using
Current Mode Control*, IEEE Applied Power Electronics Conference, 1990, pp.
779. APEC

Paper not available at time of printing. Partially revised and published in IEEE Transactions on Power Electronics, Vol. 7, No. 3, July 1992. pp. 469-479.

[JANG91B] Jang, Yungtaek, and Robert E.
Erickson, *Physical Origins of Input Filter Oscillations in
Current Programmed Converters*, APEC'91, IEEE Applied Power Electronics
Conference, 1991, pp. 439.

Paper not available at time of printing. See Jang 1992 A.

[ERIC92A] Erich, Sandra Y., and William
M. Polivka, *Input Filter Design Criteria for
Current-Programmed Regulators*, IEEE Transactions on Power Electronics,
Vol. 7, No. 1, January 1992. pp. 143-151. PELS

The design of input filters for switched-mode regulators is discussed, and it is shown that the filter's effect on the power system depends on the control method used in the regulator's dc-dc converter. Design inequalities are reviewed for duty-ratio programmed converters, and specific expressions are presented for current-programmed converters. Application examples to practical regulator circuits are given where current-programmed criteria, computer-driven measurement tools, and numerical evaluations of analytic expressions are used to design input filters. (AUTHOR ABSTRACT)

An example of a current-programmed buck converter shows analytically and experimentally that the onset of instability caused by violating the design criteria for adding an input filter is not reflected in the normal Bode plot of voltage gain, which appears to have adequate gain and phase margin at the onset of instability as measured by nearly sustained oscillation of the input current due to a transient load change. The onset of instability is also not reflected in the regulator output impedance measurements. The onset of stability would be reflected in the Bode plot of total gain, but this requires special digital modulation techniques (not usually used by most designers). For a Nyquist analysis (which includes a photograph of oscillatory input current just before going unstable) the reader is referred to the author's earlier 1990 APEC paper. This paper is a republication of the 1990 APEC paper with corrections, such as correcting the reversal of figures 1 and 2. It omits a discussion of the design of input filters from laboratory data or from specified "black box" parameters and of paralleling converters discussed in the APEC paper. (JF ABSTRACT) IBM Federal Sector Division, Owego, NY. 9 pages, 10 figures, 2 table, 19 equations, 9 references. [KP]

[KOHU92A] Kohut, Charles R., *Input Filter Design Criteria for Switching Regulators Using
Current Mode Control*, IEEE Transactions on Power Electronics, Vol. 7, No.
3, July 1992. pp. 469-479. PELS (Substantial revision of 1990 APEC paper that
is not in APEC record.)

The important transfer functions are derived for a constant-frequency current-programmed switching dc-to-dc converter with an input filter. From these transfer functions, design criteria are developed to ensure stability and prevent converter degradation. (AUTHOR ABSTRACT)

This paper examines the impact of adding a damped LC input filter to a current-programmed buck converter previously reported in the literature. The loop-gain roots are plotted as a function of input-filter damping and show a migration of roots that first produces complex zeros in the right-half plane and then complex poles as damping is further reduced. A simulation program (SCAMP), that does not contain parasitics, is used to generate both Bode plots and Nyquist plots for selected damping resistance. This is a purely analytical/simulation approach with no comparison to experiment, although it is stated that a simulation was also made with circuit parasitics included and it behaved essentially the same. In this simplified case, the onset of instability is clear in both the Bode and Nyquist plots. However, the worst case Bode plots might be interpreted as solidly stable if no determination of the existance of right-hand poles had been made. (JF ABSTRACT) Rockwell International Corporation. 11 pages, 26 figures, 1 table, 62 equations, 12 references.

[JANG92A] Jang, Yungtaek, and Robert E.
Erickson, *Physical Origins of Input Filter Oscillations in
Current Programmed Converters*, IEEE Transactions on Power Electronics,
Vol. 7, No. 4, October 1992, pp. 725-733. PELS'92

Addition of an input filter to a current-programmed converter can cause the controller to oscillate. Two instability mechanisms can typically occur: 1) the current programmed controller effective current feedback loop may become unstable, or 2) the controller effective input voltage feed forward loop, which becomes a positive feedback loop when an input filter is added, may oscillate. Design criteria are derived and interpreted here. The effective current feedback loop is unmodified by addition of the input filter provided that the usual duty-cycle-programmed design criteria are satisfied: the filter output Zs must be much smaller in magnitude than the closed-loop low-frequency regulator input impedance -R/M^2 and the reflected converter filter impedance Zei/M^2. In addition, the effective voltage loop is stable provided that a third criterion is satisfied. This criterion is active only at high frequency and/or for operating points close to the discontinuous conduction mode boundary. When all three criteria are well satisfied, then the output voltage regulation loop gain is unchanged. Hence, input filters of current programmed converters can be designed in essentially the same manner as for duty-ratio programmed converters. Results are summarized in tabular form for the basic buck, boost, and buck-boost converters. Experimental measurements for a buck converter with different input filters support the theoretical predictions. (AUTHOR ABSTRACT)

Note: The onset of instability is monitored in the paper by looking at the output voltage of the input filter, not the output of the regulator (it references [ERIC90A], that the voltage loop may not show instability, as a argument that it is caused by the current-programmed control). The paper also notes that in certain cases when the criteria developed in the paper are violated, the loop gains contain right-half-plane poles requiring the use of the Nyquist criterion to evaluate stability in some of the loops. (JF ABSTRACT) Department of Electrical and Computer Engineering, University of Colorado, Boulder, CO. 9 pages, 9 figures, 1 table, 9 equations, 17 references.

[LEWI89A] Lewis, L.R., B.H. Cho, F.C.
Lee, and B.A. Carpenter, *Modeling, Analysis and Design of
Distributed Power Systems*, IEEE Power Electronics Specialists Conference,
1989. PESC'89. Vol I, pp.152-159.

A distributed power system (DPS) featuring two cascaded stages of parallel-module switching regulators considering the dynamic impedances of the cascaded stage is presented. The design of a non-interactive EMI filter for the intermediate bus is discussed. Design considerations for parallel-modules are discussed. (AUTHOR ABSTRACT)

An analysis is included on the impact of a constant power load (negative resistance) instead of a resistive load, on current-programmed converters gain. Two gains are considered. The total loop gain is the vector sum of the current and voltage loops. Measurement of this gain requires the use of a digital modulator and the measurement point does not exist in some configurations of parallel systems. This requires using the outer voltage loop with inner current loop closed, to investigate stability. The negative impedance load can add a right-half-plane pole to this gain making the conventional use of Bode gain-phase margins, which are based on no right-half-plane poles, invalid. The full Nyquist criteria, which requires a knowledge of the number of right-half-plane poles, must be used. The analysis also points out that both the input impedance characteristics and any filter between the stages, as well as the output impedance, must be considered. (JF ABSTRACT) 8 pages, 20 figures, no tables, 9 numbered equations, 14 references. Virginia Power Electronics Center (Lewis, Cho, Lee), IBM Systems Integration Division (Carpenter).

[FLOR93A] [FLOR93A] Florez-Lizarraga,
Martin and Arthur F. Witulski, *Input Filter Design for
Multiple-Module DC Power Systems*, IEEE Power Electronics Specialists
Conference, 1993. PESC'93. pp. 108-114.

When multiple dc/dc converters are operated from a dc bus with a nonzero source impedance, the possibility exists for undesirable interactions between each individual regulator and the input impedance of other regulators on the bus. Consequently, criteria for input filter design in the presence of a significant source impedance are developed, which, when used in conjunction with already-known input filter criteria, permit the input filter to be designed so that the entire system operates reliably. Proper filter design "decouples" the negative regulator impedances from the bus, leaving only the passive input filter impedances to affect the other converters. These filter impedances appear in parallel with the source impedance and reduce the overall source impedance. Hence the use of multiple modules on the same bus actually improves the performance of the individual regulators. A specific example, the buck current mode controlled converter, is examined in detail. Extensive experimental evidence is presented to verify the analytical results. (AUTHOR ABSTRACT) 7 pages, 15 figures, no tables, 31 equations, 7 references. Dept. of Electrical and Comp. Eng., University of Arizona, Tucson, AZ. Updated and republished in PELS'96

[CHOI95A] Choi, Byungcho and Bo H. Cho,
*Intermediate Line Filter Design to Meet Both Impedance
Compatibility and EMI Specifications*, IEEE Transactions on Power
Electronics, Vol. 10, No. 5, September 1995. PELS'95.

This paper presents simple, noniterative, and practical design procedures for intermediate line filters intended for distributed power applications. The design procedures realize a line filter which simultaneously meets both impedance compatibility requirements and EMI specifications. Design examples are given for both single-stage and two-stage filters.(AUTHOR ABSTRACT) 6 pages, 7 figures, no tables, 15 equations, 7 references, 1 4-step design procedure. Power Electronics Division, Samsung Electronics Co, Korea (Choi). Dept of Elect Eng, Seoul National University, Korea (Cho).

[FLOR96A] Florez-Lizarraga, Martin and
Arthur F. Witulski, *Input Filter Design for Multiple-Module
DC Power Systems*, IEEE Transactions on Power Electronics, Vol.11, No. 3,
May 1996, pp. 472-479. PELS'96.

When multiple dc/dc converters are operated from a dc bus with a nonzero source impedance, undesirable interactions can occur between an individual regulator and the input impedance of other regulators on the bus. Consequently, criteria for input filter design in the presence of a significant source impedance are developed, which, when used in conjunction with already-known input filter criteria, permit the input filter to be designed so that each regulator operates reliably. Proper filter design tends to decouple the negative regulator impedances from the bus, leaving only the passive input filter impedances to affect the other converters. These filter impedances appear in parallel with the source impedance and reduce the overall source impedance. Hence the use of multiple modules on the same bus actually improves the performance of the individual regulators. An example, the buck current mode controlled converter, is examined in detail. Extensive experimental evidence is presented to verify the analytical results. (AUTHOR ABSTRACT) 8 pages, 11 figures, no tables, 29 equations, 8 references. International Power Systems, Sonora, Mexico and Dept. of Electrical and Comp. Eng., University of Arizona, Tucson, AZ. Update of PESC'93 paper.