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## August 05, 2003

### Current-Mode Control Articles

Current-Mode Control Articles

**Question:** Can you recommend some good articles on current mode DC-DC converters?

**Answer:** Current-mode control, also called current-programmed control and current-injected control, has existed since at least 1978 (earlier in U.S. Government reports). I have annotated some papers with abstracts that might be of interest.

C. W. Deisch, **Simple Switching Control Method Changes Power Converter Into A Current Source**, *IEEE Power Electronics Specialists Conference - 1978 Record*, pp. 300-306.

A switching converter with an LC output filter behaves as a loose-tolerance voltage-controlled current source if each switch closure is ended when switch current reaches an adjustable threshold. This converter is then combined with an external feedback to produce a precise output voltage. By generating a fixed voltage with a current source in this manner, the converter has many advantages including continuous protection of the switches, stable and equal load sharing when several converters are operated in parallel, inherent overload protection, automatic switch symmetry correction, and fast system response. (AUTHOR ABSTRACT) Bell Laboratories, Naperville, IL. 7 pages, 3 references.

Key authors since then are **Redl/Sokal**, **Ridley**, and **Middlebrook/Erickson**. I have left out a host of authors who have made major contributions, but you can search the above authors names for additional papers and find others by their co-authors and references. Also, there are many vendor application notes on current-mode controller ICs. The references below should get you started.

**R. Redl and N. O. Sokal**

Redl/Sokal published one of the early reviews of current-mode control in 1985.

R. Redl, and N. O. Sokal, **Current-Mode Control, Five Different Types, Used With the Three Basic Classes of Power Converters: Small-Signal AC and Large-Signal DC Characterization, Stability Requirements, and Implementation of Practical Circuits**, *IEEE Power Electronics Specialists Conference - 1985 Record*, pp. 771-785.

Current-mode control effectively eliminates the phase lag of the control function, associated with the output filter inductor or the energy-storage inductor. The several types of current-mode controllers differ slightly in their phase-lag characteristics, but they are all far superior to the commonly used PWM duty-ratio controllers. Unfortunately, industry has been slow to appreciate and exploit the considerable advantages of current-mode control. There seem to be two reasons for that: (a) the unavailability of integrated circuits which are well-suited to implementing current-mode controllers and (b) the lack of detailed, systematically organized, theoretical and practical information on current-mode controllers. The objective of this paper is to fill this gap by providing a well organized compendium of useful information for the design engineer who wants to understand the operation of a current-mode-controlled power converter and to accomplish an optimal design. Five different control methods are considered, used with the three basic types of regulated rectangular-wave power converters. (AUTHOR ABSTRACT) Design Automation, Inc., Lexington, MA 02173-3992. 15 pages, 18 figures, 10 tables, design equations in table form, 16 references.

Nathan Sokal has provided more information on this that is provided his comments near the end of this page.

**R. B. Ridley**

Ray Ridley published a Ph.D thesis in 1991 that contains a review of current-mode control up to that point in time.

Ridley, R. B., **A New Small-Signal Model for Current-Mode Control**, Ph.D dissertation, Virginia Polytechnic University and State University, Blacksburg, VA.

Part of which became the paper:

Ridley, R. B., **A New Continuous-Time Model for Current-Mode Control**, IEEE Transactions on Power Electronics, April, 1991, pp. 271-280.

The accuracy of sampled-data modeling is combined with the simplicity of pole-zero representation to give a new current-mode control model, accurate to half the switching frequency. All of the small signal characteristics of current-mode control are predicted, including high-frequency subharmonic oscillation which can occur even at duty cycles of less than 0.5. The best representation for the control-to-output transfer function is shown to be third-order. Model predictions are confirmed with measurements on a buck converter. (AUTHOR ABSTRACT) Virginia Power Electronics Center at VPI&SU, Blacksburg, VA. 10 pages, 18 figures, 2 tables, 31 equations, 23 appendices, 15 references.

**Ray Ridley has also published** a recent article on the subject, **Current
Mode or Voltage Mode?** in his magazine *Switching Power Magazine*, Vol. 1, Issue 2, October 2000, pp 4,5,9. You can subscribe to the magazine. at no cost if you qualify.

If you visit the Ridley Engineering website, look at the logo. It is actually a family of bode plots of a current-mode controller as the compensating ramp is increased. The upper trace is with no ramp compensation and shows the peaking near the switching frequency. Lower traces showing the effect of increasing ramp compensation until you see the characteristics of a voltage-mode controller, the double slope of the LC output filter.

You can find all of Ray Ridley's papers on his website at www.ridleyengineering.com/papers.html.

Ray Ridley's company, Ridley Engineering has been a past sponsor of this website.

**R. D. Middlebrook and R. W. Erickson**

Robert Erickson pretty much covers the Middlebrook contributions and greatly expands them with his own contributions and those of others in the chapter *Current Programmed Control*, pp. 439-487, which contains 15 references on the subject, in his text book:

Erickson, Robert W. and Dragan Maksimovic, **Fundamentals of Power Electronics, 2nd ed.**; Norwell, Mass.: Kluwer Academic, c 2001. xxi, 883 p. ISBN: 0792372700 (alk. paper); LC Control Number: 00052569

This is one of the books I recommend as part of a personal power supply design library.

Current-mode control should also be covered in most current books on power supply design and current-mode controller applications notes from IC vendors are a rich source of information and practical advice.

Speaking of advice, Ridley and many application notes emphasize keeping noise off the current sensing ramp. From my own experience and interaction with others, this advice can not be emphasized enough. Noise on the current sense ramp is nothing but design grief.

**Others may have a different perspective** on this topic. Comments are always welcome.

**Comments**

In answering the original email that had this question, I sent a copy to Robert Erickson, Nathan Sokal, and Ray Ridley.

**Comments by Robert Erickson**

"I certainly agree with the comment about noise. I think that, contrary to the discussions in many papers about selecting the artificial ramp slope to null the audiosusceptibility or to obtain deadbeat control, the most important criterion is to select the ramp magnitude large enough that good noise immunity is obtained."

[Robert Erickson suggested several other key papers with comments on the subject. Where I could, I have expanded the references and added an abstract to the papers - JF].

1. "Professor R. D. Middlebrook gave a series of very substantial seminars and papers in the late 1980's. These are notable for how they make physical sense out of this complex subject."

2."In the second edition of my textbook, Dragan Maksimovic and I have substantially revised and expanded the coverage of current mode control, including extensive tables of results for basic converters, and simulation in PSPICE using averaged models.

3."There is a chapter on current mode control in Dan Mitchell's book, DC-DC Switching Mode Regulator Analysis, McGraw Hill, 1988, ISBN 0-07-042597-3. This book is now out of print, but you might be able to order one from ejbloom.com, or to at least find a copy in the library."

4."Here is a list of basic papers on the modeling subject:"

**Middlebrook and the Caltech group**

R. D. Middlebrook, **Modelling a Current-Programmed Buck Regulator**, *IEEE Applied Power Electronics Conference*, pp. 3-13, Mar 1987

A general small-signal model for current-programmed switching power stages is used for design-oriented analysis of a 150W buck regulator.

The model, into which the current-programming minor feedback loop is absorbed, exposes the desired tendency towards "constant" output current. The regulator voltage loop remains the only explicit feedback loop, allowing the regulator closed loop properties to be easily obtained from those of the open-loop current-programmed power stage.

The design-oriented analytic results allow easy inference of the effects of element changes on the regulator performance functions. Results are obtained for the regulator line-to-output transfer functions (audio susceptibility) and output impedance. (AUTHOR ABSTRACT) California Institute of Technology, Pasadena, California. 11 pages, 8 figures, 45 equations, 11 references.

R. D. Middlebrook, **Modelling a Current-Programmed Boost Regulator**, *Proc. The Power Electronics Show & Conference*, San Jose CA, Oct 1986, pp. 273-285.

A general small-signal model for current-programmed switching power stages is used for design-oriented analysis of a 280W boost regulator.

The model, into which the current-programming minor feedback loop is absorbed, exposes the desired tendency towards "constant" output current. The regulator voltage loop remains the only explicit feedback loop, allowing the regulator closed-loop properties to be easily obtained from those of the open-loop current-programmed power stage.

The design-oriented analytic results allow easy inference of the effects of element changes on the regulator performance functions. Results are obtained for regulator line-to-output transfer function (audio susceptibility) and output impedance, for both maximum and minimum load. (AUTHOR ABSTRACT) California Institute of Technology, Pasadena, California. 13 pages, 11 figures, 64 equations, 9

references.

R. D. Middlebrook, **Topics in Multiple-Loop Regulators and
Current-Mode Programming**, *IEEE Power Electronics Specialists
Conference - 1985 Record*, pp. 716-732.

Some general considerations about multiple-loop feedback are discussed, and it is concluded that incorporation of a current-programmed power stage into a "new" power stage model is both justified and useful. A new circuit-oriented model of the current feedback path is derived which augments the well-known power stage canonical circuit model. The current loop gain, though wideband is always stable if the conventional stabilizing ramp is employed, but has a relatively small low-frequency value. Consequently, the "new" power stage is more usefully modeled by a y parameter model in which the current loop is not explicit. Expressions for the y parameters are given that are extensions of those previously derived. Although current-programming tends to make the power stage output behave as a current source, the control to output voltage transfer function exhibits, in addition to the familiar dominant pole, a second pole at the current loop gain crossover frequency, which may lie from one-sixth to two-thirds of the switching frequency. (AUTHOR ABSTRACT) California Institute of Technology, Pasadena, California. 17 pages, 21 figures, 1 table, 51 equations, 12 references.

Verghese, G. C., C. A. Bruzos, and K. N. Mahabir, Averaged and Sampled-Data Models for Current Mode Control: A Reexamination, IEEE Power Electronics Specialist Conference, 1989 pp. 484-491

A correction to the usual derivation of state-space averaged models for constant frequency, current mode controlled converters produces new averaged models. Using a buck-boost example, we compare frequency responses of the new model, the usual model, and an exact sampled-data model. Approximate sampled-data models, often written down but seldom exploited, are also highlighted. (AUTHOR ABSTRACT) MIT Cambridge, MA. 8 pages, 8 figures, 31 equations, 12 references.

Ridley -- 1991 VPEC PhD thesis and papers [see above]

Tan, F. D., and R. D. Middlebrook, **Unified Modeling and Measurement of Current-Programmed Converters**, IEEE Power Electronics Specialist Conference, 1993, pp. 380-387.

A Unified model is established for a current-programmed converter, which is both a modification and an extension of familiar models. Inclusion of the sampling effect allows the presence of an additional pole in the current-loop gain to be inferred. The resulting final double-slope asymptote is fixed in position, and the crossover frequency cannot exceed half the switching frequency. A new "stability parameter" Q, determines the additional pole and describes the degree of peaking in the closed-loop transfer functions. Experimental verification employs an analog signal injection technique. (AUTHOR ABSTRACT) Caltech. 8 pages, 12 figures, 25 equations, 16 references.

Tan, F. D., and R. D. Middlebrook, **A Unified Model for Current-Programmed Converters**, IEEE Transactions on Power Electronics, Vol. 10, No. 4, July 1995, pp. 397-408.

A unified model is established for a current-programmed converter, which is both a modification and an extension of familiar models. Inclusion of the sampling effect allows the presence of an additional pole, Wp, in the current-loop gain to be derived. The resulting final double-slope asymptote is fixed in position, and the crossover frequency cannot exceed half the switching frequency. A stability parameter, Qs, determines the additional pole and describes the degree of peaking in the closed-loop transfer function. Experimental verification employs an analog signal injection technique. (AUTHOR ABSTRACT) QSC Audio Products, Costa Mesa, CA (Tan), Caltech (Middlebrook). 12 pages, 15 figures, 41 equations, 23 references.

**Comments by Nathan Sokal**

Nathan Sokal recommended other publications co-authored by R. Redl and N. O. Sokal that could be useful. Reprints of technical papers listed below are available via postal mail on request to NathanSokalATcompuserveDOTcomRemoveThis. Also, additional papers on current-mode control were published by R. Redl without Sokal; bibliographic reference citations probably are available from RichardRedlATcompuserveDOTcomRemoveThis. (Email addresses coded for spam protection, change and remove obvious parts to decode.)

Where I had the reference, I added the abstract and other information to Mr. Sokal's list.

Kislovski, Andre S., Richard Redl, and Nathan O. Sokal, **Dynamic Analysis of Switching-Mode DC/DC Converters**, Van Nostrand Reinhold, New York, 1991. 404p. (Includes detailed analyses of several types of current-mode control. No longer available from Van Nostrand Reinhold. Reprinted with additions and corrections by Design Automation, Inc., 4 Tyler Road, Lexington, MA 02420-2404, U.S.A.; cost USD66 prepaid by check payable on a U.S.A. bank or charged to a VISA or MasterCard credit card, includes shipping via surface book mail. If desired, add USD7 for shipping via AO Air Mail.)

SMPS Technology booklist abstract of above.

Redl, Richard, and Nathan O. Sokal, **Using Current Mode Control**, *Powertechnics Magazine*, vol. 5, no. 7, July 1989. pp. 23-28.

What do constant-frequency peak-current commanding, constant-frequency valley-current commanding, constant off-time, constant on-time, hysteretic and PWM-conductance control schemes all have in common? They are all forms of current-mode control, but that is about all they do have in common. (TABLE OF CONTENTS DESCRIPTION) Although often thought of as a single method of controlling switching power supplies, current-mode control rally is an umbrella under which resides several quite different regulation schemes, each with its own unique set of advantages and disadvantages. (ARTICLE LEAD HEADLINE) 4 pages, 7 figures, no equations, 7 references.

Redl, Richard, and Nathan O. Sokal, **Superiority of Current-Mode Control, for Stability Over Wide Ranges of Output Capacitance and ESR**, Power Electronics Conference, Anaheim, CA, Feb. 1988.

General-purpose power supplies must maintain stability over wide ranges of output capacitance and capacitor ESR, as a consequence of the ways that different systems are configured. Voltage-mode controllers and current-mode controllers differ greatly in their ability to meet that requirement. Because those facts had not been generally appreciated, this important aspect of power-supply design and application had usually been overlooked. After investigating this subject in detail, we found that current-mode control is far superior to the traditional voltage-mode control in this respect, too. (AUTHOR ABSTRACT) Design Automation, Inc. 17 pages, 21 figures, 35 equations, 8 references, 2 appendices with 10 equations.

Sokal, N. O. and R. Redl, **Current-Mode Control of Capacitively Coupled Power Converters**, U.S. Patent 4,719,559, Jan. 1988. [legal version of next reference]

U.S. Patent Office full text search by patent number.

Redl, R, and N. O. Sokal, **How to Use Current-Mode Control with Capacitively Coupled Half-Bridge Converters**, *IEEE Applied Power Electronics Conference*, San Diego, CA, March 1987. pp. 257-265

Switch-peak-current commanding current-mode control produces asymmetrical operation when used in capacitively coupled symmetrical dc/dc converters. This paper discusses the causes and effects of asymmetry, gives an analytical model, and proposes a negative-feedback corrector to eliminate the asymmetry. Test results on a 150-W off-line half-bridge converter prove the effectiveness of the recommended solutions. (AUTHOR ABSTRACT) 9 pages, 15 figures, 11 equations, 4 references, 1 appendix with 10 equations.

Redl, R, and N. O. Sokal, **Near-Optimum Dynamic Regulation of DC/DC Converters, Using Feed-Forward of Output Current and Input Voltage, with Current-Mode Control**, IEEE Trans. Power Electronics, vol. PE-1, no. 3, July 1986, pp. 181-192. [additional unpublished information available from Sokal on request]

Near-optimum dynamic regulation of a dc-dc converter is obtained by adding feed-forward of output current and input voltage to a current-mode controller. The results are a) near zero output impedance and audio susceptibility, from dc to nearly the switching frequency, b) much reduced magnitude, duration , and energy content of the output-voltage transient after a transient change of output current or input voltage, and c) smaller size and lower cost for the output filter capacitor. Feed-forward is applicable to both forward and flyback types of converters and to all types of current-mode control. The cost of feed-forward for a forward-type converter is a low-power resistor and a current sensor; a flyback-type converter needs also an analog multiplier-divider integrated circuit (IC). A description is given of the control loop, conditions to achieve extremely good transient response, calculation of the peak deviation of the output voltage for a step load change, practical methods for current feed-forward, and experimental results. The theoretical predictions are in excellent agreement with the experimental results. In the experiments, adding output current feed-forward reduced the transient deviations of output voltage by factors of 6.7 in magnitude, 50 in duration, and 335 in energy content. The added components were a 1/4-W resistor and a 12-mm ferrite toroid with a 10-turn winding. (AUTHOR ABSTRACT) 12 pages, 20 figures, 23 equations, 15 references.

Redl, R., and N. O. Sokal, **Frequency Stabilization and Synchronization of Free-Running Current-Mode-Controlled Converters**, *IEEE Power Electronics Specialists Conference*, June 1986, Vancouver, BC, Canada. pp. 519-530.

Power converters with free-running current-mode control (hysteretic, constant-"off"-time, or constant-"on"-time) can be frequency stabilized or can be synchronized to a reference frequency. Those can be accomplished by feed forward, feedback, or phase-locking techniques. With hysteretic control, the frequency is controlled by varying the current hysteresis. With constant-"off"-time or constant-"on"-time control, the frequency is controlled by varying the "off" time or the "on" time, respectively. We consider all possible methods of frequency stabilization and synchronization for the three types of free-running current-mode control, used with the three basic types of power converters (buck, boost, and buck-boost). We give analyses and practical design information for the most-important combinations, and experimental data for a buck converter with constant-"off"-time control and feed-forward frequency stabilization. (AUTHOR ABSTRACT) Design Automation, Inc., Lexington, MA 02173-3992, U.S.A., 12 pages, 16 figures, 13 equations, 4 tables, 6 references.

Redl, Richard, and Nathan O. Sokal, **What a Design Engineer Should Know About Current-Mode Control**, *Power Electronics Design Conference*, Oct. 1985, Anaheim, CA. pp. 18-33. [update of PESC 1985 paper by same authors.]

In a power converter with a conventional PWM controller, the high-frequency phase lag of the control transfer function approaches 180º in the L-C part of the power circuit, plus more than 90º in the voltage-error amplifier and additional phase lag in some duty-ration modulators. High-gain feedback-control systems with so much phase lag require very careful design to ensure both stability and adequate response speed under all operating conditions.

Current-mode control effectively eliminates the 90º phase lag associated with the filter inductor (or the energy-storage inductor in a flyback converter). The several types of current-mode controllers differ slightly in their phase-lag (and other) characteristics, but all of them are far superior to PWM duty-ratio controllers. Unfortunately, industry has been slow to appreciate and exploit the considerable advantages of current-mode control. There seem to be two reasons: (a) the lack of detailed, systematically organized practical information on current-mode controllers, with theoretical back-up, and (b) the unavailability of integrated circuits which are well-suited to implementing current-mode controllers.

The objective of this paper is to fill the "information gap." We provide a swell-organized compendium of useful design information for the engineer who wants to understand the operation of a current-mode-controlled power converter and wants to accomplish an optimal design. Five different control methods are included, used with the three basic types of regulated rectangular-wave power converters. First we establish the technical basis for an informed choice among the five control methods. Them we recommend which types of current-mode control to use in each of the common applications. We point out special precautions for transformer-coupled converters, to avoid catastrophic disasters. Appropriate control ICs are scheduled to be available in early 1986, from Cherry Semiconductor and at least one alternate source. 16 pages, 13 figures, 10 tables, 16 references.

Repeating: Others may have a different perspective on this topic. Comments are always welcome.

Posted by Jerrold Foutz at August 5, 2003 03:51 PM