[MIDD75B] Middlebrook, R. D., *Measurement of Loop Gain in Feedback Systems*, International
J. of Electronics, vol. 38, no. 1, pp. 485-512, April 1975. IJE

In the design of a feedback system it is desirable to make experimental measurements of the loop gain as a function of frequency to ensure that the physical system operates as analytically predicted or, if not, to supply information upon which a design correction can be based. In high loop-gain systems it is desirable that the loop-gain measurement be made without opening the loop. This paper discusses practical methods of measuring and interpreting the results for loop gain of the closed-loop system by voltage injection or current-injection technique; extensions to the case in which measurement can be made even though the system is unstable; and extension to the case in which neither the voltage nor current-injection technique alone is adequate, but in which a combination of both permits the true loop gain to be derived. These techniques have been found useful not only in linear feedback systems but also in describing function analysis of switching-mode converters and regulators. (AUTHOR ABSTRACT) Caltech. 28 pages, 21 figures, no tables, 81 equations, 3 references. See also Middlebrook 1976D

[MIDD76D] Middlebrook, R. D., *Improved-Accuracy Phase Angle Measurement*, International J.
of Electronics, vol. 40, no.1, pp. 1-4, January 1976. IJE

A method for phase angle determination from measurement of three magnitudes described in a recent paper (Middlebrook 1975), is extended to provide improved accuracy. (AUTHOR ABSTRACT) Caltech. 4 pages, 3 figures, no tables, 1 equation, 1 reference. See also Middlebrook 1975B

[VENA80A] Venable, H. Dean, and Stephen
Foster, *Practical Techniques for Analyzing, Measuring, and
Stabilizing Feedback Control Loops in Switching Regulators and Converters*,
Proceedings of the Seventh National Power Conversion Conference,
PowerCon'7, pp. I2-1 to I2-17. (10)

Practical techniques are shown for analyzing the response of switching regulators and determining and realizing the desired feedback characteristics to achieve stable closed-loop operation. These techniques employ reactance paper to reduce the calculation time to minutes and increase understanding of circuit behavior. Measurement techniques are also shown which allow loop gain and phase margin to be determined in a few seconds while the circuit is operating. (AUTHOR ABSTRACT) Hughes Aircraft Company. 17 pages, 22 figures, 2 tables, 9 equations, 8 references, 1 appendix.

[MIDD81C] Middlebrook, R.D., *Power Electronics: Topologies, Modelling, and Measurement*,
Proceedings of the IEEE International Symposium on Circuits and Systems, 1981.
SCAS Republished in "Advances in Switch-Mode Power Conversion, Volumes I
and II," 2nd edition, TESLAco, 1983, paper 2, pp. 17-25.

A review is presented of the work of the Power Electronics Group at the California Institute of Technology. Development of a canonical model for a general switched-mode dc-to-dc converter culminated in the state-space average analysis method, complemented by corresponding experimental measurement techniques. A search for a dc-to-dc converter having improved properties led to the Cuk converter, and its coupled-inductor-transformer extensions to provide zero current ripple at input or output or both. Extensions to two-quadrant and four-quadrant outputs can be made by suitable bidirectional switch implementations. The concept of duality extended to switched networks leads to useful classification of switched-mode converters, and to new converter topologies and operating modes. (AUTHOR ABSTRACT) 8 pages, 12 figures, no tables, equations - but not numbered, 9 references.

[BARZ81A] Barzegar, Farhad, Slobodan Cuk,
and R. D. Middlebrook, *Using Small Computers to Model and
Measure Magnitude and Phase of Regulator Transfer Functions and Loop Gain*,
Proceedings of PowerCon 8, the Eighth International Solid-State Power
Electronics Conference, 1981. Republished in "Advances in Switch-Mode
Power Conversion, Volumes I and II," 2nd edition, TESLAco, 1983, paper 16,
pp. 251-278.

Applications of small computers for analysis and design of switched-mode power supplies are presented. A complete computerized frequency response analysis for any two topology converter is presented that is based on state-space averaging techniques and can analyze the general closed-loop converter with most of the parasitics included. Frequency response measurement techniques are discussed which range from the simple manual magnitude measurement to a fast, accurate and easy to use computerized system which automatically measures both magnitude and phase and displays the results in convenient from (Bode plot). Dedicated software makes both theoretical prediction and automated measurement possible on a desk-top computer, such that the accuracy of predictions can easily be verified by the measurement results. (AUTHOR ABSTRACT) Caltech 28 pages, 29 figures, no tables, 72 equations, 14 references.

[VENA82A] Venable, H. Dean, *Stability Analysis Made Simple*, Venable Industries,
1982.

A manual for Venable Industries Model 200 Frequency Response Analysis System. Partial topics include how to analyze a modulator (power stage); how to measure transfer functions of the modulator; how to stabilize a loop (including worst-casing a loop); how to synthesize an amplifier; how to measure open loop transfer functions of a circuit operating closed loop; how to measure pieces of a loop; how to measure voltage versus frequency; how to measure current versus frequency; and how to measure impedance and admittance. The manual shows how to use impedance graph paper to aid in design. (JF) 101 pages, 12 chapters, 6 appendices.

[VENA84A] Venable, H. Dean, *Testing Power Sources for Stability*, Proceedings of the
Power Sources Conference, 1984, pp. S12 1-14 (1)

Recent advances in measurement technology have made it not only possible to measure stability margins, but made it a quick and simple process. On power sources with remote voltage sensing terminals, gain and phase margins can usually be determined in a few seconds without even removing the cover. These measurements can be made while the source is operating normally, supplying power to the real load. In this way, the effects of power source performance can easily be determined. This paper will explore the causes of problems when the power source is connected to the real load -- as opposed to the resistive load normally used by the power source manufacturers -- and how to specify and test the power source to avoid those problems. (AUTHOR ABSTRACT) Venable Industries. 14 pages, 14 figures, no tables, no equations, 1 reference.

[CHO84A] Cho, B. H., and F. C. Lee,*Measurement of Loop Gain with the Digital Modulator*, IEEE Power Electronics Specialists Conference - 1984 Record, pp. 363-373.

A Loop gain measurement technique for switching regulators using a digital modulator is introduced. While the conventional technique injects and measures the analog signals, the proposed digital modulator injects a digital perturbation and measures the resultant duty cycle modulation. Since the duty cycle signal, derived from all feedback loops, provides the ultimate control of a switching regulator, the loop gain defined at the duty cycle modulator is unique. Employing the digital modulator, this loop gain can be measured even with a switching regulator employing the current injected control. Furthermore, this new technique overcomes false measurement problems found in the conventional technique when the feedback signal at the point where the loop gain is measured contains a pulsating nature. (AUTHOR ABSTRACT) Electrical Engineering Department, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061. 11 pages, 17 figures, 10 equations, 11 references.

[VENA85B] Venable, H. Dean, *Integrated Frequency Response Modelling and Measurement Systems
with FILE MATH*, PEDC'85, Proceedings of Power Electronics Design
Conference, 1985, pp. 195-202.

The Venable Industries Model 250 Frequency Response Analysis System has long been the world standard for feedback loop stability analysis and testing. Now, with the addition of FILE and VECTOR MATH, a whole new world of capabilities has been made possible. The entire process of feedback loop stabilization has been automated, and a truly integrated test and analysis system is the result. (AUTHOR ABSTRACT) Venable Industries. 8 pages, 14 figures, no tables, no equations, no references.

[VENA85C] Venable, H. Dean, *Testing Modern Power Supplies*, Test & Measurement World
Magazine, Vol. 5, No. 11, November 1985, pp. 118-121.

No abstract in this hypertext.

[VENA87A] Venable, H. Dean,*Specify Gain and Phase Margins on All Your Loops*, Proceedings of the Power Electronics Show and Conference, 1987 (2)

No abstract in this hypertext.

[VENA90A] Venable, H. Dean, and Thomas K.
Phelps, *Stability Testing of Multi-Loop Converters*,
PCIM'90, Proceedings of the Twenty-First International Power Conversion
Conference, October 1990, pp. 232-238. (11)

No abstract in this hypertext.

[VENA92A] Venable, H. Dean, *Production Testing of Power Supplies for Stability*,
Proceedings ATE and Instrumentation Conference, 1992, pp. 17-21.

No abstract in this hypertext.

[VENA93A] Venable, H. Dean, *Testing Power Factor Correction Circuits for Stability*,
Proceedings of PCIM/Power Quality International Conference, 1993. (13)

No abstract in this hypertext.

[VENA94B] Venable, H. Dean, *Testing Stability of Power Factor Correction Circuits*,
PCIM'94, PowerConversion & Intelligent Motion Magazine, Vol. 20, No. 2,
February, 1994.

No abstract in this hypertext.