By Topic

Analytic solutions of limit cycles in a feedback-regulated converter system with hysteresis

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

3 Author(s)
I. Babaa ; Bell Telephone Laboratories, Inc., Winston-Salem, NC, USA ; T. Wilson ; Yuan Yu

A mathematical model is derived for the voltage step-down dc-to-dc converter in which a hysteretic bistable trigger circuit is used to regulate the output voltage. Normalized second-order differential equations are derived for the output-voltage error, or output-voltage ripple, measured with respect to a constant reference. The method of successor functions is applied to the piecewise analytic phase plane trajectory for the errors and the conditions leading to a limit cycle are initially formulated in two transcendental equations. With the objective of obtaining an analytic solution for the period of the limit cycles these two equations are then replaced by approximate algebraic equations which are solvable in general terms. The approximations are carefully based on properties that are typical of all converters of this type, and lead to quite simple but accurate expressions for the period of the limit cycle in terms of arbitrary system parameters. Expressions for the amplitude of the limit cycle are also given, and its stability is tested. A numerical example based on an actual representive system is given. Certain unusual characteristics of the limit cycle as a function of certain system parameters are pointed out.

Published in:

IEEE Transactions on Automatic Control  (Volume:13 ,  Issue: 5 )