Modeling of DC–DC Buck Converters for Large-Signal Frequency Response and Limit Cycles

A zeroth-order-hold equivalent discrete-time model of the buck converter for computing its large-signal frequency response is developed and experimentally verified. It is shown that, with a dc bias and a sinusoidal variation of the input duty cycle, the frequency response of the output voltage from the converter shifts from underdamped behavior to damped behavior with increasing amplitude of the input sinusoid. It is observed that, with a given dc input bias and a given input amplitude beyond the range of the state-space linearized small-signal model, the converter behavior varies from exclusively continuous inductor current mode at low frequencies to behavior with continuous and discontinuous inductor current modes at high frequencies. The use of this sinusoidal input large-signal frequency response in predicting limit cycles induced by feedback of the output voltage using proportional and integral controllers for such converters is studied. Experimental results confirming the use of this large-signal frequency response are presented

[1]  E. P. Cunningham,et al.  Digital Filtering: An Introduction , 1992 .

[2]  Nicola Femia,et al.  State-space models and order reduction for DC-DC switching converters in discontinuous modes , 1995 .

[3]  Duwang Li,et al.  Comparison of simulation algorithms for accelerated determination of periodic steady state of switched networks , 2000, IEEE Trans. Ind. Electron..

[4]  W. L. De Koning,et al.  On the periodic behavior of PWM DC-DC converters , 2002 .

[5]  Gene F. Franklin,et al.  Digital control of dynamic systems , 1980 .

[6]  Kadry Al-Badwaihy,et al.  Steady-State Analysis of Static Power Converters , 1982, IEEE Transactions on Industry Applications.

[7]  K. Natarajan,et al.  System identification and PID controller tuning using band‐pass filters , 1997 .

[8]  A. Stanković,et al.  Multifrequency averaging of DC/DC converters , 1999 .

[9]  Seth R. Sanders,et al.  On limit cycles and the describing function method in periodically switched circuits , 1993 .

[10]  J. M. Noworolski,et al.  Generalized averaging method for power conversion circuits , 1990, 21st Annual IEEE Conference on Power Electronics Specialists.

[11]  G. Ledwich,et al.  Modelling and control of switch-mode DC-DC converters using state transition matrices , 1995 .

[12]  Slobodan Cuk,et al.  A general unified approach to modelling switching-converter power stages , 1976, 1970 IEEE Power Electronics Specialists Conference.

[13]  G. Siouris,et al.  Nonlinear Control Engineering , 1977, IEEE Transactions on Systems, Man, and Cybernetics.

[14]  Marian K. Kazimierczuk,et al.  Small-signal model of PWM converters for discontinuous conduction mode and its application for boost converter , 2003 .

[15]  A. Martinez,et al.  A unified discrete-time state-space model for switching converters , 1995 .