Modelling and analysis of switching DC-to-DC converters in constant-frequency current-programmed mode

Abstract

An anaZy&iA o(> dc-to-dc switching conventew> in constant-fanequency current-programmed continuous conduction modo, U> performed, and leadLs to two significant, results.The first is that a Kamp function, used to eliminate a potential insta bility, can be chosen uniquel.y to assure both stability and the fastest possible transient, response oh the programmed current.The second is the development of an extension of the statespace averaging technique by meant* of u)hich both the input and output small-signal properties of any such conveAteA may be accurately represented by a linear small-signal equivalent-circuit model. The mode^ ^ presented and experimentally νwilled for the Cuk converter and for the conventional buck, boost, and buck-boost convert.ers. Kit models exhibit basically a one-pole control-tooutput transfer function response. INTRODUCTIONOver the last several years an effort has been made to characterize the transfer properties of dc-to-dc switching converters in the frequency domain. This program has culminated in the "statespace averaging" approach, and leads to generalized equivalent circuits ("canonical models") that ex press the line-to-output and control-to-output transfer properties. So far, equivalent circuits have been derived for the continuous and the discontinuous conduction modes of a converter operated in the conventional "duty-ratio pro grammed mode" in which the duty ratio appears as the external port at which feedback for regulation purposes is applied employed.In this mode, the converter power switch duty ratio is determined by the times at which the switch current reaches a threshold value determined by a control signal. Thus, this threshold level, rather than the duty ratio, becomes the input port for feedback in the current-programmed mode. In The current-programmed mode has several advantages over the conventional duty-ratio programmed scheme. First, since the switch, usually a transistor, is turned off when its current reaches the control signal level, failures due to excessive switch current can be prevented simply by limiting the maximum value of the control signal. This measure also protects the entire converter from overload damage.Second, several converters can be operated in parallel without a load-sharing problem, because all of the power switches receive the same control signal from the regu lator feedback circuit and hence carry the same CH1461-3/79/0000-0284$00. 75 © 1979 IEEE 284

A unified model for current-programmed converters

“…The first factor in the right of (1 3) is a measure for the value of slopes since (3) shows that both M I and A42 are proportional to the ratio V o f f / L . The second factor represents the effect that the compensating ramp Mc has on the gain factor.…”

Sampled-Data Modeling and Analysis of the Power Stage of PWM DC-DC Converters

“…Recently there has been intensive research on modeling and analysis of the power stages of the PWM DC-DC converter [1, 2,3,4,5,6,7,8,9,10,11,12], especially in special configurations such as under current mode control [13,14,15,16,17,18,11] and in discontinuous conduction mode [19,20,21,22]. The better the power stage is modeled, the better closed-loop performance can be achieved as expected.…”

Modeling and Current Programmed Control of a Bidirectional Full Bridge DC-DC Converter

“…This leads to 100% the duty cycle, as a result after some cycles; the circuit is gone to its steady state in which inductor and capacitor experience only a constant source and this is when they go under short and open circuit respectively. The other important block is compensating ramp which can overcome the unstable oscillation problem described in [10,22,30]. Figures 20 and 21 show that the controllers are successful to control the converter in the presence of 1 A and 10 A step load change for boost and buck mode respectively.…”

“…This method may pose some complexity especially in nonbasic topologies. Another circuit oriented method that is introduced by Middlebrook and Cuk [21][22][23] in 1977 is the average state space. An advantage of the state-space averaging method is its efficiency compared to that of the switched model because there is not any switching frequency ripple and, consequently, the simulation time required by the averaged model is much lower than required by the switched model.…”