A Chaotic Peak Current-Mode Boost Converter for EMI Reduction and Ripple Suppression

A Chaotic Peak Current-Mode Boost Converter for

EMI Reduction and Ripple Suppression

H.Li,Student Member,IEEE,W.K.S.Tang,Member,IEEE,Z.Li,Member,IEEE,and W.A.Halang

Abstract—A novel chaotic peak current-mode boost converter is proposed.By deriving its corresponding current mapping func-tion,a thorough analysis of its chaotic behavior is carried out.As demonstrated both in simulations and experiments,the proposed design can effectively reduce electromagnetic interference and sup-press ripples of the converter’s output,resulting in a better design for power supplies.

Index Terms—Boost converter,chaotic mapping,electromag-netic interference(EMI)reduction,ripple suppression.

I.I NTRODUCTION

D URING the last two decades,the use of chaos in dc–dc

converters has attracted great interest.In the framework of peak current-mode boost converters,the distinct effect of chaos on reducing electromagnetic interference(EMI)has been largely explored[1]–[10].

The?rst design can probably be dated back to1996when Deane and Hamill[1]utilized chaos to improve the electro-magnetic compatibility(EMC)of power supplies.Their idea was later reformulated[2]and modi?ed by applying some other control schemes[3].As demonstrated by all contributions men-tioned,it is con?rmed that,in power converters,EMC can be effectively improved by the introduction of chaos via current mode control.

A detailed study on the parametric design of a chaotic dc–dc converter has also been carried out by computing its periodic spectral components[4].Based on a similar concept,but fo-cusing on chaos control and utilization of chaos,some design suggestions were given in[5],while experimental research of a low-EMI chaotic peak current-mode controlled boost converter was presented in[6].

Despite of the success of EMI suppression using chaos, two prominent problems remain unsolved.From the previous designs,it is observed that the ripples of the output current are much greater than those of periodically running dc–dc

Manuscript received August9,2007;revised November12,2007.First pub-lished June17,2008;last published August13,2008(projected).The work of H. Li was supported by the German Academic Exchange Service and Elliptec AG, Dortmund,Germany,through a matching funds scholarship.The work of W.K. S.Tang was supported in part by a grant from the Research Grants Council of the HKSAR under Project CityU120205and by a grant from City University of Hong Kong under Project No.7002015.This paper was recommended by Associate Editor S.Callegari.

H.Li,Z.Li,and W.A.Halang are with the Faculty of Mathematics and Computer Science,Fernuniversit?t in Hagen,58084Hagen,Germany(e-mail: hong.li@fernuni-hagen.de;zhong.li@fernuni-hagen.de;wolfgang.halang@fer-nuni-hagen.de).

W.K.S.Tang is with the Department of Electronic Engineering,City Uni-versity of Hong Kong,Hong Kong,(e-mail:kstang@https://www.360docs.net/doc/5116226509.html,.hk).

Digital Object Identi?er10.1109/TCSII.2008.922379converters[7].Since the basic usage of dc–dc converters is for power supply,large ripples simply imply a degradation of performance.This problem has been previously pointed out in[11],and an explicit expression between the ripples and the spectral spreading of the current was given.It is still a dif?cult task,however,to design a suitable control in order to suppress the ripples to a desirable level.Moreover,the power of the background spectra has been increased in most designs, although the peak values of the power spectrum are reduced, resulting in larger power consumption.

These two disadvantages not only exist in the peak cur-rent-mode controlled boost converters,but also in other chaotic power converters[8],[9],which have seriously impeded their popularity.Hence,answering the questions of how to improve the control method for chaos-based dc–dc converters so that low EMI and small output ripples can be achieved and how to verify the relationship between the ripples and background spectrum constitutes the concern of this paper.Obviously, once the proposed solution is made available as a marketable technology,its commercial impact is tremendous.

The organization of this paper is as follows.In Section II,a novel peak current-mode boost converter is presented,and its corresponding chaotic mapping function is derived.The char-acteristics of the mapping are then analyzed in Section III,fo-cusing on its spectrum analysis,bifurcation,and chaotic behav-iors.Its effects on EMI reduction and ripple suppression are studied and supported with simulation results given in the same section.To further verify our design,the entire system was built, and experimental results are presented in Section IV.Finally, some concluding remarks and the outline of future work are given in Section V.

II.M ODEL OF A C HAOTIC C URRENT-M ODE B OOST C ONVERTER Inspired by[4],a novel chaotic current-mode boost converter with simple circuitry implementation is proposed as depicted in Fig.1.

Unlike the design in[4],the

switch is now controlled by a clock with

period,and a lower reference current signal and an upper one,denoted

by

and,respectively.Dif-ferent inductor current waveforms can be obtained as shown in Fig.2(a)–(c),corresponding to the following three cases,re-spectively:

Case

I:

Case

II:

Case

III:

where is the rising time of

from

to is the falling time of

from

to,

and.In

1549-7747/$25.00?2008IEEE

Fig.1.Chaotic current-mode boost converter.

order to facilitate the analysis of the proposed converter,now the discrete-time mapping of is derived.

Referring to Fig.2,we consider the time interval of varying

length,in which changes

from

to,

with

de?ned as the inductor current sampled at the instants of the

clock pulses as is decreasing

[e.g.,in Fig.2(a)–(c)],and

the instants of the clock pulses when is increasing with the

switch activated twice or more within a single clock cycle

[e.g.,in Fig.2(b)and(c)].For clarity,a time mapping is

also assumed,such

that

when.Referring to

Fig.

2,is closed

at,and

hence

(1)

where is input voltage

and is the inductance.

Let be the time required for the current

from to

reach

.Based on(1),we

have

(2)

The

switch is then opened,

and is governed

by

(3)

where is the mean output voltage.

Therefore

(4)

until the next clock pulse arrives

or.

As explained in[4],it is possible to estimate the mean output

voltage by equating the mean of the aperiodic inductor cur-

rent with a periodic one.It is derived

that is governed by the

following input–output

relationship:

(5)

where based on the design given in

[4].

Fig.2.Different current waveforms i(t)obtained from the boost converter.(a)

Case I:t

T.(b)Case II:

T

T>t.(c)Case III:

T

T.

Here,a similar approximation is performed,and(5)is still

applicable,except

that not only depends

on,but also on

the values

of

and for Cases II and III(these two cases

are our main concern).It is also observed

that is proportional

to but inversely proportional

https://www.360docs.net/doc/5116226509.html,ing the?rst-order

approximation,can be expressed

as

(6)

where

and are constants to be determined.Based on ex-

tensive experimentation,it is found

that

and

and,

hence,can be obtained by solving(5).Circuit

simulation revealed that the relative errors

of are well within

2%,which is much better than what was reported in[4].