A Low Cost and High Quality Duty-Cycle Modulation Scheme and Applications

Transcription

1 World Acadey o Science, Engineering and Technology International Journal o Electrical and Coputer Engineering Vol:8, No:3, 04 A Low Cost and High Quality Duty-Cycle Modulation Schee and Applications B. Lonla Moo, J. Mbihi, L. Nnee Nnee Digital Open Science Index, Electrical and Coputer Engineering Vol:8, No:3, 04 waset.org/publication/ Abstract In this paper, a low cost duty-cycle odulation schee is studied in depth and copared to the standard pulse width odulation technique. Using a ix o analytical reasoning and electronics siulation tools, it is shown that under the sae operating conditions, ost characteristics o the proposed duty-cycle odulation schee are better than those provided by a standard pulse width odulation technique. The siulation results obtained when testing both odulation control policies on prototyping systes, indicate that the proposed duty-cycle odulation approach, appears to be a high quality control policy in a wide variety o application areas, including A/D and D/A conversion, signal transission and switching control in power electronics. Keywords Duty-cycle Modulation, Operational apliiers, Pulse width odulation, Power electronics, Signal processing. T I. INTODUCTION HE duty-cycle odulation (DCM) is used in industrial electronics, as a special signal processing technique with a switching periodic output wave. As an iplication, the dutycycle o the odulated wave evolves according to a known unction o the odulating input ([], []). A variety o DCM architectures are encountered in the literature [], each o which being characterized on by a given hardware architecture and a speciic duty-cycle structure. eally speaking, the pulse width odulation () is a subclass o DCM techniques with constant odulation requency. It is widely used in power control electronics ([3]-[7]) as a very eicient eans or controlling the power low delivered to a load. It is used also in instruentation engineering or the ipleenting o a class o analog-to-digital (A/D) and digital-to-analog (D/A) converters ([8]-[4]). However, although the technique reains very popular in a variety o application areas, the ai o this paper is to outline the attractive characteristics o the proposed DCM schee copared to the weaknesses. J. Mbihi is with the esearch laboratory o industrial coputer sciences and autoation engineering, in the Advanced Teachers Training College (ATTCO) or Technical Education, University o Douala, Caeroon (eail: bihidr@yahoo.r). B. Lonla Moo is with the esearch laboratory o industrial coputer sciences and autoation engineering, in the ATTCO or technical education o the University o Douala, and with the Departent o electrical and electronics engineering o the College o Technology, University o Buea, Caeroon (e-ail: oolb@yahoo.r). L. Nnee Nnee is with the esearch laboratory o industrial coputer sciences and autoation engineering, in the ATTCO or technical education, University o Douala, Caeroon (e-ail: leandren@gail.co). The reaining o this paper is organized as ollows: In Section II, the architecture o the proposed DCM schee and that o the standard technique are presented or the sake o coparison. In Section III, the requency analysis o the odulated wave provided in each case is conducted. Then, the results obtained when testing both odulation control policies on recent and new application areas are outlined in Section IV, whereas a coparative analysis between the two odulation techniques is done in Section V, in order to outline the erits o DCM principles and properties. II. ACHITECTUE OF MODULATION SCHEMES The standard and the proposed DCM schees are presented in Fig. or the sake o coparative study. Without loss o generality, the coon technology retained or the ipleentation o both odulation techniques, is based on the use o integrated operational apliiers. The DCM odulation circuit shown in Fig. (a) has been selected ro the class o odulation circuits studied in reerence [] or signal conditioning in industrial instruentation. It is built using a controlled negative resistance oscillator connected to a linear capacitance, whereas the standard circuit described in Fig. (b) consists o a switching coparator with two inputs (triangle wave and odulating control signal). It is iportant to observe that the hardware coplexity o a circuit is greater than that o the DCM cell. Another iportant reark between the two is that, the odulation period T or requency equivalently, is constant at the output o a circuit. Conversely, in the case o DCM technique, the period T DCM or requency DCM evolves according to the variation o the control input u, with a axiu value reached when the control input is set to u 0 volt (see Appendix or details). The coon behavior between DCM and techniques is that, the resulting output odulated signals provided in each case is a switching periodic waveor. As it will be seen later in this paper, a set o attractive properties is hidden behind the structural siplicity o the proposed DCM circuit. Furtherore, the resulting duty-cycle associated with each switching periodic odulated wave as drawn in Fig. is given by: International Scholarly and Scientiic esearch & Innovation 8(3)

2 World Acadey o Science, Engineering and Technology International Journal o Electrical and Coputer Engineering Vol:8, No:3, 04 Digital Open Science Index, Electrical and Coputer Engineering Vol:8, No:3, 04 waset.org/publication/ Fig. (a) Basic DCM circuits considered in this paper (b) Basic circuits considered in this paper Ton T Ton T or DCM or Although the odulation period T DCM depends on the control input u, its iniu value T DCM (0) is achieved or u 0. It is assued in this paper that both odulation circuits presented in Fig. have equal basic clock requencies given by (see Appendix ): / T DCM (0) / () T () In addition, within a suiciently wide neighborhood o the ixed point (0, (0)), the duty-cycle unction provided in each case behaves as linear unction o the related odulating control with intrinsic design paraeters. Thus, in the case o DCM, the duty-cycle could be coputed ater a straightorward developent as in [5]: with, p DCM DCM α ( α ) p DCM E( α ), + α log α u + (3.a) α (3.b) + In the case o circuit, the duty-cycle could be coputed as ollows [6]: International Scholarly and Scientiic esearch & Innovation 8(3)

3 World Acadey o Science, Engineering and Technology International Journal o Electrical and Coputer Engineering Vol:8, No:3, 04 with, p u p u + (4.a) ax E 4 0 (4.b) odulation circuits. A ayor discovery eerging ro the siulation results presented in Fig. is that, under the sae operating conditions, the spectru o the DCM output signal is better in ters o rapid convergence and onotonous trend, than that o the output wave. Digital Open Science Index, Electrical and Coputer Engineering Vol:8, No:3, 04 waset.org/publication/ III. FEQUENCY CHAACTEISTICS OF MODULATED WAVES The Fourier series o odulated waves presented in Fig., are given by: U + n ( u, t) ( ) C (0, u) : Low requency ter 4 E sin( nπ ) cos π n C ( n, u) High E requency t π n T ( ) u ters where the subscript stands or DCM or policy. Given equations (3) and (4), the odulating signals could be recovered in each case ro (5) using appropriate low-pass ilters with static gains: ( α ) α (5) DCM ( α ) + α K log (6.a) α K u ax E 0 (6.b) For the sake o better coparison o the spectra o DCM and waves, we resort here to the concept o noralized spectru. A noralized spectru is obtained ro the aplitude copression o haronics. The related noralized aplitudes are deined ro (5) given (3) or (4) as ollows: C Nor Sin n π p u + C ( n, u) ( n, u) (7) C (, u) Cos( π p u) For n,,, where the subscript stands or DCM or policy, and p been given by (3) or (4). Thus, in the adissible odulating range, the noralized aplitude related to the irst haronics is or any control input u. Given the odulation scheatic diagras drawn in Fig., the absolute spectru o odulated outputs resulting ro (5), has been siulated with the help o Matlab, in the odulating range [- ] volts. The values o coponents labeled on each scheatic diagra, have been appropriately chosen in order to aintain the sae operating conditions (input odulating range [- ] volts, and equal basic requencies) or both 4 Fig. (a) Spectral representation o DCM signal (b) Spectral representation o signals International Scholarly and Scientiic esearch & Innovation 8(3)

4 World Acadey o Science, Engineering and Technology International Journal o Electrical and Coputer Engineering Vol:8, No:3, 04 Digital Open Science Index, Electrical and Coputer Engineering Vol:8, No:3, 04 waset.org/publication/ As an iplication, the rapid convergence o the DCM spectru, along with the act that the DCM period T DCM depends on the odulating input, appear to be new attractive properties or a variety o application areas investigated in the Section IV. IV. APPLICATIONS AEAS OF THE POPOSED DCM TECHNIQUE A. ecent Application Areas ecent research works have shown the great erits o the DCM principle and characteristics, when using or the ipleentation o novel analog-to-digital (A/D) and digitalto-analog (D/A) converters in [7], [8] and [9] respectively. Following the indings eerging ro these pioneering works, the challenge brought by DCM-based A/D and D/A converters aong ost existing signal conversion A/D and D/A techniques (including -based technique), relies on the act that the DCM technology oers iniu hardware cost, while providing iniu digital processing coplexity. Furtherore, in power electronics, a DCM device has been used and well tested in [0], as a better switching controller or Buck power converters. B. A New Application Area The new application area o interest o the DCM technique explored in this section is a transission syste presented in Fig 3. Both DCM and are considered or the sake o coparison. It is assued the transission line is lossless in each case. In addition, the deodulation circuits used are second order low-pass ilters, with appropriate static gains K DCM or K given by (6), and the sae cut-o DCM requency. Since K > and K <, an inverter is necessary at the output stage o the ilter. Given the 3D spectra o both DCM and presented in Fig., it is obvious to predict that, i the coon cut-o requency o deodulation ilters, is suiciently greater copared to the odulating requency range, then both DCM and odulation techniques should provide siilar outputs y DCM (t) and y (t) respectively. Otherwise, using nuerical siulations, it is interesting to analyze what would happens under an increase o the odulation requency range or a ixed cut-o requency associated with these equivalent ilters. The coparative results presented ro Figs. 4 to 5, have been obtained using National Instruent Multisi sotware. In Fig. 4, the odulating input is set to u(t) sin(0 π t). As a result, Figs. 4 (a) and (b) present a zooed view o odulation signals (ic, u ) and (ic 4, u DCM ) respectively. In Figs. 4 (c) and (d), the DCM and techniques provide siilar behaviors in ters o both the shape and the overall delay related to output waves y DCM (t) in Fig. 4 (c) and y (t) in Fig. 4 (d) respectively. In addition, Fig. 5 shows how in the case, an increase o the odulating requency yields greater decreasing eects on the aplitude o the output wave y (t). In addition, the shape o u (t) as observed on Fig. 4 (a) shows that, its ean behavior is a sine wave with the save requency as the odulating control. However, this ipressive phenoenon, is not apparent on the graph o the output wave y (t) provided in Fig. 4 (b). Fig. 3 Prototyping lossless transission syste C. Coparative Study o DCM and Techniques Table I presents a suary o the coparative study between the characteristics o DCM and techniques. The ain target application areas o and DCM techniques are listed in the irst colon, whereas the coparative criteria retained or each application area written in the second colon. The characteristics o both standard and DCM techniques are provided also in the third and ourth colons respectively. The results eerging ro coparative studies indicate that, aong a set o 0 criteria retained or a variety o application areas, the DCM technique provides less weaknesses. Thus, it International Scholarly and Scientiic esearch & Innovation 8(3)

5 World Acadey o Science, Engineering and Technology International Journal o Electrical and Coputer Engineering Vol:8, No:3, 04 ight becoe a ore suitable odulation control policy in ost application areas where is coonly used today. Digital Open Science Index, Electrical and Coputer Engineering Vol:8, No:3, 04 waset.org/publication/ Fig. 4 Siulation o transission systes or a low requency input u(t) sin(0 πt). (a) Zooed view o DCM s odulation signals (b) Zooed view o s odulation signals (c) DCM input and output wave (d) input and output wave Fig. 5 Siulation o transission systes or an increase in the odulating requency International Scholarly and Scientiic esearch & Innovation 8(3)

6 World Acadey o Science, Engineering and Technology International Journal o Electrical and Coputer Engineering Vol:8, No:3, 04 TABLE I COMPAATIVE STUDY OF DCM AND TECHNIQUES UNDE THE SAME OPEATIONAL CONDITIONS Application area Coparative criteria technique Proposed DCM technique A/D conversion Hardware coplexity and cost Higher Lower Oversapling cost Higher Lower 3 Digital deodulation cost Lower Lower D/A conversion 4 Digital processing cost (ro Fourier series) Higher Lower 5 Coplexity o the hardware conversion logic Higher Lower Buck converter control 6 Hardware coplexity Higher Lower 7 High requency stresses on power switches Higher Lower Signal transission 8 Nuber o operational apliiers Higher Lower 9 Modulating bandwidth Lower Higher 0 Nonlinear range o the duty-cycle unction Lower Higher Digital Open Science Index, Electrical and Coputer Engineering Vol:8, No:3, 04 waset.org/publication/ V. CONCLUSION This paper has studied in depth the attractive properties o a proposed low cost and high quality DCM technique. It undaentally diers ro standard principle since the odulation requency involved depends on the odulating input. Copared under the sae operating conditions to the standard policy with a ixed odulation requency, the DCM technology provides better characteristics in ost application areas where they have been well tested. The contribution o this paper has been to outline a ew weaknesses o the standard odulation technique, even though it reains coonly used today in ost application areas. Thus, the challenge o DCM techniques results ro both its architectural siplicity and high quality due to a better behavior o the odulation requency spectru. It will be very ruitul to extend the use o DCM techniques to the control o other types o switching DC-DC power converters, and to the control o power DC-AC inverters with great ephasis on electronic starters or both synchronous and induction achines. It will be interesting also to developed DCM devices and drivers using FPGA-based ebedded technology. These aoreentioned issues appear to be potential opportunities or uture research works. APPENDI SHAPE OF DCM AND MODULATION FEQUENCIES ecall that the requency is constant while the DCM requency DCM is dictated by the odulating input u. A straightorward analysis o the DCM circuit presented in Figs. (a) or (a) equivalently, leads to: with T ( u ) ln ( α ) ) u ( + α )E ( α ) ) u ( α )E τ τ C and α 3 + Fig. 6 The shape o DCM and odulation requency EFEENCES [] E. oza, "Analog-to-digital conversion via duty-cycle odulation", IEEE transactions on circuits and systes II: Analog and digital signal processing, Vol. 44, No., pp , 997. [] J. Mbihi, F. Ndjali Beng and M. Mbouenda, "odelling and siulation o a class o duty-cycle odulators or industrial instruentation", Iranian Journal o Electrical and Coputer engineering, Vol. 4, No., pp. -8, 005. [3] Joachi Holtz, Pulse width odulation - a survey, IEEE transactions on industrial electronics, vol. 39, no. 5, pp , Deceber 99. [4] G. C. Ioannidis a, G. Charokopos b, P. Marabeas b & S. N. Manias, A ixed-ode controller, International Journal o Electronics, Vol. 97, No., Deceber 00, [5] T. D. Batzel and Mihai Coanesu, Instantaneous voltage easureent technique or voltage source inverter, International Journal o Power Electronics, Vol., No, pp. -5, 008. [6] M. A. Patel, Ankit. Patel, Dhaval. Vyas and Ketul M. Patel, Use o Techniques or Power Quality Iproveent, International Journal o ecent Trends in Engineering, Vol., No. 4, pp. 99-0, May 009. [7] A. K. Dewangan, N. Chakraborty, S. Shukla, V. Yadu, based autoatic closed loop speed control o DC otors, International Journal o engineering trends and technology, Vol. 3, Issue, pp. 0-, 0. [8] M. M. Abdel Aziz, Sipliied approaches or controlling DC-DC power converters, International Journal o Engineering sciences and Technology, Vol. 4, N, pp , February 0. International Scholarly and Scientiic esearch & Innovation 8(3) 04 58

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