MULTIWAY SPEAKER SYSTEMS WITH WAVE DIGITAL BRANCHING FILTER BANK

Transcription

1 MULIWAY SPEAKER SYSEMS WIH WAVE DIGIAL BRANCHING FILER BANK Adam Dąbrowski 1 Krzyszof Sozański 2 1 Ins. of Elecronics and elecommunicaion, De. of Elecrical Engineering Poznań Universiy of echnology, ul. Piorowo 3a, Poznań, dabrow@e.u.oznan.l 2 De. of Mahemaics, Physics and echnology, Pedagogical Universiy of Zielona Góra al. Wojska Polskiego 69, Zielona Góra, sozanski@asia.aw.ws.zgora.l Absrac his aer describes a digial modulaor for a class D ower audio amlifier using he oversamling and noiseshaing echniques. Resuls of he simulaion of he ouu signal secrum for he ineresing frequency band of a sinusoidal inu signal are shown. Such modulaor achieves a signalonoise raio (SNR) near o 88dB. he conce for an analogue comensaing circui for suressing he ower suly rile is also resened. I. INRODUCION he hysics of sound reroducion makes i quie difficul for a single seaker o handle he whole audiofrequency range. herefore, for high fideliy alicaions, mos seaker sysems consis of mulile seakers, each of hem reroducing a secific band of he overall audiofrequency range. In yical realizaions, his range is divided ino wo or hree bands. Using CD layers, RDA, Sony mini discs, digial audio rocessors, digial V, digial broadcasing sysems, and so on, we have a direc access o he digial signal sources. herefore i is reasonable o suly digial signal direcly o he seaker. his idea, which is based on he conce of a digial modulaor driving he classd ower audio amlifier and on he noiseshaing echnique, is resened in his conribuion. II. HE DIGIAL SPEAKER SYSEM Block diagram of he digial seaker sysem is deiced in Fig. 2 [1, 2, 3]. he digial inu signal (in he CD layer sandard, i.e. wih samling rae f s =44.1kHz) is divided ino wo channels: lef and righ, by a digial audio inerface receiver. hen i is sli ino wo bands: a lowass and a highass band using a wave digial branching filer bank. Wave digial filer bank has been chosen no only for is owercomlemenariy bu also because of oher well known advanages of wave digial filers such as small sensiiviy o coefficien variaions, robus sabiliy and so on [4]. he ne sage is a hybrid PWM modulaor. For suression of he quanizaion and he modulaion noises he oversamling echnique ogeher wih he noiseshaing echnique are imlemened in he hybrid PWM modulaor. he ouu signal from he modulaor is a square wave wih he duy raio deending on he reresened values. his signal conrols he ower ulse amlifier hrough a secialized analogue comensaing circui roosed in his aer. In he resen version, ulsewidh modulaors (PWM's) conneced o he ulse ower amlifiers serve as D/A converers. For suressing he ower suly rile, an analogue comensaing circui is used. Addiional assive LC lowass filer is used in order o suress he noise and he disurbing modulaion roducs. Power Pulse Amlifier Simlified diagram of a ower ulse amlifier is shown in Fig. 1. he inu signals G 1H and G 1L are ransformed by he gae drivers and conrol gaes of he ower MOSFE ransisors 1 and 2. he swiching frequency of his circui can be as high as ca. 1MHz [5] according o he use of he ulra low gaecharge MOSFEs and high seed gae drivers. he ower ulse amlifier is sulied by wo equal volage sources V1 and V2. Seaker is conneced o he inverer ouu hrough a assive LC lowass filer in order o suress he noise and he modulaion frequency. G1H G1L GROUND High Seed Gae Drivers 1 2 D1 D2 Us C1 SPEAKER Figure 1: Simlified diagram of a ower ulse amlifier L1 V1.5Us V2.5Us

2 fs =44.1kHz f s f s R f s =352.8kHz R f s R f s = Digial signal from CD layer DAI Receiver Filer Bank Inerolaor R Hybrid PWM Modulaor Noise Shaing D/ Converer Analog Comens. Power Sulier Pulse Amlifier o second channel o highass band LC Filer & Seaker ime resoluion r =1/(N R f s )=1/( kHz) 22.1ns Figure 2: Block diagram for he roosed digial seaker sysem INPU γ HP OUPU γ 1 γ 2 LP OUPU a 1 a 2 a 3 Figure 3: Block diagram for he digial branching filer bank Wave digial branching filer bank In a yical hree way crossover sysem, he audiofrequency range is divided ino hree searae bands. In our case, we use wo bands only, namely he weeer band and he join woofer/midrange band. In boh considered acivedigial crossover versions, hey are realized using a wave digial branching filer bank shown in Fig. 3 [3, 4]. An addiional lowass FIR filer cascaded wih he lowass branch forms a correced woofer/midrange band. he funcion of his filer can also be referred o as he midrange correcion, because, by his means, we reduce he midrangebandgain of he owercomlemenary wave digial branching filer bank, comensaing he nonuniform frequency characerisic of wo idenical woofer/midrange seakers used in he eerimenal sysem. Hybrid ulse widh modulaor he idea of he modified ulsewidh modulaion (PWM) echnique used in our sysem is deiced in Fig. 1. he modulaor inu signal (i.e., he ouu signal of he filer bank) is firs R imes inerolaed; R being he oversamling raio of his signal samled originally wih frequency f s.=44.1khz he idea of oversamling consiss in an increase of he signal samling rae o he value for which a lowresoluion quanizer is sufficien for he signal reresenaion wih required recision. herefore using oversamling, we can reduce requiremens for D/A converer (quanizer) which oherwise should be a very recise and eensive elemen. In our soluion [1, 2], he ower ulse amlifier works as a onebi D/A converer In he ne se, he quanizaion noise is shaed. he modulaed signal is hen convered ino signals conrolling he ower inverer. he chosen oversamling raio R=8 is a comromise beween he ower MOSFE swiching losses and he seleciviy of he ouu assive lowass smoohing filer. he ransisor swiching frequency is

3 R f s =352.8kHz. In he ne se, he quanizaion noise is shaed. he modulaed signal is hen convered ino signals conrolling he ower ulse amlifier. he facor N =128 is used o guaranee he required imeresoluion of he conversion of digiallycoded magniudes o ransisor swiching imes in he ower ulse amlifier. I gives he swiching frequency equal o f s R N = MHz, and he ime resoluion r =1/ MHz 22.1ns. his value is suiable for ordinary HCMOS couners. Digialoanalog converers wih noise shaing Differen circui archiecures can be used for secral shaing of he quanizaion noise, i.e. moving i away from he band of ineres f B oward higher frequencies. Block diagram of he circui using a linear quanizer model wih noise shaing is shown in Fig. 3. Ouu signal can be calculaed as Y ( z) = X( z) H ( z) E ( z) H ( z). (1) q s q n Signal and noises ransfer funcions are given by equaions Hz ( ) H ( ) s z = and 1 H ( ) 1 Hz n z =, (2) ( ) 1 Hz ( ) resecively. X(z) H(z) E q (z) Y(z) Figure 4: Block diagram circui wih noiseshaing Y q (z) A roerly designed circui wih noise shaing has fla frequency resonse H s (ω) in he signal frequency band f f B. On he oher hand, H n (ω) should have high aenuaion in he frequency band f f B and a low aenuaion in he band f B f f s. For a low oversamling raio R, an efficien way o increase he signalonoise raio is he use of a secondorder loo filer. Delasigma modulaors (DSM's) have been used eensively in many alicaions as high qualiy ADC's and DAC's [7, 8, 1]. he linear model of he second order DSM is shown in Fig. 5. Is zdomain ouu can be eressed as a sum of he signal and he quanizaion noise comonens by using a linear quaniser model. Yz ( ) = Xzz ( ) ( 1 z ) Ez ( ) (3) Noe ha he inu signal aears a he ouu hrough a single delay, corresonding o an allass funcion. he NF is he eression ha shaes he noise secrum E(z). he noise ransfer funcion of he second order delasigma modulaor is deiced in Fig. 6. For an oversamling raio R=8 DSM, he achieved noise suression facor is near 23dB. X (z) z 1 z 1 E(z) Y (z) Figure 5: Linear model of he secondorder delasigma modulaor db db 2 4 NF Magniude Resonse Hn= 1 1 R=8 order= Normalized frequency (1>fs) 2 4 rms gain = 23dB Normalized frequency (1>fB) Figure 6: he noise ransfer funcion of he second order delasigma modulaor for R=8 Digial o ime converer wih noise shaing Idea for a D/A converer [1, 2] wih he D/A conversion error comensaion can be combined wih he idea of he PWM D/A converer based on he second order DSM as deiced in Fig. 7. he inu signal X(z) is ransformed ino signals G 1H and G 1L conrolling he ower inverer MOSFE ransisors. High levels of hese signals swich on he resecive ransisors. When signal G 1H is in he high sae, he eriod 1H is calculaed using (4) and eriod 1L is calculaed using a similar equaion for signal G 1L in he high sae. ( ) 1H = for Y z < or k ( ) cyz < ON min Y( z) 1H = ONma for k c > (4) ON ma 1H = ( Y( z )) Y( z ) 1H = in kc for > and k Yz ( ) c > ON min and k Yz ( ) c < ON ma where: k c is an auiliary coefficien, ON MOSFE ransisor swich on ime.

4 4 1 he simulaed ouu secrum for he ineresing signal band for a sinusoidal inu signal wih 2/3f B frequency is shown in Fig. 8. his converer achieves he signalonoise raio (SNR) near o 88dB. X (z) z 1 z 1 Figure 7: Block diagram of PWM D/A 2 DSM PW M Ouu Secrum of fb SNR = 88.1dB R = 8 N = 496 order = 2 N = 128 G 1H D/ Converer G 1L Y(z) D/ Model Y q (z) A soluion of such a comensaion circui for he coninuous ime inu signal can be a onecycle conrol circui [9]. A simlified diagram of such a circui is shown in Fig. 1. he duyraio of a swich is conrolled in such a way ha in each cycle he average value of he swiched variable of he swiching circui is eacly equal or roorional o he conrol reference in he seady sae and in he ransien sae. Onecycle conrol recisely follows he conrol reference in one swiching cycle. his guaranees ha a wide bandwidh can be achieved. Onecycle conrol effecively rejecs he ower source rile and rocesses ower and signal in one sage, herefore, no recision dc ower source is necessary. As a maer of fac, a recified bu unregulaed ower source wih small caacior can be used as he dc ower source. Onecycle conrol auomaically correcs he ower swich ransien error and he conducion error. As a resul, no swiching comonen maching is necessary. he ouu has no crossover disorion. High lineariy is achievable. Us 4 1 D1 U L1 SPEAKER V1 Us1=.5Us dbfs 6 Gae Driver 2 D2 C1 V2 8. Us2=.5Us 1 Narrow Pulse Generaor CA1 SA3 R fb normalized sygnal band frequency 5 6 PR CL U1A 7474 D 2 CLK 3 KA1 COMP R3 R4 Uin UA1 OPAMP R2 Figure 8: Ouu secrum of hybrid PWM based on DSM Clock R5 Vin Uos Analog Comensaion Circui Simlified model of he ower ulse amlifier swich (ransisor) [6] is shown in Fig. 7. he ransfer funcion is described by equaion y = Din (5) where: reresens he suly volage, y reresens he ouu volage, D in is he inu duy raio. he suly volage rile is ransformed o he ouu signal. For high qualiy alicaions, a high erformance sulier or a secial rile comensaion circui are needed. Figure 1: Simlified diagram of a onecycle conroller Clock U U in V' in D in D in y y P Figure 11: Waveforms of a onecycle conroller P Figure 9: Simlified model of inverer swich

5 he conrol funcion of onecycle conroller is calculaed by equaion 3 1 u RC uos RC 1 A1 2 A1 ' d = v (6) in and he local average of u is roorional o he inu signal v in u 1 u = kvin d. (7) D 1 τs Figure 13: Small signal model of he comensaion circui y Us D1 1 U L1 SPEAKER V1 Us1=.5Us Gae Driver 2 D2 R1 U1 C1 V2 R2 Us2=.5Us. Digial conrol block Block of inegraor Swiches block C Uref1=.5Uref PLD UA1 R U? OPAMP SWICH Uref2=.5Uref Din Figure 12: Diagram of analogue comensaion circui he coninuousime signal used by a onecycle conroller is no convenien for a digial signal source. For his urose an analogue comensaion circui is roosed by he auhors. Simlified diagram fo his comensaion circui is shown in Fig. 12. Inu signal is a square wave wih duy raio D in and he ouu signal is a square wave wih duy raio D ou. For all comonens consan during he swiching eriod, i is ossible o calculae D ou from equaion U ref 2 D ( n) ( ) ( ( )) U ( n) D n D n U ref 1 ou = in 1 in U ( n) 1P 1P (8) U ( n ) 1N 1 ( 1 D ( n ) ou 1 ) U ( n) 1P where: U ref1, U ref2 reference volages, U 1P ouu volage when ransisor 1 is swiched on, U 1N ouu volage when ransisor 2 is swiched on. A simlified small signal model of he comensaion circui and is rile rejecions for differen duy raios D in are shown in Figs. 13 and 14. Is small signal ransfer funcion is τs y = D 1 τs where: τ inegraor ime consan. (9) Figure 14: Comensaion circui rile rejecion III. CONCLUSION In he furher research, he noise shaing circui will be develoed o achieve beer noise rejecion. In he auhors' oinion, he classd ower amlifier, and esecially ha wih he digial inu, will be more oular in near fuure, esecially for high ower audio alicaions. he imlemenaion of he resened digial modulaor for he classd audio ower amlifier is in he final design sage using MS32C31 signal rocessor. In near fuure he designed digial modulaor will be esed in he laboraory. References [1] A. Dąbrowski, K. Sozański, Alicaion of PWM echnique and a Wave Digial Filer Bank o Signal Conversion in Muliway Seaker Sysems, 4 h Inernaional Worksho Mied Design of Inegraed Circuis and Sysems MIXDES'97, Poznań, Poland, [2] A. Dąbrowski, K. Sozański, Comarison of Alernaives for Digial Branching Filering (crossover sysems) and DigialAnalog Conversion for Alicaion o Seaker Sysems, 4 h Inernaional Worksho on Sysems, Signals and Image Processing IWSSIP'97, Poznań, Poland, 1997

6 [3] A. Dąbrowski, M. Poralski, K. Sozański, Design of Digial Branching Filer Banks for Muliway Seaker Sysem, Proceedings of XIXh Naional Conference Circui heory and Elecronics Circuis, Krynica [4] A. Feweis, Wave Digial Filers: heory and Pracice, Proceedings of he IEEE, Vol. 74, NO. 2, February 1986, [5] HIP481A, 8V/2.5A, High Frequency Full Bridge FE Driver, Daa Shee, Harris Semiconducor, March [6] Lai Z., Smedley K., A Low Disorion Swiching Audio Power Amlifier, IEEE Power Elecronics Secialis Conference, Alana, June [7] Oversamling delasigma daa converers. heory, Design, and Simulaion, Edied by J. C Candy, G. C. emes, IEEE Press [8] R. Schreier, Oversamling delasigma daa converers, Oregon Sae Universiy [9] Smedley K., Ćuk S., Swiching FlowGrah Nonlinear Modeling echnique, IEEE ransacions on Power Elecronics, Vol. 9, No. 4, July [1] he DelaSigma oolbo for Malab designed by R. Schreier, Oregon Sae Universiy 1996.