Flter mplementaton for CMOS adaptve samplng Delta Modulators R. Golansk, J. Godek, J. Kolodzej, W. Machowsk, S. Kuta, Department of Electroncs, AGH-UST Unversty of Scence and Technology, Krakow, POLAND {golansk,godek,jackolo,machowsk,skuta}@agh.edu.pl Abstract We llustrate the dea of the buldng delta modulator/demodulator wth the help of the non-unform samplng method. Each of element, both analog and dgtal, that s used for ths realzaton can be put together on one chp, makng up a pece of the System on Chp crcut or the ASIC chp dedcated to specal purpose, such as: measurng, communcaton, control systems, data compresson, data encrypton wreless telecommuncaton. The Adaptve Non-unform Samplng Delta Modulators (ANS-DM) modulaton algorthm mplementatons, and the codec archtecture are descrbed n the paper also. We present a comparatve study of ntegrated CMOS contnuous tme (CT) analog flters dedcated for speech codecs wth adaptve non-unform samplng. Fve CMOS mplementatons of ths block have been studed, four of them fabrcated n.35 µm CMOS technology. The system consderatons and smulaton results are shown. Keywords adaptve delta modulaton, CMOS crcuts, swtched-capactor flters, contnuous tme flters, ant-alasng flters, non-unform samplng, speech codecs. T I. INTRODUCTION HE nvestgaton amed at the mprovement of analog to dgtal converson effcency prove that not all potental possbltes of delta modulaton analog sgnal processng have been fully utlzed, so far [1]. The concept of usng adaptve samplng to reduce the data rate of source codng s very promsng theme, however studed only fragmentarly [2]. The nvestgaton amed at the mprovement of analog to dgtal converson effcency prove that not all potental possbltes of delta modulaton analog sgnal processng have been fully utlzed, so far [1]. The concept of usng adaptve samplng to reduce the data rate of source codng s very promsng theme, however studed only fragmentarly [2]. The long-term research works [1, 3, 4] allow to affrm, that reachng hgh accuracy and large nose mmunty n wde dynamc range, wth use of the unform samplng ADM converters, s not possble. Therefore we propose use of the 2 parameters, 1-bt PCM dfferental modulaton, whch n fact depends on applcaton of adaptaton of both the step sze and samplng nterval. The results of smulatng works proved that for nonstatonary sources, the adaptve samplng delta converters expose hgher codng effcency than the former proposals, based on unform samplng methods. Classfcaton and evaluaton of the ADM converters solutons presented n the works [4, 5], ncludng conceptual studes, enabled constructon of the adaptve samplng converters (NS-DM and ANS- DM) prototype crcuts. The studes of the solutons proved that, at present, fully effcent hardware mplementaton of adaptve samplng delta converters concepton on the base of mcroprocessor standard chps, s possble. The work was amed at elaboraton of analyze methods and performance evaluaton of the flters for delta systems wth step sze and samplng rate adaptaton. It comprsed the studes of mathematcal descrpton, computer smulatons, and desgn methodology, as well as proposal of electronc crcuts mplementaton. Wthn analytcal part, the method of descrpton of the performances of the flters for adaptve samplng delta converters has been worked out. The method of desgn of the flters archtecture was proposed. In smulatng nvestgatons, performance of the flters were analyzed. The unque approach to ths nvestgatons enabled comprehensve comparson of former and new solutons. Each practcal desgn must be done n specfc technology, so ntally our choce was an 2P4M.35µm CMOS technology from austramcrosystems (AMS), and all the presented smulaton/measurements are done for ths specfc slcon foundry. However the crcut solutons are transferable nto more advanced technology node (e.g. 18nm CMOS from Unted Mcroelectroncs Corporaton) wth mproved elements especally capactors whch have sgnfcantly lower parastcs. NMOS and PMOS transstors for AMS.35 technology have threshold voltages varyng between -.68 -.72 Volt and.46.59 Volt, respectvely. In the framework of our project we nvestgated 5 dfferent flters, 4 of them were manufactured as a part of four test chps. II. PRINCIPLE OF THE ANS-DM MODULATIONS A. Functonal dagram and algorthm of the ANS-DM modulatons The ANS-DM s a modulaton, where both coder parameter s: the step sze and the samplng nstant are adopted. Changes of the nput sgnal level cause adequate a samplng frequency and a step sze adaptaton (Fg.1). Ths Issue 2, Volume 5, 211 159
modulaton has slghtly better codng qualty so SNR s closer to ts maxmal value then others delta modulatons (LDM, NS-DM) were. 1 1 nput sgnal samplng nterval adaptaton step sze adaptaton approxmatng sgnal both parameters adaptaton output data 1 Fg. 1. Tmngs of the ANS-DM modulaton. The ANS-DM scheme has been proposed and studed n [2, 5]. The block dagram of ts dea s presented n Fg.2. ANS-DM base on the Modfed Interval Functon (MIF) and the Modfed Step-sze Functon (MSF). The MIF functon modfes the samplng nterval whle the MSF modfes the step sze accordng to the tme-varyng slope characterstcs of the nput process. In ths way a starcase waveforms ft to the source sgnal better by ANS-DM than others delta modulatons (LDM, NS-DM). For the nput sgnal x(t) the predcted sgnal s(t ) s gven by expresson (1): s(t ) = s(t ) + kd n= 1 where: d = sgn [x(t ) s(t 1 and k -th step sze. )] (1) The output code stream s: 1 for d = 1 b = (2) for d = 1 Let τ s be the samplng nstant and s(t ) - the approxmaton sgnal x(t) at t. The samplng nstant τ s = t +1 - t vary accordng to the characterstcs of x(t) thus the next samplng tme t +1 s expressed as: t +1 = t + τ s (3) a) x(t) d s(t ) Quantzer Predctor Σk f S =1/τ S k D(τ S -1 ) b D(τ S -1 ) Adaptaton Logc τ S (MIF) and q (MSF) b) b D(τ S -1 ) D(τ S -1 ) Predctor y'(t) Σk q y(t) Adaptaton Logc f S =1/τ S τ S (MIF) and k (MSF) Fg. 2. Block dagram of ANS-DM modulator: a) modulator, b) demodulator. LPF x'(t) The samplng nstant τ s s changed accordng to followng algorthm: P τ s-1 for MIF > 1 τ = Q τ -1 for MIF < 1 s s (4) τ for MIF = 1 where: MIF for ANS-DM s descrbed by Table 1; P, Q are the constant factors of samplng nstant modfcaton and ther values are: Q<1 <P. In ths case τ s s placed between the upper bound τ max and the lowest one τ mn. Theτ s start samplng nstant and ts value decdes about the average output bt rate [5, 6]. Table 1. MIF and MSF functons b b -1 b -2 S T S - 1 T -1 MSF MIF 1 1 <1 1 1 >1 1 1 1 1 >1 <1 1 1 1 1 >1 <1 1 H H 1 1 1 1 H H 1 >1 1 1 H H 1 1 1 H H 1 1 1 1 1 H H 1 >1 1 1 H H 1 1 1 1 1 1 1 <1 1 1 >1 1 1 1 1 >1 <1 1 1 1 1 >1 <1 A value of step sze k s modfed accordng formula: R k 1 for MSF > 1 k = (5) k for MSF = 1 Issue 2, Volume 5, 211 16
Down Recever Up Transsmtter Fg. 4. Block dagram of the ANS-DM modulator/demodulator archtecture wth the modfed R.Laane- B.T. Murphy parcelng ntegrator [7] where MSF s descrbed by Table 1; R s the constant factor of step sze modfcaton and R>1. Formulas (4, 5) represents 3-bt Zhu adaptaton algorthm for ANS-DM modulaton [6]. The symbols: <1, >1, 1 mean: decreasng, ncreasng, and comng back to start value of coder parameters. S, T flags. The ANS-DM output bt stream carres the nformaton of not only the changng up or down of the nput sgnal but also of the samplng nstants and the step sze value of the modulator. B. Non-unform samplng CODEC archtecture The ANS-DM codec archtecture, shown on fg.3, s the result of the many research and smulaton experments. Ths soluton conssts of the fve major elements: analog antalasng nput flter, comparator, adaptaton logc block wth the samplng frequences/nstant generator, d/a converter (parcelng ntegrator) and output smooth flter (Fg.3). Codec uses Zhu algorthm [6], that s hardware mplemented as adaptaton logc block. Both encodng and decodng process are the same, therefore, block contans dentcal components: the concdence shft regster, programmable clock dvder and MIF (Fg. 4). All mentoned parts, establsh the tme duraton of the samplng nstant. The next sample s trggered by the programmable clock, but to elmnate computatonal complexty of frequency settng, all necessary parameters are calculated at the begnnng of converson and then store as a dvder value n the Frequency Table. Predctor crcut (Fg.4), whch reconstructs the nput sgnal, s known as a charge parcelng ntegraton [7, 8]. Ths ntegraton technque charges the capactor C I only by a quantum of charge. A controlled amount of the charge s current ndependent and t causes that a constant value of voltage s added to or subtracted from the ntegratng capactor C I. Snce the charge transfer s completely wthn a few nanoseconds the wdths of the pulses from output gates do not affect the charge process consequently. The use of the charge parcelng ntegraton technque avods step sze varatons due to tmng fluctuatons n the star case appearance of the predcted sgnal [7, 8]. The analog nput flter for the ADM encoder realzaton should be smlar to classcal PCM AAF (ant-alasng flters) [9]. Fg.3. Smplfed ANS-DM coder/decoder block dagram. III. FILTER SPECIFICATIONS In PCM codecs usually swtched-capactor (SC) flters are used for ant-alasng purposes. SC flters have very good performance and fulfll sharp PCM requrements passband rpple.125db, dle nose < 6dBrnc, group delay less than 11us and 32dB/16Hz roll-off. The man drawback of ths class however s hgher nose level, whch results wth worsenng sgnal-to-nose rato, as well as hgher (compared wth contnuous tme (CT) flters class) power consumpton [1, 1]. Usually SC flter needs a clock sgnal wth frequency 1 tmes larger than cut-off frequency (3.4 khz for most speech applcatons). However n the case of adaptve non-unform samplng delta modulators constant Issue 2, Volume 5, 211 161
Magntude (db) -2-4 -6 6th order 5th order -8 Phase (deg) -9-18 -27-36 -45 1 2 3 4 5 6 7 8 9 1 Frequency (Hz) Fg. 5. Frequency Response PCM ant-alasng flter frequency SC flter clock together wth varyng samplng frequency may produce on nonlnear elements of codec and flter undesred products of frequency mxng. Some of them may be located wthn the flter s passband, so for ANS-DM applcatons CT flter are recommended. In ths paper we descrbe smulaton and expermental results of nvestgated varants of CT flters dedcated for ANS-DM applcatons. Classcal PCM flters are useful as nput/output flters to the ADM codecs (wth the bt rate not lower than 16 kb/s) [4, 9, 11]. Ffth order ellptc low pass PCM flter provdes the 3,4 khz bandwdth. A 5 Hz thrd order hghpass flter completes the transmt flter paths. Receve PCM flter consst of a 3,4 khz lowpass ffth order ellptc secton and performs band-lmtng and smoothng starcase sgnal. In addton snc gan correcton s appled to the waveform to compensate for the hgher frequences attenuaton caused by the nput capactve S&H crcut [12, 13]. In ths work 1/τ max >16 khz so snc errors are very low and ths block s not mplemented. The output flter should to have a frequency response roll off wth mnmum slope 4 db/dec. and stop-band rejecton equal or greater than 45 db [13]. Flter s frequency response specfcatons are summarzed n Tab.2 [13]. For the sake of smplcty, n the project we focused on lowpass flter mplementaton, assumng that rejecton of the 5-6 Hz supply nterference, wll be consdered separately. As a desred approxmaton of the ant-alasng flter we have chosen a 5 th order ellptc flter (such an approxmaton s mostly used for SC flters n PCM codecs) and 6 th order ellptc flter (a hgher order leads to better performance, whle an even order of the flter smplfes a lttle synthess of the flter when cascadng three smlar bquadratc blocks). The magntude- and phase- frequency response of mentoned transfer functon are depcted n Fg. 5 Tab.2. Frequency Response PCM ant-alasng flter (Relatve to 1.2 khz @ dbm). Frequency (Hz) Mn (db) Typ (db) Max (db) 15 - - -4 5 - - -3 6 - - -26 165 - -3-2 -1 - -.4 3 to 3 -.2 -.15 32 -.2 -.2 33 -.35 -.15 34 -.8-36 - -3-4 - - -14 46 to 1 k - - -32 IV. CLASSIFICATION OF INVESTIGATED FILTERS IMPLEMENTATIONS Wth respect to appled supply voltage nvestgated flters may be dvded nto two basc classes. 1. flters operatng at conventonal voltage for the technology n queston (3-3.3 Volt); 2. flters dedcated for sgnfcantly reduced supply voltage (.7-.9 Volt) As mentoned before SC flters mostly use nomnal supply, CT flters for sngle (3-4) khz range and conventonal supply may be mplemented n many crcut archtectures - and we nvestgated n more detals two of them: a. RC flters wth operatonal amplfers (OpAmps); b. flters wth actve realzaton of LC prototype. Issue 2, Volume 5, 211 162
To begn let us consder 1a class: to obtan the desred relatvely low cut-off frequency a large tme constant s requred. On the other hand, n order to ft the entre flter nto reasonable chp area, capactors we use are lmted to teens of pcofarads. Ths leads to enormous value of resstors. They may be mplemented usng HR resstors avalable n AMS Foundry Desgn Kt (FDK), but t ths case they would occupy the chp area comparable to that of capactors. Therefore we decded to use actve resstors n the form of long channel MOSFETs. Ths trck sgnfcantly reduced the fnal area of the CMOS chp [14]. For 1b class the desgn consderatons are very smlar: assumed lmtatons for capactors requre the use of nductor cols (or to be more specfc ther actve equvalents) wth values of tens to one hundred Henry. The most popular method of col-less nductance s the use of gyrator. The gyrator [15] s actve two-port network descrbed wth the admttance matrx equaton (6) g m y = (6) g m gm C gm L = C z 2 gm Fg.6. A gyrator equvalent of floatng nductor u 1 1 + g m g m + Fg. 7. A gyrator amplfers 2 y = g m + g m made of two transconductance Usng sngle gyrator t s possble to obtan a grounded nductor, whle for floatng nductor (necessary for ellptc lowpass prototype) two gyrators are needed Fg. 6. The easest and most drect gyrator mplementaton, comprsng two transconductance amplfers s depcted n Fg. 7. Speech frequency range together wth lmtatons on capactor values results wth very low g m values. Moreover usually transconductance should be constant wthn dfferent nput sgnal magntudes, whle the low-power consumpton s standard requrement. All these factors cause that the use of subthreshold regon of MOSFET s very attractve for the applcatons n queston. Fg. 8. Gyrator mplementaton usng sngle nput transconductors (e.g. nverters) Standard supply voltage transconductance amplfers were based on long tal pars, snce such class of crcut s rather ntutve and no addtonal actve stages are needed to form a gyrator. Now let us consder the last class of the flters those workng wth sgnfcantly reduced supply. For supply voltages below 1 Volt (compare ths wth threshold voltages mentoned n the frst secton) almost all practcal crcuts contanng the stack of at least two MOSFETs wll have elements workng close to the weak nverson (or subthreshold) regon. Consequently the desgn of hgh or even far performance operatonal amplfer seems to be a very dffcult f not mpossble task. Therefore only gyrator based crcuts were of our nterest. As a basc buldng block we used a transconductance amplfer comprsng a CMOS nverter only. Gyrators based on such transconductor must have slghtly dfferent archtecture, snce nverter (n contrary do dff-par) has only one nput. Therefore addtonal stages were necessary. A schematc of nverter workng as a transconductance amplfer as well as gyrator mplementaton for ths case are presented n Fg. 8. The mddle and shorted transconductor n the lower path works as 1/g m resstor. The use of conventonal constant value resstor would not assure the matchng of the stages f g m were changng, whle the presented soluton guarantees t. Transconductance of sngle nverter s strongly dependent on supply voltage thus t s very senstve to any supply changes. Fg. 9. LC flter prototype Issue 2, Volume 5, 211 163
Fg. 1. Actve equvalent of LC flter prototype V. SCOPE OF THE WORK supply voltage. For reduced supply (.7-.9 Volt) an nverter based mplementaton s preferred. To acheve desred value of gm (assumng lmts for capactor values) a basc complmentary par MOSFETs should work n weak nverson mode. For AMS transstors and supply voltages endorsed by electrochemcal or photovoltac sources (.7,.9 Volt) two addtonal transstors are needed. The full schematc of the transconductor s depcted n Fg. 11. Ths flter [11, 14, 16] was desgned n two slghtly dfferent layout varants. A bt more complcated mplementatons of schematcs from Fg. 5 are based on dfferental amplfers wth current mrror load [4, 17, 18]. The schematc of a transconductance amplfer based on ths concept s presented n Fg. 12. For current range expanson usng the same supply voltage a hgh swng varant of current mrrors can be used (Fg. 13). Another mplementaton approach (wthout gyrators) can be classcal archtecture of actve RC flter based on operatonal amplfers. Ths concept can not be realzed wth reduced supply due to OpAmp supply requrements. We desgned a 5 th order flter, snce ths s qute enough to meet PCM standards. The smplfed schematc of ths crcut s depcted n Fg. 14. Fg. 11 The schematc of nverter-based transconductor As we mentoned n ntroductory secton, we nvestgated 5 crcut solutons of CT flters. Four of them realze sxth order ellptc transfer functon and are based on passve prototype showed n Fg. 9 (absolute values of nductors and capactors are of secondary mportance, vtal for approxmaton are only mutual numercal relatonshps of the elements). To elmnate nductors an equvalent gyrator mplementaton has been used see Fg. 1. To assure necessary elements rato accuracy, all the capactors were realzed usng a matrx of dentcal unty elements and the desred value were realzed by parallel connecton of approprate number of unty elements. The choce of untary capactor s subject of subtle trade-off and descrbed n more detal n [11]. An equvalent scheme from Fg. 1 may be mplemented usng varous actve elements formng the transconductor. The actual crcut soluton comes frst of all from assumed Fg. 12. The schematcs of transconductance amplfer wth smple current mrrors Tab 3. Summary of the most mportant flter parameters Type of flter LV 1 LV 2 DP DP HS OpAmp Parameter Chp area [mm 2 ].273.2873.273.297.1782 Power consumpton [µw] max.5 max.5 32 3 243 Passband rpple [db] 1.69 1.11 1.64.4.3 Average roll-off [db/khz] -59.2-43.8-16.1-4.4-27.2 Max current [µa].55.55 1.8 1. 81 RMS ddle nose [µv] 77.6 55.1 56.7 635.1 18.3 LV1, LV2 flters based on CMOS nverters, DP flter comprsng dfferental par, DP HS same as above but wth hgh-swng mrrors Issue 2, Volume 5, 211 164
Fg. 14. OpAmp based RC 5 th order ellptc flter VI. THE RESULTS All the flters have been carefully lad out and smulated usng BSIM3.3 smulaton model for Cadence provded by the slcon foundry. In Table 3 we summarzed the most mportant fgures of mert for nvestgated flters The best results are emphaszed by bold typeface and the worst ones wth talcs. All the gyrator flters occupy smlar slcon area, ndependently on transconductor mplementaton, whle OpAmp based flter fts nto sgnfcantly lower (about 3%) area. As expected gyrator flters have very low power consumpton. OpAmp based flter power s greater by at least one order of magntude. flter. In ths soluton we used the smplest current mrrors and t leads to reducton of current gans n the transconductor and consequently worsenng of adjustng nput-output crcuts effcency. Fg. 15. THD of varous flters versus nput sgnal magntude for 8Hz Fg. 13. The schematcs of transconductance amplfer wth hgh-swng current mrrors. The worst passband non-unformty has the DP flter wth smple current mrrors. The same transconductor wth mprover hgh-swng mrrors, s on the other hand, the best, as long as rpple s under consderaton. It confrms known good features of hgh-swng mrrors. OpAmp varant s also very food wth ths parameter, whch comes from smple archtecture and hgh gan stablty of feedback amplfers. The requred roll-off posses all but DP smple mrror Fg. 16. THD of varous flters versus nput sgnal magntude for 3kHz All the gyrator flters have the same adjustng resstance (4MΏ). Therefore ther dle nose depend bascally on current consumpton, whch s sgnfcantly lower for low supply voltage. For OpAmp crcut hgher current consumpton s caused by approprate basng. Very mportant parameter for speech flter s harmonc dstorton (THD). We estmated and compared ths parameter for all the smulated crcuts. Smulatons have Issue 2, Volume 5, 211 165
been performed focusng on two frequences basc for speech.e. 8kHz and harmoncs beng close to the maxmum 3kHz As t can be seen n Fgs. 15-16 at 8Hz the greatest harmonc dstorton occurs n flters workng wth reduced supply. At 3kHz, on the other hand, the OpAmp flters has the mnmal dstorton, whle LV 2 flter has maxmal dstorton. 18 the famly of frequency response curves s shown. From ths fgure t comes that maxmum tunng range for 1.b. flters cut-off frequency les between 2Hz and 5kHz. VIII. LAYOUT OF THE ANS-DM CODEC The flters n queston have been mplemented n double poly four metal.35 µm CMOS technology from austramcrosystems (AMS). In Fg. 19 we present the layout. Total chp area of the crcut wth I/Os shown n Fg. 19 s 3 sqmm, whle the core s 1 sqmm only. From Fg. 19 t s apparent that most of the core area (79%) s occuped by the flters. On the other hand n sngle flter the great majorty of slcon area (75%) s consumed by capactors, actve crcutry s only 25% n terms of area. IX. CONCLUSIONS The results presented n the paper extend the state-of-theart and contrbute a lttle to mplementaton of samplng adaptaton concept, both n analytcal and practcal aspect. Fg. 17. Magntude frequency response of 5th order OpAmp based flter for dfferent supply (descrpton n the text) VII. TUNING PROPERTIES OF IMPLEMENTED FILTERS Fabrcaton process varatons for sngle semconductor devces caused by local and/or global dsturbances durng fabrcaton process lead to slght dsperson of flter made n slcon. Therefore some tunng scheme should be provded for every ntegrated flter. Fg.19. Layout of the ANSDM codec wth marked followng arrangements: 1. Input flter, 2. Output flter 3. Integraton module, 4. Comparator Fg. 18. Tunng range of gyrator lowpass flters based on long tal pars. The OpAmp based flters 1.a. may be tuned up wthn small range by approprate change of the supply voltage. Fg. 17 shows the mpact of supply voltage on frequency response. The supply voltage was ncreased from 2*1.4 V to 2 *1.65 V. As shown n Fg. 17 the cut-off frequency changes from 2.55kHz to 3.6kHz. Gyrator flters (both wth nverter as well as long tal par based transconductors -1b,2b) tunng may be performed by transstor s gate voltage varatons. Ths approach s especally effectve for gyrator flters wth dff pars. In Fg. We llustrated the concept of the delta modulator/demodulator realzaton wth the ad of the nonunform samplng method. All elements, both analog and dgtal, that are used for ths mplementaton, can be put together n one chp, makng ASIC/SoC dedcated to specal purpose, such as: measurng, communcaton, control systems, data compresson, data encrypton wreless telecommuncaton. In the paper we descrbed modulaton the ANS-DM algorthm mplementatons, the codec archtecture but we focused on flterng aspects and flter mplementaton n CMOS technology. The results and analyss of the flters presented n the prevous secton lead to some vtal conclusons: Issue 2, Volume 5, 211 166
The flter wth transconductor realzed wth smple current mrrors has defntely the worst performance; Reduced supply voltage varants of gyrator flters fulfll all the PCM requrements. In practcal realzaton, however, ther tendency to ntroduce nonlnear dstorton should be taken nto account; The hgh swng crcut fts nto specfcatons wth all but dle nose. Ths s result of hgh current consumpton and a specal attenton must be pad on ths parameter; The OpAmp crcut s especally well suted to hgh lnearty applcatons and has the smallest slcon area. Ths benefts are however pad by hghest power consumpton. As we mentoned all the crcuts have been manufactured and systematc expermental test are currently n progress. ACKNOWLEDGMENT Ths work was supported by the Polsh Mnstry of Scence and Hgher Educaton under grants N N5154244 33 and N N515 41134. REFERENCES [1] Marvast F.: Nonunform Samplng Theory and Practce, Kluwer Academc Publshers, New York, 21 [2] Un C. K., Cho D.H.: Hybrd Compandng Delta Modulaton wth Varable-Rate Samplng, IEEE Trans. On Comm., vol.com-3, No. 4, Aprl 1982 [3] Abate J. E.: Lnear and Adaptve Delta Modulaton. Proceedngs of the IEEE, vol. 55, No. 3, march 1967. [4] Steele R.: Delta Modulaton Systems. Pentech Press, London, 1986 [5] Golańsk R., A/D and D/A Delta Converters wth Adaptve Samplng - Methods Analyss and Performance Evaluaton. (PL). AGH- Unversty of Scence and Technology Publshers, Monographs, No 151, ISSN 867-6631, pages 182, Poland, Cracow, Dec.25, [6] Zhu Y.S., Leung S.W., Wong C.M.: A dgtal audo processng system based on nonunform samplng delta modulaton. IEEE Transacton on Consumer Electroncs, vol. 42, No.1, 1996 [7] Laane R., Murphy B.T.: Delta modulaton codec for telephone transmsson and swtchng applcatons, Bell Syst. Tech. J., vol. 49, pp. 113-132, July-Aug. 197 [8] Tewksbury S. K.: Dscrete Adaptve Delta Modulaton system. Unted States Patent 3,815, 33, 1974. [9] Godek J., Golańsk R., Kołodzej J.: Antalasng Flter for NSDM codec. Proceedngs of ICSES 28 Internatonal Conference on Sgnals and Electronc Systems, Kraków, pp. 159-164. [1] Masahro Sasak, Takeyasu Saka, Takash Matsumoto: Low Power Consumpton Analog Matched Flter, 6th WSEAS Int. Multconf. on Crcuts, Systems, Communcatons and Computers pp 7391-7394 C, 22 [11] Machowsk W., Godek J.: Low voltage contnuous tme CMOS flters for audo frequency range, Elektronka: konstrukcje, technologe, zastosowana (PL) vol. 5, pp. 56-6, December 29 [12] BURR-BROWN Applcaton Bulletn, Flter Desgn Program for the UAF 42 Unversal Actve Flter, Texas Instruments Incorporated, 2 [13] 3V 13-bt Lnear PCM Codec - Flter, Freescale Semconductor Inc, 22 [14] Machowsk W., Jaselsk J., Kuta S.: Low woltage low frequency contnous tme CMOS antalasng flters, MIXDES, 27. [15] Tellegen B.D.H.: The Gyrator: a new electrc network element, Phllps Res. Rept., vol. 3, pp. 81-11, Aprl 1948 [16] Su K. L.: Analog Flters, Kluwer Academc Publshers, New York, 22 [17] Han W., Han I.: Tunable lnear conductance by two MOSFETs and ts applcaton to analogue-mxed VLSI for moble communcatons and bologcally plausble neuromorphc hardware, 8th WSEAS Int. Conf. on Electroncs, Hardware, Wreless and Optcal Communcatons, pp. 86-93 Cambrdge 29 [18] Nkhl R., Sharma R.K.: A Lnear OTA wth mproved performance n.18 mcron, 4th WSEAS Int. Conf. on Crcuts, Systems, and Sgnals pp. 115-119, Corfu 21 Issue 2, Volume 5, 211 167