Quantization Noise Cancellation of Fractional-N Frequency Synthesizers Using Pre-distortion Technique

Transcription

1 RADIOENGINEERING VOL. 3 NO. JUNE Quantzaton Nose Canellaton o Fratonal-N Frequeny Syntheszers Usng Pre-dstorton Tehnque Kang-Chun PENG Yan-Ru LU Zh-Hong HUANG 3 Dept. o Computer and Communaton Engneerng Natonal Kaohsung Frst Unversty o Sene and Tehnology No. Jhuoyue Rd. Nanzh Kaohsung Tawan Chung Shan Insttute o Sene and Tehnology No. 5 Sh Q Z Gaopng vllage Taoyuan County Tawa R.O.C. 3 Synomm Tehnology Corp. 6F-5 No. 8 Shu-L Road Hsnhu Cty Tawa R.O.C. peterpkg@nkust.edu.tw angel_nash000@yahoo.om.tw ab @msn.om Abstrat. Ths work proposes a novel pre-dstorton tehnque or the quantzaton nose anellaton o ratonal-n requeny syntheszers. The proposed tehnque utlzes the oordnate rotaton dgtal omputer (CORDIC) algorthm to pre-dstort the baseband sgnal o a wreless system wth the quantzaton nose. The pre-dstorted sgnal then modulates the nosy output sgnal o the ratonal-n requeny syntheszer. The transmtter (Tx) modulaton qualty s thereby mproved. In the reever (Rx) mode the phase nose o the Rx arrer sgnal an also be mproved by modulaton wth a pre-dstorted snusodal sgnal rather than a baseband sgnal. Expermental results demonstrate that the novel pre-dstorton tehnque eetvely mproves the modulaton qualty o a Tx by an error vetor magntude (EVM) o about 0 % under a 3 Mbps QPSK modulaton. The arrer n-band and out-band phase nose o the ratonal-n requeny syntheszer s mproved by approxmately 6 db and 0 db respetvely. Keywords Fratonal-N requeny syntheszer delta-sgma modulato quantzaton nose CORDIC pre-dstorton.. Introduton Wreless ommunaton systems always requre hgh-perormane requeny syntheszers to provde stable RF arrer sgnals or the up-onverso down-onverso modulaton and demodulaton o sgnals. Sne the latest onsumer wreless systems suh as smartphones and tablets apply orthogonal requeny-dvson multplexng (OFDM) to provde a hgh spetral eeny the n-band phase nose o the RF arrer sgnals should be as low as possble []. Furthermore the latest wreless ommunaton systems typally support multple wreless standards to be lexbly used n varous wreless applatons. Consequently the lokng tme and requeny resoluton o requeny syntheszers should be optmzed or ast and prese requeny swthng respetvely. To aheve these goals ratonal-n requeny syntheszers are developed to replae tradtonal nteger-n requeny syntheszers []-[9]. Most ratonal-n requeny syntheszers are based on phase-loked loop (PLL) arhtetures and use a dgtal delta-sgma modulator o quantze the ratonal hannel seletng normaton. The quantzed results are then used to ontrol the nteger mult-modulus dvder (MMD). Wth ths arhteture the requeny resoluton o the syntheszer nreases wth the bus wdth o the. Hene the dvson rato N o the syntheszer an be as low as possble to mprove both phase nose perormane and requeny swthng speed [4]-[6]. However a tradeo stll exsts between the phase nose perormane and the requeny swthng speed. The pushes the quantzaton nose rom the enter requeny to a hgher oset requeny and njets ths shaped quantzaton nose nto the syntheszer va the MMD. To suppress ths quantzaton nose the loop bandwdth o the syntheszer must be suently narrow. However a narrower loop bandwdth results n a longer stable tme [6]. To overome ths ssue varous quantzaton nose anellaton tehnques have been proposed. In some nvestgatons the phase-nterpolaton tehnque has been used [6] [7]. As the quantzes the ratonal normato the dgtal quantzaton nose s onverted nto the analog doman. The analogue quantzaton nose then phase-nterpolates the tunng sgnal o the voltage-ontrolled osllator (VCO) to anel the quantzaton nose whh s njeted va MMD. Sne ths arhteture requres hghly prese dgtal-toanalog onverter (DAC) synhronzaton mehansm and nterpolatng rut or nose anellato the rutry s hghly omplated. Aordngly both the de area and power onsumpton are nreased. Shekhar used a reerene sgnal wth a very hgh requeny n a ratonal-n requeny syntheszer [8]. The quantzaton nose an be pushed to a several hundred MHz oset requeny whh s ar away rom the loop bandwdth or nose suppressng. However the several hundred MHz reerene sgnal should be syntheszed by a seond PLL and the all-dgtal also operates at suh a hgh requeny so the total power onsumpton s onsderable. Wang proposed a pre-

2 67 K. C. PENG Y. R. LU Z. H. HUANG QUANTIZATION NOISE CANCELLATION OF FRACTIONAL-N FREQUENCY dstorton tehnque to elmnate ratonal spurs whh s aused by the [9]. The tehnque s based on predstortng the nputs by the addton o a seres o small snusodal sgnals n ant-phase wth the prnpal ratonal spurs. However ths tehnque elmnates ratonal spurs rather than quantzaton nose. In addto these ratonal spurs should be pre-measured and stored n a read-only-memory (ROM). Ths means that the arhteture requres a hgh-apaty ROM or storng the pre-dstortng normaton o all hannels. To eetvely overome the tradeo between the phase nose perormane and the requeny swthng speed ths work develops a novel pre-dstorton tehnque or quantzaton nose anellaton. In ontrast wth the Wang s pre-dstorton tehnque the proposed predstorton tehnque elmnates the requrement o a hghapaty ROM. The proposed pre-dstorton tehnque s based manly on the nherent baseband proessng and modulaton o a wreless system. Hene the rutry o the proposed ratonal-n requeny syntheszer s ompat and power-savng. Seton presents an overvew o the proposed pre-dstorton arhteture and analyzes the quantzaton nose anellaton mehansm. Seton 3 presents the expermental proo that the proposed tehnque eetvely mproves the arrer phase nose and the modulaton qualty. Fnally onlusons are gven n Seton 4.. Arhteture and System Analyss. Proposed Pre-dstorton Arhteture Fg. presents the proposed pre-dstorton tehnque or quantzaton nose anellaton o ratonal-n requeny syntheszers. The quantzaton nose s extrated rom the or nose anellaton. In the transmtter (Tx) mode the baseband sgnal o a wreless system s predstorted by the nverted quantzaton nose o usng a pre-dstorton lter. The pre-dstorted baseband sgnal then modulates the nosy RF sgnal whh s produed by the ratonal-n requeny syntheszer. Sne the RF sgnal has the same quantzaton nose as the extrated nose the quantzaton nose n one sgnal anels out that n the other. Thereore the loop bandwdth o the proposed ratonal-n requeny syntheszer an be more easly optmzed or low phase nose and ast hannel-swthng than an onventonal ratonal-n requeny syntheszers. The mprovement n phase nose onsequently mproves the Tx modulaton qualty o the wreless system. In the reever (Rx) mode snusodal sgnals replae the baseband sgnals or pre-dstorton. The pre-dstorted snusodal sgnals modulate the RF sgnal whh s produed by the ratonal-n requeny syntheszer to anel out the quantzaton nose. Thereore the modulaton yelds a low-nose ontnuous wave (CW) as a peret arrer sgnal or use n the Rx o a wreless system. Baseband Sgnal Snusodal Sgnal Reerene PFD Quantzaton Nose Baseband Proessor Pre-dstorton Flter LPF VCO Quadrature Modulator o Tx Fg.. Proposed pre-dstorton tehnque or quantzaton nose anellaton o ratonal-n requeny syntheszers.. Moded and Extraton o Quantzaton Nose I pd Q pd To extrat quantzaton nose a moded seond-order s developed. Fg. presents ths where L s the bus wdth o the aumulator and N (z) and N (z) are the overlow o aumulators. The proposed s based on a mult-stage nose-shapng (MASH) arhteture. It has one more rst-order derentator than the onventonal at the end o the seond aumulator to extrat the quantzaton nose. Fg.. Moded seond-order or extratng quantzaton nose. Based on Fg. the quantzaton result o the proposed s derved as K ( ) K N z eq z ( ) L L e z () where K/ L s the ratonal part o the ratonal dvson rato N; e q s the orgnal quantzaton nose and (-z - ) s the nose shapng ator whh represents a seond-order derentaton. The derentaton an push the quantzaton nose rom the enter requeny to a hgh oset requeny. Thereore RF 90 o MMD Quantzaton Result Channel Seleton Modulaton Sgnal o Tx Carrer Sgnal o Rx Fratonal-N Frequeny Syntheszer e ext (z)

3 RADIOENGINEERING VOL. 3 NO. JUNE e () z e ( z ) q () represents the shaped quantzaton nose o. Based on Fg. the extrated quantzaton nose an be derved as e z e z (3) ext() q( ) where the nose shapng order s lower than the one o the shaped quantzaton nose e (z) by one. The man reason s that the shaped quantzaton nose e (z) njets nto the requeny syntheszer wth requeny modulaton (FM) [6]. However the extrated quantzaton nose e (z) predstorts the arrer sgnal wth phase modulaton (PM) or nose anellaton. Aordng to the modulaton theory FM an be treated as a ombnaton o rst-order ntegraton and PM [0]. Ths relatonshp between PM and FM explans why the nose shapng o the extrated quantzaton nose must be one order lower than that o the shaped quantzaton nose. v d NKvKdF s Hs (8) Ns K K F s H e s Ns Ns K K F s v d. (9) The transer untons H(s) and H e (s) have a low-pass and a hgh-pass requeny response respetvely. Aordng to (5) the nose re I CP and an be suppressed by the system outsde the loop-bandwdth. The phase nose VCO an be suppressed wthn the loop-bandwdth by the system. nre () s PFD / CP K d InCP () s LPF F(s) VCO K v /s VCO() s nrf () s.3 Nose Canellaton Model and Analyss Consderng the phase nose requrement n both Tx and Rx mode Fg. 3 presents the phase nose model o the ratonal-n requeny syntheszer that s shown n Fg. to analyze the nose anellaton tehnque. The major nose soures presented n a ratonal-n requeny syntheszer manly nlude reerene rystal VCO CP and. Dgtal ruts suh as PFD and dvder manly ntrodue noses on power and ground so ther ontrbutons are not nluded []. F(s) represents the transer unton o the loop lter. K d s the ombned gan o PFD and CP and K v s the senstvty o the VCO. N s the dvson rato o the MMD. The nose rom the VCO reerene sgnal and CP s denoted VCO (s) re (s) and I CP (s) respetvely. The term (s) whh s the quantzaton nose n the phase doma an be derved rom () as j re s () s sn 3 Ns j re where re s the reerene requeny [4]. The output phase nose o the ratonal-n requeny syntheszer an be derved as nrf () s nre () s InCP () s n () s H() s where n vo() she() s npll n (4) () s () s (5) () s I () s H() s H () s (6) PLL re CP vo e () s () s H() s (7) n n Fg. 3. Phase nose model o ratonal-n requeny syntheszer. Fg. 4 dsplays the nose anellaton model o the proposed pre-dstorton tehnque n the tme doman. Based on (5) the quadrature output sgnals n the tme doman o the ratonal-n requeny syntheszer are represented as RF os t t PLL t t t PLL t t t PLL t t t PLL t t I n RF os ( ) os ( ) sn ( ) sn ( ) (0) RF sn t Q n RF sn ( ) os ( ) os ( ) sn ( ) () where s the entral requeny o the RF sgnal and n () s L () () nrf npll /N nrf s npll s n s L () (3) n L () (4) L - s the nverse Laplae transorm. The output o the quadrature modulator an be then derved as V I RF Q RF out pd I pd Q MMD / I ()os t t os pd n PLL n

4 674 K. C. PENG Y. R. LU Z. H. HUANG QUANTIZATION NOISE CANCELLATION OF FRACTIONAL-N FREQUENCY I ()sn t t ()sn t pd n PLL n Q ()sn t t os pd n PLL n Q ()os t t ()sn t (5) pd n PLL n where I pd (t) and Q pd (t) are the pre-dstorted I(t) and Q(t) respetvely. To anel out the quantzaton nose (t) shown n (5) I pd (t) and Q pd (t) are desgned as I I()os t Q()sn t pd n n tan n ( ) t It () Qt ()tan n Q Q()os t I()sn t pd n n tan n ( t) Qt () It ()tan n (6). (7) Applyng (6) and (7) to (5) yelds the output o the quadrature modulator as (8) whh s shown at the bottom o the page. Equaton (8) demonstrates that the quantzaton nose (t) an be theoretally anelled by the proposed arhteture. Based on (5) and (8) Fg. 5 presents quantzaton nose anellaton o a ratonal-n requeny syntheszer usng pre-dstorton tehnque. The quantzaton nose predstorts the baseband sgnal. When ths pre-dstorted sgnal s used to modulate the RF arrer sgnal the quantzaton nose n the arrer sgnal s anelled out. Consequently the sgnal-to-nose rato (SNR) o the output modulaton sgnal s greatly mproved and the modulaton qualty exeeds that obtaned wthout quantzaton nose anellaton..4 Pre-dstorton Flter To aheve peret anellaton o quantzaton nose a well-desgned dgtal pre-dstorton lter s requred. Based on (6) and (7) Fg. 6 presents the vetors o the phase-rotated rom the orgnal sgnals by a phase o (t). Thereore the oordnate rotaton dgtal omputer (CORDIC) algorthm an be used to smply the mplementaton o the dgtal pre-dstorton lter []. Based on the CORDIC algorthm the pre-dstorton shown n (6) and (7) an be realzed by teratng the ollowng n the dgtal doman: Baseband / Snusodal Sgnals It () Qt () Pre-dstorted I-sgnal I pd Pre-dstorton Flter n Pre-dstorted Q-sgnal Q pd RFI Fratonal-N Frequeny Syntheszer 90 o RF () Q t Fg. 4. Nose anellaton model o proposed pre-dstorton tehnque. Ipd[ ] I [ ] I [] Q [] (9) Qpd[ ] Q [ ] Q [] I [] (0) where I[] I pd [] Q[] Q pd [] are the sampled I(t) I pd (t) Q(t) Q pd (t) at the th step respetvely; and = s the dreton o the phase rotaton at the th step. Eah teraton o (9) and (0) rotates the phase o the vetor by tan - ( - ). Followng a suent number o teratons the aumulated phase rotaton approahes the desred quantzaton nose n tan 0 Quadrature Modulator o Tx. () Modulaton Sgnal / Carrer Sgnal V out (t) orgnal and pre-dstorted sgnals. Pre-dstorted sgnals are Vout os tn PLL I()os t Q()sn t os n n n Qt ()os ()sn t It ()sn t n PLL t Qt t It t t sn () ()sn () ()sn () os () n n n It ()sn os Qt ()os PLL PLL It ()os t Qt ()sn t. (8)

5 RADIOENGINEERING VOL. 3 NO. JUNE Baseband Sgnal Proposed Pre-dstorton Flter H( S) 0logN Pre-dstorted Baseband Sgnal n Quantzaton Nose Reerene & Dvder Phase Nose VCO Phase Nose nvco re dv 0logN H( S) H ( ) e S 0 Fratonal-N Frequeny Syntheszer nrf RF Phase Nose Quadrature Modulator O Tx SNR s mproved by quantzaton nose anellaton Tx Modulaton Sgnal wth Resdual Phase Nose Fg. 5. Quantzaton nose anellaton o a ratonal-n requeny syntheszer usng pre-dstorton tehnque. Q Pre-dstorted Sgnal I () t Q pd n pd Orgnal Sgnal It () Qt () I [] Q [] n [] H(z) CORDIC n [] Ipd [] Q [] pd I Pre-dstorton Flter Sne Fg. 6. Vetors o orgnal and pre-dstorted quadrature sgnals () (9) and (0) an be smpled as Ipd[ ] I[ ] (3) where Qpd[ ] Q[ ] (4) I [ ] I [ ] Q [ ] (5) Q [ ] Q [ ] I [ ]. (6) Equatons (3) (6) ndate that the CORDICbased pre-dstorton an be smply mplemented usng btshters adders and subtraters. Fg.7 dsplays the blok dagram o the proposed pre-dstorton lter where two Fg. 7. Blok dagram o proposed pre-dstorton lter. root-rased-osne (RRC) lters are used or the pulse shapng o the baseband sgnal and H() z Z H() s (7) s the dgtzed system-transer unton o the syntheszer. To smply the mplementaton o H(z) the proposed requeny syntheszer utlzes a rst-order R-C loop lter whh makes the system transer unton H(s) as a seondorder transer unton. (8) an then be re-derved as sn Hs (8) s s where KK NRC n V d n (9) n n RC. (30)

6 676 K. C. PENG Y. R. LU Z. H. HUANG QUANTIZATION NOISE CANCELLATION OF FRACTIONAL-N FREQUENCY (a) Fg. 9. Measured onstellaton ponts o a 3 Mbps QPSK modulaton sgnal (a) wthout and (b) wth pre-dstorton tehnque. (b) The dgtzed system-transer unton shown n (7) an then be derved as where H z Az Bz Cz Dz E (3) bandwdth. The seond-order hannel seletor predstorton lter and baseband sgnal generator are mplemented usng Xlnx Vrtex-5 eld-programmable gate arrays (FPGA). A n (3) n re n B ne sn re n re n ne sn os re (33) Quadrature Modulator Power Spltter VCO C (34) n re n D e os (35) re n re E e. (36) 3. Expermental Results Fg. 8 shows the mplementaton o ratonal-n requeny syntheszer usng pre-dstorton tehnque. The requeny syntheszer o ths work s a Peregrne produt wth a model number o PE335. The TRF quadrature modulator and ROS VCO are produts o Texas Instruments (TI) and Mn-Cruts respetvely. The reerene requeny and the operatng requeny o the ratonal-n requeny syntheszer s set as 0 MHz and 3 GHz respetvely. The ratonal-n requeny syntheszer s desgned wth a 50 khz loop Loop Flter Frequeny Syntheszer Fg. 8. Implementaton o ratonal-n requeny syntheszer usng pre-dstorton tehnque. In the Tx mode a 3 Mbps baseband sgnal s used to perorm a QPSK modulaton. Fg. 9 (a) and (b) presents the measured onstellaton ponts o the 3 Mbps QPSK modulaton sgnal wthout and wth pre-dstorton tehnque respetvely. Wthout pre-dstorton tehnque the onstellaton ponts o the modulaton sgnal are rotatonally spreadng out due to the onsderable quantzaton nose. As the pre-dstorton unton s turned on to anel the quantzaton nose the spreadng o the 3 Mbps QPSK onstellaton ponts are mproved and onentrated. These results ndate that the proposed predstorton tehnque mproves the peak error vetor magntude (EVM) by more than 0 %.

7 RADIOENGINEERING VOL. 3 NO. JUNE In the Rx mode MHz snusodal sgnals replae the baseband sgnals to generate a CW as a arrer sgnal. Fg. 0(a) and (b) shows the measured output spetra and phase nose respetvely. The phase nose at an oset requeny o khz and MHz s lower than -74 db/hz and -0 db/hz respetvely. The measurements ndate that the proposed pre-dstorton tehnque works very well and mproves the n-band and out-band phase nose o the arrer sgnal by approxmately 6 db and 0 db respetvely. It an be ound that there s almost no mprovement at the moderate requeny oset. The man reason s that the requeny response o the dgtal pre-dstorton lter s not ompletely dental to the one o the analog requeny syntheszer n both magntude and phase. Ths non-deal haraterst makes the mprovement o the phase nose non-unorm over all the requenes. Magntude (dbm) Phase Nose (db/hz) wth pre-dstorton Frequeny(GHz) wthout pre-dstorton (a) wthout pre-dstorton wth pre-dstorton Oset Frequeny (Hz) (b) Fg. 0. Measured (a) spetra and (b) phase nose wth and wthout pre-dstorton tehnque. Tab. summarzes the perormane o the ratonal- N requeny syntheszer usng the proposed pre-dstorton tehnque. All o the measurements demonstrate that the proposed pre-dstorton tehnque works peretly wth ratonal-n requeny syntheszers. Tab. presents the omparson o quantzaton nose anellaton tehnques. The proposed pre-dstorton tehnque aheves the hgher out-band phase nose mprovement. The remarkable phase nose mprovement results n a 0 % EVM mprovement when the arrer sgnal s modulated wth a 3 Mbps QPSK sgnal. Comparng wth the pror arts [6][9] the proposed pre-dstorton tehnque anels out the quantzaton nose wth a muh smpler rutry and a lower operatng requeny o the. Operatng requeny Reerene requeny Frequeny resoluton Lokng tme Loop bandwdth Phase nose EVM 3 GHZ 0 MHz 305 Hz < 0 μs 50 khz -74 khz -0 MHz 5% (3 Mbps QPSK) Tab.. Perormane summary o the ratonal-n requeny syntheszer usng pre-dstorton tehnque. Reerene Ths work [9] [6] Canellaton tehnque Number o DACs Hgh-apaty ROM Operatng requeny o Phase nose mprovement Modulaton qualty mprovement Pre-dstorton Pre-dstorton Phasenterpolaton MHz 05 MHz 0 MHz 0 0 % (3 Mbps QPSK) % (.5 Mbps GFSK) Tab.. Comparson o quantzaton nose anellaton tehnques. 4. Conluson Ths work develops a novel pre-dstorton tehnque or quantzaton nose anellaton o ratonal-n requeny syntheszers. The proposed tehnque smply uses the nherent baseband-proessng and modulaton o a wreless system to anel out the quantzaton nose. It thereore redues hardware omplexty. In the Tx mode the pre-dstorton tehnque mproves the EVM o a 3 Mbps QPSK sgnal by more than 0 %. In the Rx mode the pre-dstorton tehnque mproves the phase nose o the arrer sgnal by 6 db and 0 db at 30 khz and 0 MHz oset requeny respetvely. The lokng tme o the ratonal-n requeny syntheszer s shorter than 0 μs. These remarkable measurements reveal that the proposed syntheszer arhteture usng pre-dstorton tehnque s very sutable or advaned wreless systems.

8 678 K. C. PENG Y. R. LU Z. H. HUANG QUANTIZATION NOISE CANCELLATION OF FRACTIONAL-N FREQUENCY Aknowledgements The authors would lke to thank the Natonal Sene Counl (0--E ) or provdng researh undng. Reerenes [] MUSCHALLIK C. Inluene o RF osllators on an OFDM sgnal. IEEE Transatons on Consumer Eletrons 995 vol. 4 no. 3 p [] CHRISTOFFERS N. KOKOZINSKI R. KOLNSBERG S. HOSTICKA B. J. Hgh loop-lter-order sgma-delta ratonal-n requeny syntheszers or use n requeny-hoppng-spreadspetrum ommunaton-systems. In Proeedng o the 003 IEEE Internatonal Symposum on Cruts and Systems. 003 p [3] SHU K. SANCHEZ-SINENCIO E. MALOBERTI F. EDURI U. A omparatve study o dgtal ΣΔ modulators or ratonal-n synthess. In Dgest o the 8 th IEEE Internatonal Conerene on Eletrons Cruts and Systems. 00 p [4] PENG K. C. HUANG C. H. L C. J. HORNG T. S. Hgh perormane requeny hoppng transmtters usng two-pont deltasgma modulaton. IEEE Transatons on Mrowave Theory and Tehnques 004 vol. 5 no. p [5] PENG K. C. WU P. S. Hgh Perormane ratonal N requeny syntheszer usng a two-pont hannel seleton tehnque. In Dgest o the 009 IEEE Asa-Pa Mrowave Conerene. 009 p [6] PENG K. C. LIN C. C. CHAO C. H. A novel three-pont modulaton tehnque or ratonal-n requeny syntheszer applatons. Radoengneerng 03 vol. no. p [7] ZHANG L. YU X. SUN Y. PHEEW. WANF D. WANG Z. CHEN H. A hybrd spur ompensaton tehnque or ntemodulo ratonal-n phase-loked loops. IEEE Journal o Sold- State Crut 009 vol. 44 no. p [8] SHEKHAR S. GANGOPADHYAY D. WOO E. C. ALLSTOT D. A.4-GHz extended-range type-i ΣΔ ratonal-n syntheszer wth.8-mhz loop bandwdth and -0 db/hz phase nose. IEEE Transatons on Cruts and Systems II Express Bres 0 vol. 58 no. 8 p [9] WANG H. New Strateges or Low Nose Agle PLL Frequeny Synthess. Ph.D. dssertaton. London (UK): Dept. Eletron & Eletral Eng. Unv. College Londo 009. [0] HAYKIN S. Communaton Systems 5 th ed. John Wley & Sons 009. [] ZHAO B. LIAN Y. YANG H. A low-power ast-settlng bondwre requeny syntheszer wth a dynam-bandwdth sheme. IEEE Transatons on Cruts and Systems I Regular Papers 03 vol. 60 no. 5 p [] AGGARWAL S. MEHER P. K. KHARE K. Sale-ree hyperbol CORDIC proessor and ts applaton to waveorm generaton. IEEE Transatons on Cruts and Systems I Regular Papers 03 vol. 60 no. p About Authors... Kang-Chun PENG was born on February n Tape Tawan. He reeved the B.S.E.E. M.S.E.E. and Ph.D. degrees rom the Natonal Sun Yat-Sen Unversty Kaohsung Tawa n and 005 respetvely. He s urrently an Assstant Proessor wth the Department o Computer and Communaton Engneerng Natonal Kaohsung Frst Unversty o Sene and Tehnology Kaohsung Tawan. He s also the treasurer o the IEEE Mrowave Theory and Tehnques Soety (IEEE MTT-S) Tanan Chapter. Hs urrent researh nterests are n the area o delta-sgma modulaton tehnques njetonlokng tehnques wdeband requeny syntheszers and oherent demodulators. Yan-Ru LU was born on August n Kaohsung Tawan. He reeved the B.S.E.E. degree rom the Natonal Kaohsung Unversty Kaohsung Tawa n 00. He reeved the M.S.E.E. degrees rom the Natonal Kaohsung Frst Unversty o Sene and Tehnology Kaohsung Tawa n 0. He s urrently wth the Chung Shan Insttute o Sene and Tehnology Taoyuan County Tawa R.O.C. Zh-Hong HUANG was born on September 987 n Yunl Tawan. He reeved the B.S.E.E. degree rom the Natonal Kaohsung Marne Unversty Kaohsung Tawa n 009. He reeved the M.S.E.E. degrees rom the Natonal Kaohsung Frst Unversty o Sene and Tehnology Kaohsung Tawa n 0. He s urrently wth the Synomm Tehnology Corp. Hsnhu Cty Tawa R.O.C.