A 1.2 GHz Band-Pass Sigma Delta Analog to Digital Modulator with Active Inductor based Resonators

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1 Proceed of the World Conre on Eneer and Comuter Science Vol II WCECS, October 4-6,, San Francico, USA A. GHz Band-Pa Sima Delta Analo to Diital Modulator with Active Inductor baed eonator Kev Dobon, Shahrokh Ahmadi and Mona Zahloul Abtract Thi aer reent a. GHz contuou time 6 th order band-a Sima Delta Analo to Diital modulator IBM.8 um CMOS technoloy. Traditional LC circuit, with iral ductor a reonator, were relaced with active ductor baed reonator with neative imedance circuit to enhance the quality factor, reduce chi area and elimate ot roce need. Simulk and Cadence imulation yield an enhanced SND of 75 db and ower conumtion of 9 mw. The modulator occuie.9 mm of chi area. II. DESIGN OF CONTINUOUS TIME SIGMA DELTA MODULATO The eneral architecture of a CT ΣΔ modulator i hown Fi.. When de the loo filter G() for a CT ΣΔ modulator we be with a dicrete time modulator tranfer function F(z). Index Term Active Inductor, Analo to Diital Converter, Neative Imedance Circuit, Sima Delta, ixth order. I. INTODUCTION Analo to Diital Converter (ADC) allow u to convert analo al to diital rereentation uitable for roce by a diital comuter. Sima-Delta (ΣΔ) modulator utilize the rocee of overaml and noie ha to obta hih Sal to Noie atio (SN). ΣΔ modulator utilize a few critical comonent and roduce hih accuracy reult []. Thee are hihly deirable feature. The relationhi between the SN meaured at the outut of a ΣΔ modulator and the effective number of bit (ENOB) i iven by: SN = 6.ENOB +.76 () Contuou Time (CT) ΣΔ modulator offer herent antialia and are able to oerate at hiher frequencie than their dicrete time counterart. In adio Frequency (F) receiver an com al i reeatedly filtered and mixed down to lower frequencie before be diitized and roceed. A CT band-a ΣΔ modulator caable of diitiz an F carrier al would elimate the need for analo filter and mix, and thee function would be aed on to a Diital Sal Proceor (DSP). Thi reult a imler, cheaer and more efficient receiver []. Manucrit received Auut,. The author are with the Geore Wahton Univerity, Deartment of Electrical and Comuter Eneer, 8 nd Street NW, Wahton DC 5, USA. K. G. Dobon i a PhD candidate. ( kdobon@wu.edu). S. Ahmadi i an Aitant Profeor. ( : ahmadi@wu.edu). M. E. Zahloul i a Profeor, IEEE Fellow and Deartment Chair. ( zahloul@wu.edu). Fiure : Contuou Time Sima Delta Modulator Once F(z) ha been choen the imule variant method can be ued to determe the equivalent CT loo filter G() [3]. For modulator with a non-return-to-zero (NZ) feedback we et: d G ( ) e F ( z) ( z ) Z T { L [ ]} () Here d rereent the delay troduced by the ADC and Diital to Analo Converter (DAC). For a ixth order banda Sima Delta modulator the equivalent contuou time loo filter tranfer function i of the form: G( ) ( a b ( )( a )( b ) a b )( )( ω i the normalized reonator frequency with reect to the aml frequency radian er econd, and i the quality factor of the reonator. The aml frequency i T. When d i equal to.4t and the amle rate i 4 time the frequency of the ut al then the term the numerator aroximate to zero [4]. ) (3) ISBN: ISSN: (Prt); ISSN: (Onle) WCECS

2 Proceed of the World Conre on Eneer and Comuter Science Vol II WCECS, October 4-6,, San Francico, USA III. ACTIVE INDUCTO ESONATO STUCTUE A arallel LC reonator i hown Fi. below. I ' V G (5) I V (6) V ' ' G m ' I (7) C After ubtitution we et: Fiure : LC eonator The tranfer function of a arallel LC circuit reonator H() i iven by: H ( ) A Where and LC C P P L (4) V C (8) I G G m In (8) we note that the i the numerator dicat that the circuit i ductive. G and G m can be realized u CMOS device. The circuit Fi. 5 realize an active ductor with M and M act a G and G m reectively. G() cannot be realized a a cacade of reonator but can be realized by the tructure Fi. 3. Here, A H and A L rereent amlifier a, and H the reonator. The Σ block i an analo adder. Fiure 5: CMOS Active Inductor Fiure 3: Sixth order Active Inductor Baed Loo Filter Traditionally reonator for band-a CT ΣΔ modulator have been realized by LC arallel circuit with iral ductor. Such circuit occuy a lare ilicon area. Siral ductor alo have low quality factor. Active ductor baed LC circuit occuy a much maller area, and when enhancement technique are ued, hih quality factor can be achieved. The active ductor baed reonator i exlaed by the yrator C theorem a hown Fi. 4 below. A detailed mall al analyi reult an exreion for Z a hown below [5]. Z m oc o ( C Cd Cd ) [ ( C C )]( m oc d o Cd) (9) Here o i the dra-ource conductance and oc rereent the load effect of the non-ideal bia current ource. Z can be terreted to rereent the arallel LC circuit a hown Fi.. Searat the eitive, Caacitive and ductive art of (9) yield the follow: () C () C Fiure 4: Gyrator Tooloy C L () ISBN: ISSN: (Prt); ISSN: (Onle) WCECS

3 Proceed of the World Conre on Eneer and Comuter Science Vol II WCECS, October 4-6,, San Francico, USA oc o (3) m The tric elf-reonant frequency and tric quality factor of the circuit i iven reectively by: m (4) C C roortional to the ut voltae. Thi cheme work effectively at hih frequencie. We can rewrite a: C (6) L If we denote the enhanced quality factor of the circuit with a NIC a, then; n mc (5) C n nic C C L nic (7) By utiliz two imilar circuit to that Fi. 5 and a Neative Imedance Circuit (NIC), a hih fully differential reonator can be deed for ue a band-a ΣΔ modulator. Thi reonator i hown Fi. 6 below. Outut buffer are ued but not hown. Fiure 6: CMOS Active Inductor baed eonator with NIC A PMOS device i ued to coule the ut to the circuit. It draw a mall amount of current and doe not diturb the yrator function. Outut a can be controlled by vary the ize of thi MOSFET. The effect of cacod M3 with M reduce the outut conductance thereby reduc and crea the. The NIC i comried of 3 cro-couled differential air of MOSFET with dra tied to the oo ate. It rovide a neative reitance that eek to cancel the arallel reitance, further crea the. When one cro couled air of MOSFET i ued a a NIC, it rovide a neative reitance of -/ m and add a C / araitic hunt caacitance [7]. Thee imle NIC however are notoriouly nonlear. In order to obta reater learity a multi-tanh verion of the NIC circuit wa ued. Thi require the addition of two extra cro couled air of MOSFET with a : ize ratio [6][8]. When the al i lare and the ymmetrical differential air ha aturated, the unbalanced differential air can till rovide a differential current Here nic i the NIC tranconductance and C nic i the caacitance the NIC add to the circuit [6]. A can be een from (7) the cloer the tranconductance of M and the NIC the hiher the. Care mut be taken dur de to enure that the NIC tranconductance doe not exceed the tranconductance of M. The added NIC caacitance decreae the reonant frequency. Thi can be comenated for by crea bia current. While there i no limit to the voltae that can be alied to iral ductor, the maximum ut voltae to active ductor baed circuit mut not caue MOSFET to ceae oerat aturation mode. Active ductor baed circuit are alo noiier than circuit with real ductor by a factor of [6]. We were able to de and imulate Cadence active ductor baed reonator with a reonant frequency of 3MHz and a of 5 with lear oeration when the ut i le than mv -. IV. SIMULATION A Matlab roram wa ued to enerate itial value of the reonator multily coefficient, A H and A L. Pole-Zero lot were then done to confirm modulator tability. Next, Simulk imulation were ued to further refe the modulator de. The Simulk model wa eaily modified to reflect the non-idealitie of an actual circuit uch a limited a due to nonlearity and mall delay troduced by each circuit comonent. In the ideal cae with hih a the ath conta the mot reonator a theoretical Sal to Noielu-Ditortion atio (SND) of 95dB wa obtaed. When the limitation of nonlearity and circuit delay were conidered a oal of 75 db for oeration at. GHz wa ettled on. Cadence imulation followed. A block diaram of the comlete circuit imulated Cadence i hown Fi. 7 below. Fiure 7: Active Inductor baed Sixth Order Contuou Time Modulator ISBN: ISSN: (Prt); ISSN: (Onle) WCECS

4 Proceed of the World Conre on Eneer and Comuter Science Vol II WCECS, October 4-6,, San Francico, USA Fiure 8: Simulk modulator outut ower ectrum denity A erie of comarator [9] A, are ued to rovide the required delay of.4t and effective amlification of the al rior to quantization. A lare enouh al at the ut of the quantizer i neceary to revent clock feed-throuh [9]. Sce there i a non-zero delay it i neceary to add a direct loo between the DAC and the ADC ut []. The Adder ued i decribed [4]. A Differential air i ued to ubtract the DAC outut from the ut al, Fi. 9. Fiure : Cadence modulator outut ower ectrum denity Cadence imulation reult hown Fi., are imilar to Simulk imulation Fi. 8, albeit with deteriorated noie ha due to the circuit non-idealitie reviouly mentioned and other uch a ettl time of the adder outut, and offet error. Neverthele both yield a SND of 75dB. Thi comare favorably with other non-active ductor baed ixth order band-a ΣΔ modulator uch a [], which yield a SND of 68dB. Our circuit conume 9 mw which i much maller than the 6 mw conumed []. Our de occuie only.9 mm comared to the.5 mm ued by []. Fiure 9: Subtracter differential air with buffered outut A clocked comarator [9] couled with a S fli flo i ued to enerate the modulator outut. The fli flo i neceary becaue a NZ outut i required. The DAC convert the rail to rail outut w of the quantizer to a maller voltae equal to the maximum eak to eak analo ut, Fi.. Fiure : DAC V. CONCLUSION We have ucceeded de and imulat the firt ixth order CT ΣΔ modulator u active ductor baed reonator the loo filter. The ue of enhanc technique ha reulted a modulator with a hih SND, and we have avoided the ue of area conum iral ductor. When comared to the 47 db fourth order active ductor baed CT ΣΔ mentioned [] we are able to achieve a reater SND and conume rouhly the ame amount of ower. EFEENCES [] P. Benabe, M. Keramat and. Kielbaa, Synthei and Analyi of Sima-Delta Modulator Emloy Contuou-Time Filter, Analo Interated Circuit and Sal Proce, no. 3,. 4-5, Jul []. Schreier, G. Teme, Undertand Delta-Sima Data Converter 5. [3] C. Lelandai-Perrault, P. Benabe, J. De Gouy,. Kielbaa, A arallel tructure of a contuou-time filter for banda ima-delta A/D Converter, th IEEE International Conference on Electronic, Sharjah (Emirate Arabe Uni), DEC. 3. [4] S. Benabid, P. Benabe, Hih lear terated LC filter for a contuou-time banda ima-delta ADC Circuit and Sytem, 3 IEEE 46th Midwet Symoium on, Vol., 3 Dec. 3 [5] Zhiqian Gao, Myan Yu, Yizhen Ye, Jianuo Ma, A CMOS banda filter with wide-tun rane for wirele alication, Circuit and Sytem, 6. ISCAS 6. Proceed. 6 IEEE International Symoium on. [6] Yue Wu, Xiaohui D, Mohammed Imail, and Håkan Olon, F banda filter de baed on CMOS active ductor, IEEE Tranaction on circuit and ytem II: Analo and Diital Sal Proce, vol 5, no., Dec. 3. [7] Byunhoo Jun, Harjani,., A wide tun rane VCO u caacitive ource deeneration Circuit and Sytem, 4. ISCAS ao;4. Proceed of the 4 International Symoium on Volume 4, Iue, 3-6 May 4 Pae(): IV Vol.4. ISBN: ISSN: (Prt); ISSN: (Onle) WCECS

5 Proceed of the World Conre on Eneer and Comuter Science Vol II WCECS, October 4-6,, San Francico, USA [8] A. P. yan, O. McCarthy, A novel ole-zero comenationcheme u unbalanced differential air, IEEE tranaction on circuit and ytem I: eular aer, vol. 5, no., Feb. 4. [9]. Jacob Baker, CMOS, Circuit De, Layout, and Simulation, IEEE Pre Serie on Microelectronic Sytem. [] Cho-Y Lu, Silva-iva, J.F.; Kode, P.; Silva-Martez, J., Hoyo, S., A Sixth-Order MHz IF Banda Sima-Delta Modulator With Over 68 db SND MHz Bandwidth, Solid-State Circuit, IEEE Journal of, Volume: 45, Iue: 6,, Pae(): 36 [] u Chen, Kamal El-Sankary and Ezz El-Mary, A UHF contuou-time current-mode band-a delta ima modulator baed on active ductor Circuit and Sytem, 8. MWSCAS 8. 5t Midwet Symoium on ISBN: ISSN: (Prt); ISSN: (Onle) WCECS