A 100 MHz 6 th Order Continuous Time Band-Pass Sigma Delta Modulator with Active Inductor based Resonators

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1 A 100 MHz 6 th Order ontinuous Time Band-Pass Sima Delta Modulator with Active Inductor based Resonators 1 Kevin Dobson, Shahrokh Ahmadi and 3 Mona Zahloul Deartment of Electrical and omuter Enineerin, Geore Washinton University, Washinton D, USA; 1 kdobson@wu.edu, ahmadi@wu.edu, 3 zahloul@wu.edu ABSTRAT This aer resents a 6 th order, continuous time band-ass Sima Delta modulator in IBM 0.18 um MOS technoloy. We relace traditional RL circuits, containin low quality factor siral inductors with hih quality factor, active inductor based resonators utilizin neative imedance circuits. Pad to ad simulation of the extracted layout in adence yields an enhanced SNDR of 78 db with a noise bandwidth of 18 khz and a ower consumtion of 1 mw. Our modulator occuies 7.5 mm of chi area with ads. Keywords: Sima Delta; Active Inductor; Neative Imedance circuit. 1 ontinuous Time Sima Delta Modulator Loo Filter In Fiure-1 below we see the block diaram of a ontinuous Time Sima Delta (T ΣΔ) modulator. In order to desin the loo filter G(s) we start with a discrete time modulator transfer function F(z) which rovides the required noise shain. Fiure-1: ontinuous Time Sima Delta Modulator As outlined in [1], the imulse-invariant method is used to enerate the equivalent T loo filter G(s) from F(z). ds 1 1 G( s) e F( z) (1 z ) Z T { L [ ]} (1) s Here d reresents the delay introduced by the Analo to Diital onverter (AD) and Diital to Analo onverter (DA). For a sixth order band-ass Sima Delta modulator, the equivalent continuous time loo filter transfer function is iven by: G( s) ( s ωa ωb ( s )( s + s + ωa )( s + s + ωb ) a b ω0 ω1 ω + s + ω0 )( s + s + ω1 )( s + s + ω ) 0 1 () DOI: /aiv Publication Date: nd February, 015 URL: htt://dx.doi.or/ /aiv

2 Advances in Imae and Video Processin Volume 3, Issue 1, February 015 ω reresents the normalized resonator frequencies with resect to the samlin frequency in radians er second and is the quality factor of the resonators. If we denote T as the samlin frequency, when d is equal to 1.4T and the samle rate is 4 times the frequency of the inut sinal, then the term in the numerator is aroximately equal to zero []. Active Inductor Resonator structure The transfer-function of a arallel RL resonator circuit H(s) is iven by: H ( s) s As ω ω 0 (3) G(s) cannot be realized as a cascade of resonators but can be realized by the structure shown in Fiure which aroriately laces the oles and zeros. Here, A H and A L reresent amlifier ains, and H the resonators. The Σ block is an analo adder. H 0, H 1 and H are hih resonators and rovide noise shain. H 3 is a low resonator which rovides modulator stability. A review of the available literature will show that most band-ass T ΣΔ modulators have a loo filter containin arallel RL circuits with siral inductors. Such circuits occuy a lare silicon area and the siral inductors have a low. Active inductor based resonator circuits occuy a much smaller area leadin to more economical desins. When enhancement techniques are used, hih can be achieved. Active inductor based resonators are exlained by the yrator theorem as outlined in Fiure iii below. Fiure : Sixth Order Loo Filter Fiure 3: Gyrator Tooloy It is easily shown that: V in s (4) I in G G m1 m The s in the numerator of Eq. (4) indicates the inductive nature of the circuit. When MOSFETs are used to realize G m1 and G m additional arasitics are introduced formin a lossy arallel RL resonator circuit as shown in Fiure 4 below. Fiure 4: Lossy Parallel RL Resonator oyriht Society for Science and Education United Kindom 11

3 Kevin Dobson, Shahrokh Ahmadi and Mona Zahloul; A 100 MHz 6th Order ontinuous Time Band-Pass Sima Delta Modulator with Active Inductor based Resonators. Advances in Imae and Video Processin, Volume 3 No 1, Feb (015); : When two such yrators are couled with a Neative Imedance ircuit (NI), as shown in Fiure v, a hih fully differential resonator, for use in a band-ass ΣΔ modulator, can be desined. Fiure 5: MOS Active Inductor based Resonator with NI Uon erformin a small sinal analysis of the circuit in Fiure v and searatin the resistive, caacitive and inductive arts we et the followin equations [3]. o is the drain source conductance and m the transistor transconductance. nic reresents the additional caacitance introduced by the NI and nic its transconductance. 1 R ; s ; 1 o s L eff ; and o1 o3 R s (5) m1 m m 1mm3 The enhanced self-resonant frequency and quality factor of the circuit is iven resectively by: m1 m ω en (6) + nic s 1s en o 1 nic (7) nic + L eff PMOS devices are used to coule the differential inut to the circuit. They are biased to draw a small amount of current and do not disturb the yrator function. Outut ain is controlled by varyin the size of these PMOS devices. ascodin M3 and M reduces the outut conductance which reduces R s and increases the. The NI is comrised of 3 cross-couled differential airs of PMOS devices with drains tied to the oosin ates. It rovides a neative resistance that attemts to cancel the arallel resistance R which further increases the. The use of PMOS devices allows for current reuse and results in less ower consumtion. Sinle air cross-couled NIs exhibit low linearity [4]. In order to obtain reater linearity a multi-tanh version of the NI circuit is used. This requires the addition of two extra cross-couled airs of MOSFETs with a 4:1 size ratio [5][7]. When the sinal is lare and the symmetrical differential air has saturated, the unbalanced differential airs can still rovide a differential current roortional to the inut voltae. This scheme works effectively at hih frequencies. URL: htt://dx.doi.or/ /aiv

4 Advances in Imae and Video Processin Volume 3, Issue 1, February 015 While there are no limits to the voltae that can be alied to siral inductors, the maximum inut voltae to active inductor based circuits cannot cause MOSFETs to cease oeratin in saturation mode. Active inductor based circuits are also noisier than circuits with real inductors by a factor of 0, the intrinsic quality factor [5]. All current sources used are cascode in order to rovide reater linearity. 3 Active Inductor Simulation We were able to desin and simulate active inductor based resonators in adence with resonant frequencies between 15 MHz and 1.5 GHz, and were consistently able to achieve a of 50 or reater. Simulation results for one active inductor desined are shown in Fiure 6 and 7. Fiure 6: Active Inductor simulated A resonse Fiure 7: Active Inductor Linearity 4 Matlab Modulator Simulation Initial values of the loo filter multilyin coefficients, A H and A L of G(s) were used to enerate Pole-Zero lots and confirm modulator stability. The aroriate noise shain characteristics were verified by the use of the Delta-Sima toolbox [6]. Simulink simulations were then used to further refine the modulator desin. Fiure 8: Modulator Pole Zero lot The Simulink model was easily modified to reflect the non-idealities of an actual circuit such as limited ain due to nonlinearity and small delays introduced by each circuit comonent. A theoretical Sinal to Noise-lus-Distortion Ratio (SNDR) of 95dB was obtained for the ideal case when there is a hih ain in the ath containin the most resonators. When the limitations of ain and circuit delay were taken into account a oal of 80 db was deemed feasible. oyriht Society for Science and Education United Kindom 13

5 Kevin Dobson, Shahrokh Ahmadi and Mona Zahloul; A 100 MHz 6th Order ontinuous Time Band-Pass Sima Delta Modulator with Active Inductor based Resonators. Advances in Imae and Video Processin, Volume 3 No 1, Feb (015); : adence Simulation For the adence circuit desin, resonators were desined to resonate at 5 MHz with a of 30. Linear oeration was observed when the inut was limited to less than 10mv -. A block diaram of the comlete circuit simulated in adence is shown in Fiure ix. Fiure 9: Active Inductor based Sixth Order ontinuous Time Modulator A series of differential amlifiers[8] A, rovide effective amlification of the sinal rior to quantization reventin clock feed-throuh [8] and contributin to the required delay of 1.4T. A coulin caacitor with buffer for biasin the next stae of the circuit, B, eliminates dc offsets introduced after layout. This caacitor and inut resistance of the buffer must be lare enouh to form an effective hih ass filter thereby reventin attenuation. Pre-comarators rovide further amlification before quantization by a clocked comarator. Since there is a non-zero delay it is necessary to add a direct loo between the DA and the AD inut [9]. The Adder used is described in []. A inut version of the adder is used to subtract the DA outut from the inut sinal. oncetually the subtraction is the addition of the inut and the neative DA outut. A clocked comarator [8] couled with a SR fli flo enerates the (NRZ) modulator outut. The DA is described in [10]. We use searate VDD and GND for these sub-circuits. We also surround our analo sub-circuits with two uard rins searated by BFMOAT in order to rotect them from diital noise. [11] Extraction of the layout yields extra arasitics which result in larer roaation delays and lower outut sinals, resonant frequency and. Several circuit modifications were made in order to neate the effects of the added arasitics. The first was to ensure a symmetrical layout so that the arasitics added on either side of the differential circuit were equivalent. The next was to increase the size of the inut PMOS devices leadin to better coulin of inut sinals. The third was to increase the current in the current mirror I which is necessary to overcome the added imedances. The fourth was to increase the size of M3. This decreases R s which increases our deteriorated. The fifth was to lower our clock frequency to account for the increased roaation delays. When these chanes were made to the layout and Inut/ Outut ads added, the layout was re-extracted and a ad to ad simulation was conducted. This yielded a SNDR of 78dB with a noise bandwidth of 1 khz. This was quite close to the 80dB observed in the Simulink simulations. The difference is believed to be due to circuit non-idealities, such as settlin time of the adder outut, and offset errors. This result is shown in Fiure 10. It comares favorably with other non-active inductor based sixth order band-ass ΣΔ modulators such as [1], which yields a SNDR of 68dB. Our circuit consumes 1 mw and occuies 7.5 mm, includin ads. URL: htt://dx.doi.or/ /aiv

6 Advances in Imae and Video Processin Volume 3, Issue 1, February 015 Fiure 10: Extracted Layout Power Sectrum Density 6 onclusion The reatest desin limitation encountered when desinin T ΣΔ modulators with active inductor based resonators is the limited linearity. This results in a desin that is hihly suscetible to offsets. Also many extra amlification staes are necessary to raise voltaes to accetable levels rior to quantization. The extra circuitry required to comensate for offsets and amlification neates the area ains made by the avoidance of siral inductors. More research is needed to determine how to extend the linearity of active inductor based resonators. This would result in desins that are caable of oeratin at hiher frequencies and occuyin smaller areas. A review of the available literature shows only one other active inductor based band-ass ΣΔ modulator [13]. The authors included schematic simulations but not simulation results for an extracted layout. We have succeeded in desinin and simulatin the first Sixth Order T ΣΔ modulator, usin active inductor based resonators in the loo filter and rovided ad to ad simulations of the extracted layout. Our desin has been submitted for fabrication with MOSIS. REFERENES [1]. Lelandais-Perrault, P. Benabes, J. De Gouy, R. Kielbasa, A arallel structure of a continuoustime filter for bandass sima-delta A/D onverters, 10 th IEEE International onference on Electronics, Sharjah (Emirates Arabes Unis), DE [] S. Benabid, P. Benabes, Hih linear interated L filter for a continuous-time bandass simadelta AD ircuits and Systems, 003 IEEE 46th Midwest Symosium on, Vol. 1, 30 Dec. 003 [3] Fei Yuan, MOS Active Inductors and Transformers, Princile, Imlementation, and Alications, Sriner 008 [4] Byunhoo Jun, Harjani, R., A wide tunin rane VO usin caacitive source deeneration, ircuits and Systems, 004. ISAS 04. Proceedins of the 004 International Symosium on, Volume 4, 3-6 May 004, Pae(s): IV Vol.4. [5] Yue Wu, Xiaohui Din, Mohammed Ismail, and Håkan Olsson, RF bandass filter desin based on MOS active inductors, IEEE Transactions on circuits and systems II: Analo and Diital Sinal Processin, vol 50, no.1, Dec [6] Richard Schreier and Gabor. Temes, Understandin Delta-Sima Data onverters, IEEE Press oyriht Society for Science and Education United Kindom 15

7 Kevin Dobson, Shahrokh Ahmadi and Mona Zahloul; A 100 MHz 6th Order ontinuous Time Band-Pass Sima Delta Modulator with Active Inductor based Resonators. Advances in Imae and Video Processin, Volume 3 No 1, Feb (015); : [7] A. P. Ryan, O. Mcarthy, A novel ole-zero comensation scheme usin unbalanced differential airs, IEEE transactions on circuits and systems I: Reular aers, vol. 51, no., Feb [8] R. Jacob Baker, MOS, ircuit Desin, Layout, and Simulation, IEEE Press Series on Microelectronic Systems. [9] P. Benabes, M. Keramat and R. Kielbasa, Synthesis and Analysis of Sima-Delta Modulators Emloyin ontinuous-time Filters, Analo Interated ircuits and Sinal Processin, no. 3, , Jul [10] Kevin Dobson, Shahrokh Ahmadi and Mona Zahloul, A 1. GHz Band-Pass Sima Delta Analo to Diital Modulator with Active Inductor based Resonators, Lecture Notes in Enineerin and omuter Science: Proceedins of The World onress on Enineerin and omuter Science 01, WES 01, 4-6 October, 01, San Francisco, USA, [11] Haitao Dai, Differential Sensin of Substrate Noise in Mixed-Sinal um BiMOS Technoloy, Electron Device Letters, IEEE, Au. 008, Volume 9: Issue 8, [1] ho-yin Lu, Silva-Rivas, J.F.; Kode, P.; Silva-Martinez, J.; Hoyos, S., A Sixth-Order 00 MHz IF Bandass Sima-Delta Modulator With Over 68 db SNDR in 10 MHz Bandwidth, Solid-State ircuits, IEEE Journal of, Volume: 45, Issue: 6, 010, Pae(s): [13] uinin hen, Kamal El-Sankary and Ezz El-Masry, A UHF continuous-time current-mode bandass delta sima modulator based on active inductor, ircuits and Systems, 008. MWSAS st Midwest Symosium on URL: htt://dx.doi.or/ /aiv