Aghazadeh, Seyed Rasoul

Alarcón Cot, Eduardo José

Martínez García, Herminio

Saberkari, Alireza

UPCommons

Tunable wide–band second–order all–pass filter–based time delay cell using active inductor

Aghazadeh Dafsari, Seyed Rasoul

UPCommons. Portal del coneixement obert de la UPC

Tunable Wide-Band Second-Order All-PassFilter-Based Time Delay Cell Using Active InductorSeyed Rasoul Aghazadeh, Alireza SaberkariMicroelectronics Research Lab.Department of Electronics Engineering, University of GuilanRasht, Irana−saberkari@guilan.ac.irHerminio Martinez, Eduard AlarconDepartment of Electronics EngineeringTechnical University of Catalunya (UPC), BarcelonaTechBarcelona, Spain{herminio.martinez; eduard.alarcon}@upc.eduAbstract—This paper presents a CMOS RF second-ordervoltage-mode all-pass filter (APF) as a time delay cell. Theproposed filter benefits from a simple structure; consisting ofone transistor, three resistors, and one grounded capacitor andinductor. The filter reaches a group delay of 60 ps over a 10 GHzbandwidth, while achieving maximum delay-bandwidth-product(DBW) and it consumes only 10.3 mW power. On the other hand,an active inductor is used in the APF instead of a passive RLCtank in order to control the time delay and improve the size.In this case, the power consumption increases while time delaycan be tuned. The proposed APF is designed and simulated in aTSMC 180 nm CMOS process.Keywords—all-pass filter; delay; wide-band; delay-bandwidth-product; active inductorI. INTRODUCTIONAll-pass filters (APFs) as delay stages are used for real-ization of delay structures in many different radio frequency(RF) circuits and phase shift applications like synchronizingultra-wideband (UWB) impulse radios with locally generatedreference pulses, equalizers, and analog beamformers [1]−[3].All-pass-filter-based time delays provide better performancein terms of area-efficiency and loss than alternative methodsbased on transmission lines or lumped LC delay lines, whichare area consuming and impractical for on-chip implemen-tations. Therefore, implementations of wideband analog RFbeamformers using all-pass-filter-based delay approximationshave recently received attention [4], [5].In some circuits, the delay stage is usually realized bycascading first-order all-pass gm-(R)C filters. However, thesecircuit topologies suffer from limited bandwidths around low-GHz (up to 2.5GHz) [5], [6]. Generally, high-order rationalAPFs can be decomposed into several second-order APFs withcomplex-conjugate poles and first-order APFs. Therefore, asecond-order APF is a key component for realization of a delaystructure with nanosecond delay. There are several current-and voltage-mode APFs in the literature [7]−[9], most ofthem use one or more operational voltage or current amplifiersthat suffer from low bandwidth due to the presence of highimpedance nodes though. These filters are therefore limited tolow frequencies of operation.In this paper, a CMOS wide-band second-order APF usingan active inductor to control time delay is proposed. Theproposed circuit employs pade´ approximation, which providesthe best approximation of an ideal delay; because it achievesflatter group delay over a larger bandwidth than any otherapproximation [10], [11]. For achieving maximum delay-bandwidth-product (DBW), second-order APFs using Pade´technique are better selections than the cascade of two first-order APFs to realize a second-order delay structure.The structure of this paper is as follows. In Section II, theproposed APF is designed and analyzed. Section III presentsthe tunability of the proposed second-order APF. The resultsare given in Section IV and finally, Section V providesconclusions.II. PROPOSED SECOND-ORDER APFThe ideal transfer function of a second-order APF utilizingPade´ approximation is as follows:H(s) =s2 − ωnQ s+ ω2ns2 + ωnQ s+ ω2n(1)where ωn is the natural frequency of the APF and Q isthe quality factor, which determines the position of polesand zeros in the complex plane. Fig. 1 shows the proposedCMOS second-order APF as a time delay cell. If we neglectthe parasitics of the transistors, the transfer function of theproposed second-order APF is defined as below:VoutVin(s) = −RL(gm1R1−1)RL+R1 ·s2− 1C(gm1+gm2−gm1gm2R1gm1R1−1)s+ 1LCs2+ 1C (gm1+gm2)s+1LC(2)where gm1 and gm2 are the transconductances of M1 and M2,respectively. In order to have an all-pass structure, we musthave the DC gain equal to unity and the same coefficients fors in the nominator and denominator of (2), which yields to thefollowing conditions:R1 =2gm1(3a)RL  R1 (3b)gm1 + gm2  gm1gm2R1. (3c)As a result, the transfer function in (2) can be rewritten asbelow:VoutVin(s) ∼= −s2 − 1C (gm1 + gm2)s+ 1LCs2 + 1C (gm1 + gm2)s+1LC. (4)978-1-5386-5108-7/17/$31.00 c©2017 IEEEFig. 1. The proposed second-order all-pass filter.Therefore, natural frequency and quality factor of theproposed second-order APF become, respectively, as follows:ωn =1√LC(5)Q =1gm1 + gm2√CL. (6)Given that transconductances gm1,2 only affect the qualityfactor, the circuit bandwidth and quality factor can be set, inde-pendently. The pole/zero frequencies, phase, and group delayresponses of the second-order APF are given, respectively, asbelow:|ωp1,2| =|ωz1,2| =L(gm1 + gm2)±√L2(gm1 + gm2)2 − 4LC2LC(7)ϕ(ω) = −2 tan−1[L(gm1 + gm2) · ω1− LCω2](8)τg(ω) = −∂ϕ(ω)∂ω=2L(gm1 + gm2)·1 + LCω2(1− LCω2)2 + ((gm1 + gm2)Lω)2.(9)The group delay is 2L(gm1 +gm2) at DC. When Q < 0.5,the APF has two real poles in the left-half plane, whilefor Q > 0.5 a complex conjugate pole-pair appears. WhenQ = 1/√3, the maximum flat delay will be achieved and Pade´approximation is matched. Therefore, the maximum delay-bandwidth-product (DBW) will be guaranteed. Note that, thecircuit can achieve larger delay over a wider bandwidth bychoosing gm, L, and C appropriately (low transconductanceand small values of L and C) compared to the gm-(R)C filters,as the natural frequency of the proposed circuit is 1/√LC.In order to consider the effects of parasitic capacitors onthe performance of the proposed APF, the effect of Cgd isneglected due to the fact that its impedance is more than R1 athigh frequencies, corresponding to a very high frequency polewhich does not affect the performance of the APF. Therefore,Fig. 2. (a) Active inductor and, (b) and (c) its equivalent models.Cgs is just assessed for the evaluation. Considering finiteoutput impedance of M1 and the Cgs which affect the pole/zerofrequency and DC-gain, the transfer function of the second-order APF is as follows:VoutVin(s) = −CRL(gm1R1 − 1)− CgsRL(1 +R1gds)(C + Cgs)(R1 +RL + gdsR1RL)·s2 −[(gm1+gm2+gds)(1+R1gds)−(gm2+gds)(R1(gm1+gds))C(gm1R1−1)−Cgs(1+R1gds)]s+ gm1R1−1LC(gm1R1−1)−LCgs(1+R1gds)s2 +[(gm1+gm2+gds)(R1+RL)+gm2gdsR1RL(C+Cgs)(R1+RL+gdsR1RL)]s+ 1L(C+Cgs)(10)where gds is the output conductance of M1. If gm1,2  gdsand the conditions in (3) are satisfied, the transfer function canbe rewritten as below:VoutVin(s) ∼= −C − CgsC + Cgs·s2 − gm1+gm2C−Cgs s+ 1L(C−Cgs)s2 + gm1+gm2C+Cgs s+1L(C+Cgs). (11)As it can be seen, for C  Cgs, (4) and (11) will be thesame. Further analysis shows that Cgs makes variations on thegain and group delay responses at high frequencies. However,these variations can be adjusted by varying resistor R2 in theproposed APF, which is assessed in Section IV.III. THE TUNABILITY OF THE PROPOSEDSECOND-ORDER APFIn order to control time delay in the proposed second-orderAPF, active inductors are good options as they offer a varietyof advantages; e.g. small area, large and tunable inductancevalue and self-resonant frequency, and also compatibility withstandard CMOS technology [12]. Fig. 2(a) shows a one-port grounded active inductor [13], [14], which is used inthe proposed second-order APF. Assuming for simplicity thatgm(ind)  gds(ind), the input admittance of the active inductor,Yind(= 1/Zind), can be easily obtained by using its smallsignal equivalent circuit shown in Fig. 2(b) as follows:Yind =sCgs + gm(ind)sRCgs + 1=1R+1sR2CgsRgm(ind)−1 +RRgm(ind)−1(12)where pole and zero frequencies of the input admittance ofthe active inductor are ωp = gm(ind)/Cgs and ωz = 1/RCgs,respectively. The circuit has an inductive behavior in thefrequency range of ωz < ω < ωp.The obtained input admittance in (12) can now be modeledby a parallel RL circuit shown in Fig. 2(c) as below:Y′ind = GP +1sL+RS(13)where GP = 1/RP is determined as parallel and RS as seriesresistance with inductor L. From (12) and (13), the parametersof the RL equivalent circuit can be given as:RP = R (14a)L =R2CgsRgm(ind) − 1 (14b)RS =RRgm(ind) − 1 . (14c)The circuit shown in Fig. 3 is designed to tune the delayof the proposed second-order APF. In this circuit, activeinductor shown in Fig. 2(a) is replaced with parallel RLCcircuit in Fig. 1. The value of resistor RS is very small andtherefore it can be neglected. Capacitor CP is the total parasiticcapacitances at the source terminal of the transistor M1, andhence, there is no need to any additional capacitor at thisnode resulting in a smaller area. The transfer function of theproposed circuit in Fig. 3 is as follows:VoutVin(s) = −RL(gm1R1 − 1)RL +R1·s2 −[gm1RPL+L+CPRPRS−gm1R1(L+CPRPRS)LCPRP (gm1R1−1)]s+ (gm1R1−1)(RP+RS)−gm1RPRSLCPRP (gm1R1−1)s2 +[gm1RPL+L+CPRPRSLCPRP]s+ gm1RPRS+RP+RSLCPRP.(15)Fig. 3. The proposed second-order all-pass filter using an active inductor.If gm1RP  1, gm1RS  1, and conditions in (3a)-(3b)are satisfied, the transfer function can be rewritten as below:VoutVin(s) ∼= −s2 − ( gm1CP )s+ 1LCPs2 + ( gm1CP )s+1LCP(16)which is nearly the same as that in (4).IV. RESULTSThe proposed second-order APF is designed in 180nmTSMC CMOS process and the results are obtained fromHSPICE simulation with the supply voltage of 1.8V. First, theproposed circuit shown in Fig. 1 is simulated with gm1 =31.5mA/V, gm2 = 3.7mA/V, RL = 3KΩ, R1 = 65Ω, andQ = 1/√3 (for maximum DBW). In addition, the valuesof capacitor and inductor are selected as 210fF and 0.85nH,respectively.In Fig. 4 the gain and phase responses of the second-orderAPF are shown. The gain roll-off is due to the existence ofparasitic effects of the transistors. The group delay response ofthe proposed APF is shown in Fig. 5, indicating a flat groupdelay equal to 59.8ps over 10GHz bandwidth, which is veryclose to the theoretical value in (9). Fig. 6 shows the gain andgroup delay responses of the second-order APF for differentvalues of R2(= 1/gm2). It is obvious that by varying gm2,Fig. 4. Gain and phase responses of the proposed second-order all-pass filter.Fig. 5. Group delay response of the proposed second-order all-pass filter.Fig. 6. Gain and group delay responses of the proposed second-order all-passfilter with different values of R2 = 1/gm2.Fig. 7. Gain and group delay responses of the proposed second-order all-passfilter with active inductor for different values of RP (50− 850Ω).flat gain and group delay responses are achieved at higherfrequencies.Table I indicates the performance comparison of the pro-posed second-order all-pass filter and some other reportedwide-band second-order ones. As it can be seen, power con-sumption of the proposed APF is lower than the others. Fur-thermore, the proposed circuit demonstrates a larger bandwidththan the other second-order APFs having the same mode withthe exception of the filter in [10] where two inductors wereused, resulting in a larger area.Finally, the proposed second-order APF using an activeinductor shown in Fig. 3 is evaluated with gm1 = 18mA/V,Fig. 8. Monte Carlo simulation results for gain and group delay responsesof the proposed second-order all-pass filter with active inductor.Fig. 9. Corner analysis results for group delay response of the proposedsecond-order all-pass filter with active inductor.gm(ind) = 118mA/V, RL = 3KΩ, R1 = 115Ω, and RP =450Ω. In this case, an inductance of L = 1.48nH with RS =8.6Ω is obtained, while the overall active inductor-based APFconsumes 33.6mW power from a 1.8V supply voltage. Thegain and group delay responses of the proposed APF are shownin Fig. 7. As it can be seen, the delay can be controlled overthe frequency band by varying the resistor RP in the activeinductor. Tuning action can be easily performed by a binaryweighted resistor bank instead of R(= RP ) in Fig. 2(a).For further analysis, Monte Carlo and corner analysesare considered and the results are shown in Figs. 8 and 9respectively, with RP = 250Ω. The Monte Carlo simulationresults are performed for ±7% tolerance on the channel lengthTABLE I. PERFORMANCE COMPARISON OF THE PROPOSEDWIDE-BAND SECOND-ORDER ALL-PASS FILTER AND OTHER WORKS.of M1 in Fig. 3, with a Gaussian distribution and 50 iterations.In this case, maximum variation on the group delay responseof the proposed APF over the frequency band is 9.5%.V. CONCLUSIONThis paper has presented a tunable wide-band second-orderall-pass filter as a time delay cell. The proposed voltage-mode all-pass filter shows a flat group delay of 60ps over abandwidth of 10GHz, achieving maximum delay-bandwidth-product (DBW). This filter consumes only 10.3mW andreaches a larger delay across the frequency band than otherpublished second-order voltage-mode APFs using just onegrounded inductor. Additionally, an active inductor is utilizedin order to control the time delay of the proposed second-order APF and to decrease size. In this condition, the proposedfilter consumes around 33.5 mW power, while its time delayis varied for different values of tunable resistor in the activeinductor.ACKNOWLEDGMENTThis work has been partially funded by the Spanish Min-istry of Science and Innovation (project DPI2013-47799- C2-2-R).REFERENCES[1] J. Schwartz, I. Arnedo, M. Laso, T. Lopetegi, J. Azana, and D. Plant,“An electronic UWB continuously tunable time-delay system withnanosecond delays,” IEEE Microw. Wireless Compon. Lett., vol. 18,no. 2, pp. 103-105, Feb. 2008.[2] J. Buckwalter and A. Hajimiri, “An active analog delay and the delayreference loop,” in Proc. IEEE RFIC Symp. (RFIC04), Dig., Jun. 2004,pp. 17-20.[3] G. Gurun, J. S. Zahorian, A. Sisman, M. Karaman, P. E. Hasler,and F. L. Degertekin, “An analog integrated circuit beamformer forhigh frequency medical ultrasound imaging,” IEEE Trans. BiomedicalCircuits Syst., vol. 6, no. 5, pp. 454-467, Oct. 2012.[4] C. Wijenayake, Y. Xu, A. Madanayake, L. 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Tunable wide–band second–order all–pass filter–based time delay cell using active inductor

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