HTS materials are known to produce intermodulation and other nonlinear effects, and this may restrict their use in wireless communication systems. While significant efforts are being done to measure and characterize nonlinear properties of HTS materials, there are very few works that relate these properties to system parameters. In this work we attempt to bridge this gap by using harmonic balance algorithms to analyze the nonlinear performance of superconducting filters subject to the WCDMA signals specified by 3GPP for the UMTS wireless system. This is a first step to predict compliance with system parameters like adjacent channel leakage power ratio (ACLR) or error vector magnitude (EVM).Peer Reviewe

Collado Gómez, Juan Carlos

Ferrús Ferré, Ramón Antonio

Mateu Mateu, Jordi

O'Callaghan Castellà, Juan Manuel

IEEE Transactions on Applied Superconductivity

English

UPCommons. Portal del coneixement obert de la UPC

328 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003Prediction of Nonlinear Distortion in HTS Filters forCDMA Communication SystemsC. Collado, J. Mateu, R. Ferrús, and J. M. O’CallaghanAbstract—HTS materials are known to produce intermodula-tion and other nonlinear effects, and this may restrict their usein wireless communication systems. While significant efforts arebeing done to measure and characterize nonlinear propertiesof HTS materials, there are very few works that relate theseproperties to system parameters. In this work we attempt tobridge this gap by using Harmonic Balance algorithms to analyzethe nonlinear performance of superconducting filters subject tothe WCDMA signals specified by 3GPP for the UMTS wirelesssystem. This is a first step to predict compliance with systemparameters like Adjacent Channel Leakage power Ratio (ACLR)or Error Vector Magnitude (EVM).Index Terms—CDMA, harmonic balance, HTS, intermodula-tion, nonlinearities, superconducting filters.I. INTRODUCTIONTHIRD-GENERATION (3G) wireless systems are de-signed for multimedia applications, where high data rateswill be available for person-to-person communication and/oraccess to information and services on public and private net-works. These systems are based on spread spectrum techniqueswhere CDMA signals are used to multiplex users onto the samefrequency channel using Orthogonal Variable Spreading Factor(OVSF) and Gold-code scrambling. To maintain high spectralefficiency in dense electromagnetic environments, filtering isessential to separate the desired frequency band from othersignals. Passband filters with High Temperature Supercon-ductors (HTS) might be very well suited for this application,but they are known to exhibit nonlinear effects giving riseto intermodulation distortion, even at moderate power levels.These nonlinear effects in HTS filters are distributed along thestructure of the device and can degrade the performance of thewhole transceiver [1], [2].In previous works we have proposed numerical techniquesbased on Harmonic Balance (HB) to predict microwave non-linear response of HTS filters and resonators when one or twosinusoidal signals are applied to them [3]. This is not sufficientto quantify the performance of a 3G communication system,which is subject to much more complex CDMA signals andwhose nonlinearities might affect important system parametersManuscript received August 6, 2002. This work is supported by the SpanishMinistry of Science and Technology under Project TIC2000-0996 and Scholar-ship AP99-78085980 for J. Mateu, and by Generalitat de Catalunya (DURSI)under Grant 2001 SGR 0026.C. Collado, R. Ferrús, and J. M. O’Callaghan are with Universitat Politècnicade Catalunya (UPC), Campus Nord UPC D3 08034 Barcelona, Spain (e-mail:joano@tsc.upc.es).J. Mateu is with CTTC-Centre Tecnològic de Telecomunicacions deCatalunya, Edifci NEXUS, 08034 Barcelona, Spain.Digital Object Identifier 10.1109/TASC.2003.813723such as adjacent channel leakage power ratio (ACLR) or errorvector magnitude (EVM).In this work we have extended the flexibility of our numericalmethods based on HB to simulate HTS filters subject to signalswith many frequency components like those of CDMA systems.We refer to this method as Multitone Multiport Harmonic Bal-ance (MMHB). We present illustrative examples which showthe viability of this kind of analysis for HTS front-end receiversand transmitters in 3G systems.II. MULTITONE MULTIPORT HARMONIC BALANCEOur simulations model the distributed nonlinearities in HTSfilters by discretizing its structure (for example breaking downtransmission lines in segments much shorter than a wavelength).A large nonlinear equivalent circuit results (see, for example,Figs. 1 and 2 in [4]), and is analyzed using numerical methodsbased on HB [5]. Common to all HB algorithms is the splittingbetween the linear part of the circuit, characterized in frequency-domain, and the nonlinear one, characterized in time-domain.For example, in a transmission line filter, the nonlinear part ofthe circuit would model the nonlinearities in the resistance andinductance per unit length of the transmission line, and the linearnetwork would model all other (linear) elements in the circuit(the linear resistance, inductance, capacitance and conductanceper unit length of the line, the coupling between lines, etc.) [4].The linear part is a ( )-port with of its ports loadedwith nonlinear elements and the remaining one is fed by thesource(s) driving the circuit. This ( )-port is characterizedby its impedance matrix ( ) which relates the voltage droppedacross the ports ( ) to the current flowing out of the network( ) and impressed on the nonlinear elements. In principle,the values of the matrix elements have to be calculated at allfrequencies of the source current, and at all other frequencieswhere spurious signals may exist. The nonlinear part consistsof nonlinear one-port elements modeling a distributed non-linearity. In this work we will focus on nonlinearities where thevoltage across each one-port depends on the current thoughit ( ) by means of a nonlinear resistance ( ) and in-ductance ( ), i.e.,:(1)which is used to model HTS filters with transmission line [4] ordisk resonators [6]. As shown in [3], this can be extended to cav-ities with HTS endplates, or to planar filters whose resonatorshave convoluted layouts.As detailed in [5], HB is based on an iterative procedurewhich matches the voltage and current variables of the linear1051-8223/03$17.00 © 2003 IEEECOLLADO et al.: PREDICTION OF NONLINEAR DISTORTION- 329( and ) and nonlinear part ( and ). Transforma-tion algorithms are needed to convert the data from frequency totime domain and vice versa, so that the linear part can be solvedin frequency domain and the nonlinear part in time domain. Areview of such algorithms is given in [7].A key difference of MMHB algorithm with respect to othernumerical methods that we have previously used to simulateHTS devices is the need for sampling the voltages and currentsin the device equivalent circuit. Unlike in a two-tone intermodu-lation experiment, the HTS device is now fed with a broadbandsignal with a carrier frequency and bandwidth , and squarelaw nonlinearities in the device produce voltages and currentswhose spectral components will be distributed across two fre-quency bands of bandwidth 3 centered at and 3 . Under-sampling is necessary to take into account all these frequencycomponents and down convert the signal to baseband. The sam-pling rate has to be carefully chosen to avoid aliasing. Detailson these aspects will be given in a forthcoming paper.The preceding discussions result in the following outline ofthe MMHB method:1) Once the frequency resolution is decided, we calcu-late the frequencies of the spectral lines to be considered.2) Calculation of the matrix in a 3 bandwidth centeredat in steps of .3) Determination of the sampling rate and the frequenciesof the down-converted signals.4) Start the Harmonic Balance iterative algorithm (see [3,Fig. 3]):a) Propose a solution for the time-domain currentacross the nonlinear one-ports ( ). The initialestimate is calculated with the matrix , assumingthat the voltage across these one-ports is zero.b) With the down-converted version of , find thevoltage across the nonlinear one-ports by ap-plying an equivalent of (1) that takes into accountthe effects of taking a time derivative to a down-converted signal.c) Transform to frequency domain and find itsup-converted counterpart.d) With the voltage resulting from the previous point,the source current , and the matrix , solve thelinear circuit and find an updated estimate of thecurrent thought the one-ports .e) Down-convert and transform it to time domain.Compare it with in point (b) above. If conver-gence is not achieved go to point (b) and start a newiteration.III. EXAMPLESIn this section we illustrate the usefulness of MMHB by cal-culating some figures of merit (Spurious Free Dynamic Range(SFDR), ACLR and EVM) which can be affected by the non-linearities in HTS filters. We have analyzed a number of pass-band filters at UMTS frequencies with Chebyshev and quasiel-liptic designs having various types of resonators, bandwidth andorder. All the filters have been designed for a return loss of 20dB. The quasielliptic designs had a single pair of transmissionzeros, with a ratio of the bandwidth between zeros to the 3 dBbandwidth of 1.2 [8]. Three resonator types have been consid-ered: microstrip half-wave resonant lines with either a 50 or 25characteristic impedance, and disk resonators. Twodifferent bandwidths were considered: 5 and 15 MHz, to allowfor a passband with either one or three UMTS channels.In all cases we have assumed a 0.5 mm thick MgO substratewith a 700 nm thick Y-Ba -Cu -O film whose nonlinearitiesare due to a dependence of the penetration depth with currentdensity of the type:(2)with 10 Am [9]. With this dependence, wehave determined the variation with respect to the small-signalvalues of the resistance per unit length ( ) and inductanceper unit length ( ) of the halfwave transmission line res-onators, so that and can be used in (1) to findthe voltage along the line due to the nonlinearities of theHTS. The calculation of , from (2) is done fol-lowing the procedure in described in [10]. For 50 lines wehave obtained 10 m and10 Hm . For 25 lines the result is10 m and 10 Hm .For the disk resonators, the effect of the non-linearities is to create a radial electric field that willhave a nonlinear dependence with surface current density[6], [9], [11]. If the nonlinearities are predominantly reactive[11] which, combined with (2) and thevalue of above results in 10 H[9]. As detailed in [6] this can be transformed in a nonlinearinductance (where is the radial position ofthe discretization cell being considered) that can be used in anequivalent of (1).A. Two Tone Nonlinear Response: SFDRThe Spurious Free Dynamic Range (SFDR) of a device is theratio between the noise floor and the power of the sinusoidalsignals that, when applied to the device in a two-tone intermod-ulation measurement, generate intermodulation products whosepower is equal to the noise floor [12]. In this work, we haveused a noise floor of 108 dBm [13]. Since the signals appliedto the device to quantify its SFDR are sinusoidal, we can ei-ther use our previous versions of HB for HTS analysis (whichare restricted to sinusoidal signals) [3], or the MMHB describedhere (which can handle a wide variety of signals, among themsinusoidal ones). The SFDR examples shown below have beencalculated with both codes, to confirm the proper operation ofthe MMHB described here, and we found that the results of bothcodes agreed.As an example of the type of results obtained, Fig. 1 showsthe SFDR obtained for the third order intermodulation productby sweeping two tones across the band pass of three different fil-ters and keeping a constant spacing (62.5 KHz) between them.The filters simulated had 50 lines and were designed for a15 MHz bandwidth. Two of them had a Chebyshev designs oforders 8 and 12, and the third one had an 8th order quasiellipticdesign. The figure shows that for 8th order filters, the SFDR of330 IEEE TRANSACTIONS ON APPLIED SUPERCONDUCTIVITY, VOL. 13, NO. 2, JUNE 2003Fig. 1. Spurious-free dynamic range for three different filters with identical15-MHz bandwidth and 50- line resonators. Continuous line: eighth orderquasieliptic filter. Dashed line: eighth order Chebyshev filter. Dotted line:twelfth order Chebyshev filter.the quasielliptic filter is slightly better than that of the Cheby-shev filter at the center of the bandwidth, but can be 6 dB smallerif the two input tones are at the edge of the pass band. On theother hand, increasing the order in the Chebyshev filter from 8 to12 causes a degradation between 3 and 5 dB of the SFDR. Thisexample shows that for Chebyshev filters, increasing the orderof the filter reduces the SFDR. Other simulations have shownthat this has also happens in quasielliptic filters.An extensive study has been made to compare the SFDR ofvarious coupled-line filters of identical order. The study hasshown that the SFDR of various 12th order filters at the center ofthe passband changes little (less than 1 dB) with the type of filter(Chebyshev or quasielliptic). Filters with 5 MHz bandwidth and50 lines have the smallest SFDR (88 dB), which increases to90 dB if the impedance of the lines is decreased to 25 . AnSFDR of 93 dB is obtained for 15 MHz filters with 50 lines,which can be increased to 97 dB by using 25 lines.B. Multitone Nonlinear Response: ACLR and EVMAs pointed out in [14], the SFDR and the third order interceptpoint are not sufficient to quantify the performance degradationcaused by a nonlinear device when it is subject to spread spec-trum signals as those in a 3G communication systems. To char-acterize such degradation, other parameters such as ACLR andEVM are used.ACLR is a figure of merit that quantifies the leakage ofthe transmitted power into adjacent channels, and thereforeaccounts for the combined effects of filter selectivity andspectral regrowth due to nonlinear effects. Fig. 2 shows howthese effects increase the spectral components of the signaloutside the passband. Qualitatively similar results have beenobtained from measurement of HTS filters [15]. With thisspectrum, and following a procedure specified in [16], we cancalculate the ACLR of the signal.Fig. 2. WCDMA spectrum before (black) and after (grey) an HTS filter(QE D O BW ) as simulated by MMHB, showing the effect of thenonlinearities in the regrowth of the spectrum outside the passband. The inputsignal is a sequence of 77 bits (one user with a spreading factor SF = 8) withQPSK modulation and complex spreading. Carrier frequency is 2.1375 GHzand power P = 43 dBm. The resulting ACLR of the signal at the filter outputis 68.8 dB. Note that this is only an illustrative example: more users would givelower ACLR.EVM quantifies the modulation accuracy by making a bit bybit comparison between the distorted waveform and the orig-inal one. It therefore accounts, among others, for the in-channeleffects of the nonlinearities. To calculate EVM from our simu-lated data, we have used [17]:(3)being the distorted signal, the ideal signal withoutnonlinear distortion, and their respective RMSvalues and the mean value of the phase difference betweendistorted and ideal signals. Equation (3) accounts for the meanof the phase deviation , therefore it is appropriate if thereceiver is able to correct this. Otherwise, the EVM wouldbe greater and it should be calculated with (we usein that case).In order to quantify the degradation of the EVM caused onlyby the nonlinearities of the filter we have defined the ratio be-tween the EVM obtained from nonlinear simulations to that ob-tained if the filter was a linear device.(4)Table I shows the SFDR (at midband), ACLR, EVM andfor a set of filters whose input signal is made up of a sequenceof 77 bits (one user with a spreading factor ) withQPSK modulation and complex spreading. Carrier frequency is2.1375 GHz and power dBm. Even though longer bitstreams would be desirable for a more reliable quantitative char-acterization of these parameters, some qualitative statementsabout how these filters compare can be made. The first is theexpected effect on bandwidth: all parameters degrade at smallerbandwidths due to the higher circulating power in the filter. Thisis very clear by looking at the last column in the table where thevalues of show that the EVM due to the filter nonlinearitiesCOLLADO et al.: PREDICTION OF NONLINEAR DISTORTION- 331TABLE ICOMPARISON AMONG VARIOUS TYPES OF FILTERSis much higher in the filters with 5 MHz bandwidth. Similarly,higher filter orders result in steeper slopes in the transfer func-tion at the passband edge, and this is known to be detrimentalfor intermodulation performance. As a result, all parameters inTable I degrade when the order is increased. In other words, in-creasing the filter order improves its selectivity and its ability toreject out of band interfering signals, but has a detrimental ef-fect in the in-band nonlinear effects. Finally, quasielliptic filtersare slightly better than Chebyshev ones (of identical order andbandwidth) in SFDR and ACLR. Their EVM are very similar,but their indicates that Chebyshev filters produce morephase deviation ( ) due to nonlinearities.IV. CONCLUSIONSWe have described the basics of the extension of our Har-monic Balance algorithms to allow them to analyze the effects ofsignals with many frequency components on High TemperatureSuperconductors. This capability is of interest since it allowsto evaluate the effect of superconductor nonlinearities in filterssubject to CDMA signals. The extended algorithm (MMHB)compares well with the previous ones when analyzing two-toneintermodulation, and is producing reasonable results when pre-dicting the performance of HTS filters with 3G CDMA signals.REFERENCES[1] B. Willemsen, “HTS wireless applications,” in Microwave Supercon-ductivity, H. Weinstock and M. Nisenoff, Eds: NATO Science Series,2001, vol. 375, pp. 387–387.[2] B. A. Willemsen, “HTS filter subsystems for wireless telecomunica-tions,” IEEE Trans. Appl. Supercond., vol. 11, no. 1, pp. 60–67, 2001.[3] C. Collado, J. Mateu, J. Parron, J. Pons, J. M. O’Callaghan, and J. M.Rius, “Harmonic balance algorithms for the nonlinear simulation of HTSdevices,” J. Supercond., vol. 14, no. 1, pp. 57–64, 2001.[4] C. Collado, J. Mateu, and J. M. O’Callaghan, “Nonlinear simulation andcharacterization of devices with HTS transmission lines using harmonicbalance algorithms,” IEEE Trans. Appl. Supercond., vol. 11, no. 1, pp.1396–1399, 2001.[5] S. A. Maas, Nonlinear Microwave Circuits Publisher: Artech House,1988.[6] J. Mateu, C. Collado, and J. M. O’Callaghan, “Nonlinear analysis of diskresonators. Application to material characterization and filter design,”IEEE Trans. Appl. Supercond., vol. 11, no. 1, pp. 135–138, 2001.[7] V. Borich, J. East, and G. Haddad, “An efficient fourier transform formultitone harmonic balance,” IEEE Trans. Microwave Theory Tech.,vol. 47, no. 2, p. 182, 1999.[8] J.-S. Hong and M. J. Lancaster, “Design of highly selective microstripbandpass filters with a single pair of attenuation poles at finite fre-quencies,” IEEE Trans. Microwave Theory Techn., vol. 48, no. 7, pp.1098–1107, 2000.[9] C. Collado, J. Mateu, T. J. Shaw, and J. O’Callaghan, “HTS nonlineari-ties in microwave disk resonators,” Physica C, to be published.[10] T. Dahm and D. J. Scalapino, “Theory of intermodulation in supercon-ducting microstrip resonator,” J. Appl. Phys., vol. 81, no. 4, p. 2002,1997.[11] T. Dahm, D. J. Scalapino, and B. A. Willemsen, “Microwave intermod-ulation of a superconducting disk resonator,” J. Appl. Phys., vol. 86, no.7, p. 1, 1999.[12] D. M. Pozar, Microwave and RF Design of Wireless Systems. NewYork: Wiley, 2001, pp. 348–349.[13] H. Holma and A. Toskala, WCDMA for UMTS Radio Access for ThirdGeneration Mobile Communication. New York: Wiley, 2000, p. 182.[14] K. G. Gard, H. M. Gutierrez, and M. B. Steer, “Characterization of spec-tral regrowth in microwave amplifiers based on the nonlinear transfor-mation of complex gaussian process,” IEEE Trans. Microwave TheoryTech., vol. 47, no. 7, pp. 1059–1069, 1995.[15] A. P. Jenkins, D. Dew-Hughes, and D. J. Edwards, “Application ofTBCCO based HTS devices to digital cellular communications,” IEEETrans. Appl. Supercond., vol. 9, no. 2, pp. 2849–2852, 1999.[16] “BS Radio Transmission and Reception (FDD),” 3GPP TS 25.104V5.2.0 (2002–2003).[17] Design Methodology and Implementation of a 3rd Generation W-CDMA Transceiver using Deep Submicron CMOS Technologies,Project acronym: LEMON, 2000, p. 62.

Prediction of Nonlinear Distortion in HTS Filters for CDMA Communicaction Systems

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