Passive Fully Floating Emulator of Memristive Device for Laboratory Experiments

Transcription

1 Aances n Electrcal an Computer Engneerng Passe Fully Floatng Emulator of Memrste Dece for Laboratory Experments DALIBOR BIOLEK, VIERA BIOLKOVA, ZDENEK KOLKA, ZDENEK BIOLEK Departments of Mcroelectroncs an Rao Electroncs Brno Unersty of Technology Techncka 10, Brno CZECH REPUBLIC bolek@feec.utbr.cz Abstract: - A smple emulator of memrste system, contanng only passe electronc components, namely resstors, capactor, an no-dc base transstor s escrbe. Unlke other htherto publshe emulators t oes not explot DC power supply. Moreoer, t proes effecte emulaton of groune as well as floatng memrste systems. The crcut ea enables nterestng experments, emonstratng the well-known fngerprnts of memrste systems such as the pnche - hysteress loops. Key-Wors: - Memrste system, passe system, floatng two-termnal element, pnche hysteress loop. 1 Introucton The paper [1] by the Hewlett-Packar researchers, announcng the manufacture of a nano-ece resemblng the memrstor [2], sparke worlwe nterest n memrste systems [3], naccurately esgnate as memrstors, whch are currently consere the reolutonary components for the computer nustry an also analog applcatons. Snce commercal samples are not currently aalable, arous emulators hae been esgne for expermentng wth these perspecte eces, on both analog an hybr prncples [4-15]. All of them suffer from the followng rawback: They employ acte electronc components, whch requre DC supply sources, een f a passe memrste system s emulate. Ths entals other saantages, for example a large nfluence of the parastc propertes of the acte bulng blocks (such as offset an rft, lmte banwth, low ynamc range of oltages an currents, etc.) on the operaton of the emulate system, as well as serous problems when emulatng floatng two-termnal eces. On the other han, seeral papers escrbe the expermentally well-establshe manfestatons of memrste systems, partcularly the pnche hysteress loops, for some passe systems whose framework has been well-known for many years (arous types of bulbs or scharge lamps [16], rao etector calle cat s whsker use as the frst rao etector [17], etc.) or for systems wth accentally reeale memrste behaor (oe brge wth LCR flter [18]). Experments wth Home-mae memrstors [19], [20] are base on the ea from [17] that memrste effects are assocate wth mperfect electrc contact. As emphasze n [21], the current textbooks wll hae to be rese to nclue the memrstor an the new paragm t represents for electronc crcut theory. It s unerlne n [22] that the most aluable applcatons of memrstors wll most lkely come from some young stuent who learns about these eces an has an nspraton for somethng totally new. The memrste emulators can sere as a goo nput gate nto ths exctng research area for such stuents whch lke the laboratory experments. Howeer, the emulators must be of a smple constructon such that ts analyss can easly result n a efnte unerstanng of the key prncple of the operaton of the memrste system. The objecte of ths paper s the synthess of a passe memrste system from commonly aalable electronc components. The synthess wll start from equatons that efne the memrste systems an thus the prncple of the operaton of the emulator wll be obous, together wth ts parameters, aantages an lmtatons. 2 Memrstors an memrste systems The general frst-orer oltage-controlle memrste system s escrbe by ts port equaton (1) an state equaton (2) [3] x, ), (1) x / t f ( x, ), (2) ISBN:

2 Aances n Electrcal an Computer Engneerng where an are the oltage an current of the memrste port, respectely, x s the nternal state arable, an g an f are nonlnear functons of the state arable an the oltage, respectely. The functon g represents the conuctance, or memuctance, whch can be epenent on both the oltage (the sgn of nonlnearty) an the state (the sgn of memory effect). The block agram corresponng to Eqs. (1), (2) s shown n Fg. 1. As regars the memrstors (3), (4), t s obous from (4) that the eal ntegrator nees to be mplemente for ther emulaton. Howeer, ths s mpossble wthout acte electronc elements. From the opposte pont of ew, f only passe elements are aalable for mplementng the emulator, t s possble to realze a certan subclass of the general memrste systems (1), (2), whose behaor, uner specfc contons, can approach the behaor of the eal memrstors. x, ) R = x f ( x, ) t x, t x) x R = = x 3 Synthess of memrste system The propose schematc an the physcal mplementaton of passe crcut emulatng the memrste system are shown n Fgs. 2 an, respectely. Fg. 1. Block agrams of general memrste systems, eal memrstors. The memrstor, n the sense of ts axomatc efnton [2] (toay frequently enote as eal memrstor), s a specal case of the memrste system (1), (2), wth ts conuctance beng epenent only on the nternal state, an the fferentaton of the state arable wth respect to tme beng equal to the oltage, or, n other wors, the state arable s equal to the ntegral of the oltage, whch s the flux [2] (also see Fg. 1 ): R << D D D =g( c,) D S J310 G 10 M c = x R 1 M C 100 pf x), (3) x / t. (4) Snce the memuctance epens on the nternal state, the memrste systems exhbt the - pnche hysteress loop, whch s the most wely known fngerprnt of these systems. It s also known that memrstors an memrste systems can be ether passe or acte, an that the suffcent conton of the passty s the nonnegate memuctance. A specal attrbute of the memrstor (3), (4) s that t s a funamental crcut element whch cannot be substtute by any combnaton of other funamental elements (R, L, C). The controlle sources o not fall nto ths category, an thus they can be use for the constructon of memrstor emulators a acte blocks workng on the prncple of controlle sources (for example operatonal amplfers). Fg. 2. Emulator of the passe memrste system, schematc, mplementaton. The schematc starts from the block agram of a general memrste system n Fg. 1 for the case of one-mensonal state ector x, hang an ambton to emulate, wthn a certan accuracy, also the behaour of eal memrstor n Fg. 1. The RC cell wth the output C operates as passe lossy ntegrator wth the cutoff frequency f C =1/(2 RC) 1592 Hz. For frequences aboe ths alue, the characterstcs of ths crcut approxmate the characterstcs of eal ntegrator, when the oltage C correspons to the ntegral of the port oltage ISBN:

3 Aances n Electrcal an Computer Engneerng an thus the state arable x n Eq. (4). Ths oltage s concurrently the oltage across the JFET termnals G an S, whch controls the transstor conuctance between the termnals D an S. If ths conuctance were nepenent of the oltage, then the crcut coul mplement the memrstor (3), (4). The resstor n seres wth the gate G ncreases ts resstance an galancally separates the gate from the output of the RC cell. As shown herenafter, the crcut n Fg. 2 n fact emulates a more general memrste system (1), (2). It s a consequence of the non-eal passe ntegrator an specfc nonlnear characterstcs of the transstor [ma] 0 G M gs [V] s [V] [ms] [V] gs Fg. 3. Measure characterstcs of the transstor J310 [15]: ( s ) for constant oltage gs, G M ( gs ) = / s for s = 0. The measure nonlnear DC characterstcs of the transstor J310 are shown n Fg. 3 [15]. As s obous from Fg. 3, ths JFET can be use as an electroncally controlle conuctor. Fgure 3 reeals that for a fxe oltage gs the conuctance s not constant but epens on the oltage s, whch s a sgn of the memrste system (1), not the memrstor (3). Eq. (3) wll therefore be fulflle only for a small swng of s aroun zero when the nonlneartes of the characterstcs o not take effect. Conser that the characterstcs of the transstor from Fg. 3 are represente by the equaton, ). (5) gs Concrete analytc forms of Eq. (5) of arous complextes, resultng from the physcal nature of the operaton of JFET, are well known [24], but they are rreleant to the subsequent analyss. Conserng the enttes x = c, = s, takng nto conseraton the fferental equaton of the RC cell n Fg. 2 an ts hgh mpeance leel when the current through ths cell can be neglecte n comparson wth the current, the mathematcal moel of the crcut n Fg. 2 can be rewrtten n the form x, ), (6) 1 x ( x) (7) t RC A comparson wth Eq. (1) an (2) leas to the concluson that the crcut n Fg. 1 can sere as the emulator of memrste systems. A comparson wth Eq. (3), (4) yels that the crcut n Fg. 2 can successfully mmc the eal memrstor f two contons are fulflle smultaneously: 1) The memuctance s nepenent of the oltage (thus a small oltage swng). 2) The state arable must be neglgble compare to the oltage (ths wll be fulflle for relately hgh sgnal frequences when the passe ntegratng RC cell wll show aequate attenuaton). 4 Demonstraton of the emulator behaor Fgure 4 presents expermental results when the emulate system s excte by a generator of snusoal oltage wth 3V ampltue an aryng frequency. It s obous from the results that the hysteress s neglgble for a low frequency (10 Hz) because the RC cell oes not cause any sgnfcant phase shft between the port oltage an the state oltage ( C ), the latter controllng the transstor. The memory effect s eent for 100 Hz, but the loop s not symmetrcal. It ponts to the fact that the emulate system s not an eal memrstor. s s ISBN:

4 Aances n Electrcal an Computer Engneerng One reason s the non-eal operaton of the ntegrator, whose cutoff frequency s one orer hgher than the frequency of the sgnal. The loop s alreay almost symmetrcal for 1 khz. When ncreasng the frequency up to 10 khz, one can obsere the well-known fngerprnt of memrste systems: the area of the hysteress loop mnshes towars zero f the frequency ncreases a nfntum. (c) 5 Conclusons The propose emulator of memrste systems has the followng aantages: () It s bult from components that o not use power supples. () It naturally emulates both groune an floatng two-termnal eces. () It oes not labour wth the well-known rawbacks of emulators bult up from acte eces (sgnal lmtatons, offset an rft ssues, parastc nonlnear storton comng from OpAmp nonealtes, etc.). () It can be manufacture as a small two-termnal ece, reay for laboratory experments. () The frequency ban of graual sappearance of the hysteress effects can be change a ajustng the tme constant of the RC cell. In orer to ncrease the accuracy of moelng eal memrstors, further research wll focus on the lnearzaton of the element mplementng the memuctance, an also on the mofcaton of the ntegratng cell. Acknowlegments: Ths work was supporte by the Czech Scence Founaton uner grant No S. The research was performe n laboratores supporte by the SIX project, the regstraton number CZ.1.05/2.1.00/ () Fg. 4. Measure pnche hysteress loops of the memrste system from Fg. 2 uner ts snusoal exctaton wth an ampltue of 3 V an frequences of 10 Hz, 100 Hz, (c) 1 khz, an () 10 khz. The current (ertcal axs) was sense a a oltage rop at 10 Ω resstor n seres wth D-S juncton of JFET. References: [1] Struko, D.B., Sner, G.S., Stewart, D.R., Wllams, R.S., The mssng memrstor foun, Nature (Lonon), Vol. 453, 2008, pp [2] Chua, L.O., Memrstor the mssng crcut element, IEEE Transactons on Crcut Theory, Vol. 18, No. 5, 1971, pp [3] Chua, L.O., Kang, S.M., Memrste Deces an Systems, Proceengs of the IEEE, Vol. 64, No. 2, 1976, pp ISBN:

5 Aances n Electrcal an Computer Engneerng [4] Bolek, D., Memrstor emulators, the Chapter n the book Memrstor networks (Ete by A. Aamatzky an L. Chua), Sprnger, 2014, pp [5] Soh, A., Ganh, G., Crcut mmckng TO2 memrstor: A plug an play kt to unerstan the fourth passe element, Internatonal Journal of Bfurcaton an Chaos, Vol. 20, No. 8, 2010, pp [6] Wang, X. Y. et al., Implementaton of an analogue moel of a memrstor base on a lght-epenent resstor, Chnese Physcs B, Vol. 21, No. 10, 2012, [7] Muthuswamy, B., Implementng memrstor base chaotc crcuts, Internatonal Journal of Bfurcaton an Chaos, Vol. 20, No. 5, 2010, pp [8] Bolek, D. et al., Mutators for transformng nonlnear resstor nto memrstor. In: 20th European Conference on Crcut Theory an Desgn (ECCTD), Lnkopng, Sween, 2011, pp [9] Bolkoa, V., Bolek, D., Kolka, Z. Unfe approach to synthess of mutators employng operatonal transmpeance amplfers for memrstor emulaton. In Proc. of the 11th Int. Conference on Instrumentaton, Measurement, Crcuts an Systems (IMCAS'12), Roanem, Fnlan, 2012, pp [10] Km, H. et al., Memrstor emulator for memrstor crcut applcatons, IEEE Transactons on Crcuts an Systems I: Regular Papers, Vol. 59, No. 10, 2012, pp [11] Kolka, Z., Bolek, D., Bolkoa, V. Hybr moelng an emulaton of mem-systems. Internatonal Journal of Numercal Moellng. Electronc Networks, Deces an Fels, Vol. 25, No. 3, 2012, pp [12] Pershn, Y. V., D Ventra, M., Practcal Approach to programmable Analog Crcuts Wth Memrstors, IEEE Transactons on Crcuts an Systems I: Regular Papers, Vol. 57, No. 8, 2010, pp [13] Bolek, D., Bolkoa, V., Kolka, Z. Lowoltage-low-power current coneyor for battery supple memrstor emulator. In Proc. of 5th Internatonal Conference on Crcuts, Systems an Sgnals (CSS'11), Corfu, Greece, 2011, pp [14] Mutlu, R., Karakulak, E. Emulator crcut of T02 memrstor wth lnear opant rft mae usng analog multpler. In Proc. of 2010 natonal Conference on Electrcal, Electroncs an Computer Engneerng (ELECO 2010), Bursa, Turkey, 2010, pp [15] Valsa, J., Bolek, D., Bolek, Z., An analogue moel of the memrstor, Internatonal Journal of Numercal Moellng. Electronc Networks, Deces an Fels, Vol. 24, No. 4, 2011, pp [16] Proromaks, T., Toumazou, C., Chua, L., Two centures of memrstors, Nature Materals, No. 11, 2012, pp [17] Ganh, G., Aggarwal, V., Chua, L., The frst raos were mae usng memrstors!, IEEE Crcuts an Systems Magazne, Vol. 13, No. 2, 2013, pp [18] Cornto, F., Ascol, A., Memrste oe brge wth LCR flter, Electroncs Letters, Vol. 48, No. 14, 2012, pp [19] [20] [21] Johnson, R. C. Mssng lnk memrstor create: Rewrte the textbooks? EETmes D= [22] HP memrstor FAQ: [23] Kumar, B., Jan, S. B., Electronc Deces an Crcuts, PHI Learnng Pt. Lt., 2013, pp ISBN: