Characteristics for series and parallel circuits of fluxcontrolled

Transcription

1 LETTER IEICE Electroncs Express, Vol.4, No., Characterstcs for seres and parallel crcuts of fluxcontrolled memrstors Juan He, Ch Bao Huang, and Shua Kang a) School of Physcs & Electrcal Engneerng, Zuny Normal College, Zuny 563, People s Republc of Chna a) kngshua@tom.com Abstract: Wth the closed prncple of flux-controlled memrstors, the parallel, seres, and array crcuts of flux-controlled memrstors are made dscussed. The parameters for equvalent flux-controlled memrstors of these memrstor systems are deduced theoretcally. The mathematcal relatonshps between the parameters of equvalent flux-controlled memrstors and those of correspondng component memrstors are attaned. The results are nterestng for the applcaton of sere, parallel, and array crcuts of flux-controlled memrstors. Keywords: flux-controlled memrstors, memrstor arrays, seres-parallel crcuts Classfcaton: Electron devces, crcuts and modules References IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7 [] L. O. Chua: Memrstorthe mssng crcut element, IEEE Trans. Crcut Theory 8 (97) 57 (DOI:.9/TCT ). [] L. O. Chua and S. M. Kang: Memrstve devce and systems, Proc. IEEE 64 (976) 9 (DOI:.9/PROC.976.9). [3] D. B. Strukov, et al.: The mssng memrstor found, Nature 453 (8) 8 (DOI:.38/nature693). [4] M. D Ventra and Y. V. Pershn: Memory materals: A unfyng descrpton, Mater. Today 4 () 584 (DOI:.6/S369-7()799-). [5] S. H. Jo, et al.: Hgh-densty crossbar arrays based on a s memrstve system, Nano Lett. 9 (9) 87 (DOI:./nl837689). [6] A. Buscarno, et al.: A chaotc crcut based on hewlett-packard memrstor, Chaos () 336 (DOI:.63/.47935). [7] B. Muthuswamy and P. P. Kokate: Memrstor-based chaotc crcuts, IETE Tech. Rev. 6 (9) 47 (DOI:.43/ ). [8] A. I. Ahamed, et al.: Observaton of chaotc beats n a drven memrstve chua s crcut, Int. J. Bfurcat. Chaos () 737 (DOI:.4/ S ). [9] Y. S. La, et al.: Bstable resstance swtchng of poly(n-vnylcarbazole) flms for nonvolatle memory applcatons, Appl. Phys. Lett. 87 (5) (DOI:.63/.58). [] Z. J. L, et al.: Memrstve chaotc crcut based on modfed sc-cnns, Acta Physca Snca 63 (4) 5 (n Chnese) (DOI:.7498/aps.63.5). [] Y. V. Pershn and M. D Ventra: Practcal approach to programmable analog crcuts wth memrstors, Crcuts & Systems I Regular Papers IEEE

2 IEICE Electroncs Express, Vol.4, No., Transactons on 57 () 857 (DOI:.9/TCSI ). [] Z. K. Dong, et al.: Two types of nanoscale nonlnear memrstor models and ther seres-parallel crcuts, Acta Physca Snca 63 (4) 85 (n Chnese) (DOI:.7498/aps.63.85). [3] Z. J. L: Emulatng electrcal characterstcs of memrstor and ts applcatons n chaotc, Ph.D Dssertaton, Xangtan Unversty, Chna (4). [4] M. Itoh and L. O. Chua: Memrstor oscllators, Int. J. Bfurcat. Chaos 8 (8) 383 (DOI:.4/S ). [5] B. Muthuswamy: Implementng memrstor based chaotc crcuts, Int. J. Bfurcat. Chaos () 335 (DOI:.4/S874654). Introducton The memrstor was put forward by Chua n 97 as the fourth fundamental crcut element, n addton to the resstor, nductor and capactor []. Chua and hs coauthors generalzed the theory of memrstors and memrstve systems n 976 []. In 8, Strukov and hs co-authors, the research team at Hewlett-Packard Laboratores, reported n Nature that they found memrstors based on an analyss of a thn flm of ttanum doxde [3]. Snce then a lot of researchers have payed attenton to the memrstors and memrstve systems. Nowadays the researches of memrstor have attracted wdely nterest of researchers n physcs, materals, electroncs, nformatons and other felds because of ther potental applcatons n chaotc secure communcaton, artfcal neural networks, mage processng, ntellgent computers, the new memores, and electronc measurng systems. And the researchs on the memrstor are manly n several ways, such as the physcal mechancs and mathematcal models of memrstor [4, 5, 6, 7], the manufacturng methods and new manufacturng processes of memrstor [, 5, 8, 9], the characterstc analyses and the knetc behavors of memrstors [, ], and so on. In addton, on characterstcs analyss ways of the seres-parallel crcut wth multple memrstor, some works have also been reported []. However, these works are not suffcent. In ths paper, we would analyze the characterstcs for the parallel crcuts, seres crcuts, and array crcuts of memrstors. The parallel and seres of flux-controlled memrstors IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7 The memrstor s a non-lnear passve two-termnal electrcal component wth nonvolatlty property. The electrcal resstance of memrstor depends on the magntude of electrc charge whch prevously flowed n what drecton through the devce. In ths paper, we dscuss the mathematcal models for parallel, seres, and array crcuts of flux-controlled memrstors base on the closed prncple of memrstors. All the dscussons are base on the closed prncple of memrstors, whch was put forward by Chua n 976 []. And the detaled theoretcal analyss was llustrated by L [3]. Followng the closed prncple of memrstors, the memrstve systems of parallel crcuts and seres crcuts of flux-controlled memrstors can be represented by equvalent flux-controlled memrstors.

3 IEICE Electroncs Express, Vol.4, No.,. The parallel of flux-controlled memrstors We consder the memrstve systems of parallel crcut of multple flux-controlled memrstors at frst. It s well known that for flux-controlled memrstors, the memconductances depend on voltage load on devces as well as depend on process of load. The memrstor can be characterzed by a smooth contnuous cubc nonlnear functon as [4, 5]: q ¼ þ 3 where q and º are the charge and the magnetc flux through the memrstor, respectvely. and are constants. And then the memductance WðÞ can be expressed as WðÞ ¼ dq d ¼ þ 3 : ðþ For memrstors beng drectonal electronc components, we should dstngush the same drecton parallel case and the dfferent drecton parallel case when we dscuss the parallel crcuts of multple flux-controlled memrstors... The same drecton parallel case To facltate dscusson, for the same drecton parallel crcut of multple fluxcontrolled memrstors, we suppose that the memconductance, current, voltage, and ntal magnetc flux of the multple flux-controlled memrstors be W ðtþ, ðtþ, v ðtþ, and ( ¼ ; ;...;n), respectvely, and the equvalent memconductance, equvalent current, equvalent voltage, and equvalent ntal magnetc flux of whole memrstve systems be WðtÞ, IðtÞ, IðtÞ, and, respectvely. Then the memconductances of the multple flux-controlled memrstors are gven as W ðtþ ¼ þ 3 þ v ðtþdt ; ¼ ; ;...;n ð3þ Whle the equvalent memconductance of whole memrstve system s gven as ðþ IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7 WðtÞ ¼A þ 3B þ VðtÞdt ; ð4þ where A, B, and are undetermned coeffcents. It s well known that the relatons between the equvalent voltage, equvalent current, and equvalent memconductance of whole memrstve system and voltages, currents, and memconductances of the multple memrstor components should meet the general law of parallel crcut at any tme. Thus VðtÞ ¼v ðtþ; ¼ ; ;...;n; WðtÞ ¼ W ðtþ ð5þ From Eq. (3), (4), and (5), we obtan WðtÞ ¼ þ 3 X n þ VðtÞdt ¼ þ 3 3 þ 3 Therefore the parameters A, B, and are gven as " Z # ð6þ t þ VðtÞdt 3

4 IEICE Electroncs Express, Vol.4, No., A ¼ ½ þ 3 Š 3 ; B ¼ ; ¼ : ð7þ Obvously, for the case of same drecton parallel crcut of multple dentcal memrstor components, we obtan A ¼ n ; B ¼ n ; ¼ : ð8þ.. The dfferent drecton parallel case For the dfferent drecton parallel crcut of multple flux-controlled memrstors, we suppose that the parallel drecton of the frst n memrstors be the same as reference drecton, whle those of the last m memrstors be dfferent wth reference drecton. For ths case, the relatons between the equvalent voltage, and equvalent memconductance of whole memrstve system and voltages and memconductances of the multple memrstor components should also meet the general law of parallel crcut at any tme. Thus IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7 VðtÞ ¼v ðtþ ¼ v j ðtþ; ð ½;nŠ; j½nþ;nþ mšþ; WðtÞ ¼ þm W ðtþ: ð9þ From Eq. (3), (4), and (9), we obtan X WðtÞ ¼ þm þ 3 nþm 3 X m nþ ðnþþ þm þ 3 X nþm X 3 : ðþ m Z nþ t ðnþþ 4 þm þ VðtÞdt5 and From Eq. (4), and (), the parameters A, B, and are gven as A ¼ Xnþm þ 3 Xnþm 3 X m nþ ðnþþ þm ; ðþ B ¼ Xnþm ; ¼ X m nþ ðnþþ þm : ð3þ For the case of both same drecton parallel of the frst n memrstors and dfferent drecton parallel of the last m memrstors, the parameters A, B, and are gven as A ¼ n þ nm ; B ¼ðnþmÞ ; ¼ n m ðn þ mþ n þ m : ð4þ ðþ 4

5 IEICE Electroncs Express, Vol.4, No.,. The seres of flux-controlled memrstors Just as the parallel crcuts of multple flux-controlled memrstors, we should also dstngush the same drecton seres case and the dfferent drecton seres case when we dscuss the memrstve systems of seres crcut of multple flux-controlled memrstors. However, t s very dffcult to dscuss the relatons between the equvalent and memconductance equvalent voltage for seres of flux-controlled memrstor systems usng the same method as those for flux-controlled memrstor seres systems. Therefore, we adopt a dfferent method for the latter. IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7.. The same drecton seres case For the cases of the same drecton seres crcuts of flux-controlled memrstors, the relatons between the equvalent voltage, equvalent current, and equvalent memconductance of whole memrstve system and voltages, currents, and memconductances of the multple memrstor components should alse meet the general law of seres crcut at any tme. Thus, VðtÞ ¼ v ðtþ; IðtÞ ¼ ðtþ; ¼ ; ;...;n; WðtÞ ¼ ð5þ W ðtþ The dervatves of Eq. (3) and (4) are Z dw ðtþ t ðtþ ¼ 6 þ v ðtþdt dt W ðtþ ; ¼ ; ;...;n Z dwðtþ t ð6þ IðtÞ ¼ 6B þ VðtÞdt dt WðtÞ To take advantage of the dervatves of Eq. (5) and Ohm s Law, from Eq. (3), (5), and (6), we obtan B þ VðtÞdt W 3 ¼ Xn þ v ðtþdt ðtþ W 3 ðtþ ð7þ To take advantage of the dervatves of Eq. (7) and Ohm s Law, from Eq. (5) and (6), we obtan B B þ VðtÞdt W 4 8 ðtþ W 5 ¼ Xn Xn þ v dt ðtþ W 4 8 ðtþ W 5 ðtþ ð8þ From Eq. (7) and (8), we obtan 8 3 >< B ¼ W 5 ðtþ WðtÞ W 4ðtÞ 8 X þ v dt n 6 4 W 5ðtÞ 7 5 >: 3 9 ð9þ þ8 X þ v ðtþdt > n = 6 4 W 3ðtÞ 7 5 >; When t ¼, from Eq. (3), (4), and (5), we obtan 5

6 IEICE Electroncs Express, Vol.4, No., W ðþ ¼ þ 3 ; ð ¼ ; ;...;nþ; WðÞ ¼ X n þ 3 From Eq. (9) and (), the parameter B s gven as Xn " Xn B ¼ X n 5 þ 3 ð þ 3 Þ4 þ 3 8 þ 8 X # n ð þ 3 Þ5 ð þ 3 Þ3 From Eq. (7) and (), the parameter s gven as ðþ ðþ ¼ 6 4 þ 3 ð þ 3 Þ3 Xn þ 3 ð þ 3 8 Þ4 þ8 X n ð þ 3 Þ3 From Eq. (4), (), and (), the parameter A s gven as A ¼ f 3B g þ 3 ð þ 3 Þ5! ðþ ð3þ Thus, the relatons of equvalent voltage, and equvalent memconductance for seres crcuts of multple flux-controlled memrstors are gven. For the case of same drecton seres crcut of multple dentcal memrstor components, t s easy to fnd that A ¼ n ; B ¼ n 3 ; ¼ n : ð4þ.. The dfferent drecton seres case For the cases of the dfferent drecton seres crcuts of flux-controlled memrstors, we suppose that the seres drecton of the frst n memrstors be the same as reference drecton, whle those of the last m memrstors be dfferent wth reference drecton. For ths case, the relatons between the equvalent voltage, equvalent current, and equvalent memconductance of whole memrstve system and voltages, currents, and memconductances of the multple memrstor components should alse meet the general law of seres crcut at any tme. Thus, IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7 VðtÞ ¼ v ðtþ þm v ¼nþ ðtþ IðtÞ ¼ ðtþ; ¼ ; ;...;nþ m ð5þ WðtÞ ¼ þm W ðtþ 6

7 IEICE Electroncs Express, Vol.4, No., Here the reference drecton of equvalent voltage s the same as those of the former n flux-controlled memrstors but dfferent wth those of the latter m flux-controlled memrstors. Whle the reference drecton of equvalent current s the same as those of all the n þ m flux-controlled memrstors. Smlar to the dscusson of the same drecton seres crcuts of flux-controlled memrstors, t s easy to get the relatons between the equvalent voltage and equvalent memconductance for the dfferent drecton seres case. The correspondng parameter s gven as B ¼ ¼ Xnþm Xn Xnþm þ 3 þm þ8 þm þm ð þ 3 Þ3 X m þ 3 A ¼ þm þ8 þm þm ð þ 3 8 þm Þ4 ð þ 3 Þ5 ð þ 3 Þ3 5 ; þ 3 ð6þ nþ ðnþþ ð nþ þ 3 nþ ðnþþ Þ3 Xnþm ð þ 3 8 þm Þ4 ð þ 3 Þ3 3B ; ð þ 3 Þ! þ 3! ð þ 3 Þ5 : ð7þ ð8þ For the case of seres systems of both n the same drecton dentcal fluxcontrolled memrstors and m dfferent drecton dentcal flux-controlled memrstors, the parameters of equvalent flux-controlled memrstor are gven as A ¼ n þ m nm ðn þ mþ 3 ; B ¼ ðn þ mþ 3 ; ¼ðn mþ : ð9þ IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7.3 The hybrd crcut of flux-controlled memrstors The hybrd crcut of flux-controlled memrstors s very complcated. When hybrd crcuts of flux-controlled memrstors are appled n mage processng and ntellgent computer, the same dentcal array of memrstors are the most common. Therefore, n ths paper only the same dentcal hybrd flux-controlled memrstors arrays are consdered. We suppose that n m same dentcal flux-controlled memrstors consttute a hybrd array crcut. That s, the array crcut s the same drecton seres of m crcuts whch are the same drecton parallel n dentcal flux-controlled memrstors. Combned wth the prevous dscusson above, the parameters of equvalent fluxcontrolled memrstor of ths array are gven as A ¼ m n ; B ¼ m n 3 ; ¼ n : ð3þ 7

8 IEICE Electroncs Express, Vol.4, No., Fg.. The same drecton parallel crcut of two flux-controlled memrstors. (a) The relaton of equvalent memconductance WðtÞ and tme s; (b) the dfference of between the equvalent memconductances equvalent from Eq. (7) and those wth realtme parallel crcut method; (c) The relaton of equvalent current and equvalent voltage. 3 Result In order to further llustrate the correctness of the theoretcal analyss derved n ths paper, we smulate and analyze the parameters of equvalent flux-controlled memrstor for some parallel crcuts and seres crcuts of flux-controlled memrstors. In all smulatons heren, the nput sgnals are chosen to be snusodal voltage source IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7 vðtþ ¼v snft ð3þ where the parameters of nput sgnal are chosen as v ¼ 5 V and f ¼ :5 s. In Fg. we present our results for the same drecton parallel crcut of two flux-controlled memrstors. The parameters of the two memrstors are chosen as ¼ 3 S, ¼ 6 S/Wb, ¼ 4 Wb, ¼ 3 S, ¼ 8 6 S/Wb, and ¼ Wb. For the case of the same drecton parallel crcut of two flux-controlled memrstors, from Eq. (9), (), and (), the parameters of equvalent flux-controlled memrstor are gven as A ¼ 4:67 3 S, B ¼ 9 6 S/Wb, and ¼ : Wb. We have presented our results for the dfferent drecton parallel crcut of the two flux-controlled memrstors n Fg., The parameters of both the two memrstors and nput sgnal are chosen as the same as those of parallel case. From Eq. (5), (6), and (7), the parameters of equvalent flux-controlled memrstor are gven as A ¼ :6 3 S, B ¼ 9 6 S/Wb, and ¼ 3:333 Wb. Our results of the same drecton seres crcut of the two flux-controlled memrstors are shown n Fg. 3. For ths case, the parameters of equvalent flux- 8

9 IEICE Electroncs Express, Vol.4, No., Fg.. The dfferent drecton parallel crcut of two flux-controlled memrstors. (a) The relaton of equvalent memconductance WðtÞ and tme s; (b) the dfference of between the equvalent memconductances equvalent from Eq. (), (), and (3) and those wth real-tme parallel crcut method; (c) The relaton of equvalent current and equvalent voltage. IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7 controlled memrstor are gven as A ¼ 6:667 3 S, B ¼ :963 7 S/Wb, and ¼ 6 Wb. We have presented our results for the dfferent drecton seres crcut of the two flux-controlled memrstors are shown n Fg. 4. For ths case, the parameters of equvalent flux-controlled memrstor are gven as A ¼ 3:5 3 S, B ¼ :963 7 S/Wb, and ¼ Wb. The relatons of equvalent memconductance WðtÞ and tme s for all the four crcut cases of composed of two flux-controlled memrstors are shown n Fgs. (a), (a), 3(a), and 4(a). Obvously, the curves affected by not only the parameters of nput sgnal but also the parameters of equvalent flux-controlled memrstors. For all the four crcut cases of composed of two flux-controlled memrstors, the dfferences of between the equvalent memconductances and those from real-tme calcuaton methods are shown n Fgs. (b), (b), 3(b), and 4(b). For the all crcuts of two flux-controlled, the progress procedures of real-tme calcuaton methods as followng: At every tme, the memconductances of the two flux-controlled memrstors are calcluted at frst. And then the equvalent memconductances at that tme are calcluted wth the well known conductance formula of parallel crcuts or seres crcuts. From these fgures, t s easy to see that the dfferences for all the four cases are very lttle. There are ffteen or sxteen orders of magntude between the equvalent memconductances and the dfferences. These dfferences should come from the calculaton error. Therefore, the results between our methods and real-tme calcuaton methods are the same. 9

10 IEICE Electroncs Express, Vol.4, No., Fg. 3. The same drecton seres crcut of two flux-controlled memrstors. (a) The relaton of equvalent memconductance WðtÞ and tme s; (b) the dfference of between the equvalent memconductances equvalent from Eq. (), (), (3) and those from Eq. (5), the real-tme seres crcut method; (c) The relaton of equvalent current and equvalent voltage. IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7 Fg. 4. The dfferent drecton seres crcut of two flux-controlled memrstors. (a) The relaton of equvalent memconductance WðtÞ and tme s; (b) the dfference of between the equvalent memconductances equvalent from Eq. (6), (7), (8) and those from Eq. (5), real-tme parallel crcut method; (c) The relaton of equvalent current and equvalent voltage.

11 IEICE Electroncs Express, Vol.4, No., From Fgs. (c), (c), 3(c), and 4(c), t s easy to see that for all the four crcut cases of composed of two flux-controlled memrstors, the I-V characterstcs curve of equvalent flux-controlled memrstor are all the exstence of a pnched hysteress effect. 4 Concluson Wth the closed prncple of flux-controlled memrstors, the parallel crcuts, seres crcuts, and array crcuts of flux-controlled memrstors are made dscussed. The parameters for equvalent flux-controlled memrstors of these memrstor systems are theoretcal deduced n detaled. The mathematcal relatonshps between the parameters of equvalent flux-controlled memrstors and those of correspondng component memrstors are attaned. The results are nterestng for the applcaton of seres, parallel, and array crcuts of flux-controlled memrstors. To further llustrate the correctness of the relatonshps, we smulate and analyze the parameters of equvalent flux-controlled memrstor for the same drecton parallel crcut case, the dfferent drecton parallel crcut case the same drecton seres crcut case, and the dfferent drecton seres crcut case of two flux-controlled memrstors. The results show that our theoretcal deductons are relable. At the same tme, snce our works are base on the closed prncple of memrstors, the results llustrate that the closed prncple s correct agan. Our works on seres and parallel crcuts of flux-controlled memrstors are helpful for the potental applcaton of memrstor n a conventonal crcut. Whle our works on array crcuts of flux-controlled memrstors are helpful for the potental applcaton of non-volatle memores. Acknowledgments Ths work s supported by the Natonal Natural Scence Foundaton of Chna (Grant Nos. 4645, 565), the Specal Foundaton of Governor of Guzhou Provnce for Scence and Technology and Educaton Talents (Grant No. [] 87), the Scence and Technology Foundaton of Guzhou Provnce (Grant Nos. J [5] 46, LKZS [4] 5, LH[5] 743, and LH[6] 78), the Key Project of Educaton Department of Guzhou provnce (Grant No. [KY(3) 7]), the Educaton Department of Guzhou Provnce Electronc Manufacturng Producton Base (NO. [4] 3), the Specal Fund Project of the Constructon of the Eghth Batch of Scentfc and Technologcal Innovaton Talent Team n Guzhou Provnce [No. (5)47], the Scence and Technology Project of Zuny cty Honghuagang Dstrct (No. [5] 8), and the Key Dscplne of Guzhou provnce (Grant No. [3] 8). IEICE 7 DOI:.587/elex.4.73 Receved March 9, 7 Accepted Aprl 7, 7 Publczed May 9, 7 Copyedted June, 7