Design and Implementation of a Floating Meminductor Emulator upon Riordan Gyrator

Design and Implemen a ion o a Floa ing Meminduc o Emula o 1 upon Rio dan Gy a o 2 F ancisco J. Rome o1,*, Al edo Medina-Ga cia2, Manuel Escude o3, Diego P. 3 Mo ales1 and Noel Rod iguez1 4 1 Dep . Elec onics and Compu e Technology, Facul y o Sciences, Uni e si y 5 o G anada, 18071 G anada, Spain. 6 2 In ineon Technologies AG, 85579 Neubibe g, Ge many 7 3 In ineon Technologies Aus ia AG, 9500 Villach, Aus ia 8 * Email: [email p o ec ed] 9 Abs ac 10 In his communica ion we p esen he design, simula ion and implemen a ion o 11 a loa ing lux-con olled meminduc o emula o based on he Rio dan gy a o . 12 Fi s ly, he ci cui is p esen ed heo e ically, om i s o iginal e sion o emula e 13 induc o s o i s adap a ion o loa ing meminduc o s. Once i s heo e ical 14 equa ions a e p esen ed, using SPICE simula ions, we demons a e he easibili y 15 o his implemen a ion by means o o - he-shel componen s and a mem is o , o 16 a mem is o emula o , o di e en inpu s signals and equencies in bo h 17 g ounded and loa ing con igu a ions. Finally, a low- equency b eadboa d-le el 18 implemen a ion is included o p o e i s p ac icali y. 19 Keywo ds: ci cui heo y, emula o , eedback, gy a o , meminduc o , mem is o 20 21 22 1. In oduc ion 23 Nea ly 50 yea s ago, P o . Leon Chua p esen ed o he i s ime he passi e 24 ci cui elemen which es ablished he ela ion be ween lux (𝜙, ime-in eg al o he 25 inpu - ol age) and cha ge (q) [1]. This elemen was called mem is o (memo y- 26 esis o ) since i demons a ed ha , o a gi en ol age, i s esis ance a an ins an 27 = 1 depends no only on he cu en a 1, bu also on he cu en h ough he 28 de ice om = -∞ o = 1, hence p esen ing a memo y cha ac e is ic. Howe e , 29 i was no un il 2008 ha a g oup o esea che s om Hewle -Packa d Labs (HP) 30 epo ed he i s solid-s a e de ice exhibi ing mem is i e beha io [2]. I was hen 31 when he concep o mem is o ushe ed in unp eceden ed elec onic de ices and 32 applica ions, ex ending om ReRAMs (Resis i e Random-Access Memo y) o 33 ealis ic neu al ne wo ks [3]. Thus, he mem is o , and i s non- ola ile memo y 34 e ec , has aised as one o he mo e subs an ial e olu ions in he ield o 35 elec onic ci cui s heo y since he in en ion o he ansis o [4]. 36 In 2009, a e he g ea in e es a oused by mem is i e de ices, M. Di Ven a, 37 Y.V. Pe shin and L. Chua gene alized he concep o memo y de ices o 38 capaci o s and induc o s, hus de ining he memcapaci o and he meminduc o 39 [5]. In hese de ices, bo h capaci ance and induc ance, as in he case o 40 mem is o s, p esen a non- ola ile memo y e ec which depends no only on i s 41 p esen s a e bu also on he his o y o he de ice. In his way, apa om he 42 de ini ion o mem is o (RM, Eq.1), hey de ined he concep s o memcapaci o 43 (CM, Eq. 2), as he n h-o de sys em ha es ablishes a nonlinea ela ion be ween 44 he cha ge (q) o he de ice and i s ol age (V); and he meminduc o (LM, Eq. 3), 45 as he n h-o de sys em which es ablishes he nonlinea ela ion be ween cu en 46 (I) and lux (𝜙) [6]. 47 𝑉(𝑡)=𝑅𝑀(𝒙𝑵 󰇍 󰇍 󰇍 󰇍 󰇍 ,𝐼,𝑡)·𝐼(𝑡) (1) 48 𝑞(𝑡)=𝐶𝑀(𝒙𝑵 󰇍 󰇍 󰇍 󰇍 󰇍 ,𝑉,𝑡)·𝑉(𝑡) (2) 49 𝜙(𝑡)=𝐿𝑀(𝒙𝑵 󰇍 󰇍 󰇍 󰇍 󰇍 ,𝐼,𝑡)·𝐼(𝑡) (3) 50 Being 𝒙𝑵 󰇍 󰇍 󰇍 󰇍 󰇍 a ec o ep esen ing he n in e nal s a e a iables o he sys em. 51 These de ices, memcapaci o and meminduc o , a e expec ed o cause a 52 dis up ion in he ield o elec onics, which has led o se e al s udies on di e se 53 applica ions, such as neu omo phic and quan um compu a ion [7], [8], logic ga es 54 [9], [10], sel -adap a i e il e s [11]–[13] o chao ic ci cui s [14]–[18]. Howe e , in 55 con as o mem is o s, which can be al eady ab ica ed elying on di e en 56 ma e ials and esis i e swi ching mechanisms [2], [19]–[21], solid-s a e 57 memcapaci o s and meminduc o s a e ye elusi e. 58 Fo his eason, in ecen yea s many SPICE models as well as some p ac ical 59 implemen a ions o memcapaci o s and meminduc o s emula o s ha e been 60 p oposed. These ci cui s ollow di e en al e na i es o achie e he same goal: 61 sa is ying he cons i u i e equa ions o he emula ed de ice. These al e na i es 62 can be g ouped in o wo main g oups; i) hose using ano he mem-de ice (in 63 pa icula a mem is o ) o mu a e i s beha io o he desi ed mem-de ice and ii) 64 hose no based on mem-de ices. Thus, many o he di e en memcapaci o s 65 and meminduc o s emula o s use a mem is o (o a mem is o emula o ) o 66 ans o m i s cons i u i e equa ions in o he cons i u i e ela ion o he mem- 67 de ice emula ed [22]–[28], as i is done in his wo k, while he es o hem make 68 use o classical ol age-mode op-amps (VOAs), cu en eedback ope a ional 69 ampli ie s (CFOAs), ope a ional ansconduc ance ampli ie (OTAs) and/o 70 cu en con eyo s o emula e he desi ed mem-de ice [14], [29]–[36]. 71 Howe e , he implemen a ion o mos o hese ci cui s limi s he emula ed de ice 72 o g ounded con igu a ions, hence educing hei po en ial applica ions. In o de 73 o a oid his, in his wo k we p esen a simple and low-cos loa ing meminduc o 74 emula o based on a modi ica ion o he Rio dan gy a o , ypically used o emula e 75 loa ing induc o s and whose design is based on classical op-amps [37]. 76 The manusc ip is s uc u ed as ollows: a e his in oduc ion, Sec ion 2 p esen s 77 he heo e ical modi ica ions o e he Rio dan gy a o o achie e a meminduc i e 78 beha io , oge he wi h SPICE simula ions demons a ing he easibili y o he 79 p oposed ci cui o loa ing and g ounded con igu a ions. A e ha , a simple low- 80 equency b eadboa d-le el implemen a ion using o - he-shel componen s is 81 p esen ed in Sec ion 3 and, inally, he main conclusions a e d awn in Sec ion 4. 82 2. Meminduc ance and he modi ied Rio dan gy a o . 83 As de ined by Chua [6], he meminduc i e sys ems can be ei he cu en - 84 con olled o lux-con olled depending on he ela ion o he meminduc ance wi h 85 hese pa ame e s. This wo k is ocused on lux-con olled meminduc i e sys ems, 86 which a e desc ibed by he ollowing equa ions: 87 𝐼(𝑡)=𝐿𝑀 −1(𝑥1,𝑥2,…,𝑥𝑛,𝜙,𝑡)·𝜙(𝑡) (4) 88 𝑑𝒙𝑵 󰇍 󰇍 󰇍 󰇍 󰇍 𝑑𝑡 =𝑓(𝒙𝑵 󰇍 󰇍 󰇍 󰇍 󰇍 ,𝜙,𝑡) (5) 89 being he ime, 𝒙𝑵 󰇍 󰇍 󰇍 󰇍 󰇍 he N-componen ec o de ining he N s a e a iables o he 90 sys em and 𝑓 a con inuous n h-dimensional ec o unc ion. 91 A pa icula case o his gene al de ini ion is he lux-con olled meminduc o , a 92 meminduc i e sys em wi h one single s a e a iable whose meminduc ance 93 depends only on he inpu lux. In ha case, Eq. 4 and Eq. 5 can be educed o 94 Eq. 6 [6]: 95 𝐼(𝑡)=𝐿𝑀 −1[∫𝜙(𝜏)𝑑𝜏 𝑡 𝑡0]·𝜙(𝑡) (6) 96 p o ided ha ∫𝜙(𝜏)𝑑𝜏=0 𝑡0 −∞ . No e ha a lux-con olled meminduc o is no only 97 an induc o whose induc ance depends on he ime in eg al o he inpu lux, bu 98 also whose cu en – lux cha ac e is ic p esen s a pinched hys e esis loop (in 99 which he cu en is ze o whene e he lux is ze o) [6]. 100 On his basis, he e we demons a e ha he Rio dan gy a o [37], a e ce ain 101 modi ica ions (see Figu e 1), is sui able o he emula ion o loa ing lux-con olled 102 meminduc o s. 103 104 Figu e 1. (a) Modi ied Rio dan gy a o using an impedance Z3 whose alue 105 depends on he double ime in eg al o he inpu ol age. (b) Adap a ion o he 106 ci cui shown in (a) o emula e lux-con olled meminduc o s. (c) Ci cui equi alen 107 o he one shown in (b). 108 Fi s ly, o a loa ing impedance, he inpu cu en a e minal one mus be equal 109 o he ou pu cu en o e minal wo: 110 𝐼1=−𝐼2 (7) 111 Neglec ing he inpu bias cu en o he op amps, he inpu cu en a e minal one 112 co esponds o he cu en h ough he impedance Z1, and he e o e, i can be 113 ob ained as indica ed in Eq. 8. 114 𝐼1=𝑉𝐼𝑁1−𝑉𝐵 𝑍1=(𝑉𝐼𝑁1−𝑉𝐼𝑁2)· 𝑍2𝑍4 𝑍5𝑍3𝑍1=𝑉𝐼𝑁·𝑍2𝑍4 𝑍5𝑍3𝑍1 (8) 115 In he same way, he cu en a e minal wo co esponds o he sum o he cu en 116 h ough Z6 and Z5, which can be de i ed as exp essed in Eq. 9. 117 𝐼2=𝑉𝐼𝑁2−𝑉𝐼𝑁1 𝑍5+𝑉𝐼𝑁2−𝑉𝐶 𝑍6=𝑉𝐼𝑁·(𝑍7 𝑍8𝑍6+𝑍2𝑍4𝑍7 𝑍3𝑍5𝑍6𝑍8−1 𝑍5) (9) 118 Thus, in o de o sa is y Eq. 7, he ci cui shown in Figu e 1a needs o ul ill he 119 ollowing condi ion: 120 1 𝑍5=1 𝑍1=𝑍7 𝑍6𝑍8 (10) 121 In ha case, and conside ing Z3 as a lux-con olled impedance, he alue o he 122 lossless loa ing lux-con olled inpu impedance o he ci cui can be exp essed 123 as indica ed in Eq. 11 in Laplace’s domain. 124 𝑍1→2(𝜌(𝑠))=𝑍1𝑍3(𝜙(𝑠) 𝑠)𝑍5 𝑍2𝑍4 (11) 125 This impedance, a e he subs i u ions shown in Figu e 1b, can be di ec ly ela ed 126 o a lux-con olled induc ance (see Eq. 12) conside ing 𝑅1=𝑅2=𝑅5=𝑅6= 127 𝑅7=𝑅8=𝑹, and a esis ance 𝑅3(𝜌) con olled by he ime in eg al o he lux (𝜌). 128 𝑍1→2(𝜌(𝑠))=𝒔𝑅𝐶4𝑅3(𝜙(𝑠) 𝑠)=𝒔𝐿(𝜙(𝑠) 𝑠) (12) 129 This also makes easible he ci cui o Figu e 1b sa is ies he cons i u i e equa ion 130 o a meminduc o , gi en ha : 131 𝐼1=1 𝑅𝐶4𝑅3(𝜙(𝑠) 𝑠)·𝑉𝐼𝑁 𝑠→ 𝐼1(𝑡)=1 𝐿(𝜌)·𝜙(𝑡) (13) 132 Mo eo e , i we u he analyze his ci cui conside ing close o ideal ope a ional 133 ampli ie s, i can be de i ed ha he ol age ac oss R3(𝜌) can be exp essed as a 134 unc ion o he inpu lux (𝜙) (Eq. 14). 135 𝑉𝑅3(𝑡)= 𝑉𝑅3+(𝑡)− 𝑉𝑅3−(𝑡)= 1 𝑅5𝐶4∫(𝑉𝑖𝑛1(𝑡)−𝑉𝑖𝑛2(𝑡))𝑑𝑡= 1 𝑅5𝐶4∫𝑉𝑖𝑛(𝑡)𝑑𝑡= 𝜙(𝑡) 𝑅5𝐶4 (14) 136 The e o e, gi en ha he esis ance R3(𝜌) changes i s alue acco ding o he ime- 137 in eg al o he inpu lux (𝜌), i is eally changing i s alue as a unc ion o he ime- 138 in eg al o i s own inpu , hence beha ing as a ol age-con olled mem is o [6]. 139 On his basis, R3(𝜌) could be eplaced by a ol age-con olled mem is o , as 140 illus a ed in Figu e 1c, which would allow o o mula e Eq. 12 in e ms o 141 mem is ance, as indica ed in Eq. 15. 142 𝑍1→2(𝜌(𝑠))=𝒔𝑅𝐶4𝑅𝑀=𝒔𝐿(𝜌(𝑠)) (15) 143 To p o e he easibili y o he ci cui o emula e a meminduc o , we ha e 144 conside ed he simple wo-s a es meminduc o implemen a ion depic ed in Figu e 145 2. 146 147 Figu e 2. Two-s a es meminduc o emula o based on he Rio dan gy a o . 148 In he ci cui o Figu e 2, he alue o he ime in eg al o he inpu lux is ob ained 149 by in eg a ing he inpu ol age wice (e.g., using di e en ial op-amp ol age- 150 mode in eg a o s [39]). This alue is hen used o con ol a ol age-con olled 151 swi ch ha will connec (o no ) he addi ional esis o o he eedback loop. Unde 152 his con igu a ion, he lux-con olled induc ance gi en in Eq. 12 can be exp essed 153 as ollows: 154 𝐿(𝜌)={𝑅2𝐶𝑖𝑓 𝜌<𝜌𝑇𝐻 𝑅2𝐶 2𝑖𝑓 𝜌≥𝜌𝑇𝐻 (16) 155 whe e 𝜌𝑇𝐻 is he de ined h eshold alue which igge s he swi ch. 156 This bis able con igu a ion has been simula ed wi h SPICE in o de o con i m i s 157 meminduc i e beha io . Fo ha , we conside ed he ollowing con igu a ion: R = 158 1 kΩ, C = 47 nF and 𝜌TH = 0 V·s2, which esul s in he ollowing alues o 159 induc ance acco ding o Eq. 16: L(𝜌) = 47 mH o 𝜌 < 0 and L(𝜌) = 23.5 mH o 𝜌 160 > 0. 161 162 Figu e 3. Simula ion o he wo-s a es meminduc o emula o using a sinusoidal 163 inpu signal wi h a equency o 1 kHz (a) and a squa e inpu signal o 500 Hz (a). 164 The esul s shown in Figu e 3 demons a e ha he ci cui p oposed beha es as 165 a wo-s a es meminduc o ega dless o he inpu signal. As seen, he emula o 166 sa is ies he cons i u i e equa ion o he meminduc o (Eq. 6), since he inpu 167 cu en is ze o whene e he inpu lux is ze o and i s wa e o m is a unc ion o 168 he inpu lux and he s a e o induc ance (which in u n depends on he ime- 169 in eg al o inpu lux as indica ed by Eq. 16). In he same way, he meminduc i e 170 beha io is also mani es ed in he closed pinched hys e esis loop o i s i-𝜙 171 cha ac e is ic (Figu e 4), which has been ob ained using a sinusoidal inpu signal 172 wi h di e en equencies (1 kHz and 10 kHz). In addi ion, he i- cha ac e is ic o 173 R3 (inse o Figu e 4) also p o es ha he ol age-con olled esis o beha es as 174 5. Conclusions. 268 In his communica ion he easibili y o a modi ied e sion o he Rio dan gy a o 269 o emula e loa ing meminduc i e sys ems has been demons a ed. The ci cui 270 p oposed has been i s ly desc ibed heo e ically, om he modi ica ions on he 271 classical Rio dan gy a o o i s connec ion wi h he cons i u i e equa ions o lux- 272 con olled meminduc o s. The heo e ical app oach has been suppo ed wi h 273 SPICE simula ions using di e en inpu s signals and equencies o a simple wo- 274 s a es meminduc o implemen a ion as well as o a meminduc o -based low- 275 pass il e . Finally, a b eadboa d-le el implemen a ion o a con inuous s a es 276 meminduc o demons a es he simplici y, p ac icali y and e sa ili y o he 277 emula o p oposed. 278 Decla a ion o Compe ing In e es 279 The au ho s decla e no con lic o in e es . 280 Acknowledgmen s 281 This wo k was suppo ed by he Spanish Minis y o Educa ion, Cul u e, and Spo 282 (MECD)/FEDER-EU h ough he g an FPU16/01451 and he p ojec TEC2017- 283 89955-P. 284 Re e ences 285 [1] L. Chua, “Mem is o -The missing ci cui elemen ,” IEEE T ansac ions on 286 Ci cui Theo y, ol. 18, no. 5, pp. 507–519, Sep. 1971, doi: 287 10.1109/TCT.1971.1083337. 288 [2] D. B. S uko , G. S. Snide , D. R. S ewa , and R. S. Williams, “The missing 289 mem is o ound,” Na u e, ol. 453, no. 7191, A . no. 7191, May 2008, doi: 290 10.1038/na u e06932. 291 [3] P. 01 M. 2008 | 15:57 GMT, “The Mys e ious Mem is o - IEEE Spec um,” 292 IEEE Spec um: Technology, Enginee ing, and Science News. 293 h ps://spec um.ieee.o g/semiconduc o s/design/ he-mys e ious-mem is o 294 (accessed Oc . 26, 2020). 295 [4] R. C. Johnson, “EETimes - Will mem is o s p o e i esis ible? -,” EETimes, 296 Sep. 01, 2008. h ps://www.ee imes.com/will-mem is o s-p o e-i esis ible-2/ 297 (accessed Oc . 26, 2020). 298 [5] M. D. Ven a, Y. V. Pe shin, and L. O. Chua, “Pu ing Memo y In o Ci cui 299 Elemen s: Mem is o s, Memcapaci o s, and Meminduc o s [Poin o View],” 300 P oceedings o he IEEE, ol. 97, no. 8, pp. 1371–1372, Aug. 2009, doi: 301 10.1109/JPROC.2009.2022882. 302 [6] M. Di Ven a, Y. V. Pe shin, and L. O. Chua, “Ci cui Elemen s Wi h Memo y: 303 Mem is o s, Memcapaci o s, and Meminduc o s,” P oceedings o he IEEE, 304 ol. 97, no. 10, pp. 1717–1724, Oc . 2009, doi: 305 10.1109/JPROC.2009.2021077. 306 [7] Y. V. Pe shin and M. Di Ven a, “Neu omo phic, Digi al, and Quan um 307 Compu a ion Wi h Memo y Ci cui Elemen s,” P oceedings o he IEEE, ol. 308 100, no. 6, pp. 2071–2080, Jun. 2012, doi: 10.1109/JPROC.2011.2166369. 309 [8] C. Chen, H. Bao, M. Chen, Q. Xu, and B. Bao, “Non-ideal mem is o synapse- 310 coupled bi-neu on Hop ield neu al ne wo k: Nume ical simula ions and 311 b eadboa d expe imen s,” AEU - In e na ional Jou nal o Elec onics and 312 Communica ions, ol. 111, p. 152894, No . 2019, doi: 313 10.1016/j.aeue.2019.152894. 314 [9] S. K a insky e al., “MAGIC—Mem is o -Aided Logic,” IEEE T ansac ions on 315 Ci cui s and Sys ems II: Exp ess B ie s, ol. 61, no. 11, pp. 895–899, No . 316 2014, doi: 10.1109/TCSII.2014.2357292. 317 [10] S. K a insky, N. Wald, G. Sa a , A. Kolodny, U. C. Weise , and E. G. 318 F iedman, “MRL — Mem is o Ra ioed Logic,” in 2012 13 h In e na ional 319 Wo kshop on Cellula Nanoscale Ne wo ks and hei Applica ions, Aug. 2012, 320 pp. 1–6, doi: 10.1109/CNNA.2012.6331426. 321 [11] N. Yang, C. Yang, Y. YU, X. LU, L. Wang, and T. Nyima, “S udy on Ac i e 322 Fil e Based on Mem is o and Memcapaci o ,” in 2018 Fi een h In e na ional 323 Con e ence on Wi eless and Op ical Communica ions Ne wo ks (WOCN), 324 Feb. 2018, pp. 1–4, doi: 10.1109/WOCN.2018.8556125. 325 [12] H. Gan, D. Yu, D. Li, and H. Cheng, “Bina y memcapaci o based i s - 326 o de ac i e il e ,” Ci cui Wo ld, ol. 46, no. 2, pp. 117–124, Jan. 2020, doi: 327 10.1108/CW-06-2019-0061. 328 [13] M. Wang, Y. Yu, N. Yang, C. Yang, and H. Ma, “New band-pass and band- 329 s op il e s wi h h ee memo y de ices,” in 2019 14 h IEEE Con e ence on 330 Indus ial Elec onics and Applica ions (ICIEA), Jun. 2019, pp. 1985–1989, 331 doi: 10.1109/ICIEA.2019.8834352. 332 [14] Q. Zhao, C. Wang, and X. Zhang, “A uni e sal emula o o mem is o , 333 memcapaci o , and meminduc o and i s chao ic ci cui ,” Chaos, ol. 29, no. 334 1, p. 013141, Jan. 2019, doi: 10.1063/1.5081076. 335 [15] F. Yuan and Y. Li, “A chao ic ci cui cons uc ed by a mem is o , a 336 memcapaci o and a meminduc o ,” Chaos, ol. 29, no. 10, p. 101101, Oc . 337 2019, doi: 10.1063/1.5125673. 338 [16] F. Yuan, G. Wang, and X. Wang, “Chao ic oscilla o con aining 339 memcapaci o and meminduc o and i s dimensionali y educ ion analysis,” 340 Chaos, ol. 27, no. 3, p. 033103, Ma . 2017, doi: 10.1063/1.4975825. 341 [17] X. Wang, J. Yu, C. Jin, H. H. C. Iu, and S. Yu, “Chao ic oscilla o based on 342 memcapaci o and meminduc o ,” Nonlinea Dyn, ol. 96, no. 1, pp. 161–173, 343 Ap . 2019, doi: 10.1007/s11071-019-04781-5. 344 [18] M. Yildi im and F. Kaca , “Chao ic ci cui wi h OTA based mem is o on 345 image c yp ology,” AEU - In e na ional Jou nal o Elec onics and 346 Communica ions, ol. 127, p. 153490, Dec. 2020, doi: 347 10.1016/j.aeue.2020.153490. 348 [19] E. Gale, “TiO2-based mem is o s and ReRAM: ma e ials, mechanisms 349 and models (a e iew),” Semicond. Sci. Technol., ol. 29, no. 10, p. 104004, 350 Sep. 2014, doi: 10.1088/0268-1242/29/10/104004. 351 [20] F. J. Rome o e al., “Lase -Fab ica ed Reduced G aphene Oxide 352 Mem is o s,” Nanoma e ials, ol. 9, no. 6, A . no. 6, Jun. 2019, doi: 353 10.3390/nano9060897. 354 [21] F. J. Rome o e al., “Resis i e Swi ching in G aphene Oxide,” F on . 355 Ma e ., ol. 7, 2020, doi: 10.3389/ ma s.2020.00017. 356 [22] D. Biolek and V. Biolko a, “Mu a o o ans o ming mem is o in o 357 memcapaci o ,” Elec onics Le e s, ol. 46, no. 21, pp. 1428–1429, Oc . 358 2010, doi: 10.1049/el.2010.2309. 359 [23] M. Pd. Sah, R. K. Budha hoki, C. Yang, and H. Kim, “Expandable ci cui s 360 o mu a o -based memcapaci o emula o ,” In . J. Bi u ca ion Chaos, ol. 23, 361 no. 05, p. 1330017, May 2013, doi: 10.1142/S0218127413300176. 362 [24] X. Y. Wang, A. L. Fi ch, H. H. C. Iu, and W. G. Qi, “Design o a 363 memcapaci o emula o based on a mem is o ,” Physics Le e s A, ol. 376, 364 no. 4, pp. 394–399, Jan. 2012, doi: 10.1016/j.physle a.2011.11.012. 365 [25] D. S. Yu, Y. Liang, H. Chen, and H. H. C. Iu, “Design o a P ac ical 366 Memcapaci o Emula o Wi hou G ounded Res ic ion,” IEEE T ansac ions 367 on Ci cui s and Sys ems II: Exp ess B ie s, ol. 60, no. 4, pp. 207–211, Ap . 368 2013, doi: 10.1109/TCSII.2013.2240879. 369 [26] Y. V. Pe shin and M. D. Ven a, “Mem is i e ci cui s simula e 370 memcapaci o s and meminduc o s,” Elec onics Le e s, ol. 46, no. 7, pp. 371 517–518, Ap . 2010, doi: 10.1049/el.2010.2830. 372 [27] D.-S. Yu, Y. Liang, H. H. C. Iu, and Y.-H. Hu, “Mu a o o ans e ing a 373 mem is o emula o in o meminduc i e and memcapaci i e ci cui s,” Chinese 374 Phys. B, ol. 23, no. 7, p. 070702, Jul. 2014, doi: 10.1088/1674- 375 1056/23/7/070702. 376 [28] S.-F. Wang, “The gy a o o ans o ming nano mem is o in o 377 meminduc o ,” Ci cui Wo ld, ol. 42, no. 4, pp. 197–200, Jan. 2016, doi: 378 10.1108/CW-01-2016-0002. 379 [29] F. Yuan, Y. Jin, and Y. Li, “Sel - ep oducing chaos and bu s ing oscilla ion 380 analysis in a meminduc o -based conse a i e sys em,” Chaos, ol. 30, no. 381 5, p. 053127, May 2020, doi: 10.1063/5.0008313. 382 [30] F. J. Rome o e al., “Memcapaci o emula o based on he Mille e ec ,” 383 In e na ional Jou nal o Ci cui Theo y and Applica ions, ol. 47, no. 4, pp. 384 572–579, 2019, doi: 10.1002/c a.2604. 385 [31] M. E. Fouda and A. G. Radwan, “Cha ge con olled mem is o -less 386 memcapaci o emula o ,” Elec onics Le e s, ol. 48, no. 23, pp. 1454–1455, 387 No . 2012, doi: 10.1049/el.2012.3151. 388 [32] Yan L., Dong-Sheng Y., and Hao C., “A no el meminduc o emula o 389 based on analog ci cui s,” wlxb, ol. 62, no. 15, pp. 158501–158501, Aug. 390 2013, doi: 10.7498/aps.62.158501. 391 [33] M. Konal and F. Kaca , “Elec onically unable meminduc o based on 392 OTA,” AEU - In e na ional Jou nal o Elec onics and Communica ions, ol. 393 126, p. 153391, No . 2020, doi: 10.1016/j.aeue.2020.153391. 394 [34] M. E. Fouda and A. G. Radwan, “Mem is o -less cu en - and ol age- 395 con olled meminduc o emula o s,” in 2014 21s IEEE In e na ional 396 Con e ence on Elec onics, Ci cui s and Sys ems (ICECS), Dec. 2014, pp. 397 279–282, doi: 10.1109/ICECS.2014.7049976. 398 [35] M. E. Fouda and A. G. Radwan, “Meminduc o Response Unde Pe iodic 399 Cu en Exci a ions,” Ci cui s Sys Signal P ocess, ol. 33, no. 5, pp. 1573– 400 1583, May 2014, doi: 10.1007/s00034-013-9708-y. 401 [36] F. J. Rome o, M. Escude o, A. Medina-Ga cia, D. P. Mo ales, and N. 402 Rod iguez, “Meminduc o Emula o Based on a Modi ied An oniou’s Gy a o 403 Ci cui ,” Elec onics, ol. 9, no. 9, A . no. 9, Sep. 2020, doi: 404 10.3390/elec onics9091407. 405 [37] R. H. S. Rio dan, “Simula ed induc o s using di e en ial ampli ie s,” 406 Elec onics Le e s, ol. 3, no. 2, pp. 50–51, Feb. 1967, doi: 407 10.1049/el:19670039. 408 [38] R. Senani, D. R. Bhaska , A. K. Singh, and V. K. Singh, “Simula ion o 409 Induc o s and O he Types o Impedances Using CFOAs,” in Cu en 410 Feedback Ope a ional Ampli ie s and Thei Applica ions, R. Senani, D. R. 411 Bhaska , A. K. Singh, and V. K. Singh, Eds. New Yo k, NY: Sp inge , 2013, 412 pp. 49–80. 413 [39] D. V. Kama h, “O e iew o OPAMP and OTA based In eg a o s,” 414 In e na ional Jou nal o Inno a i e Resea ch in Elec ical, Elec onics, 415 Ins umen a ion and Con ol Enginee ing, ol. 3, no. 9, pp. 74–79, Sep. 2015, 416 doi: 10.17148/IJIREEICE.2015.3915. 417 [40] X.-Y. Wang, A. L. Fi ch, H. H. C. Iu, V. S ee am, and W.-G. Qi, 418 “Implemen a ion o an analogue model o a mem is o based on a ligh - 419 dependen esis o ,” Chinese Phys. B, ol. 21, no. 10, p. 108501, Oc . 2012, 420 doi: 10.1088/1674-1056/21/10/108501. 421 422