Design and Implemen a ion o a Floa ing Meminduc o Emula o
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upon Rio dan Gy a o
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F ancisco J. Rome o1,*, Al edo Medina-Ga cia2, Manuel Escude o3, Diego P.
3
Mo ales1 and Noel Rod iguez1
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1 Dep . Elec onics and Compu e Technology, Facul y o Sciences, Uni e si y
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o G anada, 18071 G anada, Spain.
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2 In ineon Technologies AG, 85579 Neubibe g, Ge many
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3 In ineon Technologies Aus ia AG, 9500 Villach, Aus ia
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* Email: [email p o ec ed]
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Abs ac
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In his communica ion we p esen he design, simula ion and implemen a ion o
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a loa ing lux-con olled meminduc o emula o based on he Rio dan gy a o .
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Fi s ly, he ci cui is p esen ed heo e ically, om i s o iginal e sion o emula e
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induc o s o i s adap a ion o loa ing meminduc o s. Once i s heo e ical
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equa ions a e p esen ed, using SPICE simula ions, we demons a e he easibili y
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o his implemen a ion by means o o - he-shel componen s and a mem is o , o
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a mem is o emula o , o di e en inpu s signals and equencies in bo h
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g ounded and loa ing con igu a ions. Finally, a low- equency b eadboa d-le el
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implemen a ion is included o p o e i s p ac icali y.
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Keywo ds: ci cui heo y, emula o , eedback, gy a o , meminduc o , mem is o
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21
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1. In oduc ion
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Nea ly 50 yea s ago, P o . Leon Chua p esen ed o he i s ime he passi e
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ci cui elemen which es ablished he ela ion be ween lux (𝜙, ime-in eg al o he
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inpu - ol age) and cha ge (q) [1]. This elemen was called mem is o (memo y-
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esis o ) since i demons a ed ha , o a gi en ol age, i s esis ance a an ins an
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= 1 depends no only on he cu en a 1, bu also on he cu en h ough he
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de ice om = -∞ o = 1, hence p esen ing a memo y cha ac e is ic. Howe e ,
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i was no un il 2008 ha a g oup o esea che s om Hewle -Packa d Labs (HP)
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epo ed he i s solid-s a e de ice exhibi ing mem is i e beha io [2]. I was hen
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when he concep o mem is o ushe ed in unp eceden ed elec onic de ices and
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applica ions, ex ending om ReRAMs (Resis i e Random-Access Memo y) o
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ealis ic neu al ne wo ks [3]. Thus, he mem is o , and i s non- ola ile memo y
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e ec , has aised as one o he mo e subs an ial e olu ions in he ield o
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elec onic ci cui s heo y since he in en ion o he ansis o [4].
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In 2009, a e he g ea in e es a oused by mem is i e de ices, M. Di Ven a,
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Y.V. Pe shin and L. Chua gene alized he concep o memo y de ices o
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capaci o s and induc o s, hus de ining he memcapaci o and he meminduc o
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[5]. In hese de ices, bo h capaci ance and induc ance, as in he case o
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mem is o s, p esen a non- ola ile memo y e ec which depends no only on i s
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p esen s a e bu also on he his o y o he de ice. In his way, apa om he
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de ini ion o mem is o (RM, Eq.1), hey de ined he concep s o memcapaci o
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(CM, Eq. 2), as he n h-o de sys em ha es ablishes a nonlinea ela ion be ween
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he cha ge (q) o he de ice and i s ol age (V); and he meminduc o (LM, Eq. 3),
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as he n h-o de sys em which es ablishes he nonlinea ela ion be ween cu en
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(I) and lux (𝜙) [6].
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𝑉(𝑡)=𝑅𝑀(𝒙𝑵
󰇍
󰇍
󰇍
󰇍
󰇍
,𝐼,𝑡)·𝐼(𝑡) (1)
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𝑞(𝑡)=𝐶𝑀(𝒙𝑵
󰇍
󰇍
󰇍
󰇍
󰇍
,𝑉,𝑡)·𝑉(𝑡) (2)
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𝜙(𝑡)=𝐿𝑀(𝒙𝑵
󰇍
󰇍
󰇍
󰇍
󰇍
,𝐼,𝑡)·𝐼(𝑡) (3)
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Being 𝒙𝑵
󰇍
󰇍
󰇍
󰇍
󰇍
a ec o ep esen ing he n in e nal s a e a iables o he sys em.
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These de ices, memcapaci o and meminduc o , a e expec ed o cause a
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dis up ion in he ield o elec onics, which has led o se e al s udies on di e se
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applica ions, such as neu omo phic and quan um compu a ion [7], [8], logic ga es
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[9], [10], sel -adap a i e il e s [11]–[13] o chao ic ci cui s [14]–[18]. Howe e , in
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con as o mem is o s, which can be al eady ab ica ed elying on di e en
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ma e ials and esis i e swi ching mechanisms [2], [19]–[21], solid-s a e
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memcapaci o s and meminduc o s a e ye elusi e.
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Fo his eason, in ecen yea s many SPICE models as well as some p ac ical
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implemen a ions o memcapaci o s and meminduc o s emula o s ha e been
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p oposed. These ci cui s ollow di e en al e na i es o achie e he same goal:
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sa is ying he cons i u i e equa ions o he emula ed de ice. These al e na i es
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can be g ouped in o wo main g oups; i) hose using ano he mem-de ice (in
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pa icula a mem is o ) o mu a e i s beha io o he desi ed mem-de ice and ii)
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hose no based on mem-de ices. Thus, many o he di e en memcapaci o s
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and meminduc o s emula o s use a mem is o (o a mem is o emula o ) o
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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-
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de ice emula ed [22]–[28], as i is done in his wo k, while he es o hem make
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use o classical ol age-mode op-amps (VOAs), cu en eedback ope a ional
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ampli ie s (CFOAs), ope a ional ansconduc ance ampli ie (OTAs) and/o
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cu en con eyo s o emula e he desi ed mem-de ice [14], [29]–[36].
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Howe e , he implemen a ion o mos o hese ci cui s limi s he emula ed de ice
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o g ounded con igu a ions, hence educing hei po en ial applica ions. In o de
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o a oid his, in his wo k we p esen a simple and low-cos loa ing meminduc o
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emula o based on a modi ica ion o he Rio dan gy a o , ypically used o emula e
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loa ing induc o s and whose design is based on classical op-amps [37].
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The manusc ip is s uc u ed as ollows: a e his in oduc ion, Sec ion 2 p esen s
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he heo e ical modi ica ions o e he Rio dan gy a o o achie e a meminduc i e
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beha io , oge he wi h SPICE simula ions demons a ing he easibili y o he
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p oposed ci cui o loa ing and g ounded con igu a ions. A e ha , a simple low-
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equency b eadboa d-le el implemen a ion using o - he-shel componen s is
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p esen ed in Sec ion 3 and, inally, he main conclusions a e d awn in Sec ion 4.
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2. Meminduc ance and he modi ied Rio dan gy a o .
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As de ined by Chua [6], he meminduc i e sys ems can be ei he cu en -
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con olled o lux-con olled depending on he ela ion o he meminduc ance wi h
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hese pa ame e s. This wo k is ocused on lux-con olled meminduc i e sys ems,
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which a e desc ibed by he ollowing equa ions:
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𝐼(𝑡)=𝐿𝑀
−1(𝑥1,𝑥2,…,𝑥𝑛,𝜙,𝑡)·𝜙(𝑡) (4)
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𝑑𝒙𝑵
󰇍
󰇍
󰇍
󰇍
󰇍
𝑑𝑡 =𝑓(𝒙𝑵
󰇍
󰇍
󰇍
󰇍
󰇍
,𝜙,𝑡) (5)
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being he ime, 𝒙𝑵
󰇍
󰇍
󰇍
󰇍
󰇍
he N-componen ec o de ining he N s a e a iables o he
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sys em and 𝑓 a con inuous n h-dimensional ec o unc ion.
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A pa icula case o his gene al de ini ion is he lux-con olled meminduc o , a
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meminduc i e sys em wi h one single s a e a iable whose meminduc ance
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depends only on he inpu lux. In ha case, Eq. 4 and Eq. 5 can be educed o
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Eq. 6 [6]:
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𝐼(𝑡)=𝐿𝑀
−1[∫𝜙(𝜏)𝑑𝜏
𝑡
𝑡0]·𝜙(𝑡) (6)
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p o ided ha ∫𝜙(𝜏)𝑑𝜏=0
𝑡0
−∞ . No e ha a lux-con olled meminduc o is no only
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an induc o whose induc ance depends on he ime in eg al o he inpu lux, bu
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also whose cu en – lux cha ac e is ic p esen s a pinched hys e esis loop (in
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which he cu en is ze o whene e he lux is ze o) [6].
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On his basis, he e we demons a e ha he Rio dan gy a o [37], a e ce ain
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modi ica ions (see Figu e 1), is sui able o he emula ion o loa ing lux-con olled
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meminduc o s.
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Figu e 1. (a) Modi ied Rio dan gy a o using an impedance Z3 whose alue
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depends on he double ime in eg al o he inpu ol age. (b) Adap a ion o he
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ci cui shown in (a) o emula e lux-con olled meminduc o s. (c) Ci cui equi alen
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o he one shown in (b).
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Fi s ly, o a loa ing impedance, he inpu cu en a e minal one mus be equal
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o he ou pu cu en o e minal wo:
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𝐼1=−𝐼2 (7)
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Neglec ing he inpu bias cu en o he op amps, he inpu cu en a e minal one
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co esponds o he cu en h ough he impedance Z1, and he e o e, i can be
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ob ained as indica ed in Eq. 8.
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𝐼1=𝑉𝐼𝑁1−𝑉𝐵
𝑍1=(𝑉𝐼𝑁1−𝑉𝐼𝑁2)· 𝑍2𝑍4
𝑍5𝑍3𝑍1=𝑉𝐼𝑁·𝑍2𝑍4
𝑍5𝑍3𝑍1 (8)
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In he same way, he cu en a e minal wo co esponds o he sum o he cu en
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h ough Z6 and Z5, which can be de i ed as exp essed in Eq. 9.
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𝐼2=𝑉𝐼𝑁2−𝑉𝐼𝑁1
𝑍5+𝑉𝐼𝑁2−𝑉𝐶
𝑍6=𝑉𝐼𝑁·(𝑍7
𝑍8𝑍6+𝑍2𝑍4𝑍7
𝑍3𝑍5𝑍6𝑍8−1
𝑍5) (9)
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Thus, in o de o sa is y Eq. 7, he ci cui shown in Figu e 1a needs o ul ill he
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ollowing condi ion:
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1
𝑍5=1
𝑍1=𝑍7
𝑍6𝑍8 (10)
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In ha case, and conside ing Z3 as a lux-con olled impedance, he alue o he
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lossless loa ing lux-con olled inpu impedance o he ci cui can be exp essed
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as indica ed in Eq. 11 in Laplace’s domain.
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𝑍1→2(𝜌(𝑠))=𝑍1𝑍3(𝜙(𝑠)
𝑠)𝑍5
𝑍2𝑍4 (11)
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This impedance, a e he subs i u ions shown in Figu e 1b, can be di ec ly ela ed
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o a lux-con olled induc ance (see Eq. 12) conside ing 𝑅1=𝑅2=𝑅5=𝑅6=
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𝑅7=𝑅8=𝑹, and a esis ance 𝑅3(𝜌) con olled by he ime in eg al o he lux (𝜌).
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𝑍1→2(𝜌(𝑠))=𝒔𝑅𝐶4𝑅3(𝜙(𝑠)
𝑠)=𝒔𝐿(𝜙(𝑠)
𝑠) (12)
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This also makes easible he ci cui o Figu e 1b sa is ies he cons i u i e equa ion
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o a meminduc o , gi en ha :
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𝐼1=1
𝑅𝐶4𝑅3(𝜙(𝑠)
𝑠)·𝑉𝐼𝑁
𝑠→ 𝐼1(𝑡)=1
𝐿(𝜌)·𝜙(𝑡) (13)
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Mo eo e , i we u he analyze his ci cui conside ing close o ideal ope a ional
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ampli ie s, i can be de i ed ha he ol age ac oss R3(𝜌) can be exp essed as a
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unc ion o he inpu lux (𝜙) (Eq. 14).
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𝑉𝑅3(𝑡)= 𝑉𝑅3+(𝑡)− 𝑉𝑅3−(𝑡)= 1
𝑅5𝐶4∫(𝑉𝑖𝑛1(𝑡)−𝑉𝑖𝑛2(𝑡))𝑑𝑡= 1
𝑅5𝐶4∫𝑉𝑖𝑛(𝑡)𝑑𝑡= 𝜙(𝑡)
𝑅5𝐶4 (14)
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The e o e, gi en ha he esis ance R3(𝜌) changes i s alue acco ding o he ime-
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in eg al o he inpu lux (𝜌), i is eally changing i s alue as a unc ion o he ime-
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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
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mem is ance, as indica ed in Eq. 15.
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𝑍1→2(𝜌(𝑠))=𝒔𝑅𝐶4𝑅𝑀=𝒔𝐿(𝜌(𝑠)) (15)
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To p o e he easibili y o he ci cui o emula e a meminduc o , we ha e
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conside ed he simple wo-s a es meminduc o implemen a ion depic ed in Figu e
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2.
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Figu e 2. Two-s a es meminduc o emula o based on he Rio dan gy a o .
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In he ci cui o Figu e 2, he alue o he ime in eg al o he inpu lux is ob ained
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by in eg a ing he inpu ol age wice (e.g., using di e en ial op-amp ol age-
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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)
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whe e 𝜌𝑇𝐻 is he de ined h eshold alue which igge s he swi ch.
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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
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induc ance acco ding o Eq. 16: L(𝜌) = 47 mH o 𝜌 < 0 and L(𝜌) = 23.5 mH o 𝜌
160
> 0.
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Figu e 3. Simula ion o he wo-s a es meminduc o emula o using a sinusoidal
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inpu signal wi h a equency o 1 kHz (a) and a squa e inpu signal o 500 Hz (a).
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The esul s shown in Figu e 3 demons a e ha he ci cui p oposed beha es as
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a wo-s a es meminduc o ega dless o he inpu signal. As seen, he emula o
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sa is ies he cons i u i e equa ion o he meminduc o (Eq. 6), since he inpu
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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
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he inpu lux and he s a e o induc ance (which in u n depends on he ime-
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in eg al o inpu lux as indica ed by Eq. 16). In he same way, he meminduc i e
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beha io is also mani es ed in he closed pinched hys e esis loop o i s i-𝜙
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cha ac e is ic (Figu e 4), which has been ob ained using a sinusoidal inpu signal
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wi h di e en equencies (1 kHz and 10 kHz). In addi ion, he i- cha ac e is ic o
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R3 (inse o Figu e 4) also p o es ha he ol age-con olled esis o beha es as
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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
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p oposed has been i s ly desc ibed heo e ically, om he modi ica ions on he
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classical Rio dan gy a o o i s connec ion wi h he cons i u i e equa ions o lux-
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con olled meminduc o s. The heo e ical app oach has been suppo ed wi h
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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
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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
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[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