Emulation of floating memcapacitors and meminductors using current conveyors

0.32 MB·English

by  Yuriy V. Pershin

1
Emulation of floating memcapacitors and
meminductors using current conveyors
Yuriy V. Pershin and Massimiliano Di Ventra
Abstract—We suggest circuit realizations of emulators trans- aa L[[t]]=
formingmemristivedevicesintoeffectivefloatingmemcapacitive V1 = V2 RRM [t]C
1 and meminductive systems. The emulator’s circuits are based
1 on second generation current conveyors and involve either four Y X X Y
0 single-output or two dual-output current conveyors. The equa- V11 ZZ R ZZ V22
2 tions governing the resulting memcapactive and meminductive
systems are presented. CC
n
a Index Terms—Memory, Analog circuits, Analog memories.
J THE class of memory circuit elements [1] involves mem- ZZ YY

5
ristors [2], [3], memcapacitors [1] and meminductors Y X X Z
2
[1], namely resistors, capacitors and inductors, respectively, R
M
] which retain memory of the past dynamics. While there
t are many discovered experimental realizations of memristive
e CC[[tt]]=
d systems, the number of systems showing memcapacitive and b
V V L/(RR [t])
- meminductive behavior is still very limited [1]. Therefore, 1 = 2 M
s RR
M
n electroniccircuitsthatemulatethebehaviorofmemcapacitive
Y X X Y
s.i awnadymtoeombitnadinucmtiveemcealepmaceintitvseaorremoefmsiingdnuificctiavnetrienstpeorensste. iOsntoe VV1 Z Z VV2
c
i use mutators [4], [5]. However, recently suggested mutators LL
s
have some limitations [4], [5]. For instance, the mutators
y
h discussedinreference[4]realizegroundedmemcapacitiveand Z Y
p meminductivesystemsconnectedinserieswitharesistor.The
[ mutator from reference [5] simulates a grounded memcapaci- YY XX XX ZZ
R
2 tive system. For applications in electronics, however, it is de-
v sirabletohaveemulatorsofmemcapacitiveandmeminductive
0 systems that can be connected between any two voltages, and Fig. 1. Emulators of meminductive (a) and memcapacitive (b) systems
2 employing single-output current conveyors. Here, [t] denotes implicit and
that do not involve any additional resistances. Such circuits
6 explicittimedependenceofcorrespondingelements.
are proposed in this work.
4
. Thesuggestedcircuitstransformatime-dependentresponse
1
of a memristive system into effective floating memcapacitive
1
0 and meminductive responses. The memristive system is de- or it could be emulated as suggested by the present authors in
1 fined by the following equations: Refs. [4], [7], [8].
:
v I = [R (x,V ,t)]−1V , (1) Figure 1 shows circuits of mutators employing four single-
i M M M M output second generation current conveyors (CCII+) [9], [10].
X dx
= f(x,V ,t), (2) Themaincircuit’stopologyisbasedonthefloatinginductance
r dt M
a simulation circuit [11]. In addition to four active elements,
where IM and VM are the current through and the voltage eachcircuitusesthreepassiveelementssuchasthememristive
across the memristive system, respectively [3], RM is the system RM described by Eqs. (1-2), and standard linear
memristance (time-dependent resistance), x is a vector of the R, C and L. The operation of a current conveyor can be
internal state variables and f is a device-specific function. characterized by the following relations: V = V , I = I ,
x y x z
The memristive system could be realized by a physical mate- I = 0. By straightforward analysis of the circuit shown in
y
rial/system[1](withf given,e.g.,bytheequationsinRef.[6]) Fig. 1(a) we find that the circuit’s response between terminals
1 and 2 is described by
Yu.V.PershiniswiththeDepartmentofPhysicsandAstronomyandUSC
Nanocenter,UniversityofSouthCarolina,Columbia,SC,29208
e-mail:[email protected]. I = 1 φ≡[L(x,φ,t)]−1φ, (3)
M.DiVentraiswiththeDepartmentofPhysics,UniversityofCalifornia,
CRR (x,φ/(RC),t)
SanDiego,LaJolla,California92093-0319 M
e-mail:[email protected]. dx
= f(x,φ/(RC),t) (4)
ManuscriptreceivedNovemberXX,2010;revisedJanuaryYY,2011. dt
2
L[[t]]= same as Eqs. (3-4) and Eqs. (5-6), respectively.
aa
V1 = V2 RRM [t]C In conclusion, we have presented emulators of floating
memcapacitive and meminductive systems using second gen-
Y Z- eration current conveyors involving either four single-output
VV11 X Z YY ZZ- or two dual-output current conveyors. The resulting circuits
mutate memristive system’s dynamics into an effective mem-
X Z
capacitive and meminductive response. Since memristor emu-
V
C 2 lators can be easily made from off-the-shelf components [7],
R RR
MM [8], [4], we expect these mutators to find widespread use in
electronic applications with memdevices.
REFERENCES
CC[[tt]]= [1] M. Di Ventra, Y. V. Pershin, and L. O. Chua, “Circuit elements with
b memory:Memristors,memcapacitors,andmeminductors,”Proc.IEEE,
V1 = V2 L/(RRM [t]) vol.97,no.10,pp.1717–1724,2009.
[2] L. O. Chua, “Memristor - the missing circuit element,” IEEE Trans.
Y Z- CircuitTheory,vol.18,pp.507–519,1971.
[3] L.O.ChuaandS.M.Kang,“Memristivedevicesandsystems,”Proc.
VV
11 X Z YY ZZ- IEEE,vol.64,pp.209–223,1976.
[4] Y.V.PershinandM.DiVentra,“Memristivecircuitssimulatememca-
X Z pacitorsandmeminductors,”ElectronicsLetters,vol.46,pp.517–518,
L V2 2010.
RM R [5] D. Biolek and V. Biolkova, “Mutator for transforming memristor into
memcapacitor,”El.Lett.,vol.46,p.1428,2010.
[6] Y.V.Pershin,S.LaFontaine,andM.DiVentra,“Memristivemodelof
amoebalearning,”Phys.Rev.E,vol.80,p.021926,2009.
[7] Y. V. Pershin and M. Di Ventra, “Practical approach to programmable
analogcircuitswithmemristors,”IEEETrans.Circ.Syst.I,vol.57,p.
1857,2010.
Fig. 2. Emulators of meminductive (a) and memcapacitive (b) systems [8] ——, “Experimental demonstration of associative memory with mem-
employingdual-outputcurrentconveyors.Thedual-outputcurrentconveyors ristiveneuralnetworks,”NeuralNetworks,vol.23,p.881,2010.
satisfytherules:Vx=Vy,Ix=Iz,Iy =0,andIz−=−Iz. [9] A.SedraandK.Smith,“Asecond-generationcurrentconveyorandits
applications,”IEEETrans.Circ.Th.,vol.CT17,p.132,1970.
[10] B.Wilson,“Recentdevelopmentsincurrentconveyorsandcurrent-mode
circuits,”IEEProc.G,vol.137,pp.63–77,1990.
where the flux φ is given by φ(t) = (cid:82)t(V1(t(cid:48))−V2(t(cid:48)))dt(cid:48). [11] Won.cKuirrraennotncoannvdePy.oPrsa,w”aErlaencgtrkoonoincs,“LFeltoteartsin,gvoinl.d3u3c,tapnpc.e1s7i4m8u–l1a7ti4o9n,b1a9s9e7d.
0 [12] K.Pal,“Modifiedcurrentconveyorsandtheirapplications,”Microelec-
The analysis of the circuit presented in Fig. 1(b) results in the tronicsJournal,vol.20,p.37,1989.
following system’s equations: [13] A. M. Soliman, “Current conveyor filters: Classification and review,”
MicroelectronicsJournal,vol.29,pp.133–149,1998.
L [14] W.TangsriratandW.Surakampontorn,“Highoutputimpedancecurrent-
Q = RR (x,(V −V ),t)(V1−V2)≡ modeuniversalfilteremployingdual-outputcurrent-controlledconvey-
M 1 2 orsandgroundedcapacitors,”AEU-InternationalJournalofElectronics
≡ C(x,(V −V ),t)(V −V ), (5) andCommunications,vol.61,pp.127–131,2007.
1 2 1 2
dx
= f(x,(V −V ),t). (6)
dt 1 2
It is readily seen that Eqs. (3-4) and (5-6) describe float-
ing flux-controlled meminductive systems [1] and voltage-
controlled memcapacitive systems [1], respectively. If we
consider equation (3) and algebraically solve it with respect
to the flux φ (assuming a unique solution at any given time),
we can then substitute the result into (4) and obtain equations
of a current-controlled meminductive system. The same can
be done for Eqs. (5) and (6) thus transforming a voltage-
controlledmemcapacitivesystemintoacharge-controlledone,
providedauniquesolutionofEq.(5)existsatanygiventime.
Itwaspreviouslydemonstratedthatdual-outputcurrentcon-
veyorscanbeusedtoreducethenumberofactivecomponents
indifferentcircuits[12],[13],[14].Fig.2representsemulators
of meminductive and memcapacitive systems based on a
floating-inductor simulation circuit [12]. Each of the circuits
in fig. 2 employs one memory element (memristor), two other
passive and two active elements. The equations governing the
effective meminductive and memcapacitive behaviors are the