Memristor-Based Timing Circuit Şuayb Çagrı Yener
Reşat Mutlu
Department of Electrical and Electronics Engineering, Sakarya University, Sakarya, Turkey
[email protected]
Dept. of Electronics and Telecommunication Engineering, Namık Kemal University Çorlu, Tekirdağ, Turkey
[email protected]
Tuba Yener
H. Hakan Kuntman
Department of Metallurgy and Materials Engineering, Sakarya University, Sakarya, Turkey
[email protected]
Dept. of Electronics and Communication Engineering, Istanbul Technical University, Istanbul, Turkey
[email protected]
Abstract—Memristor has been proposed as the fourth missing fundamental circuit element in 1971. This new circuit element has a charge controlled resistance, saturation mechanism and zero-crossing hysteresis loop which cannot be mimicked by previously known circuit elements. It is a promising candidate for both digital and analog electric circuit applications. In this work, a memristor based timer circuit is proposed. Concept of the circuit is presented and its analysis is done. Simulation of the timer is done using the linear drift model of the TiO2 memristor and the result is compared to the analytical calculations. Keywords—Memristor; TiO2; timer; resistive switching;
I. INTRODUCTION Memristor has been claimed as a fundamental circuit element by Chua in 1971 [1]. Then, in 1976, he and his student Sung Mo Kang, generalized the concept of the memristor to a class of dynamical systems as memristive devices [2]. A memristive device behaving as a memristor at least for some part of its operation has been declared in 2008 [3]. This solid state realization was based on a TiO2 thin film containing doped and undoped regions between two metal contacts at nanometer scale [3]. The new circuit element is under consideration for both analog and digital circuit applications. Memristor has been researched in a number of applications like in terms of analog applications has already been studied for programmable gain amplifiers, programmable filters, integrators, oscillators, biomedical and chaotic systems [4]–[8]. A memristor can replace the functionality of resistor/transistor thanks to its switching capability. Resistive switching behavior has also been observed in different materials such as nickel oxide, zirconium oxide, zinc oxide, and titanium oxide. Several fabrications exhibiting memristor behavior have also been studied literature [9]–[12]. However, since no practically available commercial memristor exists yet, memristor models and physical implementations have great importance from the point of view real-world circuit design [13]–[17].
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In his seminal paper, Chua not having a memristor at that time has given an electrolytic cell (E-cell) as an example to a memristor and showed it can be used as a timer because of the fact that this cell switches its state at a certain charge value [1]. Therefore, timers may also be done with memristors or memristive systems reported in literature. In this letter, it is demonstrated that a timer can also be done with TiO2 memristor reported in literature [1]–[3]. II. THE TIO2 MEMRISTOR MODEL The linear dopant drift model of TiO2 memristor is commonly used in literature and also used in this study. TiO2 memristor model given in [2] is different than the E-cell model given in [1]. The charge dependent of TiO2 memristor memristance with linear dopant drift system is given as d R (1) ROFF 1 V 2ON q t dq D Where µV is mobility of vacancies in memristor, D is the length of the memristor, ROFF and RON correspond high and low resistances, respectively. Memristance function is also expressed as following M q
M q M 0 Kq q t
(2)
Where M0=ROFF is the maximum memristance and Kq is the charge coefficient. If memristor get saturated at q=qSAT, i.e. its memristance is defined by M SAT M 0 K q qSAT
(3)
III. TIMER CIRCUIT WITH MEMRISTOR In this study, a timer circuit shown in Fig. 1 is designed. The switches S1, S2, S3 and S4, can be either mechanically or electronically controllable. The memristor is placed in this circuit in a way that if the switches S1 and S2 are turned on, its memristance starts increasing. S3 and S4 are controlled to reset the memristor to the minimum memristor state. If S1 and S2 are turned on, the memristor current is
iS
VS VS RS M q RS M SAT K q q
M q M SAT K q
(4)
Where MSAT is the minimum memristor memristance and Kq is the memristor charge coefficient.
VS t RS
(9)
When Q is turned on: VS VS R2 t VS M SAT K q RS RS R1 R2 The turn-on time of Q, τ, can be found as V V
RS K qVS
(10)
R2 RS M SAT R R 2 1
(11)
RS2 RM R2 S SAT K qVS ( R1 R2 ) K qVS
Fig. 1. The memristor-based timer circuit.
If the resistor RS is chosen to be much greater than memristor memristance for all its operation (RS>>M(q)), it can be assumed that the memristor is fed with a constant current: VS (5) RS The Op-Amp in Fig. 1 is used as a comparator and also to drive the transistor Q. The positive and negative input voltages of the Op-Amp are iS
V iS M q
VS M SAT K q q RS
(6)
and
As can be seen from (11), τ is linearly dependent on R2 when R1+R2 is constant. With the memristor parameters D=10nm, µ=10-10cm2/Vs, MSAT=100Ω and M0=38kΩ, which are taken from [2], and choosing R1+R2=100kΩ, R2=2.08kΩ and RS=300kΩ, a timing value of τ=5s is obtained. The simulated waveforms are shown in Fig.s 2-4. The opamp output voltage is shown in Fig. 2. The memristance and the charge of the memristor are shown in Fig. 3. The memristor voltage and current are shown in Fig. 4. A timing value of τ=4.99s is obtained from simulation calculated from (11) with an error below 1%. As shown in Fig. 2, even though the timing pulse is obtained, the memristor voltage, current, memristance and charge continue varying until memristor gets saturated with the maximum memristance value as shown in Fig. 2-4. If the memristor is reset, the waveforms shown in Fig. 2-4 would repeat. For a working design, it must be provided that
R2 VSAT . (7) R1 R2 R1 and R2 are obtained using a potentiometer whose resistance is divided into R1 and R2. For V+V-, the output voltage is equal to the positive saturation voltage V+SAT=VSAT and the transistor Q is on. V- controlled by the resistance since R1+R2 is constant R2 defines the time when the Op-Amp output voltage takes its positive saturation voltage and transistor Q is turned on. Note that the resistors can be realized as active resistors employing MOS transistors which enables and simplifies IC realization phase.
M SAT R2 M0 M SAT RS R1 R2 M 0 RS
V
Transistor can drive a relay and the relay can be used to drive a load as shown in Fig.1. When a reset occurs, the memristor memristance and charge become equal to MSAT and qSAT respectively. In this case, its memristance is a linearly increasing function with respect to time since its current is assumed to be constant. If the timer is reset and then start running again at t=0; its charge and memristance are t
q t i d qSAT iS t 0
and
(8)
(12)
15 10
o
v (V)
5 0 -5 -10 -15 0
2
4
6 t (s)
Fig. 2. The output voltage of the timing circuit.
8
10
[4] 100
[5] 20
50
q M
q (µC)
Memristance (k)
40
[6]
[7] 0 0
5
10
15
20 t (s)
25
30
35
0 40
[8]
Fig. 3. The memristance and charge of the memristor with respect to time. [9] 0.15
3.4
0.1
3.2
v
vMem 0.05
0 0
3
5
10
15
20 t (s)
25
30
35
(µA) Mem
Mem
iMem
i
(V)
[10]
2.8 40
[11]
[12]
Fig. 4. Memristor voltage and current with respect to time. [13]
IV. CONCLUSION We have shown that a timer circuit can be done using a memristor. The idea is originated from Chua’s seminal paper. To validate the design, both analytical calculations and numerical simulations are done. Simulation results are in good agreement with the calculations. Using a memristor, a timer which can have timing values from milliseconds to days can be designed by choosing appropriate circuit parameters. To the best of our knowledge, DC applications of the memristors are limited with computer memories. This timing circuit application is a new one. REFERENCES [1] [2] [3]
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