Most of us have heard of resistors, varistors, thermistors and so on….There are so many ‘ISTORS’ to bug our minds. Here’s one more its called a MEMRISTOR, anyway it’s a really cool thing.
We all have heard of resistors which vary with many physical factors like temperature (anyway all resistors vary with temperature) , force ,pressure , voltage and so on.
MEMRISTOR somehow stands apart from all of these.
What is a MEMRISTOR??
It is the consolidation of two words namely, MEMORY and RESISTOR. As the name suggests its resistance (dV/dI) depends on the charge that HAD flowed through the circuit. When current flows in one direction the resistance increases, in contrast when the current flows in opposite direction the resistance decreases. However resistance cannot go below zero. When the current is stopped the resistance remains in the value that it had earlier.
To put it in other words MEMRISTOR’S resistance depends on the integral of the input applied to the terminals rather than the instantaneous values like say in a varistor.
To consolidate we can say that the MEMRISTOR “REMEMBERS” the current that had last flowed through it.
How to represent a MEMRISTOR??, i.e., the circuit symbol
Here is how we represent a MEMRISTOR:
How to describe the MEMRISTOR mathematically??
Let’s now define the memristor a bit mathematically:
It maintains a functional relationship between ∫Idt (called Charge) and ∫Vdt (called Flux).
The slope of this function is called as Memresistance M (similar to resistance R). Memristor is similar to R,L and C being that it is a passive device but R,L and C can however be considered under LTI theory, memristors have a non – linear characteristic/function and may be described by a variety of functions of net charge. . There is no such thing as a standard memristor. Instead, each device implements a particular function, wherein the integral of voltage determines the integral of current, and vice versa. A linear time-invariant memristor is simply a conventional resistor.Other scientists had already proposed fixed nonlinear flux-charge relationships, but Chua's theory introduced generality.
Like other two-terminal components (e.g., resistor, capacitor, inductor), real-world devices are never purely memristors ("ideal memristor"), but will also exhibit some amount of capacitance, resistance, and inductance. Note however that a "memristor" with constant M and a resistor with constant R (i.e. not a varistor) are the same thing.
How to consolidate MEMRISTOR as a mathematical equation??
Or
What are the V- I characteristics of a MEMRISTOR??
A little more mathematical equations now…
Resistance, R = dV/dI Ohm
Capacitance, C = dQ/dV Farad
Inductance, L = dΦm / dI Henry
Memresitance, M = dΦm / dQ Ohm
where Q is defined by I = dQ/dt, and Φm is defined by V = dΦm/dt. Note that the above table covers all meaningful ratios of I, Q, Φm, and V. No device can relate I to Q, or Φm to V, because I is the derivative of Q and Φm is the integral of V.
Hence M(q) = dΦm / dQ
i.e., M( q(t) ) = (dΦm /dt)/ (dQ/dt)
Hence M( q(t) ) = V(t)/I(t)
The power equation is,
P(t) = V(t)I(t) = I2(t)M(q(t))
After all these, the final question one is bound to ask is,
There are also MEMCAPACITORS and MEMINDUCTORS whose properties depend on the state and history of the system.
What are the applications of a MEMRISTOR??
Non-volatile memory applications: Memristors can retain memory states, and data, in power-off modes. Non-volatile random access memory, or NVRAM is the first application that comes to mind when we hear about memristors. There are already 3nm Memristors in fabrication now.
Low-power and remote sensing applications: Coupled with memcapacitors and meminductors, the complementary circuits to the memristor which allow for the storage of charge, memristors can possibly allow for nano-scale low power memory and distributed state storage, as a further extension of NVRAM capabilities. These are currently all hypothetical in terms of time to market.
Programmable Logic and Signal Processing, and a variety of Control System memristor patents are out there, waiting for the microchips to fall where they may. The memristive applications in these areas will remain relatively the same, because it will only be a change in the underlying physical architecture, allowing their capabilities to expand, however, to the point where their applications will most likely be unrecognizable as related.
There are many more applications but for now all these are hypothetical so I have mentioned only a few above.