Memristor Basics: Understanding the Memory Resistor

This page covers memristor basics, including its definition, analogy, and properties.

As we know, there are three fundamental two-terminal circuit elements: the resistor, capacitor, and inductor. These are defined in terms of the relationship between two circuit variables out of four: current (i), charge (q), voltage (v), and flux (φ).

• Current is defined as the time derivative of charge: $i = \frac{dq}{dt}$
• Voltage is defined as the time derivative of flux: $v = \frac{d\phi}{dt}$

Now let’s look at each of the basic elements:

• Resistor: Defined by the relationship between voltage and current: $dv = R \cdot di$
• Capacitor: Defined by the relationship between charge and voltage: $dq = C \cdot dV$
• Inductor: Defined by the relationship between flux and current: $d\phi = L \cdot di$

The element known as a memristor (short for memory resistor) provides a relationship between charge and flux: $d\phi = M \cdot dq$, where M is the memristance. Figure 1 (above) depicts the four basic circuit elements: resistor, capacitor, inductor, and memristor.

Memristor Definition

The term “memristor” refers to a passive device that provides a functional relationship between charge and flux. It’s defined as a circuit element where the flux (φ) between two terminals is a function of the amount of charge (q) passed through the device. It is not an energy storage element.

Figure 2 (above) depicts the symbol for a memristor.

The memristor is considered a charge-controlled device when the relationship between flux and charge is represented as a function of electric charge (q): $\phi = f(q)$.

Conversely, it’s known as a flux-controlled memristor when the relationship is expressed as a function of flux linkage: $q = f(\phi)$.

Memristor Properties

• Memristance: This is the key property of a memristor. The memristor’s resistance increases when charge flows in one direction and decreases when it flows in the opposite direction.
• Non-Volatility: When the applied voltage is switched off, the charge flow stops, and the memristor remembers its last resistance.
• State Retention: When the flow of charge is started again, the device will exhibit a resistance equal to the value it had when it was last active.
• Analogy: A resistor is analogous to a pipe through which water flows, while a memristor is like a special pipe whose diameter increases or decreases based on the direction of water flow through it.
• Dissipative Nature: As a memristor is purely dissipative, it acts like a resistor. The φ-q curve of a memristor is always a monotonically increasing function. This is illustrated in Figure 3 (above).