The I–V characteristics – also known as the characteristics – of an electronic device is the relationship between its voltage and its current. There are two ways to express this relationship: by means of an equation or by means of a graph. For example, the I–V characteristics of a resistor is the equation that expresses Ohm’s Law for the resistor, or

| | (2.1) |

where *V* is the voltage applied to the resistor, *R* is its resistance value, and *I* is the current through the resistor. Notice that for any voltage applied to the resistor there is a current associated with it and, vice-versa, for any current through the resistor there is a corresponding voltage. This relationship is the only fact we need to know in order to completely understand the *behavior* of the resistor. This is the reason why we call Eq. 2.1 the **characteristics **of the device.

Another way to represent the I-V characteristics is by means of a graph of the characteristics equation. In particular, for resistors and some other devices the plot of *I* vs. *V* will always be a straight line through the origin. This should be clear to the reader from the fact that Eq. 2.1 is the equation of a straight line.

**Type of Devices**

Based on the form of the characteristic equation the electronic devices can be divided into two broad classes according to the following definitions:

**Definition 2.1 Linear Devices** *The characteristic equation of a *__linear device__ is expressed by means of a linear equation^{[1]}*. ** This means that both the current and the voltage are *directly proportions* to each other. An example of this is Eq. 2.1 for a resistor. The characteristic curve of a resistor is a straight line.*

**Definition 2.2 Non-linear Devices** *For these devices the characteristic equation is a non-linear equation. This means that either the voltage (V) or the current *(*I*) - *or both in some cases - appear in the equation with an exponent not equal to one or they may be an argument of a non-linear function. Or, in mathematical terms, the current and the voltage are not directly proportional to each other. The plot of such an equation will not produce a straight line. An example of these type of devices is the diode. The diode characteristic equation is expressed as*

| | (2.2) |

*where**I*_{D} and V_{D}*are the diode current and diode voltage respectively, e is the natural log base (e = 2.718282), and the other symbols are constants. *

As you can see in the above equation, the current is a function of an exponential with an exponent which is a function of the voltage.

Figure 2.1(a) represents the characteristic curve of a linear device (a resistor with a resistance value of 2 KΩ and Figure 2.1(b) is an example of a non-linear device (a diode).

One important feature of a linear device is the fact that its resistance is the same *at any voltage* (or current). The resistance of such a device can be calculated by taking two points in its characteristics and finding the inverse of the slope of the line connecting these two points. In other words

Then,

or,

| | (2.3) |

For a non-linear device – like the diode shown in Fig. 2.1(b) – the resistance is different at different points in its curve. In other words, we can state that a linear device is a device with a constant resistance; whereas in a non-linear device, the resistance changes from point to point in its characteristics. As an exercise^{[2]}, the reader should prove these statements by taking several points in both characteristics shown in Fig. 2.1 and calculating the resistances at these points.

^{[1]} A linear equation is an equation where both the *independent *and the *dependent *variables appear as a linear combination of each other. This implies that the graph of the equation will be a straight line.

^{[2]} But for God’s sake, do it!

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