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Electronics I Laboratory Manual

I-V Characteristics

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)

whereID and VDare 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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