Lab 2 Updated

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Gwinnett Technical College *

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123

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Electrical Engineering

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Apr 3, 2024

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Linear and Non-Linear Devices Introduction n this lab, three different circuit components will be evaluated: a basic resistor, a light bulb, and a light- emitting diode (LED). Load line analysis and graphical representations are used to analyze these devices. Theoretical values and measured values are compared, showing that the theory learned in class supports the measurements taken in the lab setting. The previously mentioned circuit components fall into two different categories referred to as linear and non-linear devices . A linear device is defined as a device in which the input into the device (such as voltage) is linearly related to the output of the device (such as current). As one would expect, a non-linear device has a non-linear relationship between input and output. Understanding the difference between linear and non-linear devices is essential to thoroughly understanding this lab. Background and Theory Comparing the voltage-current relationship given by Ohm’s Law to the basic form of a linear equation ( 𝑦𝑦 = 𝑚𝑚𝑚𝑚 + 𝑏𝑏 ) yields 𝑽𝑽 = 𝑰𝑰𝑰𝑰 → 𝑰𝑰 = 𝟏𝟏 𝑰𝑰 ∙ 𝑽𝑽 ∴ 𝒎𝒎 = 𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔𝒔 = 𝟏𝟏 𝑰𝑰 This linear relationship between the applied voltage and the current across a resistor is why a resistor is known as a linear device . Figure 1 shows a plot of current (I) vs. applied voltage (V). In contrast with the resistor, the light bulb used in the second section of this lab does not have a set resistance. The resistance of the bulb, more specifically the resistance of the bulb’s filament, is a function of its temperature. As a result a light bulb is known as a non-linear device . An LED or light-emitting diode is also a non-linear device . LEDs are electric light sources that operate differently from a standard light bulb. They have a non-linear relationship between I Figure 1: Linearity (Ohm's Law)

voltage and current given by an exponential function that will not be discussed in this lab. The idea is to gain a basic understanding of the component. Load line analysis is a graphical concept that is used in the analysis of non-linear devices experiencing a direct current. Initially, a non-linear device is analyzed in a given circuit, varying the source voltage and measuring the corresponding voltage across and current through the non- linear device. From these measurements, current through the non-linear device vs. voltage across the device is plotted. The non-linear device is now placed in series with a linear device (as in Figure 3) in the same circuit used previously. This circuit is analyzed using KVL, resulting in the load line equation . The load line equation gives a relationship between the source voltage, the voltage across the resistor (linear device) and the voltage across the non-linear device (in this case, a light bulb or LED) at some location that is yet to be determined. By applying two boundary conditions, (1) when the voltage across the non-linear device is zero and (2) when the current through the non-linear device is zero, and solving for the corresponding voltage across or current through the non-linear device yields two sets of voltages and their corresponding current values. The two sets of data are plotted as two points on the graph formed from the analysis of the non-linear device alone (see circuit shown in Figure 4) and are connected by a straight line referred to as the load line . The intersection of the load line and the original data points plotted from Figure 4 (as shown in the example Graph below) form the operating point . The operating point is the location where the responses from the nonlinear device alone are equal to that of the responses from the combination of the linear and non-linear device. Figure 3: Load Line Circuit (1) Figure 4: Load Line Circuit (2)

Example 1: Load Line Analysis Example Graph 1: Load Line Analysis The plot above denoted by the blue diamonds is obtained by measurements taken from the circuit shown in Figure 4. Applying Kirchhoff’s Voltage Law to the circuit shown in Figure 3 yields the following 𝑽𝑽 𝒔𝒔 = 𝑰𝑰𝑰𝑰 + 𝑽𝑽 𝑵𝑵𝑵𝑵𝑵𝑵 Using the boundary conditions of 𝑰𝑰 = 𝟎𝟎 → 𝑽𝑽 𝑵𝑵𝑵𝑵𝑵𝑵 = 𝑽𝑽 𝒔𝒔 and 𝑽𝑽 𝑵𝑵𝑵𝑵𝑵𝑵 = 𝟎𝟎 → 𝑰𝑰 = 𝑽𝑽 𝒔𝒔 𝑰𝑰 This analysis yields the points ( 𝑽𝑽 𝒔𝒔 , 𝟎𝟎 )& �𝟎𝟎 , 𝑽𝑽 𝒔𝒔 𝑰𝑰 � These points are plotted as squares and connected by the red line. This line is referred to as the Load Line . The location where the original plot intersects the load line is called the operating point . At the operating point, the response from the circuit containing both a non-linear and linear device is the same as the response from the circuit containing only the non-linear device. The above analysis implies that in both circuit configurations the non-linear device has a current of approximately 12 mA when a voltage of 10.5 V is applied to it. 0 5 10 15 20 25 0 5 10 15 20 25 Current (mA) Voltage (non-linear device) (V) Load Line Analysis Non-Linear Device Operating Line

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