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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Experiment and Procedure Figure 5: 1. Assemble the circuit as shown in Figure 5. 2. Measure the resistor R1 using the DMM and record its value. 3. Vary the power supply from 0 V to +20.0 V in increments of 2 Volt and record the corresponding values of V R and I R in the closed circuit. (Values corresponding to the resistor. V R = voltage across the resistor) 4. Plot the data as an I R vs. V R graph.(slope =1/R) 5. Determine the slope and calculate the resistance. 6. Compare the resistance obtained in step 5 with the measured value in step 2, and calculate the percent error. Now write the Load Line Equation (equation for the loop) for the circuit below by applying Kirchhoff’s Voltage Law. Note that this is purely a mathematical problem. Figure 7: Load line analysis circuit 7. Use this equation to determine two points to develop your load line analysis. Label them A and B. C I R C U I T 1

8. Plot A B points on the I-V curve you made in circuit 1 of the lamp and connect A and B point (which will be a line across the curve). Find the intersection point of the line and the curve. label it Q1 (Operating Point). Now we will repeat these steps for the Light Emitting Diode. Assemble the circuit as show below to develop the characteristic curve of the diode: Figure 9 1. Vary the power supply from 0V to 10V with increments of 1V. Record the values of V Diode and I Diode in each case. 2. Record the voltage across the diode when it first lights up. 3. Plot I Diode vs V Diode . Now write the Load Line Equation (equation for the loop) for the circuit below. This circuit, like Circuit 3, is purely mathematical and does not need to be constructed. Figure 10: Load line analysis circuit 4. Use this equation to determine two points to develop your load line. Label them C and D. 5. Plot C D points on the I-V curve you made in circuit 2 of the LED and connect C and D point (which will be a line across the curve). Find the intersection point of the line and the curve. label it Q2 (Operating Point). C I R C U I T 2

6. Record the value of I and V, which are the coordinates of Q2. (through the circuit and across the LED) 7. Find the percent error between the actual values you measured in step 1 and the theoretical values for Q2. 8. What happens to the voltage drop across the LED if the resistor value is changed? How does it affect the current in the circuit?

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Online Lab Instruction 1. Create an Account: o Go to the TinkerCad website ( https://www.tinkercad.com/ ). o Click on "Sign Up" to create a new account. o Select “Create Personal Account” → “Sign up with Email”. o Be sure select your age older than 18, otherwise it will ask you for parent approval. o Verify your email address by clicking the confirmation link sent to your email. 2. Access Circuits: o After verifying your email, log in to your TinkerCad account with your email and password.

o Once logged in, you'll be on your TinkerCad dashboard. Click on the "+ New Design" tab at the top right corner of right corner of your profile. Click on the “Circuit”. o Then select “All” electric component, you now can drag and drop the electric components. o In lab 2 we are going to use ONLY Resistor, LED, Power Supply, Multimeter. Please do NOT use Bread board component on TinkerCad for Circuit 1 and Circuit 2, as it will not output the correct amperage. 3. When plotting the I-V Characteristic Curve for Circuit 1 and Circuit 2, be sure your power supply current stays at 0.01 (A).