ECE 231 Laboratory Exercise 4 Thévenin and Norton Theorems, Study notes of Law

Download ECE 231 Laboratory Exercise 4 Thévenin and Norton Theorems and more Study notes Law in PDF only on Docsity! ECE 231 Laboratory 4 Thévenin and Norton Theorems 1 R. Frank Smith, Cal Poly Pomona University, 2016 ECE 231 Laboratory Exercise 4 Thévenin and Norton Theorems Laboratory Group (Names) _______________ ______________ _______________ OBJECTIVES  Learn various ways to measure Thévenin's voltage and resistance.  Validate the maximum power theorem. BACKGROUND Thévenin's theorem (1883) states that any linear circuit can be replaced by a single voltage source and a single series resistance. In 1926 Norton’s Theorem was shown to be equal to Thévenin’s Theorem, see Figure 1. You might wonder why the 57 year delay between the theorems. Batteries were easy to construct and incorporate into a circuit. No one knew how to make a good constant current source. We do not have current sources available in the lab to verify Norton's theorem, but it can be calculated using Ohm’s Law. Constructing constant current sources is beyond the scope of this course. Thévenin's Voltage Source Thévenin's Resistance Vout Norton Current Source Thévenin's Resistance Vout = Figure 1. Thévenin's and Norton’s equivalent circuits for a Linear Circuit Procedure for Finding the Thèvenin Equivalent Circuit Mathematically A. Circuits with independent sources only. No Dependent sources. Step 1. Find R Thèvenin 1. Deactivate all of the independent sources by shorting all batteries or DC supplies and opening all current sources. 2. The equivalent resistance between the terminals for which you would like to know the Thèvenin resistance is found by combining all of the resisters into one equivalent resistance between the appropriate terminals. These are usually designated “a” and “b.” ECE 231 Laboratory 4 Thévenin and Norton Theorems 2 R. Frank Smith, Cal Poly Pomona University, 2016 3. A load resistor which is equivalent to the Thèvenin resistance will result in maximum power being dissipated in the load resistor and of ½ the input voltage will be across the load. 2 maximum 4 th th V Power R  Step 2. Find V Thèvenin between terminals “a” and “b.” 1. Use the original circuit and nodal analysis to find the voltage between terminals "a" and "b." B. Circuits with independent and dependent sources. Step 1. Find R Thèvenin 1. Deactivate all of the independent sources by shorting all batteries or DC supplies and opening all current sources. 2. Connect a 1 amp your current source between terminals "a" and "b." 3. Find the voltage between terminals "a" and "b” using nodal analysis. This voltage will be the Thèvenin resistance by the use of Ohm's law. Resistance 1 ab ab Thevenin VVoltage R R Current     Step 2. Find V Thèvenin between terminals “a” and “b.” 1. Use the original circuit and nodal analysis to find the voltage between terminals "a" and "b." C. Circuits with dependent sources only. No independent sources. These circuits cannot output any power as such they reduce to a Thèvenin resistance only. Step 1. Find R Thèvenin 1. Connect a 1 amp your current source between terminals "a" and "b." 2. Find the voltage between terminals "a" and "b.” This voltage will be the Thèvenin resistance by the use of Ohm's law. ECE 231 Laboratory 4 Thévenin and Norton Theorems 5 R. Frank Smith, Cal Poly Pomona University, 2016 Table 1. Measured and calculated data. 1 2 3 4 5 6 7 8 RThevenin Measured with sources removed (shorted) RThevenin Calculated 1 with sources removed % Error between measured and calculated RThevenin Calculated 2 using Ohm’s Law and Rload % Difference between calculated 1 and calculated 2 Vab Measured Vab Calculated % Error Thévenin voltage measured and calculated Part 2 1. Now construct the network shown in Figure 2, but replace Rload with a potentiometer connected between “a” and “b.” The equivalent circuit is shown in Figure 3. We will now determine rthevenin using the potentiometer. 2. Measure the voltage between “a” and “b” as the potentiometer is adjusted. 3. Adjust the potentiometer wiper until the voltmeter reads VThevenin/2 NOT Vsource/2. The potentiometer is now set at the maximum power load which is equal to rthevenin 4. Calculate the maximum power delivered to the load using equation (2). 5. Measure the value of the potentiometer and determine how close it is to the value of rthevenin determined above. 𝑀𝑎𝑥𝑖𝑚𝑢𝑚 𝑝𝑜𝑤𝑒𝑟 = ( 𝑉𝑇ℎ𝑒𝑣𝑒𝑛𝑖𝑛 2 ) 2 𝑅𝑙𝑜𝑎𝑑 = 𝑉𝑎𝑏 2 𝑅𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟 (2) Figure 3. Maximum power network. 6. Now prove that this is the load for maximum power. Prove it by measuring the voltage Vab across the potentiometer after the potentiometer is rotated 1 turn CW. Then measure the potentiometer resistance at this position. Calculate the power delivered to the potentiometer using equation (3). 0 Rload 0 V1 V Potentiometer Wiper Thevenin V1 Thevenin VRload Thevenin Thevenin R R ECE 231 Laboratory 4 Thévenin and Norton Theorems 6 R. Frank Smith, Cal Poly Pomona University, 2016 𝑝𝑜𝑤𝑒𝑟 = (𝑣𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟) 2 𝑅𝑝𝑜𝑡𝑒𝑛𝑡𝑖𝑜𝑚𝑒𝑡𝑒𝑟 (3) 7. Repeat step 4, but this time rotate the potentiometer 2 turns CCW (1 turn to get back to the maximum power resistance then one additional turn). Calculate the power delivered to the potentiometer using equation (3). Compare results. P1 turn CW= __________ Pmax= _________ P2turns CCW= ___________ This value must be less than Pmax This value must be less than Pmax Conclusion _____________________________________________________________ _____________________________________________________________ _____________________________________________________________