EK307 Lab: Thévenin Equivalent Circuits

EK307 Lab: Thévenin Equivalent Circuits Laboratory Goal: Learning Objectives: Suggested Tools:Reverse engineer a “mystery circuit”Parallel and series resistors, modeling, Thévenin equivalent circuit.Voltage source, multimeter, waveform generator, oscilloscopePre Lab Assignment:This is a design question:You are an electrical engineer working on a commercial product. The User interface (UI) group wouldlike you to add an LED to the front panel to indicate the power supply is on. The power supply engineersaid she can provide up to 24 mA from the 15 Volt power supply for the indicator. The manufacturingengineer said you have these values of resistors available: 2.2M Ohm 1/8 Watt, 100 Ohm, 1/4 Watt, 1000Ohm 1/8 Watt. Note; you do not have to use all the different resistor values. They are available to you ifyou need them. The manufacturing engineer also said you can use a maximum combination of any threeresistors and that the LED you must use has a terminal Voltage of 3 Volts at 20 mA. Design a circuit thatfits within the requirements of the UI, Power supply, manufacturing specs, and won’t go up in smoke. Forthe answer draw the schematic with the resistor values. Why might the manufacturing engineer care aboutlimiting the number and values of resistors used to implement this?Assignment (For Level 2: Complete BOTH Level 1 and 2 material):LEVEL 1:a) Build the circuit you designed for the prelab on your breadboard and test it: Instead of usingan LED for the load (a load is the device absorbing power and/or performing some type of work)we will use a resistor.** We can use a resistor as a ‘stand in’ for an LED or other types of passive devices where weknow the current and voltage relationship: We know the LED in the prelab will pass 20mA ofcurrent when 3 volts is applied across its terminals. Using Ohm’s law we can assume at theseoperating conditions that the equivalent resistance of the load (LED) is 3 V/0.02 A or 150 Ohms.This approximation is only valid when there are three volts across or 0.02 A through the LED.Likewise if we only knew some other operating point the computed resistance is only valid at thatpoint. The reason is because an LED is a nonlinear device. **b) Now that we have determined the equivalent resistance of the LED, get a 150 Ohm resistor fromthe cabinet by the door or make an equivalent one by series parallel connections of availableresistors.c) Insert the 150 Ohm resistor into your circuit.d) Measure the voltage across and current through the 150 Ohm resistor. Does the circuit perform asyou expect?9/28/2017

e) Calculate the Thevenin equivalent of the prelab circuit as ‘seen’ by the 150 Ohm resistor? This isthe prelab circuit without the 150 Ohm resistor (or LED) present. You may already have done thisstep while completing the prelab.f) Build the Thevenin equivalent circuit on your breadboard and attach the 150 Ohm load load toverify it works. For each circuit, the prelab and the Thevenin equivalent) the voltage and current ofthe 150 Ohm resistor should be the same (within circuit and instrument tolerances).g) Characterize the Thevenin equivalent of an unknown circuit: Obtain a four-terminal“Thévenin” box from your TA or from the parts counter. Connect the box to the power supply onby your lab bench using the connections shown below. The 6-V external voltage source is to beconsidered an integral part of the mystery box.** The behavior of your mystery box, as observed between terminals A and B, can be modeled by the“Thévenin Equivalent Circuit” shown below. If you were to build the simple network to the right withproperly chosen values of VTh and RTh, , it would behave in all respects exactly like the circuit insidethe mystery box. **h) Devise an experiment to determine the values of VTh and RTh for your mystery box.(Hint: Apply at least two different resistive test loads between A and B and measure the resultingdecrease in VAB. Plot these results on a current vs. voltage graph. Or use the open circuit voltage shortcircuit current method.END OF LEVEL 19/28/2017

LEVEL 2:a) Complete all the steps in Level 1b) Measure the Thevenin equivalent of the output of the function generator: In this section youwill be introduced to another test instrument, the waveform generator. The waveform generatorproduces various cyclical waveforms such as sine waves and square waves. The amplitude andfrequency are adjustable via the front panel controls.The waveform generator can be modeled by the Thévenin equivalent circuit shown in the figurebelow on the right.Your task is to devise an experiment to determine the values of VTh and RTh.Red signal output (node A)Black ground (node B)** The connector on the function generator is called a BNC connector. The inner pin is the signalwire, the metal case of the connector is the ground. When you plug a test lead into the functiongenerator both of these connections are made simultaneously. There are cables in the lab that havethe BNC connector on one end and alligator clips or terminals on the other end. The Red clip isthe signal line. The black clip is the ground line. **c) To get started:Turn on your waveform generator and set it to the following settings:a. Voltage: 3-V (peak to peak)b. Frequency: 100 Hzc. Waveform: Square wave, 50% duty cycled) As we saw in Level 1 and learned in class, there are multiple methods of finding the Theveninequivalent resistance. Since the output is AC, you can use the AC voltage measurement function9/28/2017

on the multimeter and/or the oscilloscope to make voltage and current measurements. We will useboth methods and show they are equivalent.e) Use the multimeter to find the short circuit current and open circuit voltage of the functiongenerator. With these values you can compute the Thevenin equivalent of the circuit.** The multimeter measures Root Mean Square Voltage (RMS) which is a method of measuringpower delivered into a load. You will learn about RMS in lecture. For now it is important to knowthat the RMS Voltage will be less than or equal to the peak to peak Voltage depending on thewaveform. For the purpose of this lab we are looking at relative changes in Voltage so if youignore the fact that the Voltage measurement is RMS it will not affect your answer. **f) Use two known test resistances and the oscilloscope to find the Thevenin equivalent of thefunction generator. The oscilloscope is a more sophisticated way to measure the Voltage output ofthe waveform generator. An oscilloscope measures voltage vs. time and displays it on a graph onits screen. The TAs will be glad to give you a brief introduction and help you set it up.g) Choose two resistors from the stock to use as your test resistors. Note that finding resistances thatare in the same order of magnitude as the Thevenin equivalent of your circuit will make themeasurements much more accurate. For this lab choose values in the 20 Ohm to 500 Ohm range.** The known test resistance method relies on adding known resistive loads across the output(node A and node B). When the load is added you will observe a drop in the output voltage. Whenyou add a known resistive load and measure the voltage you can also compute the current becauseyou know V and R. If you take at least two known load measurements you will have a two pointsin two dimensions. Remember from the LED lab when you made voltage vs. current plots of theLED? **h) Use your two test resistance voltage and current pairs and plot them on a sketched voltage vs.current (V-I plot) in your notebook. The above plot is an example V-I plot.9/28/2017

i) Find the slope of the line. The Thevenin equivalent resistance is compute by taking the negativereciprocal of the slope. Do the two methods of finding the Thevenin resistance produce the sameresult?j) Using the V-I plot, estimate the open circuit voltage and short circuit current. Compare these toyour multimeter measurements. Are they the same?END OF LEVEL 2!BackgroundResistor CombinationsResistors connected in series can be modeled as a single resistor having a value equal to the sum of theindividual resistors. Hence if R1, R2, and R3 are connected serially, they can be thought of as just oneresistor of value REQ R1 R2 R3:R1R2REQR3REQ R1 R2 R3Resistors connected in parallel sum together according to their conductances. Remember that theconductance G of a resistor, measured in siemens, is equal to the reciprocal of its resistance: G 1/R Thus,if RA, RB, and RC are connected in parallel, their total conductance will be GEQ GA GB GC. Theequivalent resistance of the parallel combination will be REQ 1/GEQ, orRARBREQRCREQ 1111 R A RB RCNote that for the case of just two resistors in parallel, the above formula simplifies to the familiar “parallelresistor” formula:R RREQ A BRA RB9/28/2017

About Resistor Tolerance:Remember that the actual value of a 5%-tolerance resistor may vary by as much as 5% of its nominalvalue. Thus, a 10-k resistor could have a value as high as10 k (0.05)(10 k ) 10.5 k or as low as10 k (0.05)(10 k ) 9.5 k As a result, two 10-k resistors connected in series may have a value as high as 2 10.5 k 21 k oras low as 2 9.5 k 19 k . Similarly, two 10-k resistors in parallel may have an equivalent value ashigh as 5.25 k or as low as 4.75 k .9/28/2017

Thévenin EquivalenceWe will learn a lot about the Thévenin equivalent circuit this semester, as it is one of the more importanttheorems in linear circuit theory. Leon Thévenin was a French telegraph engineer in the late 1800’s towhom the theorem is attributed. Thévenin’s theorem states that the behavior of a linear circuit as seenfrom any two nodes of the circuit (considered as “terminals”) can be represented by an equivalent circuitcomprising a voltage source and a resistance, as shown in Figure 2. A resistive circuit is considered linearif is made only from voltage sources, current sources, and resistors.One parameter of a linear resistive circuit that is easily measured is its open circuit voltage, that is, thevalue of vX when iX 0. Another might be the short circuit current, that is, the current iX that flows whenvX 0. These two quantities are, in fact, the axes intercepts in the plot shown below.Any twonodes1LinearResistiveNetwork2vXiXVTh vXVThRThiXThe behavior of a Thévenin circuit can be described by the equation: vX VTh iX RTh9/28/2017

9/28/2017 EK307 Lab: Thévenin Equivalent Circuits Laboratory Goal: Reverse engineer a “mystery circuit” Learning Objectives: Parallel and series resistors, modeling, Thévenin equivalent circuit. Suggested Tools: Voltage source, multimeter, waveform generator, oscilloscope Pre Lab Assignment: This is a design question: