Lab 3 Thevenin Equivalent Circuit2022

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Jan 9, 2024

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Lab 3: Thevenin equivalent circuits Instructions: Fill out these first few pages following the procedure starting on page 5 1. ( Paper calculation - to be done before lab.) Determine how to analytically compute the input resistance from the measurements made in Section 4.3. To do this, imagine that the circuit under test (the inverting op amp circuit in this case) is replaced by a resistor equal to it input resistance: i.e., the op amp circuit on the left below is analyzed as the circuit on the right, where R in is the input resistance of the op amp circuit. Knowing V test , R test , and V in you can find an expression for the input resistance R in . 1. Equation for R in : Vtest (Rin/(Rin + Rtest)) = Vin (VTest - Rin) / (Rin +Rtest) Vtest - Rin = Vin(Rin + RTest) Rin(Vtest - Vin) = Vin + Rtest Rin(Vtest - Vin) = Vin + Rtest Name: Lishuo Liu ________________

R in = (Vin + Rtest)/ (Vtest - Vin) 2. (Experimental determination of Thevenin equivalent circuit) Build the circuit shown below on your breadboard, omitting the resistor R. (When making the measurements of voltage, follow the instructions below. Best practices in making measurements is to have all the grounds connected together – multimeter, scope, and power supply.) a) Measure the voltage at point a) with the multimeter. .922 V b) Measure the voltage at point b) with the multimeter. 9.145 V c) Subract b) from a). The result is the open circuit voltage Voc=Vth. .922 - 9.145 = -8.223 Pick a resistor from the stock in the lab between 500  and 20K  . Put it into the circuit as above. d) Use the method above to measure Vtest=Vab across the known resistor R. Vab = 2.238 = Vtest

e) Use equation (2) to find Rth. Rth = -3198.519 f) Fill in your values for the complete Thevenin equivalent of the circuit below. 1. -8.21/1.006 = 8.161 Voc = 8.21 Rth = 3.2 K  3. (Verification of Thevenin equivalent circuit) The purpose of the next part of the lab is to verify that Thevenin equivalent circuit is equivalent to the original circuit. a) Wire up the Thevenin equivalent circuit on your breadboard. Combine as best you can the resistors available to achieve Rth. b) Move the resistor R from the original circuit to the Thevenin equivalent circuit you just wired,

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c) Measure the voltage across R in the Thevenin equivalent circuit, and compare it to the voltage in the original circuit) d) Comment on the accuracy of the Thevenin equivalent circuit. How could it be made more accurate? Vr (original circuit) = ___ 8.0 Vr (Thevenin equivalent circuit)= _____8.6_________ % Error (V Roriginal circuit/V RThevein equivalent circuit ) *100= ___7.5%___________ Comment on accuracy:

4. (Measuring Input Resistance of an amplifier circuit) The purpose is to learn how to experimentally determine the input impedance of an active circuit. Wire up the op- amp circuit shown below using 2 10K resistors for R1 and R2 (gain of about -1). a) Choose an R test with a value of 1 kΩ and set the 6V source to a voltage of 1V for Vtest and connect them as shown below . Record the value of Vin. Use your pre-lab results to compute the input resistance of this circuit. b). Power down the circuit and replace R 1 in the op amp circuit with a 1kΩ resistor; then re-apply power to the circuit c). Repeat Step 3. You have now measured R in of the inverting op amp circuit for two different values of R 1 . From these measurements, formulate a general rule for expressing the input resistance of the inverting op amp configuration. R in (R1=10K)= ______10Kohm_____________ R in (R1=1K)= _______1K ohm__________ R in (in terms of R1)=_______R1__________ If you wish to connect this amplifier to an arbitrary signal, what should the output resistance of that signal be for no reflection from the amplifier? R out = ________Rin___________________

Lab 3: Thevenin Equivalent Circuits - Instructions 1. Purpose The purpose of this lab is to learn how to obtain a Thevenin Equivalent circuit by making measurements of the I-V (current-voltage) characteristics at a pair of terminals. 2. Introduction Any linear DC circuit as seen at a pair of terminals can be modeled as an ideal voltage source in series with a resistor as shown in Error: Reference source not found. Figure 1: The idea of Thevenin equivalent circuit. The linear circuit on the left can be modeled by the simple ideal voltage source and ideal resistor connection shown on the right. Figure 1: Thevenin Equivalent Circuit In order to obtain the Thevenin Equivalent circuit, two quantities must be calculated or measured: • v oc : The open circuit voltage drop from terminals a to b and • i sc : The short circuit current from terminals a to b. Once the values for v oc and i sc have been obtained, the Thevenin resistance R Th can be determined from the relation R Th = V oc I sc (1) The problem with using this method in practice is that you might damage the circuit by shorting its output terminals together. So we often need a different method to measure R Th in the lab. Here are two practical methods. R Th Method #1 : If the circuit contains no dependent sources , then R Th may also be found by turning off all of the independent sources and using resistance reduction rules to determine the resistance between terminals ab; however, this method assumes that you have access to the internal sources of a circuit, which you might not. This method is primarily an analytic one… i.e., you work it out on paper. R Th Method #2 : Connect a known test resistance across terminals ab. Measure the voltage across the test resistance, call it V test . Then, referring to Error: Reference source not found, we can see that V test will behave according to V test = [ R test R test + R Th ] V oc (2) Thus, having accurately measured V oc , R test , and V test , you can then calculate the value of R Th .

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Figure 2: Using a known test resistor to measure R TH The Thevenin idea is used to simplify the analysis of how some “driving” circuit interacts with a variety of loads. Once you have determined the Thevenin equivalent circuit you can use it to analyze the effect of a load resistance being placed across terminals ab. However, many times it isn’t simply a resistor that is placed across terminals ab but rather some other circuit as shown in Error: Reference source not found. Figure 3: Two linear circuits connected. Suppose that circuit #1 is to be viewed as supplying a voltage to Circuit #2; that is Circuit #1 is the driving circuit and Circuit #2 is the driven circuit (the loading circuit). To analyze this case we use a concept closely related to Thevenin Equivalent circuits: the idea of input resistance of a circuit being driven as the load. In that case we wish to model the entire “driven” circuit as a simple resistive load and also model the driving circuit with its Thevenin equivalent circuit. Technically, we should model the driven circuit using a complete Thevenin equivalent circuit (V OC and R TH ) to account for any sources inside the driven circuit. However, many times the driven circuit is known to not have any sources… then we can model the driven circuit just as shown in Error: Reference source not found. Figure 4: Modeling a driving circuit with its Thevenin equivalent and modeling a driven circuit with its equivalent input resistance. In this lab, we will do both things! a) Experimentally determine a Thevenin equivalent circuit through measurements! b) Experimentally find the input impedance of an op-amp amplifier circuit.