Lab Report: Thévenin Equivalent Circuit Theorem and Superposition Principal, Schemes and Mind Maps of Kinesiology

Download Lab Report: Thévenin Equivalent Circuit Theorem and Superposition Principal and more Schemes and Mind Maps Kinesiology in PDF only on Docsity! Superposition and Equivalent Circuits [5pts for header, and formatting] Author: Evelyn Helms Section: 018 Date: 3/4/2022 Abstract [5 pts] In this lab, we focused on two main ideas for simplifying complicated circuits: the Thévenin equivalent circuit theorem and the superposition principal. The Thévenin and Norton equivalent theorems can take a complicated, messy circuit and simplify them to a single source and resistor. The Thévenin theorem states that a particular node in a linear circuit has an equivalent circuit that contains only one independent voltage source in series with a resistor. The source is written as Voc and the resistor is written as Rth. This theorem is used in the second task of the experiment to simplify the circuit given and to find the beginning resistance and voltage values. The Norton theorem is very similar but states that the equivalent circuit will contain one independent current source parallel with one resistor. The source is written as Isc and the resistor is written as Rn (which is equivalent to Rth). The superposition principal also can be used to reduce the complexity of a circuit. This principal states that for linear systems with multiple inputs, the output is a linear combination of the responses due to each input using the additivity and scalability properties. In task three, we used SPICE to simulate and support the superposition principal using a given circuit with multiple inputs and a single output. In task one of the experiment, we used a voltage buffer to measure the effects of a loading. A voltage buffer mitigates the loading caused by a large source resistance by transforming the source resistance of the function generator to a smaller one. A buffer provides multiple benefits, such as a low output resistance derived from external power, a large input resistance (sometimes not easily measured), and a voltage gain of one where the input signal equals the output. 1. Objectives [10 pts] The overall objective of this experiment is to utilize the Thévenin equivalent theorem and to support the superposition principal through a simulation. 1.1. Loading with a Real Signal The objective of this task is to use a voltage buffer to measure the effects of loading on a circuit. After measuring the RMS voltage across a speaker without the buffer, we need to measure the RMS voltage with the buffer and compare the two results. 1.2. Thévenin Equivalent Circuit Design The objective of this task is to design a given circuit with a two-terminal network to have a specific Thévenin equivalent voltage and resistance. 1.3. Simulate the Superposition Principal with SPICE The objective of this task is to create a SPICE simulation to verify the superposition principal by comparing these results with previous prelab results. 2. Theory [20 pts] The two main theories used in this experiment are the Thévenin equivalent circuit theorem and the superposition principal, both which are used to simplify complex circuits. The Thévenin theorem states that a particular node in a linear circuit has an equivalent circuit that contains only one independent voltage source in series with a resistor. The source is written as Voc and the resistor is written as Rth. Figure 1 is the Thévenin equivalent circuit model that circuits are simplified down to after use of the theorem. Rth is equal to the equivalent resistance of a given complex circuit, so when simplifying the circuit, Req must be found. When a circuit has two parallel resistors, Equation 1 can be used to find the equivalent resistance. 3.2. Thévenin Equivalent Circuit Design This task of the experiment asked us to design a given circuit to have a Thévenin equivalent voltage of 2.5 V and resistance of 1.5 kΩ. As seen by the circuit from Figure 4, we had to find Vs, R1, R2, and R3. We found these values by reversing the superposition principal to make a circuit that would have these Thévenin equivalent values. Figure 4: Given Circuit to Design from its Thévenin Equivalent After finding the values, we had to build the circuit and test these values. We used the power supply with a current limit of .5 A and a set voltage of our found Vs value in order to measure the equivalent voltage and resistance of the Thévenin equivalent. 3.3. Simulate the Superposition Principal with SPICE This final task of the experiment asks us to create a SPICE simulation for the circuit in Figure 5 and then plot the individual Vout responses as well as the output waveform for all three inputs together. In order to plot each voltage input separately, we ground the voltage sources we are not focused on, plotting only the one source we want. Figure 5: Circuit for Observing the Superposition Principal 4. Results [30 pts] 4.1. Loading with a Real Signal Before the buffer is connected, the voltage across the speaker is lower than calculated (seen in Table 1), and the sound is quite soft. After the buffer is connected, the measured voltages are much more accurate (seen in Table 2), and the sound is much louder than without the buffer. Measured RMS (V) Calculated RMS (V) Percent Error (%) .1362 .1768 22.96 % Table 1: RMS Voltages Across Speaker Before Buffer Measuring Position Measured RMS (V) Calculated RMS (V) Percent Error (%) Across Speaker .1594 .1768 9.84% Input of Buffer .1769 .1768 .057% Table 2: RMS Voltages with Buffer Figure 6: Estimating the Thévenin Equivalent Resistance of the Buffer Output 4.2. Thévenin Equivalent Circuit Design We designed a circuit to have a Thévenin equivalent voltage of 2.5 V and resistance of 1.5 kΩ. After the calculations seen in Figure 7, we found all three resistances to be 1kΩ and Vs to be 5 V. We then built the designed circuit and measured Req and Voc. Figure 7: Calculations Using Thévenin Equivalent Given Values Measured Given Percent Error (%) Req (kΩ) 1.496 1.5 .267% Voc (V) 2.4911 2.5 .356% Table 3: Measured vs Given Thévenin Equivalent Values 4.3. Simulate the Superposition Principal with SPICE We used SPICE to simulate the circuit from Figure 5 and then plotted each individual Vout response from each inputted voltage separately. To do this, we grounded the two sources we were not plotting while plotting a single response. Then we turned all of the sources on to graph Vout with all inputs on simultaneously. The plots are very similar to the prelab results, which proves that these are consistent with the superposition principal. Figure 8: Superposition Circuit With Values Figure 9: V1 Plot Using DC Voltage of 2.25 V