ECE210 - Lab 3 - LTSpice and Nodal analysis

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University of Massachusetts, Amherst *

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210

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Electrical Engineering

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Jan 9, 2024

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UMass ECE 210 – Fall 2023 Lab 3: LTSpice and Nodal Analysis GOALS: • Solve a simple DC circuit by hand using nodal analysis (Part 1) • Verify calculations by simulating the circuit’s DC operating point in LTspice (Part 2+3) • Investigate circuit behavior via DC sweep analysis (Part 4) • Meet design specification via DC sweep analysis (Part 5) Lab report (Due in 1 week): 1. Introduce justification for experiment. a. Validate theoretical calculations via simulation b. Investigate circuit behavior via simulation 2. Properly label and document theoretical calculations, simulation schematics, and simulation results a. Label all voltages, currents (with direction). b. Label components, interesting nodes 3. Present measurements with figures that are clearly labeled 4. Analysis for each figure 5. Conclusion – Summary of concepts (See template for more details) You will need to RECORD all of your data independently. The simulation data required for your lab report are listed in a black box like this at throughout the following parts. FOLLOW ALL STEPS AND INCLUDE ALL REQUIRED DATA IN YOUR REPORT!

Introduction: Theoretical Calculations and Simulations Simulation programs (like LTspice) are powerful tools that let us quickly and efficiently analyze a circuit’s behavior without needing to build the physical circuit or repeat tedious calculations by hand (e.g., solve the circuit again for every new resistor value we want to test). However, it is still valuable to first solve the circuit by hand to develop some intuition or understanding of its behavior, and then verify these results and perform further testing via simulation. To illustrate this process, you will first solve a circuit using nodal analysis by hand to find two specific node voltages (note that there are more than two node voltages in the circuit!). You will then simulate this circuit to verify your calculations of the voltages, as well as other quantites (e.g., current, power). Finally, you will use the simulation to investigate the circuit behavior, develop some intuition related to nodal analysis, and implement a design.

Part 1: Nodal Analysis Pictured aboved is a relatively complex circuit. Note the 8 nodes in this circuit, each with it’s own voltage: 7 nodes are labeled with black speech bubbles, and the 8 th node is labeled with the “ground” symbol. Although we know the values of every source and resistor, we do not immediately know the voltages at any of these nodes (other than ground, which is 0V). It turns out we can use nodal analysis to efficiently calculate two of these node voltages, V 1 and V 2 , and then use other techniques to easily calculate the remaining node voltages and branch currents. For this lab, we will just calculate V 1 , V 2 , and the branch currents by hand. Use nodal analysis to find the voltages V 1 and V 2 in the circuit above. After finding V 1 and V 2 , calculate the 4 branch currents leaving/entering the V 1 node and verify that KCL is satisfied. Do the same for the 3 branch currents leaving/entering the V 2 node.

In your lab report : 1. Re-draw the circuit schematic, including… a. Draw arrows indicating the directions you assigned for each branch current. b. Draw the polarities you assigned across each current source and resistor. 2. Show your work for nodal analysis, including… a. Your symbolic nodal equations before solving them (one for node V 1 , one for node V 2 ) b. The values of V 1 and V 2 c. KCL check for node V 1 d. KCL check for node V 2 Some hints : • When deriving each nodal equation, it helps to imagine all the currents leaving (or all entering) the node, so that the sum of all these currents is equal to 0. In other words, you do not need to try to predict the direction of every current, or use the polarity of a voltage source to determine the direction of the current through it. • You should end up with a system of equations with only two unknowns (V 1 and V 2 ). • In each nodal equation, when there are multiple terms proportional to V 1 or V 2 , you should find that EVERY term has the same sign (if you have chosen all currents leaving (or all entering). It might be positive or negative, depending on exactly how you apply nodal analysis, but they must all be the same. • Work symbolically! Form your nodal equations and do as much of the algebra as possible with symbols before plugging in numbers.

Part 2: LTspice Next, you will use LTspice to simulate the circuit and verify your calculations. Visit https://www.analog.com/en/design-center/design-tools-and-calculators/ltspice-simulator.html and download the appropriate version of LTspice for your machine. Follow the on-screen prompts of the installer to install LTspice, and then open the program. You should see a window similar to the left image (Windows) or right image (MacOS). In this window, select File à New Schematic (Windows) or Start a new, blank schematic (MacOS). This will open a blank workspace, which is where you will build your circuit model and simulate its behavior. Be sure to save your schematic file (.asc) now, and as you work. Building the circuit model First, we must build the circuit model by placing each resistor and source and connecting them via wires. Let’s start with the leftmost 2 branches in the circuit above. Helpful hotkeys are listed throughout; see the Appendix for a complete list. 1. Place an independent current source 1.1. Select Edit à Component (Windows) or right click à Draft à Component (MacOS). 1.1.1. Use F2 as a hotkey for the component menu 1.2. In the search bar, type “current,” and click the corresponding result to select the source. 1.3. You will be returned to the schematic window and your cursor will be replaced with the current source. 1.4. press Ctrl + R (CMD + R) to rotate the source 90deg clockwise. Rotate it until it matches the direction of the 1A source in the given circuit, then left click to place it. 1.5. Your cursor will still be a source in case you want to place another instance. Press escape, or right click, to return to a normal cursor. 1.5.1. If you want to delete or move the component you just placed, go to the edit menu (right click the schematic window on MacOS), and select the delete or move tools to change your cursor to the corresponding tool (or press hotkeys F5 for delete, F7 for move). With the delete tool, click on the component to delete it. With the move tool, click on the component to select it, then move the component and click again to place it. Press escape or right click to stop using either tool. 1.5.2. You can use your mouse wheel or the zoom options on the toolbar or under the view dropdown to change your view of the schematic. A helpful option is "Zoom to fit," which resets your view to your circuit (hotkey = spacebar ).

2. Change the source parameters 2.1. This source has two labels: a name, I1, and a value, I. 2.2. Right click the name (I1) and change it to Ia, to match the given circuit diagram. 2.3. Right click the source or the I to edit it’s properties. Since this is an independent DC current source, we can only change the current. Change the current to 1A (the unit is listed within the pop-up). 2.4. The two blue blocks on the top and bottom of the source are its terminals. We will use these later to wire up the circuit. 3. Place some resistors 3.1. Select Edit à Component (Windows), or right click à Draft à Component (MacOS), search “resistor,” and select the component. 3.1.1. You could also press R in the schematic window, or select the resistor element from the toolbar. 3.2. Place a resistor above the current source, Ia, and then 3 more resistors as in the 2nd leftmost branch. Match the circuit diagram but leave enough room so you can clearly see the component parameters. 3.3. Change their values and labels to match the circuit. 3.4. Make sure the resistor above the 1A source is named R1 – we will use this later. 4. Wire up the components 4.1. Select Edit -> Draw Wire (Windows), or right click à Draft à Wire (MacOS). Your cursor will change to 2 perpendicular dotted lines. 4.1.1. You could also use the F3 hotkey. 4.2. Click on the blue box above Ia, and then move your cursor away. You will see a line following your cursor, which is the wire. 4.3. Click the blue box at the bottom of resistor R1 (above the current source) to connect them via the wire. 4.3.1. If you mess up, you can use the delete tool ( F5 ). 4.4. Wire up the other components, matching the circuit diagram. 4.4.1. If you want to place a path of wiring (e.g. a 90deg turn), you can click in open space to place one segment of wire, then move your cursor again to continue the wire path in a different direction. 4.4.2. You may notice a solid blue square forming when more than 2 wires are connected. This indicates a junction where multiple branches meet.

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