EP2E04 Topic 1 Notes - DC Resistive Network Analysis

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McMaster University *

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2E04

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Electrical Engineering

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Dec 6, 2023

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1. DC Resistive Network Analysis 1.1. Introduction 1.1.1. Intended Learning Outcomes (ILOs): 1. Review of basic skills; KVL, KCL, Ohm's law 2. Details of resistive network analysis (analyzing circuits containing only sources and resistors). If you use phasors, the techniques here can also apply to AC steady-state analysis for networks containing resistors, capacitors, and inductors, so it's more general than it sounds at first. Skills and info to be gained: a. Node Analysis (Method to analyze resistive networks) b. Mesh Analysis (Method to analyze resistive networks) c. Superposition (Method to analyze resistive networks which relies on linearity) d. Thévenin & Norton Equivalent Circuits (Methods for simplifying source networks) e. Further Study (beyond scope of tests): Maximum Power Transfer (Information about impedance matching to get the most out of a source network) Note that applying KVL & KCL is also a circuit analysis method, and unlike some of the other methods doesn't itself rely on linearity. While it is a valid method and perhaps the easiest to understand why it works, it's typically not as fast as the methods above. Each of the above methods is best for a particular type of circuit. Here's the sort of circuit you'll be able to analyze after this topic: 1.1.2. Topic 1 Videos: 1. Multisim & DC Resistive Analysis Intro: https://www.youtube.com/watch? v=vdhn3GjsbKs&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index=1 2. Nodal Analysis: https://www.youtube.com/watch?v=hSNeqDJe- qE&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index=2 3. 4. Mesh Analysis: https://www.youtube.com/watch? v=rXIFmaLHj4M&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index=3 5. Superposition: https://www.youtube.com/watch? v=FwuC_7JMQzQ&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index=4
6. Thévenin Equivalents: https://www.youtube.com/watch? v=QxzSa_TZe4o&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index=6 7. Max Power Transfer: https://www.youtube.com/watch? v=Qjxi5SfMjrM&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index=7 8. Lab Skills Videos: a. https://www.youtube.com/watch? v=JrveDVs2fCQ&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index= 5 b. https://www.youtube.com/watch? v=AqybJURSgKU&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index =8 9. Hantek Lab Modification Videos: a. Lab kit unboxing vids: https://www.youtube.com/watch? v=bukI2s27PEg&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index=9 b. DC Voltage measurement: https://www.youtube.com/watch? v=Q4SASV0s88I&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&index= 12 c. Full lab 1 Hantek modification version: https://www.youtube.com/watch? v=NsR1MMAEOnU&list=PLhbHWgMknRJT_eKLFXB843NkaNHfJ37Pw&ind ex=13 1.1.3. Deliverables Note: As always, your full objective for this topic is to review these notes, the videos, practice problems, live class sessions and forum content, then to write-up creating and tri-solving a variation problem of the week's topic that demonstrates you've mastered the content. With that all still in mind, following are some specific guidelines & tips for this week. See the Outline and Deliverable Rubric files for information for the write-ups in general. Specific tasks for your H1 deliverable are as follows: 1. Design a circuit using resistors and your power distribution board (header board from the component kit) that has a. Two voltage supplies (one 5 V and one 3.3 V) which have their low sides connected to ground (having them connected is mandatory because the header board has the low side of each supply connected together already. Defining it as "ground" for your circuit is not mandatory, but it will help keep things a bit consistent) b. At least 5 resistors that are at least 1k (need high enough resistance of a load to avoid shorting your supply) c. At least 3 meshes d. No shorting of the power supplies (putting a low resistor or wire across the supply or any too low of a resistance path from one end to the other) or making them fight (putting the two voltage supplies in parallel)** 2. Make your tri-solve objective to find: a. at least two nontrivial currents and b. at least three nontrivial voltages in your circuit. 3. Analytically solve your circuit 4 separate ways: a. using Kirchoff's laws,
b. mesh analysis, c. nodal analysis, and d. superposition. 4. Use Multisim to model your circuit and measure the target voltages and currents. Do this using multisim's voltage and current probes and using the multimeters. 5. Physically build your circuit on the breadboard and measure the same voltages and currents ( Note: watch all of the above videos and review the rest of these notes before doing any of the steps, but especially the physical build, because you can break, burn, or even explode your equipment and seriously hurt yourself and your house if you use it wrongly enough ). a. Note: remember that your multimeter is an open in voltmeter mode, a short in ammeter mode, and applies a voltage in ohmmeter mode. The most common problems people have are 1) trying to measure resistance in an assembled [or worse, assembled & powered] circuit; and 2) accidentally putting an ammeter in parallel with something and shorting it out, possibly breaking their power supply. b. Note: For all measurements, include uncertainty due to the instrument you're using on the setting you're using it. c. Note: Take a picture of your student card and your finished circuit together. Mark this up to explain how it's implementing your desired circuit (i.e., which resistor and supply are which). d. Note: Take a picture of the multimeter output for all measurements. e. Before wiring up the circuit, measure all resistor values f. Measure the voltage outputs of the supplies while the circuit is operating; if they drop by more than a few percent you have a short (or are drawing too much current because your resistors are too small). g. Get your current measurements two ways: i. by using the ammeter, and ii. by measuring a voltage across a resistor in that branch where you want the current and using Ohm's law. 6. Write this all up in a clean report that satisfies all the steps in the rubric; e.g., includes an analysis section comparing [and reconciling] the results and a reflection on the topic and its applicability. Hints: 1. Consider the resistor values you actually have in the kit before deciding on your resistor values. You can even measure them at the start and use the measured values as your selected resistance for your sample circuit. Alternatively, you can update the values in the sample circuit to the measured values and recalculate & resimulate like I do in the video. 2. Don't draw the circuit by hand; use the image from multisim and mark that up with a paint program; it's faster (once you get used to it) and will make your writeup look much better. 3. When comparing your results, ensure you are comparing the same things. e.g., if your actual measured supply voltages and resistor values were different than ones used in your analytical calculation & simulation, you need to update those and recalculate & re- simulate before comparing.
4. Propagating the error in voltage or resistance measures in this calculation is difficult because the calculation involves solving a linear system. With Maple you can solve the system analytically and deduce the impact of uncertainty in various quantities. You can also test how well the error propagation formula works here by re-calculating quantities using maxes and mins of measured ranges to determine the range on the output values. **What does "No shorting the supplies or making them fight" mean?? Here's V2 shorted: (there's a wire, AKA a short circuit, connecting each side of V2 so there's a short cut for current around it. Since it's a supply, it'll try to put infinite current to maintain 9V and will actually reach a current limit at close to 0 V (the wire will win the fight). Since it's not a good supply, your kit's supply will overheat and break when it does this) Here's V2 fighting V1: (V1 says the voltage at the top is 5 V, while V2 says it's 9 V. They're in parallel, so will compete, and each try to put out infinite current to make that happen. In reality they can't, so will reach some current limit at a different voltage, as when they're shorted, and will likely overheat and burn out.) 1.2. Electricity and Circuit Fundamentals This chapter focuses on details of resistive network analysis (analyzing circuits containing only sources and resistors). If you use phasors (Chapter 4), the techniques here can also apply to AC steady-state analysis for networks containing resistors, capacitors, and inductors, so it's more general than it sounds at first. First we will go over some background information which you should know already from previous courses.
1.2.1. Symbols Below are the main passive and active circuit elements you will be dealing with in this class: [note: In this class we deal with ideal sources and ignore imperfections that are associated with real-world power supplies. The symbols above indicate ‘ideal’ sources] 1.2.2. Terminology and Definitions Voltage: Represented with the symbol ( V ), voltage is the measure of potential difference between two points in a given circuit. Measured in volts (V). Current: Represented by the symbol (I), current is the rate of flow of electric charge, traditionally this is specifically the flow of positive charge. Measured in amps (A). Power: Electrical power is the rate at which energy is dissipated across an element or load. Measured in Watts, which is equivalent to Joules/second. (W or J/s). Ideal voltage source: always has its set voltage across its terminals (i.e., an ideal 5 V source supplies any current necessary to make its positive terminal 5 V higher than its negative terminal) Ideal current source : always supplies its set current (i.e., an ideal 2 A current source produces any voltage necessary across its terminals to supply 2 A.) Ground : An electrical connection of a circuit or conductor to the earth. The node attached to the ground is used as a reference voltage of 0V. Branch: A group of elements along a single path. Node: A point at which lines or pathways intersect or branch; a connecting point. The image below has labelled all nodes in the circuit.
Mesh: A closed path around a circuit (contains no smaller closed paths) Loop : Any closed path (physical or ortherwise). This implies that all meshes are loops, but not all loops are meshes.
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