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Course: MAE 140, Spring 2010
School: UCSD
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Word Count: 815

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8 Lesson Node Voltage Analysis (Section 3-1)(CLO 3-1) One of the basic understandings that will help students write node voltage equations is to recognize that this technique is nothing more than applying KCL. The first thing to ask the students to do is to count and label the nodes, and then to select one of the nodes as the reference node or ground. Although any node can be selected as a ground, if they choose...

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8 Lesson Node Voltage Analysis (Section 3-1)(CLO 3-1) One of the basic understandings that will help students write node voltage equations is to recognize that this technique is nothing more than applying KCL. The first thing to ask the students to do is to count and label the nodes, and then to select one of the nodes as the reference node or ground. Although any node can be selected as a ground, if they choose wisely they can simplify the analysis. Ask them to look for voltage sources. If one or more share a common node, that node makes a good reference candidate. Encourage them to select the negative terminal of a voltage source as their reference. That will automatically make the positive node equal to the voltage of the source that is one less node they have to worry about. The node labels are ground symbol (0V) and VA, VBVN. Some of the node voltages may be known since they are connected to a source whose other end is connected to ground e.g. VA = VS. Writing the node voltage equations follows from KCL. Here the trick is to always assume that the currents leaving the node are positive (i.e. the sum of currents leaving a node is zero). VA is connected to ground via a voltage source VS. Hence, VA is known and we write equations at each unknown node (VB and VC) VA IX VS I R1 VB R3 IS VC + VI _ VA = VS VB VS VB 0 VB VC + + =0 R1 R2 R3 VC VB + IS = 0 R3 R2 Tell the students that they should collect all the unknown terms on the left side of the equation and all the sources on the right. This will enable the students to reduce the equations to a set of linear equations that are then ready to be solved using one of several analytical techniques and or computer tools. Draw the currents this one time to help them see that we are indeed summing currents at a node, but then erase the currents because they can easily get confused if they draw them at each node. Stress to the students that they can and should write node equations without drawing in the currents. VB ( 1 1 1 1 V + + ) VC ( ) = S R1 R2 R3 R3 R1 VV B + C = IS R3 R3 These equations are simple enough to solve by hand using substitution or simultaneously. If the parameters numeric had values, they could be solved using MATLAB or their hand calculators. If they are in literal form, they will need to use the symbolic processor in MATLAB. For up to a 3 3, they could solve it by hand using Cramers Rule. Anyway, they should already know how to solve a set of linear equations. It is also important for the students to know how to find a desired current or a voltage across a particular circuit element. Once they have found the node voltages the desired current can be found by appealing to the desired element equation. For example the current identified in the circuit above is I = (VS VB)/R1. Point out to the students that had the arrow gone the other way the current would be found as I = (VB VS)/R1. VI, the voltage across the current source, is simply VC0 or VC. Draw a circuit that does not have the ground node at the bottom of the circuit. That is, place the voltage source on top of the page. Students at times get used to the ground at the bottom and place it there even if that is not the best place to put it. Another issue is that students like to write node equations even at known nodes VA for example. This can be done but is not normally necessary; moreover, it often adds undesired complexity to the solution. If one really wants to write a node equation at a known node then one must identify a current through the voltage source and include it in the equation, IX, in the example circuit. The equation at node VA then would be: VA VB + IX = 0 R1 The last thing to cover is how to handle a circuit with a voltage source connecting two nonground nodes. We will use the Supernode technique. Consider the circuit below. Regardless of where one picks a ground one source will always be connected between two non ground nodes. To use a super node you draw a node around the non-grounded source i.e. VS2. Then treat the currents exiting that supernode as if they were exiting from one node. Supernode V S2 V A R 1 V B V R 3 C VA 0 VA VS1 VC VS1 + + + IS = 0 R2 R1 R3 Then we need the equation relating nodes VA and VC namely, VA VC=VS2. Since VB is known this will allow the node voltages to be solved. R 2 V S1 IS
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UCSD - MAE - 140
Lesson 9 Mesh Current Analysis and Linearity. (Sections 3-2 and 3-3)(CLO 3-1 and 3-2) Students generally do not have serious problems in understanding Mesh Current analysis. You might mention that it is the dual of Node Voltage analysis. Mesh Current anal
UCSD - MAE - 140
Lesson 10 Superposition and Thvenin/Norton Theorems (Sections 3-3 and 3-4) (CLOs 3-2 and 3-3) Superposition is more of a learning technique than a useful tool since most simulation tools can solve multiple source problems with no extra effort. However, th
UCSD - MAE - 140
Lesson 11 Signal Transfer and Interface Design (Section 3-6) (CLOs 3-4 and 3-5) This is a key lecture for students to understand circuit limitations. In this type of interface circuit design loading is not bad it is intentional! We have taught students th
UCSD - MAE - 140
Lesson 12 Comparison of Analysis Techniques (Chapter 3 review)(CLOs 3-1thru 3-5) This lesson offers students with the ability to sit back and review all of the different analysis techniques we have been teaching them. They need practice in deciding which
UCSD - MAE - 140
Lesson 13 Dependent Sources #1 (Sections 4-1 and 4-2) (CLO 4-1) This and the next lesson are very important to the students understanding of electronic modeling especially the Op-Amp section that follows. Some students do not appreciate what a dependent s
UCSD - MAE - 140
Lesson 14 Dependent Sources #2 (Section 4-2) (CLO 4-1) This is a challenging lesson to both teach and to learn. It is important because it sets the underlying concept for the operation of Op-Amps namely feedback. To reinforce what the students are to lear
UCSD - MAE - 140
Lesson 15 Dependent Sources #3 (Section 4-2) (CLO 4-1) This lesson looks at input and output resistance of a dependent source circuit. A very important concept involves the effect of feedback on RIN and ROUT. If there is no feedback resistor, the input re
UCSD - MAE - 140
Lesson 16 Op-Amps #1 (Sections 4-3 and 4-4) (CLO 4-2) There are seven lessons dedicated to Op-Amps. By the end of this module the students should feel comfortable analyzing and designing Op-Amp circuits. The lessons are as follows: 1. The basics (this les
UCSD - MAE - 140
Lesson 17 Op-Amps #2 (Section 4-4) (CLO 4-2) This is the second lesson on Op-Amps. The goal is to get through developing the four basic building blocks: Inverter, Non-inverter (and Follower), Summer, and Subtractor. It is important that the students learn
UCSD - MAE - 140
Lesson 18 Op-Amps #3 (Section 4-4) (CLO 4-2) The third lesson on Op-Amps focuses on cascading Op-Amp building blocks and the concept of loading. Last lesson we developed several Op-Amp building blocks. Those along with the voltage divider are very useful
UCSD - MAE - 140
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UCSD - MAE - 140
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UCSD - MAE - 140
Lesson 21 Op-Amps #6 (Section 4-6) (CLO 4-3) The sixth lesson on Op-Amps focuses on designing Instrumentation Systems. After this and the next lesson, the students should be able to design simple instrumentation systems.KInput Transducer Gain+ +Bias,
UCSD - MAE - 140
Lesson 22 Op-Amps #7 (Section 4-6) (CLO 4-3) This last lesson on Op-Amps focuses on designing Instrumentation Systems with passive transducers.KInput Transducer Gain+ +Bias, b Output TransducerAs mentioned previously, passive transducers require an e
UCSD - MAE - 140
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UCSD - MAE - 140
Lesson 24 Signals II (Section 5-4, 5-6 and 5-7) (CLOs 5-1 and 5-3) This is the second lesson of a three-lesson block on signals. The first lesson was on Singularity functions and exponentials. This one is on sinusoids and partial descriptors (VP, VPP, VMA
UCSD - MAE - 140
Lesson 25 Signals III (Section 5-5 and 5-7) (CLO 5-1 through 5-3) This is the last lesson of a three-lesson block on signals. This section focuses on composite signals and how to construct them using OrCAD and MATLAB. We start by discussing the various co
UCSD - MAE - 140
Lesson 26 Capacitors and Inductors I (Sections 6-1 and 6-2) (CLO 6-1) This is the first of two lessons on Capacitors and Inductors. The first lesson introduces the i-v characteristics of the devices and includes power and energy considerations. The second
UCSD - MAE - 140
Lesson 27 Capacitors and Inductors II (Sections 5-5 and 5-7) (CLOs 6-2 and 6-3) This is the second of two lessons on Capacitors and Inductors. This lesson discusses combining multiple devices and introduces two new operational modules, the integrator and
UCSD - MAE - 140
Lesson 28 RL and RC Circuits (Natural Response) (Section 7-1) (CLO 7-1) The next three lessons on First-Order Circuits can be a bit challenging for the students because they involve calculus. The first looks at deriving the equations that describe first-o
UCSD - MAE - 140
Lesson 29 RL and RC Circuits (Step Response) (Sections 7-2 and 7-3) (CLO 7-1) This lesson starts out challenging but fortunately becomes easy for the students to use once the derivations are done and they can apply solutions to a template. That this analy
UCSD - MAE - 140
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UCSD - MAE - 140
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UCSD - MAE - 140
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UCSD - MAE - 140
Lesson 33 AC Circuit Analysis I (Sections 8-1 and 8-2) (CLOs 8-1 and 8-2) This is the beginning of a four-lecture block on doing all those things we did with dc (KVL, KCL, Node Voltage, Mesh Current, Thvenin Equivalent, Voltage and Current dividers, Super
UCSD - MAE - 140
Lesson 34 AC Circuit Analysis II (Sections 8-2 and 8-3) (CLO 8-3) This lesson begins to apply all of the theorems learned back in Chapters 2 and 3 to ac circuits. But, before we start we bring in one very important concept involving impedance. It is very
UCSD - MAE - 140
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UCSD - MAE - 140
Lesson 36 Transfer Functions and Cascade Connections (Variant of Sections 11-1 and 11-2) (Variant of CLOs 11-1) This is the first lecture of a three-lecture block on learning how filters work and designing first-order filters. The end result is for the st
UCSD - MAE - 140
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