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MIT6_01F09_lec08

# MIT6_01F09_lec08 - 6.01 Introduction to EECS 1 Week 8 6.01...

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6.01: Introduction to EECS 1 6.01: Introduction to EECS I Solving Circuits Circuit Abstractions Week 8 October 27, 2009 Analyzing Complicated Circuits All circuits can be analyzed by systematically applying Kirchoﬀ’s voltage law (KVL), Kirchoﬀ’s current law (KCL), and current-voltage laws (constituitive relations) for the components and then solving the resulting equations. Developing a systematic approach is especially important for auto- mated simulation tools (such as CMax). Week 8 October 27, 2009 Analyzing Simple Circuits Simple circuits (of the type that we have been building in lab) can usually be analyzed by recognizing equivalent representations (that are even simpler) e.g., series and parallel combinations recognizing common patterns e.g., voltage and current dividers serendipitous formulation of circuit equations Analyzing complicated circuits requires a more algorithmic approach. Step 1: KVL The sum of the voltages around any closed path is zero. + v 1 V 0 + v 2 + v 4 + v 3 v 6 + v 5 + + Check Yourself How many KVL equations can be written for this circuit? + V 0 + v 1 + v 2 + v 3 + v 4 + v 5 + v 6 Example: v 1 + v 2 + v 4 =0 KVL Equation Solver To solve circuits algorithmically using KVL, we must enumerate a complete set of linearly independent KVL equations eliminate those that are linearly dependent on others. This task is not trivial, even for just moderately complicated circuits. + + + + v 2 v 3 v 1 V 0 + v 6 + + v 4 v 5 1

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6.01: Introduction to EECS 1 Week 8 October 27, 2009 Alternative Representation: Node Voltages Node Voltages Node voltages represent the voltage between each node in a circuit Node voltages are linear combinations of component voltages. and an arbitrarily selected ground. Component voltages are diﬀerences between node voltages. e 0 e 0 + V 0 e 1 + v 2 + v 4 + v 6 + + v 3 + + V 0 e 1 + v 2 + v 4 + v 6 v 3 + v 1 e 2 v 1 e 2 + + v 5 v 5 gnd gnd Node voltages and component voltages are diﬀerent but equivalent representations of voltage. Examples: e 0 = v 2 + v 4 v 2 = e 0 e 1 component voltages represent the voltages across components. node voltages represent the voltages in a circuit. Node Voltages Node voltages automatically satisfy KVL. e 0 e 1 V 0 + v 2 + v 4 + v 3 + + v 1 e 2 + v 6 + v 5 gnd using component voltages: v 1 + v 2 + v 4 =0 using node voltages e 0 +( e 0 e 1 )+( e 1 ) 0 Check Yourself The following voltages are not consistent with KVL but can be made consistent by changing just one. Which one? 1 2 2 1 3 2 2 3 4 2 3 0 d c a b 1. a 2. b 3. c 4. d 5. none of the above Node Voltages Check Yourself Node voltages eliminate the need to enumerate any KVL equations.
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MIT6_01F09_lec08 - 6.01 Introduction to EECS 1 Week 8 6.01...

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