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LectR1EEE 2021 Exam #1 Review Dr. Holbert February 18, 2008

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LectR1EEE 2022 Basic Circuit Analysis Methods While Obeying Passive Sign Convention Ohm’s Law; KCL; KVL Voltage and Current Division Series/Parallel Resistance combinations

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LectR1EEE 2023 Default Sign Convention Passive sign convention : current should enter the positive voltage terminal Consequence for P = I V –Positive (+) Power: element absorbs power –Negative (-) Power: element supplies power Circuit Element + – I

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LectR1EEE 2024 Ohm’s Law V = I R The Rest of the Circuit V I + – R

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LectR1EEE 2025 KCL (Kirchhoff’s Current Law) The sum of currents entering the node is zero: Analogy: mass flow at pipe junction i1(t)i1(t) i2(t)i2(t)i4(t)i4(t) i5(t)i5(t) i3(t)i3(t)

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LectR1EEE 2026 KVL (Kirchhoff’s Voltage Law) The sum of voltages around a loop is zero: Analogy: pressure drop through pipe loop v1(t)v1(t) + + – – v2(t)v2(t) v3(t)v3(t) +–+–

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LectR1EEE 2027 KVL Polarity A loop is any closed path through a circuit in which no node is encountered more than once Voltage Polarity Convention –A voltage encountered + to – is positive –A voltage encountered – to + is negative

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LectR1EEE 2028 In General: Voltage Division Consider N resistors in series: Source voltage(s) are divided between the resistors in direct proportion to their resistances

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LectR1EEE 2029 In General: Current Division Consider N resistors in parallel: Special Case (2 resistors in parallel)

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LectR1EEE 20210 Equivalent Impedance If we wish to replace two parallel resistances with a single resistor whose voltage-current relationship is the same, the equivalent resistance has a value of: Parallel elements share the same two (distinct) end nodes

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LectR1EEE 20211 Steps of Nodal Analysis 1.Choose a reference (ground) node, V=0. 2.Assign node voltages to the other nodes. 3.Apply KCL to each node but the reference node; express currents in terms of node voltages. 4.Solve the resulting system of linear equations for the nodal voltages. V1V1 V2V2 R

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LectR1EEE 20212 Steps of Mesh/Loop Analysis 1.Identify mesh (loops). 2.Assign a current to each mesh. 3.Apply KVL around each loop to get an equation in terms of the loop currents. 4.Solve the resulting system of linear equations for the mesh/loop currents. I1I1 +– VRVR I2I2 V R = (I 1 – I 2 ) R R

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LectR1EEE 20213 Nodal and Loop Analyses Nodal Analysis Recipe 1&2) Identify and label N nodal voltages plus the ground node (V=0) 3) Apply KCL at N nodes (supernode makes constraint eq.) 4) Solve for the nodal voltages Loop Analysis Recipe 1&2) Identify and label M mesh currents 3) Apply KVL at the M meshes (a current source makes a constraint equation) 4) Solve for the mesh currents

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LectR1EEE 20214 Superposition Procedure 1.For each independent voltage and current source (repeat the following): a)Replace the other independent voltage sources with a short circuit (i.e., V = 0). b)Replace the other independent current sources with an open circuit (i.e., I = 0). Note: Dependent sources are not changed! c)Calculate the contribution of this particular voltage or current source to the desired output parameter. 2.Algebraically sum the individual contributions (current and/or voltage) from each independent source.

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LectR1EEE 20215 Source Transformation A voltage source in series with a resistor is transformed into a current source in parallel with that resistor; and vice versa. VsVs RsRs IsIs RsRs +–+–

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LectR1EEE 20216 Basic Approach to Finding the Thevenin/Norton Equivalent Circuits with independent sources: –Find V oc and/or I sc –Compute R Th (= V oc / I sc ) Circuits without independent sources: –Apply a test voltage (current) source –Find resulting current (voltage) –Compute R Th (= V test / I test )

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LectR1EEE 20217 Thevenin/Norton Equivalent R Th V oc Thevenin equivalent circuit +–+– R Th Norton equivalent circuit I sc

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LectR1EEE 20218 Op Amps Generally apply KCL or nodal analysis Ideal Op-Amp Relations i – = 0 = i + v – = v + + –

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