Exam #1 ReviewBasic Circuit Analysis MethodsDefault Sign ConventionOhm’s LawKCL (Kirchhoff’s Current Law)KVL (Kirchhoff’s Voltage Law)KVL PolarityIn General: Voltage DivisionIn General: Current DivisionEquivalent ImpedanceSteps of Nodal AnalysisSteps of Mesh/Loop AnalysisNodal and Loop AnalysesSuperposition ProcedureSource TransformationBasic Approach to Finding the Thevenin/Norton EquivalentThevenin/Norton EquivalentOp AmpsLectR1 EEE 202 1Exam #1 ReviewDr. HolbertFebruary 18, 2008LectR1 EEE 202 2Basic Circuit Analysis Methods•While Obeying Passive Sign Convention•Ohm’s Law; KCL; KVL•Voltage and Current Division•Series/Parallel Resistance combinationsjNser iesRRRRR 21iMparRRRRR1111121LectR1 EEE 202 3Default 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 powerCircuit Element+–ILectR1 EEE 202 4Ohm’s LawV = I RThe Rest of the CircuitVI+–RLectR1 EEE 202 5KCL (Kirchhoff’s Current Law)The sum of currents entering the node is zero:Analogy: mass flow at pipe junctioni1(t)i2(t) i4(t)i5(t)i3(t)njjti10)(LectR1 EEE 202 6KVL (Kirchhoff’s Voltage Law)The sum of voltages around a loop is zero:Analogy: pressure drop through pipe loop0)(1njjtvv1(t)++––v2(t)v3(t)+–LectR1 EEE 202 7KVL 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 negativeLectR1 EEE 202 8In General: Voltage Division•Consider N resistors in series:•Source voltage(s) are divided between the resistors in direct proportion to their resistancesjiSRRRtVtVki)()(LectR1 EEE 202 9In General: Current Division•Consider N resistors in parallel:•Special Case (2 resistors in parallel)iNparjparSRRRRRRRRtitikj11111)()(21212)()(1RRRtitiSRLectR1 EEE 202 10Equivalent 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 nodes2121RRRRReqLectR1 EEE 202 11Steps of Nodal Analysis1. 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 thenodal voltages.V1V2RVVI21RLectR1 EEE 202 12Steps of Mesh/Loop Analysis1. 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 themesh/loop currents.I1+ –VRI2VR = (I1 – I2 ) RRLectR1 EEE 202 13Nodal and Loop AnalysesNodal Analysis Recipe1&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 voltagesLoop Analysis Recipe1&2) Identify and label M mesh currents3) Apply KVL at the M meshes (a current source makes a constraint equation)4) Solve for the mesh currentsLectR1 EEE 202 14Superposition Procedure1. 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.LectR1 EEE 202 15Source TransformationA voltage source in series with a resistor is transformed into a current source in parallel with that resistor; and vice versa.VsRsIs RssssIRV +–LectR1 EEE 202 16Basic Approach to Finding the Thevenin/Norton Equivalent•Circuits with independent sources:–Find Voc and/or Isc–Compute RTh (= Voc / Isc)•Circuits without independent sources:–Apply a test voltage (current) source–Find resulting current (voltage)–Compute RTh (= Vtest / Itest)LectR1 EEE 202 17Thevenin/Norton EquivalentRThVocThevenin equivalent circuit+–RThNorton equivalent circuitIscLectR1 EEE 202 18Op Amps•Generally apply KCL or nodal analysis •Ideal Op-Amp Relationsi– = 0 = i+v– =