Circuit w/ Dependent Source ExampleUsing Equivalent ResistancesThe Wheatstone BridgeFinding the value of RxIdentifying Series and Parallel CombinationsResistive Circuits: SummaryCircuit Analysis Methods …Node-Voltage Circuit Analysis MethodNodal Analysis: Example #1PowerPoint PresentationNodal Analysis: Example #2Slide 12Nodal Analysis w/ “Floating Voltage Source”Nodal Analysis: Example #3Slide 15Slide 16Slide 17Slide 18Week2bEECS 42, Spring 2005 Prof. WhiteFind i2, i1 and ioCircuit w/ Dependent Source ExampleWeek2bEECS 42, Spring 2005 Prof. WhiteSimplify a circuit before applying KCL and/or KVL: +7 VUsing Equivalent ResistancesR1 = R2 = 3 kR3 = 6 kR4 = R5 = 5 kR6 = 10 kIR1R2R4R5R3R6Example: Find IWeek2bEECS 42, Spring 2005 Prof. WhiteThe Wheatstone Bridge•Circuit used to precisely measure resistances in the range from 1 to 1 M, with ±0.1% accuracyR1 and R2 are resistors with known valuesR3 is a variable resistor (typically 1 to 11,000)Rx is the resistor whose value is to be measured+V–R1R2R3Rxcurrent detectorbatteryvariable resistorWeek2bEECS 42, Spring 2005 Prof. WhiteFinding the value of Rx•Adjust R3 until there is no current in the detector Then,+V–R1R2R3RxRx = R3R2R1Derivation:i1 = i3 and i2 = ixi3R3 = ixRx and i1R1 = i2R2i1R3 = i2RxKCL =>KVL =>R3R1RxR2=i1i2ixi3Typically, R2 / R1 can be varied from 0.001 to 1000 in decimal stepsWeek2bEECS 42, Spring 2005 Prof. WhiteSome circuits must be analyzed (not amenable to simple inspection) -+R2R1VIR4R3R5Special cases:R3 = 0 OR R3 = R1 +R4R5R2VR3Identifying Series and Parallel CombinationsWeek2bEECS 42, Spring 2005 Prof. WhiteResistive Circuits: Summary•Equivalent resistance of k resistors in series:Req = Ri = R1 + R2 + ••• + Rk•Equivalent resistance of k resistors in parallel:•Voltage divided between 2 series resistors:•Current divided between 2 parallel resistors:i=1k1Req= ••• + i=1k1Ri1R11R21Rkv1 = vsR1R1 + R2i1 = isR2R1 + R2Week2bEECS 42, Spring 2005 Prof. WhiteCircuit Analysis Methods …Given: a circuit with voltage and/of current sources, and components(Rs, Cs, Ls, diodes, transistors, etc.) connected by wiresTask: find all the voltages and currents of interestApproaches:1. Use Ohm’s Law, KCL and KVL piecemeal 2. Nodal analysis – node voltages are the unknowns3. Mesh (loop) analysis – mesh currents are the unknowns4. Superposition (linear circuits) – work with only one voltage or current source at a time) and use #1, #2 or #35. Computer simulation of circuit behaviorWeek2bEECS 42, Spring 2005 Prof. White1. Choose a reference node (“ground”)Look for the one with the most connections!2. Define unknown node voltagesthose which are not fixed by voltage sources3. Write KCL at each unknown node, expressing current in terms of the node voltages (using the I-V relationships of branch elements)Special cases: floating voltage sources 4. Solve the set of independent equations N equations for N unknown node voltagesNode-Voltage Circuit Analysis MethodWeek2bEECS 42, Spring 2005 Prof. White1. Choose a reference node.2. Define the node voltages (except reference node and the one set by the voltage source).3. Apply KCL at the nodes with unknown voltage.4. Solve for unknown node voltages.R4 V1R2+ -IS R3R1Nodal Analysis: Example #1Week2bEECS 42, Spring 2005 Prof. WhiteWeek2bEECS 42, Spring 2005 Prof. WhiteV2V1R2R1R4R5R3I1VaNodal Analysis: Example #2Week2bEECS 42, Spring 2005 Prof. WhiteWeek2bEECS 42, Spring 2005 Prof. WhiteA “floating” voltage source is one for which neither side is connected to the reference node, e.g. VLL in the circuit below:Problem: We cannot write KCL at nodes a or b because there is no way to express the current through the voltage source in terms of Va-Vb.Solution: Define a “supernode” – that chunk of the circuit containing nodes a and b. Express KCL for this supernode. Incorporate voltage source constraint into KCL equation. R4R2 I2VaVb+ -VLL I1Nodal Analysis w/ “Floating Voltage Source”Week2bEECS 42, Spring 2005 Prof. WhitesupernodeEq’n 1: KCL at supernodeSubstitute property of voltage source:R4R2 I2VaVb+ -VLL I1Nodal Analysis: Example #3Week2bEECS 42, Spring 2005 Prof. WhiteWeek2bEECS 42, Spring 2005 Prof. WhiteNode-Voltage Method and Dependent Sources•If a circuit contains dependent sources, what to do?Example:–+–+80 V5i20 10 200 2.4 AiWeek2bEECS 42, Spring 2005 Prof. WhiteNode-Voltage Method and Dependent Sources•Dependent current source: treat as independent current source in organizing and writing node eqns, but include (substitute) constraining dependency in terms of defined node voltages.•Dependent voltage source: treat as independent voltage source in organizing and writing node eqns, but include (substitute) constraining dependency in terms of defined node voltages.Week2bEECS 42, Spring 2005 Prof. White–+–+80 V5i20 10 200 2.4
View Full Document