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EE 221 Review 2

EE 221 Review 2. Nodal and Mesh Analysis Superposition Source transformation Thevenin and Norton equivalent Operational Amplifier. Nodal Analysis - Approach. Redraw circuit to emphasize nodes . Assign reference node and voltages . N nodes result in N-1 unknown voltages.

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EE 221 Review 2

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  1. EE 221 Review 2 Nodal and Mesh Analysis Superposition Source transformation Thevenin and Norton equivalent Operational Amplifier

  2. Nodal Analysis - Approach • Redraw circuit to emphasize nodes. • Assign reference node and voltages.N nodes result in N-1 unknown voltages. • Use KCL to find N-1 equations. • Relate dependent sources to node voltages. • Form supernode to enclose voltage sources and apply KCL. Add voltage equations.

  3. At node 1: (KCL) At the “supernode:” (KCL) At the “supernode:” (KVL) Nodal analysis - Example KCL requires that all currents flowing into the region must sum to zero, or we would pile up or run out of electrons.

  4. (I) (II) (III) variables Independent voltage source (supernode containing reference) v1 = -12 Nodal analysis - Example

  5. Mesh analysis - approach • Redraw planar circuit to emphasize meshes. • Assign clockwise mesh currents.M meshes result in M unknown currents. • Apply KVL around each mesh. • Relate dependent sources to mesh currents. • Use supermesh for current source shared between two meshes. Add current equation.

  6. Creating a “supermesh” from meshes 1 and 3: -7 + 1 ( i1 - i2 ) + 3 ( i3 - i2 ) + 1 i3 = 0 [1] Around mesh 2: 1 ( i2 - i1 ) + 2 i2 + 3 ( i2 - i3 ) = 0 [2] Finally, we relate the currents in meshes 1 and 3: i1 - i3 = 7 [3] Rearranging, i1 - 4 i2 + 4 i3 = 7 [1] -i1 + 6 i2 - 3 i3 = 0 [2] i1 - i3 = 7 [3] Solving, i1 = 9 A, i2 = 2.5 A, and i3 = 2 A. Mesh analysis - Example

  7. Circuit analysis (a) A voltage source set to zero acts like a short circuit. (b) A current source set to zero acts like an open circuit.

  8. Superposition (a) Linear circuits allow superposition. (b) Keep only one independent sourceat a time activate. (c) Always keep dependent sources.

  9. Source transformation A general practical current sourceconnected to a load resistor RL. A general practical voltage sourceconnected to a load resistor RL. • Convert between the two - Sources are related by: • RS = Rp, and • Vs = Rs Is = Rp Is • Useful when asked for: • Maximum terminal voltage (vs) and/or current (is) • (Maximum) power transferred (PL = vL iL when RL = Rs)

  10. Thevenin and Norton • "Dead" network to find equivalent source resistance RTH and RN • Open loop voltage to determine VTH (any method) • Short circuit current determines IN

  11. Thenenin - Example Source transformation is used here. • Open loop voltage to determine VTH and short circuit current determines IN • Find equivalent source resistance RTH and RN • use "Dead" network • use RTH = RN = VTH / IN(the only way in case of dependent sources)

  12. Operational Amplifier (a) Electrical symbol. (b) “Minimum" op amp. Neglected: (1) Output voltage saturation. (2) Input/output resistance. (3) Limited open loop gain. (4) Input bias current. (5) Input offset voltage. Ideal: (1) No input current. (2) No voltage difference between input terminals.

  13. Operational Amplifier - Circuits Op amp connected as an Inverting amplifier. Vout = - (Rf / R1) Vin Output characteristics. • 1st step: Determine voltage at input terminals • 2nd step: Determine current i • 3rd step: Find output voltage vout

  14. (c) Operational Amplifier - Circuits (a) An op amp used to construct a noninverting amplifier circuit. (b) Circuit with currents and voltages labeled. (c) Output characteristics. Vout = (1 + Rf / R1) Vin

  15. b a c d OpAmp - Example Difference amplifier • Your choice: Nodal analysis and/or superposition • vout = -Rb/Rc v1 + Rd(Ra+Rb) / (Ra(Rc+Rd)) v2

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