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ECE 2006

ECE 2006. Lecture for Chapter 3 S.Norr. Circuit Analysis Methods. Nodal Analysis: Applicable to ANY circuit Uses KCL to determine voltages in cricuit Mesh Analysis: ONLY applicable to planar circuits Uses KVL to determine currents in circuit. Nodal Analysis. Procedure:

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ECE 2006

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  1. ECE 2006 Lecture for Chapter 3 S.Norr

  2. Circuit Analysis Methods • Nodal Analysis: • Applicable to ANYcircuit • Uses KCL to determine voltages in cricuit • Mesh Analysis: • ONLY applicable to planar circuits • Uses KVL to determine currents in circuit

  3. Nodal Analysis • Procedure: • Select One Node as Reference • Assign a Voltage Variable to each remaining Node • Apply KCL at each non-reference Node • Solve the resulting set of simultaneous equations

  4. Grounding • Any SINGLE node in a circuit can be grounded without impact on the performance of the circuit. • Connecting one node of a circuit to ground provides a Zero Voltage reference at that point • Symbols for the Ground Plane:

  5. Example of Nodal Analysis • Assign a Reference Node

  6. Nodal Analysis Example • Assign a Voltage to all Other Nodes:

  7. Nodal Example (Cont.) • Write KCL at One or More Nodes: i1 + i2 + i3 = 0 • Re-Write the Currents using Ohm’s Law: i1= (Va - 5)/2 ; i2 = (Va + 3)/4 ; i3 = (Va – 0)/8 • Substitute: (Va - 5)/2 + (Va + 3)/4 + (Va – 0)/8 = 0 Va = 2 Volts

  8. Nodal Analysis Example… • Use the Resulting Node Voltages to Solve for Currents: Example: i3 = (Va – 0)/8 = (2 – 0)/8 = 1/4 Amps

  9. Example of Nodal Analysiswith a Dependent Source • Establish a Reference Node:

  10. Example of Dependent (Cont.) • Assign a voltage at all other nodes:

  11. Example of Dependent (Cont.) • Applying KCL at Node V2: ix + i + 2i = 0

  12. Example of Dependent (Cont.) Describe Ix using Ohm’s Law: ix = Vx/5 ; Vx = V2 – V1 = V2 – 5 Volts ix = (V2 – 5) /5 Also, Relate ito V2: V2 =i * 10 Result: ix = (i * 10 – 5) /5 = 2i -1 Substitute back into KCL: ix + i + 2i = 0 2i -1 + i + 2i = 0 i = 1/5 Amps ; V2 = 2 Volts

  13. MESH Analysis • ONLYused with PLANAR circuits • Planar meaning the circuit can be drawn on a two-dimensional plane without any branches crossing over another branch • A MESH is a Loop that contains no other Loops within it.

  14. MESH Analysis: • Assign a currentvariable to each MESH in a circuit • Apply KVL to each Mesh, using Ohm’s law to express each Voltage in terms of the assigned currents • Solve the resulting set of simultaneous equations

  15. Mesh Example: • Assign Mesh Currents:

  16. MESH Example… • Write KVL in terms of Mesh Currents: • Mesh 1: -5 + 2i1 + 8(i1 –i2) = 0

  17. Mesh Example…. • Mesh 2 Equation: 8(i2 – i1) + 4i2 – 3 = 0

  18. Mesh Example… • Solve the Set of Simultaneous Equations: 10i1 – 8i2 = 5 -8i1 + 12i2 = 3 14i1 + 0i2 = 21 i1 = 3/2 Amps i2 = 5/4 Amps

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