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3. Analysis Techniques

3. Analysis Techniques. CIRCUITS by Ulaby & Maharbiz. Overview. Node-Voltage Method. Node 1. Node 3. Node 2. Node 2. Node 3. Node-Voltage Method. Three equations in 3 unknowns: Solve using Cramer’s rule, matrix inversion, or MATLAB. Supernode.

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3. Analysis Techniques

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  1. 3. Analysis Techniques CIRCUITS by Ulaby & Maharbiz

  2. Overview

  3. Node-Voltage Method Node 1 Node 3 Node 2 Node 2 Node 3

  4. Node-Voltage Method Three equations in 3 unknowns: Solve using Cramer’s rule, matrix inversion, or MATLAB

  5. Supernode A supernode is formed when a voltage source connects two extraordinary nodes • Current through voltage source is unknown • Less nodes to worry about, less work! • Write KVL equation for supernode • Write KCL equation for closed surface around supernode

  6. KCL at Supernode = • Note that “internal” current in supernode cancels, simplifying KCL expressions • Takes care of unknown current in a voltage source

  7. Example 3-3: Supernode Solution: Supernode Determine: V1 and V2

  8. Mesh-Current Method Two equations in 2 unknowns: Solve using Cramer’s rule, matrix inversion, or MATLAB

  9. Example 3-5: Mesh Analysis But Mesh 1 Hence Mesh 2 Mesh 3

  10. Supermesh A supermesh results when two meshes have a current source( with or w/o a series resistor) in common • Voltage across current source is unknown • Write KVL equation for closed loop that ignores branch with current source • Write KCL equation for branch with current source (auxiliary equation)

  11. Example 3-6: Supermesh Solution gives: Mesh 1 Mesh 2 SuperMesh 3/4 Supermesh Auxiliary Equation

  12. Nodal versus Mesh When do you use one vs. the other? What are the strengths of nodal versus mesh? • Nodal Analysis • Node Voltages (voltage difference between each node and ground reference) are UNKNOWNS • KCL Equations at Each UNKNOWN Node Constrain Solutions (N KCL equations for N Node Voltages) • Mesh Analysis • “Mesh Currents” Flowing in Each Mesh Loop are UNKNOWNS • KVL Equations for Each Mesh Loop Constrain Solutions (M KVL equations for M Mesh Loops) Count nodes, meshes, look for supernode/supermesh

  13. Nodal Analysis by Inspection • Requirement: All sources are independent current sources

  14. Example 3-7: Nodal by Inspection Off-diagonal elements Currents into nodes G11 G13 @ node 1 @ node 2 @ node 3 @ node 4

  15. Mesh by Inspection Requirement: All sources are independent voltage sources

  16. Linearity • A function f(x) is linear if f(ax) = af(x) • All circuit elements will be assumed to be linear or can be modeled by linear equivalent circuits • Resistors V = IR • Linearly Dependent Sources • Capacitors • Inductors A circuit is linear if output is proportional to input We will examine theorems and principles that apply to linear circuits to simplify analysis

  17. Superposition Superposition trades off the examination of several simpler circuits in place of one complex circuit

  18. Example 3-9: Superposition Contribution from I0 Contribution from V0 alone alone I1 = 2A I2 = ‒3A I = I1 + I2 = 2 ‒ 3 = ‒1 A

  19. Cell Phone Today’s systems are complex. We use a block diagram approach to represent circuit sections.

  20. Equivalent Circuit Representation • Fortunately, many circuits are linear • Simple equivalent circuits may be used to represent complex circuits • How many points do you need to define a line?

  21. Thévenin’sTheorem Linear two-terminal circuit can be replaced by an equivalent circuitcomposed of a voltage source and a series resistor voltage across output with no load (open circuit) Resistance at terminals with all independent circuit sources set to zero

  22. Norton’s Theorem Linear two-terminal circuit can be replaced by an equivalent circuit composed of a current source and parallel resistor Current through output with short circuit Resistance at terminals with all circuit sources set to zero

  23. How Do We Find Thévenin/Norton Equivalent Circuits ? • Method 1: Open circuit/Short circuit 1. Analyze circuit to find 2. Analyze circuit to find Note: This method is applicable to any circuit, whether or not it contains dependent sources.

  24. Example 3-10: Thévenin Equivalent

  25. How Do We Find Thévenin/Norton Equivalent Circuits? Method 2: Equivalent Resistance 1. Analyze circuit to find either or 2. Deactivate all independent sources by replacing voltage sources with short circuits and current sources with open circuits. 3. Simplify circuit to find equivalent resistance Note: This method does not apply to circuits that contain dependent sources.

  26. Example 3-11: RTh (Circuit has no dependent sources) Replace with SC Replace with OC

  27. How Do We Find Thévenin/Norton Equivalent Circuits? Method 3:

  28. Example

  29. To find

  30. Power Transfer In many situations, we want to maximize power transfer to the load

  31. Tech Brief 5: The LED

  32. BJT: Our First 3 Terminal Device! • Active device with dc sources • Allows for input/output, gain/amplification, etc

  33. BJT Equivalent Circuit Looks like a current amplifier with gain b

  34. In Out 0 1 1 0 In Out Digital Inverter With BJTs BJT Rules: Vout cannot exceed Vcc=5V Vin cannot be negative Output high Input low Output low Input high

  35. Nodal Analysis with Multisim See examples on DVD

  36. Multisim Example: SPDT Switch

  37. Tech Brief 6: Display Technologies

  38. Tech Brief 6: Display Technologies Digital Light Processing (DLP)

  39. Summary

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