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EECS 70A: Network Analysis

Announcements: Announcements. EECS 70A: Network Analysis. Lecture 5. (Monster HW problem). i 1. 3 V. 3 V. 3 V. 3 V. 3 V. 3 i 1. 3 i 1. 7 W. 7 W. 7 W. 2 W. 2 W. 3 W. 7 W. 7 W. 5 W. 5 W. 7 W. 7 W. 7 W. 2 W. 3 W. 5 W. 7 W. 2 W. 7 W. 7 W. 7 W.

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EECS 70A: Network Analysis

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  1. Announcements: Announcements EECS 70A: Network Analysis Lecture 5

  2. (Monster HW problem) • i1 • 3 V • 3 V • 3 V • 3 V • 3 V • 3 i1 • 3 i1 • 7 W • 7 W • 7 W • 2 W • 2 W • 3 W • 7 W • 7 W • 5 W • 5 W • 7 W • 7 W • 7 W • 2 W • 3 W • 5 W • 7 W • 2 W • 7 W • 7 W • 7 W • 7 W • 7 W • 7 W • 7 W • 7 W • 5 W • 7 W • 7 W • 7 W • 7 W • 7 W • 7 W • 3 A • 3 A • 3 A • 3 A • 3 A • 3 A • 3 A • 3 A • 2 i1 • + • + • + • + • + • + • + • - • - • - • - • - • - • -

  3. + + Nodal analysis (simplified) Nodal analysis (complete) • + • + • - • - Later in course: All our methods can also be used with these elements.

  4. + + Mesh analysis (simplified) Mesh analysis (complete) • + • + • - • -

  5. Diode Nodal/mesh analysis won’t work on this but… Radio wave detector is a diode. Behaves like: Solar cell is a diode. Behaves like: Detector • Vdc = 0.1 xVac • Vac • + • - b Nodal/mesh analysis works on these equivalent circuits!

  6. Transistors drain Nodal/mesh analysis won’t work on this but… gate source In some cases behaves like switch: In some cases behaves like potentiometer: In some cases behaves like VCCS: drain drain drain • R • 5 x Vgate • aR source source source • Rsd = (constant) x Vgate Nodal/mesh analysis works on these equivalent circuits!

  7. Nodal vs. mesh analysis Consider 2 examples, each with 2 resistors. For both problems, find i1, i2, V1, V2. Is it easier to solve for the currents or the voltages first? • i2 • i2 • i1 + + + • R1 • R2 • R2 • V1 • V2 • V2 - - - • i2 • i1 + + • R2 • i0 • R1 • V1 • V2 • 3 V • 3 A • + • - - - • i1 + • R1 • V1 -

  8. Notation: two elements in series Textbook chapter 2 notation: a • i • i + • R1 • V1 • R1 - • i • i b + • R2 • R2 • V2 - • i • i c c • Vab is the voltage drop across resistor 1 • V1 is the voltage drop across resistor 1

  9. Nodal analysis • Define a reference node. • Label remaining nodes a • i • R1 • i b • R2 • i c • Vab is the voltage drop across resistor 1

  10. Example (Ch. 2 notation) • R7 • R12 • R2 • R6 • R1 • R11 • i4 • i5 • i8 • i9 • i10 • i3 - - - - - - + + + + + + • V1 • V12 • V7 • V6 • V2 • V11 + + + + + + - - - - - - • i7 • i1 • i6 • i2 • R4 • R3 • R5 • V8 • V3 • V9 • V4 • V10 • V5 • 3 A • R8 • R9 • R10 • i11 • i12 Typical notation: V1 is voltage drop across R1. i1 is current through R1. Label voltages as drops across resistors.

  11. Same circuit: Nodal analysis • Define a reference node. • Label remaining nodes. • Apply KCL + ohm. • R7 • R12 • R2 • R6 • R11 • R1 • i4 • i5 • i3 • i9 • i10 • i8 • i2 • i1 • i7 • i6 • R3 • R4 • R5 • 3 A • R9 • R8 • R10 • i11 • i12 Typical notation: i1 is current through R1. (Same as before) V1 is voltage of node 1 relative to reference node. (Different from before)

  12. Kramer’s rule Solve for x,y,z in terms of known constants a1-3, b1-3, c1-3, d1-3:

  13. Determinants: Solve for x,y,z in terms of known constants a1-3, b1-3, c1-3, d1-3:

  14. Nodal analysis example • 7 W • 3 W • i3 • i4 • i5 • 2 W • 4 W • 2 A • i5 • i2 • i1

  15. Ground? ?

  16. Nodal analysis example • 7 W • 2 W • 3 W • 5 W • 5 A • 2 A • i1 • i2 • i3 • i4

  17. Questions?

  18. KCL examples From Lecture 3, Week 2: Find a relationship among i1,i2, i3,i4… • i1 • i3 • i2 • i8 • i4 • i7 • i5 • i6

  19. “Supernode” A node with a voltage source in it… • i2 KCL: • i3 • + • - • i1 • i4 Must define a supernode if a voltage source appears when doing nodal analysis… (unless one end of voltage source connected to reference node) • Define a reference node. • Label remaining nodes. • Apply KCL + ohm to all nodes and supernodes • Apply KVL to loop with voltage source

  20. Example nodal w/voltage source • 10 V • 2 W • 3 A • 5 A • + • 3 W • 2 W • -

  21. Questions?

  22. Example nodal w/voltage source • 5 W • 5 A • 3 W • 3 A • 2 W • 7 W

  23. Example nodal w/voltage source • 3 W • 2 W • 2 W • 4 W • 2 i1 • + • - • 10 V

  24. Symbol library • Iab • I=5 A + + a + a - - b b - a b

  25. Symbol library • + • + • - • i7 • i7 • i7 • 3 V • 3 i1 • 2 W • 3 A • 2 i1 • + • + • - 2 • - • - • + • -

  26. Symbol & circuit library

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