1. ELECTRIC CIRCUITS ECSE-2010 Spring 2003 Class 21

2. ASSIGNMENTS DUE Today (Tuesday/Wednesday): Experiment #7 Report Due (1 Per Team) Will do Computer Project #3 in Class Activities 21-1, 21-2 (In Class) Thursday: Activities 21-3, 22-1 (In Class) Next Week – Spring Break: No Classes!! Monday, March 17: Homework #8 Due (1 Per Team) Computer Project #3 Report Due (1 Per Student) Activities 23-1, 23-2 (In Class)

3. AC STEADY STATE

4. REVIEW AC Steady State: Input = x(t) = Steady State Output = y F (t) = y ss (t) y ss (t) = Phasors; Express x(t) as Phasor X:

5. REVIEW A

6. COMPLEX MATH Addition: A + B = (a r + j a i ) + (b r + j b i ) = (a r + b r ) + j (a i + b i ) Subtraction: A - B = (a r + j a i ) - (b r + j b i ) = (a r - b r ) + j (a i - b i ) => Do Addition/Subtraction in Rectangular Form

7. COMPLEX MATH Multiplication: Difficult to do in Rectangular Form Use Euler or Polar Form Division: Do Multiplication/Division in Polar Form

8. RATIONALIZATION Division in Rectangular Form:

9. COMPLEX CONJUGATES A = a r + j a i A* = a r - j a i = Complex Conjugate of A A x A* = a r 2 + a i 2 = Angle of A* = - (Angle of A)

10. ACTIVITY 21-1

12. ACTIVITY 21-2

17. K’S LAWS FOR PHASORS Circuit in AC Steady State: Can Express All v’s and i’s in Circuit as Phasors:

18. K’S LAWS FOR PHASORS KCL: If i 1 + i 2 = i; => I 1 + I 2 = I KVL: If v 1 + v 2 = v; => V 1 + V 2 = V K’s Laws Work for Phasors! Complex Addition, not Simple Addition Will do Activity 21-3 Tomorrow Will do Computer Project #3 Today

19. COMPUTER PROJECT 3

21. Transient Simulation of 2 nd Order Ckt: Model of an Op Amp Ckt: Real Messy to do this Analytically! Input = Rectangular Pulse; 1 V, 1 msec duration Use a Piece-Wise Linear model of Input R 1 = 10,000 x b; R 2 = 10,000 / b b =.25,.5, 1.0, 2.5 Transient Analysis for 0 < t < 3 msec Identify Over, Under and Critical Damping

22. COMPUTER PROJECT 3

23. Piece-Wise Linear Model – Schematics: Use Source Named VPWL Doubleclick on VPWL Set T1, V1; T2, V2, T3, V3, etc

24. PSPICE TRANSIENTS Transient Analysis - Schematics: Click on Setup Analysis Check Transient Doubleclick on Transient Set Print Step = Final Time Set Final Time Save Click on Simulate

25. PSPICE TRANSIENTS Transient Analysis - Schematics: Also Need to Set Initial Conditions on L and C Create Circuit using L and c Doubleclick on L and c Set Value Set Initial Conditions (Amps, Volts)

26. PSPICE TRANSIENTS Transient Analysis – Circuit File:. tran Statement.tran t f t f uic Start time for analysis is t = 0, End time = t f uic = use initial conditions

27. PSPICE TRANSIENTS Transient Analysis with PSpice: Need to put in initial conditions for L, C C1 2 3 4u IC = 4  Capacitor C1 connected between nodes 2 and 3, value = 4 uF, v C (0 + ) = 4 Volts

28. COMPUTER PROJECT 3 Piece-Wise Linear Model – Circuit File: Vin 1 0 pwl 1m,1 1.01m,0 Resistors: R1 1 2 {10000*b} R2 2 3 {10000/b} Initial Conditions: IC = 0 for both C’s

29. COMPUTER PROJECT 3 Circuit File Computer Project 3 Spring 2003 vin 0 1 pwl 1m,1 1.01m,0 R1 1 2 {10000*b} R2 2 3 {10000/b} C25 2 5 10n ic=0 R34 3 4 50 C40 4 0 10n ic=0 E50 5 0 (3,0) 2.param b=.25.step param b list.25.5 1 2.5.tran 3m 3m uic.probe.end