Electrical Engineering 348: ELECTRONIC CIRCUITS I

1. Electrical Engineering 348:ELECTRONIC CIRCUITS I Dr. John Choma, Jr. Professor of Electrical Engineering University of Southern California Department of Electrical Engineering– Electrophysics University Park; Mail Code: 0271 Los Angeles, California 90089-0271 213-740-4692 [Office] 626-715-0944 [Fax] 818-384-1552 [Cell] johnc@almaak.usc.edu Spring Semester 2001

2. EE 348:Lecture Supplement Notes SN1 Review of Basic Circuit Theory and Introduction To Fundamental Electronic System Concepts 01 January 2001 J. Choma, Jr.

3. Outline Of Lecture • Thévenin’s & Norton’s Theorems • Basic Electronic System Concepts • Steady State Sinusoidal Response • Transient Response J. Choma, Jr.

4. Thevénin’s Theorem • Concept • Two Terminals Of Any Linear Network Can Be Replaced By Voltage Source In Series With An Impedance • Thévenin Voltage Is “Open Circuit” Voltage At Terminals Of Interest • Thévenin Impedance Is Output Impedance At Terminals Of Interest • Linear Load • Thévenin Concept Applies To Linear Or Nonlinear Load • Voltage VL Is Zero If No Independent Sources Are Embedded In The Load J. Choma, Jr.

5. Thévenin Model Parameters • Thévenin Voltage • Zero Load Current • Voc Vth • Thévenin Impedance • “Ohmmeter” Calculation • Thévenin Voltage Is Set To Zero By Nulling All Independent Sources In Linear Network • Superposition J. Choma, Jr.

6. Thévenin Example • Bipolar Emitter Follower Equivalent Circuit • Load Is The Capacitor, Cl • Calculate: • Thévenin Voltage Seen By Load • Thévenin Impedance Seen By Load • Transfer Function, Vo(s)/Vs(s) • 3–dB Bandwidth J. Choma, Jr.

7. Thévenin Voltage And Impedance • Thévenin Voltage Gain • Thévenin Impedance J. Choma, Jr.

8. Thévenin Output Model • Gain • Resistance J. Choma, Jr.

9. Transfer Function (Gain) • Gain At Zero Frequency Is Ath • Bandwidth Definition • 3–dB Bandwidth (Radians/Sec) J. Choma, Jr.

10. Frequency and Phase Responses 0.776 –45° J. Choma, Jr.

11. Input Impedance • Very Large Zero Frequency Input Impedance • Other Characteristics • Left Half Plane Pole And Left Half Plane Zero • Non-Zero High Frequency Impedance J. Choma, Jr.

12. Voltage Delivery To Load • Load Voltage • If |Zl| << |Zs|, Much Of The Source Voltage Is “Lost” In The Source Impedance • If |Zl| = |Zs|,50% Of The Source Voltage Is Lost, Resulting In A factor Of Two Attenuation Or 6 dB Gain Loss. • Many Systems Are Intolerant Of Such A Loss • System Problem • Voltage Generated By Some Linear Network Is To Be Supplied To A Fixed Load Impedance, Zl • Because The Source Network Is Linear, Its Output Can Be Represented By A Thévenin Circuit (Vs— Zs) • Assume Thévenin Source and Load Impedances are Fixed J. Choma, Jr.

13. Insertion Of Voltage Buffer J. Choma, Jr.

14. Impact Of Voltage Buffer • Practical Buffer • Zout Very Small • Zin Very Large • Abuf Near Unity • Effect Of Ideal Buffer J. Choma, Jr.

15. Norton’s Theorem • Concept • Two Terminals Of Any Linear Network Can Be Replaced By A Current Source In Shunt With An Impedance • Norton Current Is “Short Circuit” Current At Terminals Of Interest • Norton Impedance Is Output Impedance At Terminals Of Interest And Is Identical To Thévenin Output Impedance • Linear Load • Norton Concept Applies To Linear Or Nonlinear Load • Voltage VL Is Zero If No Independent Sources Are Embedded In The Load J. Choma, Jr.

16. Norton Model Parameters • Norton Current • Zero Load Voltage • Isc Ino • Norton Impedance • “Ohmmeter” Calculation • Norton Current Is Set To Zero By Nulling All Independent Sources In Linear Network • Superposition J. Choma, Jr.

17. Thévenin–Norton Relationship • From Thévenin Model: • From Norton Model: • Thévenin–Norton Equivalence: J. Choma, Jr.

18. Current and Voltage Sources • Ideal Voltage Source • Ideal Current Source J. Choma, Jr.

19. Voltage Amplifier • Ideal Properties • Infinitely Large Input Impedance, Zin • Zero Output Impedance, Zout • Sufficiently Large Voltage Gain, Av, Independent Of Input Voltage, VI and Output Voltage Vo • Circuit Schematic Symbol J. Choma, Jr.

20. Transconductor • Ideal Properties • Infinitely Large Input Impedance, Zin • Infinitely Large Output Impedance, Zout • Sufficiently Large Transconductance, Gm, Independent Of Input Voltage, VI and Output Voltage Vo • Circuit Schematic Symbol J. Choma, Jr.

21. Current Amplifier • Ideal Properties • Zero Input Impedance, Zin • Infinitely Large Output Impedance, Zout • Sufficiently Large Current Gain, Ai, Independent Of Input Voltage, VI and Output Voltage Vo • Circuit Schematic Symbol J. Choma, Jr.

22. Transresistance Amplifier • Ideal Properties • Zero Input Impedance, Zin • Zero Output Impedance, Zout • Sufficiently Large transresistance, Rm, Independent Of Input Voltage, VI and Output Voltage Vo • Circuit Schematic Symbol J. Choma, Jr.

23. Max Voltage & Current Transfer • Voltage Transfer • Current Transfer  Maximum Voltage Transfer Requires Very Small Zth  Maximum Current Transfer Requires Very Large Zth J. Choma, Jr.

24. Power Dissipated In The Load • Sinusoidal Steady State • Load Power J. Choma, Jr.

25. Maximum Power Transfer • Condition: • Max Power: J. Choma, Jr.

26. Example–50  Transmission Line • Parameters • Antenna RMS Voltage Signal Is 10 V • Transmission Line Coupling To RF Stage Behaves Electrically As A 50 Ohm Resistance • Power To RF Input Port • Maximized When RF Input Impedance Is 50 Ohms • dBm Value: J. Choma, Jr.

27. Second Order Lowpass Filter • Lowpass Filter • Unity Gain Structure (Gain At Zero Frequency Is One) • Ideal Transconductors • KVL (Solve For Vo/Vs) J. Choma, Jr.

28. Filter Transfer Function • Generalization: • Parameters • DC Gain = H(0) = 1 • Undamped Resonant Frequency = o = (gm1gm2/C1C2)1/2 • Damping Factor =  = (gm2C1 / 4gm1C2)1/2 J. Choma, Jr.

29. Lowpass 2nd Order Function • Poles At s = –p1 & s = –p2 • Undamped Frequency: • Damping Factor: • P1 & P2 Real Results In  >1 (Overdamping) Or = 1 (Critical Damping) • P1 & P2 Complex Requires P1 & P2 Conjugate Pairs, Whence  < 1 (Underdamping) J. Choma, Jr.

30. Lowpass – Critical Damping • Critical Damping  = 1  p1 = p2 • Frequency Response • Bandwidth Constraint • Bandwidth |H(j)| in dB |H(0)| Slope = –40 db/dec -3 dB  B J. Choma, Jr.

31. Lowpass – Overdamping • Overdamping  > 1  p1 < p2 • Poles Are Real Numbers • Dominant Pole System Implies p1 << p2 • Dominant Pole Bandwidth • Transfer Function Approximation • Bandwidth Approximation • Gain-Bandwidth Product J. Choma, Jr.

32. Lowpass Frequency Response 3-dB Down J. Choma, Jr.

33. Lowpass Phase Response J. Choma, Jr.

34. Lowpass Step Response • Input Is Unit Step [X(s) = 1/s] • Overdamped ( > 1) • Critical Damping ( = 1 o = p1 = p2) J. Choma, Jr.

35. Real Pole Step Response Plots 95% Line J. Choma, Jr.

36. Lowpass – Underdamping • Overdamping  < 1  p1 = p2* = oe j • Circuit Bandwidth • Proportional To o • Equal To o For  = 0.707 • Frequency Response Peaking • |H(j)| Not Monotone Decreasing Frequency Function If  < 0.707 • Non-Zero Frequency Associated With Maximal |H(j)| J. Choma, Jr.

37. Underdamped Frequency Response 3-dB Line J. Choma, Jr.

38. Underdamped Phase Response J. Choma, Jr.

39. Delay Response • Steady State Sinusoidal Response • If Phase Angle Is Linear With Frequency • Constant Time Shift, Independent Of Signal Frequency • No Phase Angle Is Ever Perfectly Linear Over Entire Passband • Envelope Delay J. Choma, Jr.

40. Underdamped Delay Response J. Choma, Jr.

41. Underdamped Step Analysis • Input Is Unit Step [X(s) = 1/s] • Underdamped ( < 1) • Characteristics • Damped Oscillations • Oscillation For Zero Damping ( = 0) • Undamped Frequency Is Oscillatory Frequency For Zero Damping J. Choma, Jr.

42. Underdamped Step Response J. Choma, Jr.