1. Impedance Matching (1)

2. Maximum Power Transfer Choose an RL in order to maximize power delivered to RL.

3. Power Delivered to the Load

4. Numerical Example V TH =1 V R TH =50 Ω

5. Conclusion! Maximum power is delivered to the load resistor when R L is equal to R TH.

6. Max Power Transfer for Complex Source Impedance At resonant frequency, the series impedance of the inductor and capacitor is zero.

7. Summary R L >R S R S >R L

8. L Network Different L netowrk Difference bewteen highpass and low pass Examine butterworth filter from the point of view of matching….

9. Resistance Transformation (See derivation in the handout) R P must be larger than R S

10. Matlab Calculation

11. Simulation Results

12. High Pass Match Note: There is not a DC path to ZL. RS must be larger than RL! See derivation! QS=sqrt(RS/RL-1) QS=1/(ωR L C) QS=RS/(ωL)

13. Matlab Calculation

14. ADS Simulation

15. Dealing With Complex Load Absorption Approach Resonance Technique

16. Match Via Absorption Approach Ignore stray component Match the load resistance to the source resistance with an L-match Subtract the stray component from the L-match value

17. Absorption Example

18. Calculation Neglecting Stray Components

19. Account for Stray Components This technique will not work if the stray components is much larger than L match components. E.g. if 2pF is replaced by 6 pF, then this technique will not work.

20. Resonant Approach Resonate any stray reactance with an equal and opposite reactance at the frequency of interest!

21. Example Resonate the 40 pF with a parallel L.

22. Parallel Resonant Network

23. Determine the Matching Network

24. Resonant Approach Example

25. Series to Parallel Conversion for RC Circuits

26. Series to Parallel Conversion for RL Circuits

27. Intuition If the Q is sufficiently large, L S ≈L P and C S ≈C P. R P is Q 2 times R S.

28. Summary R L >R S R S >R L

29. Smith Chart Derivation

30. Smith Chart Derivation (2)

31. Smith Chart Construction (The center line represents an axis where X=0.) (+) (-)

32. z L =1±j

33. Adding a Series Capacitance to an Impedance

34. Use Smith Chart Matching

35. SmithChartMatch

36. Smith Chart Utility 1. Select Smith Chart Match 2.Click on Tools, then select Smith chart utility 3. Select first option

37. Change the Load Impedance to 75 Ohms

38. Lock Load/Source Impedance

39. Add a Shunt Capacitance

40. Negative Capacitance! Negative capacitance

41. Add a Series Inductor (1) (2) Double click on the smith chart to drop the component

42. Build ADS Circuit

43. Comparison with Matlab Vs. ADS ADSMatlab Shunt Cap1.511 pF1.5 pF Series L5.72 nH5.627 nH

44. Adding an Inductor in Series Insertion of a series inductor to an impedance moves the impedance upward, causing a rotation clockwise along a constant circle of resistance

45. Series Inductance Neg L High LLow L fixed frequency Insertion of a series inductor to an impedance moves the impedance upward, causing a rotation clockwise along a constant circle of resistance

46. Adding a Capacitor in Series Insertion of a series capacitor to an impedance move impedance downward, causes a rotation counter clockwise along a constant circle of resistance

47. Series Capacitance High C Low L Neg C fixed frequency Insertion of a series capacitor to an impedance move impedance downward, causes a rotation counter clockwise along a constant circle of resistance

48. Admittance

49. Admittance Example

50. Method 1

51. Method 2 1. Find the Z. 2. Rotate Smith Chart 180 degrees

52. Smith Chart Construction (The center line represents an axis where X=0.) (+) (-) Conductance circle Inductive susceptance Rotate the impedance chart by 180 degrees Capacitive susceptance

53. Enable Admittance Chart

54. Adding a Shunt Capacitance Insertion of a shunt capacitor causes a rotation clockwise along a constant circle of admittance

55. Adding a Shunt Capacitance High C Low C Neg C fixed frequency Insertion of a shunt capacitor causes a rotation clockwise along a constant circle of admittance

56. Adding a Shunt Inductance Insertion of a shunt inductor causes a rotation counter clockwise along a constant circle of admittance

57. Shunt Inductance Neg Ind High L Low L fixed frequency Insertion of a shunt inductor causes a rotation counter clockwise along a constant circle of admittance

58. Next Class Pi Network T Network Smith Chart Genesis

59. The Pi Network The virtual resistance must be less than RS and RL.