Impedance Matching (1)

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 • VTH=1 V • RTH=50 Ω

5. Conclusion! • Maximum power is delivered to the load resistor when RL is equal to RTH.

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

7. Summary RL>RS RS>RL

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

9. Resistance Transformation RP must be larger than RS (See derivation in the handout)

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/(ωRLC) 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, LS≈LP and CS≈CP. • RP is Q2 times RS.

28. Summary RL>RS RS>RL

29. Smith Chart Derivation

30. Smith Chart Derivation (2)

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

32. zL=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 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

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 Low L High L Neg 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 seriescapacitor to an impedance move impedance downward, causes a rotation counterclockwise along a constant circle of resistance

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

48. Admittance

49. Admittance Example

50. Method 1