1. Lecture-2 Microwave Engineering Instructor: Athar Hanif

2. 1.2-Dimensions and Units  To understand the upper frequency limit, beyond which conventional circuit theory can no longer be applied to analyze an electric system, we should recall the representation of an electromagnetic wave.

3. 1.2-Dimensions and Units

4.  Propagation constant/Phase constant represents the change in phase per meter along the path travelled by the wave at any instant and is equal to the wave number of the wave.

5. 1.2-Dimensions and Units  Intrinsic impedance: the ratio between electric and magnetic field components.  TEM Waves: field components are perpendicular to each other and both are perpendicular to the direction of propagation.

6. 1.2-Dimensions and Units  TE Waves: in this magnetic field component is perpendicular to the direction of propagation.  TM Waves: in this electric field component is perpendicular to the direction of propagation.

7. 1.2-Dimensions and Units  The phase velocity of the TEM wave can be found as  Example1.1:

8. 1.2-Dimensions and Units (Problems)

10. 1.4-RF Behavior of Passive Components  From the knowledge of circuit theory  ‘R’ is frequency independent  ‘C’ and ‘L’ are frequency dependent  Capacitive and inductive reactance

11. 1.4-RF Behavior of Passive Components  For; C=1pF and L=1nH  X C =  X L =  For the low frequency; R, C and L are created by wires, plates and coils respectively  For the RF/Microwave frequency, single straight wire or a copper segment of a

12. 1.4-RF Behavior of Passive Components printed circuit board (PCB) layout has frequency dependent resistance and inductance

13. 1.4-RF Behavior of Passive Components  DC excitation  AC excitation  Skin effect  For high frequency condition(f≥500MHz)  xx

14. 1.4-RF Behavior of Passive Components  Conclusion  Conductivity  Copper σ =64.516х10 6 S/m  Aluminum σ =40.0х10 6 S/m  Gold σ =48.544х10 6 S/m

15. 1.4-RF Behavior of Passive Components

16. From this we conclude that resistance increases inversely proportional to the cross-sectional skin area

17. 1.4-RF Behavior of Passive Components 1.10- 1.11-

18. 1.4-AWG System  Diameter of the wire is determined by its AWG value  General rule: the diameter of the wire is doubles every six wire gauges starting with 1mil for a AWG 50 wire

19. 1.4-AWG System Example-1.2

20. 1.4.1-High Frequency Resistors c

21.  Electric equivalent circuit representation of the resistor

22. 1.4.1-High Frequency Resistors  Electric equivalent circuit representation for high frequency wire-wound resistance

23. Example 1.3

25. 1.4.2-High Frequency Capacitors  In RF/Microwave circuits chip capacitors find widespread applications  Tuning of filters  Matching networks  Biasing active components

26. 1.4.2-High Frequency Capacitors  Displacement current  At high frequency, dielectric becomes lossy, there is a conduction current flow  Current flow at DC is due to the conductance,

27. 1.4.2-High Frequency Capacitors  Loss tangent is defined by the angle between the capacitor’s impedance vector and the negative reactive axis

28. 1.4.2-High Frequency Capacitors

29. Electric equivalent circuit for a high frequency capacitor

30. Example 1.4

32. Loss Tangent  Loss tangent can also be defined as the ratio of an equivalent series resistance to the capacitor’s reactance

33. Problems 1.12 1.14

34. Problems 1.15

35. 1.4.3-High Frequency Inductors  RF/Microwave biasing networks  RFCs (Matching and Tuning)  Distributed capacitance and series resistance in the inductor coil

36. 1.4.3-High Frequency Inductors  Equivalent circuit of the high-frequency inductor

37. 1.4.3-High Frequency Inductors  Example 1.5:

38. 1.4.3-High Frequency Inductors

39.  Quality factor: determines the resistive loss in the passive circuit

40. High Frequency Inductors (Problems)