Lecture-2 Microwave Engineering Instructor: Athar Hanif

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.

1.2-Dimensions and Units

 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.

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.

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.

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

1.2-Dimensions and Units (Problems)

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

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

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

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

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

1.4-RF Behavior of Passive Components

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

1.4-RF Behavior of Passive Components

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

1.4-AWG System Example-1.2

1.4.1-High Frequency Resistors c

 Electric equivalent circuit representation of the resistor

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

Example 1.3

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

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,

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

1.4.2-High Frequency Capacitors

Electric equivalent circuit for a high frequency capacitor

Example 1.4

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

Problems

Problems 1.15

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

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

1.4.3-High Frequency Inductors  Example 1.5:

1.4.3-High Frequency Inductors

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

High Frequency Inductors (Problems)