Lecture-2

Microwave EngineeringInstructor: 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

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)

1.2-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 XC=

XL=

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 =64.516х106S/m Aluminum σ =40.0х106S/m Gold σ =48.544х106S/m

1.4-RF Behavior of Passive Components

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

1.10-

1.11-

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

1.4.1-High Frequency Resistors

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

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

1.4.2-High Frequency Capacitors

• Electric equivalent circuit for a high frequency capacitor

Example 1.4

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

1.12

1.14

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

1.4.3-High Frequency Inductors

Quality factor: determines the resistive loss in the passive circuit

High Frequency Inductors (Problems)