Lecture-2Microwave EngineeringInstructor: Athar Hanif

1.2-Dimensions and UnitsTo 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 UnitsPropagation 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 UnitsIntrinsic 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 UnitsTE 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 UnitsThe 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 ComponentsFrom the knowledge of circuit theoryR is frequency independentC and L are frequency dependentCapacitive and inductive reactance

1.4-RF Behavior of Passive ComponentsFor; C=1pF and L=1nHXC=XL=For the low frequency; R, C and L are created by wires, plates and coils respectivelyFor 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 ComponentsDC excitationAC excitationSkin effectFor high frequency condition(f500MHz)

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1.4-RF Behavior of Passive Components

ConclusionConductivityCopper =64.516106S/mAluminum =40.0106S/mGold =48.544106S/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 Components1.10-

1.11-

1.4-AWG SystemDiameter of the wire is determined by its AWG valueGeneral rule: the diameter of the wire is doubles every six wire gauges starting with 1mil for a AWG 50 wire

1.4-AWG SystemExample-1.2

1.4.1-High Frequency Resistors

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1.4.1-High Frequency ResistorsElectric equivalent circuit representation of the resistor

1.4.1-High Frequency ResistorsElectric equivalent circuit representation for high frequency wire-wound resistance

Example 1.3

Example 1.3

1.4.2-High Frequency CapacitorsIn RF/Microwave circuits chip capacitors find widespread applicationsTuning of filters Matching networksBiasing active components

1.4.2-High Frequency CapacitorsDisplacement currentAt 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 CapacitorsLoss tangent is defined by the angle between the capacitors impedance vector and the negative reactive axis

1.4.2-High Frequency Capacitors

1.4.2-High Frequency CapacitorsElectric equivalent circuit for a high frequency capacitor

Example 1.4

Example 1.4

Loss TangentLoss tangent can also be defined as the ratio of an equivalent series resistance to the capacitors reactance

Problems1.12

1.14

Problems1.15

1.4.3-High Frequency InductorsRF/Microwave biasing networksRFCs (Matching and Tuning)Distributed capacitance and series resistance in the inductor coil

1.4.3-High Frequency InductorsEquivalent circuit of the high-frequency inductor

1.4.3-High Frequency InductorsExample 1.5:

1.4.3-High Frequency Inductors

1.4.3-High Frequency InductorsQuality factor: determines the resistive loss in the passive circuit

High Frequency Inductors (Problems)