ELCT564 Spring 2012

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Chapter 3: Waveguides and Transmission Lines

Waveguides

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Metal Waveguides

Dielectric Waveguides

Comparison of Waveguides and Tlines

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Transmission Line Waveguide

Two or more conductors separated by some insulating medium (two-wire, coaxial, microstrip, etc.

Metal waveguides are typically one enclosed conductor filled with an insulating medium while a dielectric waveguide consists of multiple dielectrics

Normal operating mode is the TEM or quasi-TEM mode (can support TE and TM modes but these modes are typically undesirable.

Operating modes are TE or TM modes (can not support a TEM mode)

No cutoff frequency for the TEM mode. Tline can transmit signals from DC up to high frequency

Must operate the waveguide at a frequency above the respective TE or TM mode cutoff frequency for that mode to propogate

Significant signal attenuation at high frequencies Lower signal attenuation at high frequencies

Small cross section line can transmit only low power levels

Can transmit high power levels

Large cross section tlines can transmit high power leves.

Large cross section waveguides are impractical due to large size and high cost.

General Solutions for TEM, TE and TM Waves

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General Solutions for TEM, TE and TM Waves

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TEM Waves

TE Waves

TM Waves

Attenuation due to Dielectric Loss

Parallel Plate Waveguide

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TEM Waves

Parallel Plate Waveguide

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TM Waves

Parallel Plate Waveguide

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TE Waves

Summary of Results for Parallel Plate Waveguide

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Rectangular Waveguide

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TE Waves

Rectangular Waveguide

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TM Waves

Summary of Results for Rectangular Waveguide

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Example I

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Consider a length of Teflon-filled (εr=2.08, tanδ=0.0004) copper K-band rectangular waveguide, having dimensions a=1.07 cm and b=0.43 cm. Find the cutoff frequencies of the first five propagating modes. If the operating frequency is 15 GHz, find the attenuation due to dielectric and conductor losses.

Example II

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Circular Waveguide

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TE Waves

Circular Waveguide

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TM Waves

Summary of Results for Cirular Waveguide

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Example I

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Find the cutoff frequencies of the first two propagating modes of a Teflon-filled (εr=2.08, tanδ=0.0004) circular waveguide with a=0.5cm. If the interior of the guide is gold plated, calculated the overall loss in dB for a 30cm length operating at 14GHz.

Example II

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Attenuation of Waveguides

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Coaxial Line

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Higher Order Modes

Coaxial Line: Example

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Consider a piece of RG-401U coaxial cable, with inner and outer conductor diameter of 0.0645’’ and 0.215’’, and a Teflon dielectric(εr=2.2). What is the highest usable frequency before the TE11 waveguide mode starts to porpagate?

=563.4 m-1

=18.15GHz

Field lines for TEM mode of a coaxial line

Field lines for TE11 mode of a coaxial line

Coaxial Connectors

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Connector Type Other names

Female Male Maximum Frequency

Phone plugs and jacks

TS, TRS 100 kHz

RCA Phono plugs and jacks

10MHz

UHF PL-259 300MHz

F Video 250MHz to 1 GHz

BNC 2GHz

C 12 GHz

Type N 12GHz or more

SMA 12 GHz or more

2.4mm 50GHz

Strip Line

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Strip Line: Example

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Find the width for a 50Ω copper stripline conductor, with b=0.32 cm and εr=2.2. If the dielectric loss tangent is 0.001 and the operating frequency is 10 GHz, calculate the attenuation in dB/λ. Assume a conductor thickness of t=0.1mm.

Microstrip Line

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MicroStrip Line: Example

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Calculate the width and length of a 50Ω copper microstrip line, with a 90o phase shift at 2.5GHz. The substrate thickness is d=0.127 cm, with εr=2.2.

Wave Velocities and Dispersion

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Dispersion: If the phase velocity is different for different frequencies, then the individual frequency components will not maintain their original phase relationships as they propagate down the transmission line or waveguide, and signal distortion will occur.

Group Velocity

Calculate the group velocity for a waveguide mode propagating in an air-filled guide. Compare this velocity to the phase velocity and speed of light.

Summary of Transmission Lines and Waveguides

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Characteristic Coax Waveguide Stripline Microstrip

Modes: Preferred Other

TEMTE, TM

TE10TM, TE

TEMTM,TE

Quasi-TEMHybrid TM, TE

Dispersion None Medium None Low

Bandwidth High Low High High

Loss Medium Low High High

Power Capacity Medium High Low Low

Physical Size Large Large Medium Small

Ease of Fabrication Medium Medium Easy Easy

Integration with Others Hard Hard Fair Easy

Other Lines and Guides

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