ECE

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ECE TCOM 590Microwave Transmission for
Telecommunications

• Introduction to Microwaves
• January 29, 2004

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Microwave Applications

• Wireless Applications
• TV and Radio broadcast
• Optical Communications
• Radar
• Navigation
• Remote Sensing
• Domestic and Industrial Applications
• Medical Applications
• Surveillance
• Astronomy and Space Exploration

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Brief Microwave History

• Maxwell (1864-73)
• integrated electricity and magnetism
• set of 4 coherent and self-consistent equations
• predicted electromagnetic wave propagation
• Hertz (1873-91)
• experimentally confirmed Maxwells equations
• oscillating electric spark to induce similar
  oscillations in a distant wire loop (?10 cm)

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Brief Microwave History

• Marconi (early 20th century)
• parabolic antenna to demonstrate wireless
  telegraphic communications
• tried to commercialize radio at low frequency
• Lord Rayleigh (1897)
• showed mathematically that EM wave propagation
  possible in waveguides
• George Southworth (1930)
• showed waveguides capable of small bandwidth
  transmission for high powers

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Brief Microwave History

• R.H. and S.F. Varian (1937)
• development of the klystron
• MIT Radiation Laboratory (WWII)
• radiation lab series - classic writings
• Development of transistor (1950s)
• Development of Microwave Integrated Circuits
• microwave circuit on a chip
• microstrip lines
• Satellites, wireless communications, ...

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Ref text by Pozar
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Microwave Engr. Distinctions

• 1 - Circuit Lengths
• Low frequency ac or rf circuits
• time delay, t, of a signal through a device
• t L/v T 1/f where Tperiod of ac signal
• but f?v so 1/f ?/v
• so L ?, I.e. size of circuit is generally much
  smaller than the wavelength (or propagation times
  ? 0)
• Microwaves L? ?
• propagation times not negligible
• Optics L ?

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Transit Limitations

• Consider an FET
• Source to drain spacing roughly 2.5 microns
• Apply a 10 GHz signal
• T 1/f 10-10 0.10 nsec
• transit time across S to D is roughly 0.025 nsec
  or 1/4 of a period so the gate voltage is low and
  may not permit the S to D current to flow

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Microwave Distinctions

• 2 - Skin Depth
• degree to which electromagnetic field penetrates
  a conducting material
• microwave currents tend to flow along the surface
  of conductors
• so resistive effect is increased, i.e.
• R ? RDC a / 2 ?, where
• ? skin depth 1/ (? f ?o ?cond)1/2
• where, RDC 1 / (? a2 ?cond)
• a radius of the wire
• R ?waves in Cu gtR low freq. in Cu

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Microwave Engr. Distinctions

• 3 - Measurement Technique
• At low frequencies circuit properties measured by
  voltage and current
• But at microwaves frequencies, voltages and
  currents are not uniquely defined so impedance
  and power are measured rather than voltage and
  current

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Circuit Limitations

• Simple circuit 10V, ac driven, copper wire, 18
  guage, 1 inch long and 1 mm in diameter dc
  resistance is 0.4 m? and inductance is 0.027 ?H
• f 0 XL 2 ? f L ? 0.18 f ?10-6 0
• f 60 Hz XL ? 10-5 ? 0.01 m?
• f 6 MHz XL ? 1 ?
• f 6 GHz XL ? 103 ? 1 k ?
• So, wires and printed circuit boards cannot be
  used to connect microwave devices we need
  transmission lines

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High-Frequency Resistors

• Inductance and resistance of wire resistors
  under high-frequency conditions (f ? 500 MHz)
• ?L/RDC ? a / (2 ?)
• R /RDC ? a / (2 ?)
• where, RDC /(? a2 ?cond) the 2 here
  accounts for 2 leads
• a radius of the wire
• length of the leads
• ? skin depth 1/ (? f ?o ?cond)1/2

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Reference Ludwig Bretchko, RF Circuit Design
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High Frequency Capacitor

• Equivalent circuit consists of parasitic lead
  conductance L, series resistance Rs describing
  the losses in the the lead conductors and
  dielectric loss resistance Re 1/Ge (in
  parallel) with the Capacitor.
• Ge ? C tan ?s, where
• tan ?s (??/?diel) -1 loss tangent

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Reference Ludwig Bretchko, RF Circuit Design
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Reference Ludwig Bretchko, RF Circuit Design
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Reference Ludwig Bretchko, RF Circuit Design
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Reference Ludwig Bretchko, RF Circuit Design
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Maxwells Equations

• Gauss
• No Magnetic Poles
• Faradays Laws
• Amperes Circuit Law

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Characteristics of MediumConstitutive
Relationships
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Fields in a Dielectric Materials
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Fields in a Conductive Materials
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Wave Equation
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General Procedure to Find Fields in a Guided
Structure

• 1- Use wave equations to find the z component of
  Ez and/or Hz
• note classifications
• TEM Ez Hz 0
• TE Ez 0, Hz ? 0
• TM Hz 0, Ez ? 0
• HE or Hybrid Ez ? 0, Hz ? 0

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General Procedure to Find Fields in a Guided
Structure

• 2- Use boundary conditions to solve for any
  constraints in our general solution for Ez and/or
  Hz

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Plane Waves in Lossless Medium
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Phase Velocity
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Wave Impedance
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Plane Waves in a Lossy Medium
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Wave Impedance in Lossy Medium
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Plane Waves in a good Conductor
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Energy and Power
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