CHARACTERIZING LOSSES INMICROSTRIP TRANSMISSION LINES

CHARACTERIZING LOSSES INMICROSTRIP TRANSMISSION LINES

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  • dissertation
CHARACTERIZING LOSSES IN MICROSTRIP TRANSMISSION LINES by Rashmi Pathak A dissertation submitted in partial fulfillment of the requirements for the degree of Master of Science (Electrical and Computer Engineering) at the UNIVERSITY OF WISCONSIN–MADISON Summer 2005
  • test fixture halves
  • rashmi pathak
  • 2.1 transmission lines
  • nd resonance of the slot
  • final setup
  • equivalent circuit model
  • microstrip

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Astro110-01 Lecture 8
The Copernican Revolution
(Cont’d)
or the revolutionaries:
Nicolas Copernicus (1473-1543)
Tycho Brahe (1546-1601)
Johannes Kepler (1571-1630)
Galileo Galilei (1564-1642)
Isaac Newton (1642-1727)
who toppled Aristotle’s cosmos
4/02/09 1Astro 110-01 Lecture 8Johannes Kepler
(1571–1630)
• In the interplay between quantitative
observation and theoretical construction that
characterizes the development of modern
science, Brahe was the master of the first but
was deficient in the second.
• The next great development in the history of
astronomy was the theoretical intuition of
Johannes Kepler (1571-1630), a German who
went to Prague to become Brahe's assistant.
4/02/09 2Astro 110-01 Lecture 8Kepler and the Elliptical Orbits
• Unlike Brahe, Kepler believed firmly in the
Copernican system.
• Kepler realized that the orbits of the planets were
not the circles but were instead the "flattened
circles" called ellipses
The difficulties with the Martian orbit derive
precisely from the fact that the orbit of Mars was
the most elliptical of the planets for which Brahe
had extensive data.
4/02/09 3Astro 110-01 Lecture 8What is an ellipse?
An ellipse looks like an elongated circle.
4/02/09 4Astro 110-01 Lecture 8Eccentricity of an Ellipse
Eccentricity and Semimajor Axis of an Ellipse
4/02/09 5Astro 110-01 Lecture 8Kepler’s three laws of planetary
motions
4/02/09 6Astro 110-01 Lecture 8Kepler’s First Law:
The orbit of each planet around the Sun is an
ellipse with the Sun at one focus.
[Greek: near [Greek:
the Sun] away from
the Sun]
4/02/09 7Astro 110-01 Lecture 8Kepler’s Second Law:
As a planet moves around its orbit, it sweeps
out equal areas in equal times.
 A planet travels faster when it is nearer to the
Sun and slower when it is farther from the Sun.
4/02/09 8Astro 110-01 Lecture 8Kepler's 2nd Law
4/02/09 9Astro 110-01 Lecture 8Kepler’s Third Law
• The ratio of the squares of the revolutionary periods for two
planets is equal to the ratio of the cubes of their semimajor axes:
• Choosing subscript 1 for the Earth, the relation can be rewritten
as:
2 3
p = a
with p = orbital period in years
and a = average distance from Sun in AU
4/02/09 10Astro 110-01 Lecture 8