ENE 429 Antenna and Transmission lines Theory

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ENE 429Antenna and Transmission lines Theory
DATE 21/08/06 18/08/06

• Lecture 6 Transmission lines problems and
  microstrip lines

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Review

• Input impedance for finite length line
• Quarter wavelength line
• Half wavelength line
• Smith chart
• A graphical tool to solve transmission line
  problems
• Use for measuring reflection coefficient, VSWR,
  input impedance, load impedance, the locations of
  Vmax and Vmin

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Ex1 A 0.269?- long lossless line with Z0 50 ?
is terminated in a load ZL 60j40 ?. Use the
Smith chart to find a) ?L b) VSWR c)
Zin d) the distance from the load to the first
voltage maximum
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Impedance matching

• To minimize power reflection from load
• Zin Z0
• Matching techniques
• 1. Quarter - wave transformers
  for real load
• 2. single - stub tuners
• 3. lumped element tuners
• The capability of tuning is desired by having
  variable reactive elements or stub length.

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Simple matching by adding reactive elements (1)

• EX2, a load 10-j25 ? is terminated in a 50 ?
  line. In order for 100 of power to reach a load,
  Zin must match with Z0, that means Zin Z0 50
  ?.
• Distance d WTG (0.5-0.424)? 0.189 ?
• 0.265 ?
• to point 1 j2.3. Therefore cut TL and insert a
  reactive element that has a normalized
  reactance of -j2.3.
• The normalized input impedance becomes
• 1 j2.3 - j2.3 1
• which corresponds to the center or the Smith
  chart.

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Simple matching by adding reactive elements (2)

• The value of capacitance can be evaluated by
  known frequency, for example, 1 GHz is given.

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Single stub tuners

• Working with admittance (Y) since it is more
  convenient
• to add shunt elements than series elements
• Stub tuning is the method to add purely reactive
  elements
• Where is the location of y on Smith chart?
• We can easily find the admittance on the Smith
  chart by
• moving 180? from the location of z.

Ex3 let z 2j2, what is the admittance?
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Stub tuners on Y-chart (Admittance chart) (1)

• There are two types of stub tuners
• Shorted end, y ? (the rightmost of the Y chart)
• opened end, y 0 (the leftmost of the Y chart)

Short-circuited shunt stub
Open-circuited shunt stub
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Stub tuners on Y-chart (Admittance chart) (2)

• Procedure
• Locate zL and then yL. From yL, move clockwise to
  
• 1 ? jb circle, at which point the
  admittance yd 1 ? jb.
• On the WTG scale, this represents length d.
  
• 2. For a short-circuited shunt stub, locate the
  short end at
• 0.250? then move to jb, the
  length of stub is then
• l and then yl jb.
• 3. For an open-circuit shunt stub, locate
  the open end at 0?,
• then move to jb.
• 4. Total normalized admittance ytot ydyl
  1.

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Ex5 What about the open-circuited stub?
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Microstrip (1)

• The most popular transmission line since it can
  be fabricated using printed circuit techniques
  and it is convenient to connect lumped elements
  and transistor devices.
• By definition, it is a transmission line that
  consists of a strip conductor and a grounded
  plane separated by a dielectric medium

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Microstrip (2)

• The EM field is not contained entirely in
  dielectric so it is not pure TEM mode but a
  quasi-TEM mode that is valid at lower microwave
  frequency.
• The effective relative dielectric constant of the
  microstrip is related to the relative dielectric
  constant ?r of the dielectric and also takes into
  account the effect of the external EM field.

Field lines where the air and dielectric have
been replaced by a medium of effective relative
permittivity, ?eff
Typical electric field lines
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Microstrip (3)
Therefore in this case and
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Evaluation of the microstrip configuration (1)

• Consider t/h lt 0.005 and assume no dependence of
  frequency, the ratio of w/h and ?r are known, we
  can calculate Z0 as

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Evaluation of the microstrip configuration (2)

• Assume t is negligible, if Z0 and ?r are known,
  the ratio w/h can be calculated as

The value of ?r and the dielectric thickness (h)
determines the width (w) of the microstrip for a
given Z0.
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Characteristic impedance of the microstrip line
versus w/h
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Normalized wavelength of the microstrip line
versus w/h
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Ex5 A microstrip material with ?r 10 and h
1.016 mm is used to build a TL. Determine the
width for the microstrip TL to have a Z0 50 ?.
Also determine the wavelength and the effective
relative dielectric constant of the microstrip
line.
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Wavelength in the microstrip line
Assume t/h ? 0.005,
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Attenuation

• conductor loss
• dielectric loss
• radiation loss

where ?c conductor attenuation (Np/m)
?d dielectric attenuation (Np/m
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Conductor attenuation
If the conductor is thin, then the more accurate
skin resistance can be shown as
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Dielectric attenuation