DISP-2003_ Introduction to Digital Signal Processing - faculty_3_

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DISP-2003_ Introduction to Digital Signal Processing - faculty_3_ Powered By Docstoc
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     Dr. Hugh Blanton

   ENTC 4307/ENTC 5307
Transmission Line Transformations
• A lossless transmission line is a cascade of series
  inductors and parallel capacitors.
    • Cascading a transmission line to a complex termination
      has a rotating effect on the Smith Chart.




 Dr. Blanton - ENTC 4307 -   Introduction          3 / 30
  • To calculate the input impedance (ZIN) of a
    lossless transmission line (having
    characteristic impedance ZTL and electrical
    length q) cascaded to ZT.
      1. Locate the normalized termination (zT) on a Smith
         Chart that is normalized to Zo = ZT.
      2. Draw a concentric circle (constant VSWR) through
         zT and rotate clockwise on this circle twice the
         electrical length (2q in degrees) of the line.
      3. Mark the end of the rotation of the circle and read
         the normalized value of zIN.
      4. Multiply zIN by Z0 to find ZIN.


Dr. Blanton - ENTC 4307 -   Introduction           4 / 30
• Textbooks recommend different procedures for
  transmission line transformations on the Smith
  Chart:
   • one for movement towards loads and
   • another toward sources.
        • Instead of having two different directions, always rotate
          clockwise from the starting impedance to find a new
          impedance along the line.




Dr. Blanton - ENTC 4307 -     Introduction                    5 / 30
• Since the Chart is a reflection coefficient tool, a
  wave must travel twice (incident and reflected)
  through the transmission line.
    • Accordingly, we must rotate through an angle in
      degrees that is two times the electrical length of the
      line.




 Dr. Blanton - ENTC 4307 -   Introduction              6 / 30
• Find the input impedance (ZIN) of the circuit
  shown at f = 1 GHz.




 Dr. Blanton - ENTC 4307 -   Introduction    7 / 30
             ZT    30  j15
1. Find zT                 0.4  j 0.2 on a Smith Chart
             ZTL      75
   that is normalized to ZTL.

2. Draw a constant VSWR circle through zT rotate 2q=90
   clockwise (154 to 64) from zT.

3. Read the normalized input impedance zIN = 1 +j1.

4. Unnormalize, ZIN = zIN Zo =( 1 +j1)75W.

5. Read GIN75=O.45Z64 in the 75~ system
6. 6. NOTE THAT Zin ALWAYS falls on the constant
   VSWR circle that passes thru Z~
Dr. Blanton - ENTC 4307 -   Introduction             8 / 30
Dr. Blanton - ENTC 4307 -   Introduction   9 / 30
• At a given frequency, lumped capacitors and
  inductors may be replaced by their equivalent
  open circuited or short circuited transmission line
  stubs.




Dr. Blanton - ENTC 4307 -   Introduction     10 / 30
• If a transmission line of less than 90 electrical
  length is open circuited at one side, the other end
  becomes similar to a capacitor.
   • This element can be used as an open-circuited parallel
     stub.




Dr. Blanton - ENTC 4307 -   Introduction           11 / 30
The input reflection coefficient of an open-circuited line is found on
the Smith Chart by starting at an open circuit termination (ZT =)
and rotate clockwise twice the electrical length (2 x 45 = 90)


 Dr. Blanton - ENTC 4307 -    Introduction                  12 / 30
• If a transmission line of less than 90 electrical
  length is short circuited at one end, the other side
  behaves like an inductor.
   • When used as a parallel branch, it represents a parallel
     short circuited stub.




 Dr. Blanton - ENTC 4307 -   Introduction            13 / 30
Dr. Blanton - ENTC 4307 -   Introduction   14 / 30

				
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posted:10/21/2012
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