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Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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Transmission Lines and Antennas

Introduction to Tx Lines

Javier Leonardo Araque Quijanof! "#3 $ %&"

(t. 1"&)3jlaraqueq*unal.edu.co

Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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L/2 dz

L/2 dz

C dz

i(z,t) i(z+dz,t)

+

v(z,t)

-

+

v(z+dz,t)

-

i(z,t) i(z+dz,t)

Transmission Lines

v+t -

/

0

. . .

. . .

d1

Telegrapher'sequations

Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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Waves in Transmission Lines Partial derivation of equations above (one w.r.t. t, other w.r.t. z

followed by substitution of the element with crossed differentials)results in identical (wave) equations for v(z,t) and i(z,t):

General solutions have the form:

2nits +sm4,the inverse of asquare velocit5

Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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Terminated Transmission Lines (2)

v+t -/

0L

L6nitiall5 onl5 a 7 8ro8a/atin/ wavee(ists. 9hen it im8in/es on the load, it

cannot b5 itself satisf5 the circuit relation:;6

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Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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Terminated Transmission Lines(Time Domain)

v+t -

/

0L

L

6n /eneral both forward and bac>ward waves are required tosatisf5 boundar5 conditions +volta/ecurrent ratio at lum8ed loads.9henever 0c and the terminatin/ load are different, a reflectedwave is /enerated, the reflection coefficient is +see ne(t slides!

Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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Terminated Transmission Lines (2)

/

0L

L

v+t -

A similar reflection ta>es8lace at the /eneratorconsiderin/ its =h@veninim8edance /.

Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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Lossy Transmission Lines(Frequency Domain)

L% d

L% d

B d

i+ i+7d

7

v+

C

7

v+7d

Ci+ i+7d

L% d % d

% d

Dd

1

Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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LossyTransmissionLines (Freq.

Dom.) (2)

=imeCdomain form, forwardC8ro8a/atin/ wave!

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Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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Distorting and Distortionless Lines

Deneric loss5 lines are!Dispersive = phase velocity depends on frequencyDistortin = !ttenuation constant depends on f requency

"hen any of the a#ove holds, the line is ter$ed %distortin&

Fistortionless lines have attenuation constant and 8hase velocit5 inde8endent from w!

Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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Terminated Lossy Line(Frequency Domain)

:

-

/

l

0L

0c,

0in

z=0z=-l

Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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Lossless Line Terminated in Sort!ircuit

l

0c,

0in

Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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"xercise

Comute the inut imedance of these

terminated !" lines: #hort$circuit lossless line

%en$circuit lossless line

&uarter$wavelen'th lossless line with realtermination

alf$wavelen'th line with arbitrarytermination

Comute * and $ in the circuit before.

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Javier Araque, this material cannot be used outside the course where it was obtained without author's written consent.

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#e$erences

+- . /. Collin, 01oundations of 2icrowave/n'ineerin'3, 4/// ress, 566.

+5- 7. 2. Pozar, 02icrowave /n'ineerin'3, 8ohn

9iley sons, ;;