Transmission Lines

ULTRA HIGH FREQUENCY (U.H.F) TRANSMISSION LINES-1

by amsh

ULTRA HIGH FREQUENCY (U.H.F) TRANSMISSION LINES (TRANSMISSION LINES AS CIRCUIT ELEMENTS)

Ultra High Frequency lines commonly abbreviated as U.H.F lines are one of the types of the transmission lines. Ultra high frequency lines have operational frequency range from 300 to 3000 MHz or wavelength from 100 cm to 10 cm.

Under normal frequencies the transmission lines are used as wave guides for transferring power and information from one point to another.

At Ultra High Frequencies, the transmission lines can be used as circuit elements like capacitor or an inductor . It means they can be used in circuits like a capacitor or an inductor.

Assuming line to be lossless ,that is α=0.

As Input impedance of a lossless line

Zi=z0[Zr+j Z0tab β l/Z0+jZRtan β l]

Cases

  1. Input Impedance Zi for open circuited line

A voltage difference will exist between two wires but no current can flow in open circuit.Thus at the open end termination of this line there exist a maximum voltage and zero current. Therefore impedance at the open end will be infinite.

That is                                        ZR=∞

Ir=0                                                                      [zr=Vr/IR]

Now dividing numerator and denominator of R.H.S in expression of Zj,we get

Zi=Z0[1+jZ0/Zrttan βL/Z0/ZR+j tan βL]

= Z0[1+0/0+jtan βL]                              (ZR=∞]

=Z0/j tan βL

Or                                                           (Zi)OC= -j Z0cot βl

2. Input Impedance Zi for short circuited line

For the short –circuited end between the two transmission lines wires there will be no voltage difference ,but there will be a maximum current flow. Therefore ,at the short –circuited termination ,the current is maximum ,the voltage is zero and impedance will also be zero.

That is             ZR=0

This implies                              V­r=0                                            [zr=vR/iR]

THUS EQUATION 31(B) BECOMES

Zi=Z0[0+j Zotan βl/Z0+0]

Thus                                                 (Zi)SC=jZ0tan βl

As                                       Zi=R0+j X0

Thus by comparing above two equations, we get

X0=Z0tan βl

Thus Ziof a short circuited line is pure reactive.

For a short length line,

Tan βl= βl

Therefore Zi=j Z0 βl

= j L/C ш LC l       [Z0=L/C and β=ш LC]

Zi= jшLl               (inductive Reactance]

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