Transmission Line (Final)

1Lab: Transmission Line

Table of Contents

Introduction·································································································2

Objective······································································································2

Equipment·································································································3

Procedure·································································································3

Results·······································································································5

Analysis and

Discussion··················································································6

Conclusion·····································································································

10

Appendix

A······································································································11

References ·····································································································

13


Transmission Line

Introduction:

Transmission lines are used to transfer energy of waves or signals from one

node to another node via line circuit. Standing wave ratio (SWR) is defined as to

determine the maximum voltage and current on a transmission line and to determine

how a transmission is perfect? A standing wave ratio of 1:1 shows the perfect

characteristic impedance of transmission line. Nodes are the places on transmission

line where opposite phase of two waves cancel

out the effect of each other. While anti-nodes are the places where maximum current is

obtained and two waves of the same phase added up to enforce each other’s effect.

Objective:

The objective of this experiment is the study of characteristics of transmission

lines by examining standing wave ratio (SWR) measurement. The purpose of this

experiment is to determine the minimum and maximum current values via transmission

lines and to take the points on the transmission line to measure the distance between

anti-node and node so that we will be able to measure wavelength of the signal and to


determine the velocity propagation of the waves. We can plot SWR versus resistance

and can measure characteristic impedance.

Equipment:

Varnier Calliper

Wire Air Dielectric Transmission Line

Meter Rule

Travelling Ammeter $ detector

HP 8654A Signal Generator

Procedure:

Meter rule was used to calculate the length of the transmission line and recorded

measurement form the point of transmission line matching network (Generator

input point) to the point where two wires are connecting together ( short circuit

point) and recorded the length which is 747 cm long.

After that by using Vernier Calliper, we measured the diameter of two wires and

also measured the distance between two wires. And noted down the diameter

d=1mm and distance between two wires= 39mm.

Adjusted the frequency of the HP8564A signal generator to 150 MHz and power

to 0 dBm and turned on the signal generator and turned on the power amplifier

EIN Model 310RF.


Put the travelling detector on the two wires and hold down the Ammeter steadily

and make sure that the travelling Detector will be able to move easily on the

wires by pushing gently and set the reading of the Ammeter to zero before

measuring.

Start detecting the reading on the generator input point and moved the travelling

detector slowly towards the load side and check the ammeter reading

continuously till first node 1st anti-node or node is obtained and mark that

position.

Current has minimum value at node terminal.

Current has maximum value at anti-node terminal.

Move the detector toward load side till we will get all the anti-nodes and nodes

and record all the values in table-2.

After that we measured the distance between adjacent nodes and adjacent anti-

nodes and recorded the readings in table 3.

By using following formula, we can determine velocity of propagation V

V= f x λ

After that we replaced the copper conductor with inductance (216+j15Ω) and

capacitance 9312-j77Ω) at the same node. Repeated the steps and recorded the

values in table 4, 5, 6 and 7.

From the data recorded, determined the value of SWR for each case by using

following equation

SWR = ImaxImin


Results:

The distance of the source form load is LLine= 6910 mm.

Transmission line dimensions are

L (mm) 43.5 44 41

D (mm) 1.5 1.4 1.5

Table 1: Dimensions of transmission line

After terminating the transmission line with the inductance resistance 216-

j15Ω

Current Imax1 Imin1 Imax2 Imin2 Imax3 Imin3 Imax4

Ammeter

Reading (µA)18 2 20 1.8 19 2 20.5

Table 2: Ammeter reading at nodes and anti-nodes

Distance LN1= MIN1-MIN2 LN2= MIN2-MIN3 LN3= MIN3-MIN4

Length (mm) 1005 990 1030

Table 3: Distance between adjacent nodes- 216+j15Ω

After terminating the transmission line with the inductance resistance 312-

j77Ω.


Current Imin1 Imax1 Imin2 Imax2 Imin3 Imax3 Imin4

Ammeter

Reading (µA)6 8 6 10 6.1 7.9 6.8

Table 4: Ammeter reading at nodes and antinodes-312-j77Ω

Distance LN1= MIN1-MIN2 LN2= MIN2-MIN3 LN3= MIN3-MIN4

Length (mm) 870 980 1020

Table 5: Distance between adjacent nodes- 312-j77Ω

Analysis & Discussion:

Calculation of Velocity of Propagation:

We know the velocity of propagation of waves is defined as

V= f x λ, where f is the frequency of the signal.

From the data in above tables,

λ = [(1115 + 980 + 1050) + +1030+ 990+1005) + +1020+ 980 +870)] *2/9

= 2.01 m

Hence,

Vp= ¿) * (2.010

= 3.01* 108m /s

This velocity is greater than the speed of light.

Calculation of Velocity Factor:

The ratio of velocity in transmission line to the velocity in free space is called velocity factor and can be defined as follows:

Vf= Vp/c


Vf= 3.01∗108

3∗108

≈ 1

Analysis of short circuit transmission line:

From the data in above tables,

In all the three cases, the maximum value of current is bigger in short circuit

transmission line than the other two cases (shorted circuit, 216+j15Ω, and 312-j77Ω).

In short circuit transmission line, the minimum value of current is theoretically zero. But

it is not zero but very close to zero. That’s why, there is large SWR.

Calculation of Standing wave ratio:

We know that SWR= Imin/Imax. SWR will be large if Imax will be low.

By changing the transmission line with inductance value of 216+j15Ω

Current Imax1 Imin1 Imax2 Imax2 Imin3 Imin3

Reading (µA) 10 1 11.8 1.2 12 1.8

SWR= Imax/Imin 10 9.83 6.67

Table 6: Calculation of SWR with impedance value 216+j15Ω

Average SWR= (10.0+9.831+6.68)/3 = 8.831

By changing the transmission line with inductance value of 312+j77Ω

Current Imax1 Imin1 Imax2 Imax2 Imin3 Imin3

Reading (µA) 8 6 10 6 7.9 6.1

SWR= Imax/Imin 1.33 1.67 1.30


Average SWR= (1.331+1.671+1.31)/3 = 1.431

From this data, it is concluded that different values of SWR were obtained with different

values of loads of transmission line; this shows the different level of reflection.

Calculation of Characteristics Impedance Z0:

Characteristic impedance Z0 can be determined by using following equation:

Z0 = 276

√ε r log10

2Da

From the given data, we can calculate Z0

D=L-d (mm) D (mm) Z0 (Ω)

42 1.5 483

42.6 1.4 492

39.5 1.5 475

Average D = (42.0+42.60+39.50)/3=41.370mm

Average d = (1.50+1.40+1.50)/3 = 1.470mm

By putting values in the above values,

Z0 = 483 Ω

Characteristic Impedance Estimation

By using SWR values calculated and the corresponding resistance, we can draw the

diagram


Figure 1: Characteristic Impedance Estimation

For pure resistance:

If the load is a pure resistance, SWR has following formulas

SWR= R/ Z0; R>Z0

=1; R=Z0

= Z0/R; R<Z0

Figure 2: Relation between SWR and pure resistance R


Calculation of Reflection Coefficient:

For SWR= 8.83,

Reflection Coefficient = 0.8

For SWR = 1.43,

Reflection Coefficient = 0.18

From this, we concluded that the value reflection coefficient increase with the increase of SWR. Different values represent different levels of reflection.

Conclusion:

It is concluded that the propagation velocity is very close to speed of light in transmission line but it is always lower than the speed of light and it can be measured by dielectrics of transmission lines.The characteristic impedance of a lossless transmission line can be measured by the dielectric permittivity and dimension of transmission line.

Propagation waves will occur along the transmission line if characteristics impedance is not equal to the load of transmission line. Different levels of reflection in transmission line are due to different levels of mismatching and are described below:

1 <SWR < ∞ or 0 << 1, partial reflection.

SWR= or =0, no reflection

SWR= or =1, total reflection.

If a short transmission line is used or transmission line is opened or load is pure reactance, total reflection will occur. Maximum values is the twice of the incident value of the current and the minimum value is zero. The maximum and minimum value of the current will repeat after every half wavelength.

Current changing rule in transmission line is same like the voltage changing rule but both are 90 degree out of phase.


Appendix(A):

Figure 3: Matching Transmission load with load 216+j15Ω


Figure 4: Matching transmission line with 312-j77Ω


REFERENCES:

Beasley, J. S., & Miller, G. M. (2008). Modern electronic communication. New

Jersey, the United States of America: Pearson Education.

Black Magic Design. (2010). The complete Smith Chart. Retrieved from

http://www.sss-mag.com/pdf/smithchart.pdf.

Blake, R. (2002). Electronic communication systems. New York, the United States

of America: Delmar.

Roddy, D., & Coolen, J. (1984). Electronic communications. Virginia, the United

States of America: Reston Publishing Company.

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Transmission Line (Final)