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CH.4
Transmission Lines
(16 marks)
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2. Basic Principle
Transmission line is a current carrying conductor.

3. Fundamentals of Transmission Line
There are two types of commonly used transmission lines.
Transmission Line
 Co-axial cable Parallel wire
( Unbalanced) (Balanced)
• Balanced line is made of two parallel conductors spaced from one another by a distance of 1/2 inch upto several inches.
• Insulating spacers may be used in the wires to be separated.
• Unbalanced line has one conductor at the center and outer braided conductor which is grounded.
• Of the two types of transmission lines, co-axial is most widely used

4. Co-axial Cable

5. Continued…. Frequency Range:
Co-axial cables carries signals of higher-frequency ranges from 100 kHz to 500 MHz.
Applications:
Co-axial cable is used when unbalanced properties are needed, as in interconnection of a broadcast transmitter to its grounded antenna.
It is also employed at UHF and microwave frequencies to avoid risk of radiation from the transmission line itself.
1. Telephone cables.
2. Cable TV system (for cable connections).
3. Local Area Networks (LAN) for computers.

6. Fig.: Connection between Dish Antenna and TV Receiver
Continued….
Fig.: Connection between Dish Antenna and TV Receiver

7. Comparison between Parallel Wire and Co-axial Cable

8. Equivalent Circuit Of Transmission Line
Fig. General Equivalent Circuit of Transmission Line

9. Fig. Transmission Line RF Equivalent Circuit

10. Primary Constants of Transmission Line
Consider a long transmission line consisting of two parallel uniform conductors carrying current, there is a magnetic field around the conductors and voltage drop along them.
• The existence of magnetic field indicates that the lines have series inductance (L) and voltage drop indicates the presence of series resistor (R).
Effect of Primary Constant on Transmission line:
The primary constants take into account both the forward and return lines.
They are constant, in that they do not vary with voltage or current, however, they are frequency dependent to some extent.
The series resistance R increases with frequency as a result of skin effect.

11. Continued…
The inductance is almost independent of frequency for open lines, but tends to decrease with increasing frequency for screened cables.
The capacitance C is almost independent of frequency whereas the conductance G tends to increase with frequency because of increasing dielectric loss with increase in frequency.
Voltage applied across the conductor produces an electric field between the conductor and charge them. This shows that lines have Shunt capacitance (C) and Shunt conductance (G).
The four constants R, G, L and C are called primary constants of transmission line.
When these constants are uniformly distributed along the line it is called uniform transmission line shown in Fig.
Four primary constants:
R - Series resistance, ohms/unit length
L - Series inductance, heneries/unit length
C - Shunt capacitance, farads/unit length
G - Shunt conductance, susceptance/unit length

12. Secondary Constants of Transmission Line
There are two secondary constants of transmission line.
Characteristic impedance (ZO) and
Propagation constant ().

13. Characteristic Impedance (ZO)
Any circuit that consists of series and shunt impedances must have an input impedance.
For the transmission line this input impedance will depend on the type of line, its length and termination at the far end.
Definition:
Characteristic impedance of a transmission line, ZO is the impedance measured at the input of this line when its length is infinite.
Method of Calculation:
If a line has infinite length, all the power fed into it will be absorbed, because the voltage drops across the inductance and leakage current through capacitance.

14. Continued…

15. Continued….

16. Continued…. Therefore, Zo=√R+jwL / √G+jwc
Equation shows the characteristic impedance of transmission line may be complex.
At radio frequencies, (or at high frequencies) the resistive components are ignored.
L >> R, C >> G
 ZO = √L/√c 
... L is measured in H/m and C in f/m.
At low frequencies
R >> L, G >> C
 Zo= √R/√G
The characteristic impedance ZO for a telephone line is between 200 to 600 .

17. Advantages/ Disadvantages of Transmission Line
(i) Simple construction.
(ii) Flexible.
(iii) Higher mechanical strength.
(iv) Less expensive.
Disadvantages
(i) Increase in power loss with increase in frequency.
(ii) Cannot handle high voltages.

18. Losses in Transmission Line
There are three ways in which energy, applied to a transmission line may be dissipated before reaching the load are −
1. Radiation loss.
2. Conductor heating loss (or I2R loss).
3. Dielectric heating loss.

19. Continued…. Radiation Loss
Radiation losses occur because a transmission line may act as an antenna if the separation between conductors is an appreciable fraction of a wavelength.
This occurs more to parallel-wire lines than co-axial lines.
Radiation losses increase with frequency for a given transmission line.
Conductor Heating (or I2R) Loss
Conductor heating loss is proportional to the current and therefore inversely proportional to the characteristic impedance.It is also increased with frequency, because of skin effect.

20. Continued…. 3. Dielectric Heating Loss
Dielectric heating is proportional to the voltage across the dielectric and hence inversely proportional to the characteristic impedance for any power transmitted.
This loss also increases with frequency for any given dielectric medium.
For air, dielectric heating remains negligible.
For co-axial lines at 1 GHz, these losses vary from as much as 200 dB/100 m for a solid-dielectric, flexible 6 mm line.

21. (i) An open circuit and (ii) A short circuit
Standing Waves
Definition:
The forward and reflected waves on the incorrectly terminated transmission line produce an interference pattern known as standing wave.
A standing wave is the unique distribution of voltage and current along the transmission line that is not terminated in its characteristic impedance.
The concept of standing wave can be best understood by considering the two cases of impedance mismatch at load or the antenna end of the transmission line.
(i) An open circuit and (ii) A short circuit

22. Fig. Standing Waves on a Shorted Transmission Line
Shorted Load
Fig. Standing Waves on a Shorted Transmission Line

23. Continued…..
The waveform below the transmission line shows the voltage and current at each point on the line.
•We can measure these voltages and current at each point with the help of multimeter.
•As shown the voltage is zero while the current is maximum because short circuit means zero impedance.
•All the power is reflected back towards the source.
•The voltage and current variations distribute themselves according to the wavelength of the signal.
•The pattern repeats for every one-half wavelength.
•The voltage and current levels at the source will be dependent on the signal wavelength and actual line.

24. Fig. Standing Waves on an Open-Circuit Transmission Line
Open Load
Fig. Standing Waves on an Open-Circuit Transmission Line

25. Open circuit means an infinite impedance, so that voltage at the end of the line is maximum and the current is zero.
• All the energy is reflected, thereby setting up this stationary pattern of voltage and current standing waves.
• Practically, transmission line won’t have a short or open.
• Instead, the load impedance will not be equal to the transmission line (characteristics) impedance.

26. Mismatch in Load:
The antenna will have reactive component, either inductive or capacitive as well as its resistance.
•The mismatch will produce standing waves, but with less amplitude, their distribution is shown in Fig
Fig. Transmission Line with Mismatched Load with resulting Standing Waves

27. Resonant Line
A line terminated in other than characteristic impedance is called a resonant line.
Non-Resonant Line
•A line terminated in its characteristics impedance is called a non-resonant or flat line

28. Reflection in Transmission Lines
Reflection of energy occurs when there is an impedance irregularity i.e. when the primary constants of the line are not uniform along the line or the terminated impedance at the far end is different from ZO.
•This reflection will be maximum when line is open circuit (terminating impedance ZR = ).
•This reflection will be negligible (or zero) when line is short circuit (i.e. ZR = 0).
•This reflection normally is undesirable on transmission line.
•If a line is terminated by its characteristic impedance does not reflect power, such a line is called non-resonant line. The reflection coefficient of such line is zero If ZRZO Zo = ZR- Z0/ ZR+ Z0

29. Standing Wave Ratio (SWR)
If ZR  ZO, some of the power is absorbed in the load and rest is reflected back.
Fig. Standing Wave
•Thus as shown in Fig. , one set of waves V and I travelling towards the load and the reflected set is travelling back to source.

30. Reflection in Transmission Lines
Reflection of energy occurs when there is an impedance irregularity i.e. when the primary constants of the line are not uniform along the line or the terminated impedance at the far end is different from ZO.
•This reflection will be maximum when line is open circuit (terminating impedance ZR = ).
•This reflection will be negligible (or zero) when line is short circuit (i.e. ZR = 0).•This reflection normally is undesirable on transmission line.
If a line is terminated by its characteristic impedance does not reflect power, such a line is called non-resonant line. The reflection coefficient of such line is zero.
If ZR  ZO

31. Standing Wave Ratio (SWR)
If ZR  ZO, some of the power is absorbed in the load and rest is reflected back.
Fig. Standing Wave
• Thus as shown in Fig, one set of waves V and I travelling towards the load and the reflected set is travelling back to source.

32. Continued….. Definition of Standing Wave:
The two sets of travelling wave travelling in opposite direction set-up an interference pattern known as standing waves.
Standing Wave Ratio (SWR) - Definition:
The ratio of maximum and minimum magnitudes of current or voltage on the line having standing wave is called Standing Wave Ratio (SWR).

33. The magnitude of standing waves on a transmission line is determined by the ratio of the maximum current to the minimum current along the line.
SWR = Vmax = Imax
Vmin Imin
•For a properly terminated transmission line,
Load impedance = Characteristic impedance
i.e. ZL = ZO
 No reflection takes place.
 Vmax = Vmin
  For ideal case

34. Definition of Standing Wave:
The two sets of travelling wave travelling in opposite direction set-up an interference pattern known as standing waves.
Standing Wave Ratio (SWR) - Definition:
The ratio of maximum and minimum magnitudes of current or voltage on the line having standing wave is called Standing Wave Ratio (SWR).

35. SWR = Vmax/Vmin =Imax/Imin
The magnitude of standing waves on a transmission line is determined by the ratio of the maximum current to the minimum current along the line.
SWR = Vmax/Vmin =Imax/Imin
•For a properly terminated transmission line,
Load impedance = Characteristic impedance
i.e. ZL=ZO
 No reflection takes place.
 Vmax=Vmin
  For ideal case
SWR = Imax/Imin =Vmax/Vmin
SWR= 1

36. Reflection Coefficient (K or R)
If a finite piece of line is terminated in an impedance not equal to characteristic impedance (i.e. ZR  ZO) then some of the power will be absorbed by termination and remaining power will be reflected towards source.
If Vi is the incident voltage and Vr is the reflected voltage wave, then their ratio will tell us what is happening along the line.
Definition:
The ratio of reflected voltage to incident voltage is called reflection coefficient (K).
K= Vr/Vi or K= Ir/Ii

37. If the line is terminated in its characteristic impedance i. e
If the line is terminated in its characteristic impedance i.e. ZL = ZO, then there is no reflected voltage so that .K=0
If the line is open or shorted, the total reflection occurs. ZL  ZO. That is Vr and Vi are same.
In this case K=1

38. Voltage Standing Wave Ratio (VSWR)
The ratio of maximum voltage to minimum voltage along a transmission line is called VSWR.
Taking only r.m.s. values,
Vmax = |Vi| + |Vr|
Vmin = |Vi| − |Vr|
Vi  r.m.s. value of incident voltage
Vr  r.m.s. value of reflected voltage
By definition,
VSWR=|Vmax|= |Vi| + |Vr|
|Vmin| |Vi| − |Vr|

39. Continued….

40. Continued….

41. Quarter and Half Wavelength Line
Transmission lines that are exactly quarter wavelength or a half wavelength long have important impedance-transforming properties and for this purpose these are used at radio frequencies.

42. Impedance Inversion by Quarter-Wavelength Lines
Consider Fig.shows a load impedance ZL connected to a piece of transmission line of length s, having characteristic impedance ZO.
Fig.Loaded Line
•When the length s is exactly a quarter wavelength line (or odd number of quarter-wavelength) and the line is lossless, then the impedance Zs, when looking towards the load is given by,
 (4.10)
•This relation is called reflective impedance, means the quarter wavelength reflects the opposite of its load impedance (also known as impedance inversion).

43. Properties of Quarter Wavelength Line:
Equation represents a very important and fundamental relation which shows important properties as follows:
1.Unless a load is resistive and equal to characteristic impedance of the line, standing waves of voltage and current are set-up along the line with node and antinode repetition rate of /4 shown in Fig.

44. Properties of Quarter Wavelength Line:
Equation represents a very important and fundamental relation which shows important properties as follows:
1.Unless a load is resistive and equal to characteristic impedance of the line, standing waves of voltage and current are set-up along the line with node and antinode repetition rate of /4 shown in Fig.
Fig.Standing Waves along a Mismatched Transmission Line; Impedance Inversion

45. Continued… Note that, (i)The voltage and current minima are not zero.
(ii)The load is not a short circuit so that SWR is not infinite.
(iii)The current nodes are separated from the voltage nodes by a distance of /4.
•At point A (current node, voltage antinode) the line impedance is high.
•At point B (current antinode, voltage node) it is reverse i.e. line impedance is low.
•In order to change the impedance at A, it is necessary to change the SWR of the line.

46. Continued…. Equation above states this relation mathematically.
Another interesting property of the quarter-wave line is seen if in equation the impedances are normalized with respect to the ZO.
Dividing by ZO to both the sides,
We have, Zs/Zo=Zo/Zs
But, Zs/Zo= Zs
and ZL/Zo =ZL
Hence, Zo/ZL =1/ZL
Substitute this in equation (4.11),
Zs =1/ZL
Zs =ZL where, Y is the normalized admittance of the load.

47. Quarter-Wave Transformer and Impedance Matching
Properties:
1. Quarter-wave transformer has a length of /4 at only one frequency.
It is highly frequency dependent and in this respect similar to a high – Q tuned circuit.
The practical behaviour of transmission line transformer and ordinary tuned transformer is identical but difference in construction.
Quarter-wave transformer used as a filter, to prevent unwanted frequencies from reaching the load, such as antenna.
If impedance matching is required for broadband, the transformer must be constructed with high resistance wire to reduce its Q, thereby increasing bandwidth.

48. Properties of Lines of Various Lengths
We know that a piece of transmission line /4 long and short circuited at far end (or /2 long and open circuited at far end) behaves exactly like a parallel tuned circuit.
Fig. Transmission Line Sections and their LC Equivalents

49. Continued….
If the frequency of operation is reduced, then there is reduction in shunt inductive reactance and increase in shunt capacitance reactance.
• Inductive current predominates and thus the impedance of circuit is purely inductive.
• Now same piece at the new frequency is less than /4 long, since how the wavelength is greater and length of line is unchanged.
• Thus, we have important property that a short circuited line less than /4 long appears as a pure capacitance.
• The various possibilities are shown in Fig which is nothing but table of various line lengths, termination and their equivalent LC circuits.

50. Impedance Matching
The best way to prevent a mismatch between the antenna and transmission lines is correct design.
•But, practically mismatches occurs.
i.e. the antenna resistance may be other than the characteristic impedance of the line or the antenna may be inductive or capacitive.
•One solution is to tune the antenna, by adjusting its length.
•Also, we can insert impedance matching circuit or antenna tuner between the transmitter and the transmission line.
•This can be balun (balance to unbalance transformer) or LC, L, T or  network.
•These circuits will make the transmitter to behave properly but will not reduce the SWR on the transmission line.

51. Stubs
It is possible to connect sections of open or short circuited line known as stub or tuning stub in shunt with the main line at a certain point to effect the impedance matching.
• The matching with the help of tuning stub or stub is called stub matching and it has following advantages.
(i) Length (l) and characteristic impedance (ZO) remains unchanged.
(ii) Mechanically, it is possible to add adjustable susceptance in shunt with the line.
•A stub matching is of two types.
Stub Matching
Single Stub Matching Double Stub Matching

52. Fig.: Single Stub Matching
A type of transmission lines frequently employed for single stub matching is shown in Fig.
Fig.: Single Stub Matching

53. Continued….
The main element of this transformer is a short circuited section of line whose open end is connected to the main line at a particular distance from the load end.
•Where the input conductance at that point is equal to the characteristic conductance of the line, and the stub length is adjusted to provide a susceptance equal in value but opposite in sign, to the input susceptance of the main line at that point.
•So that, the total susceptance of the main line at that point is zero.
•The combination of stub and the line will thus present a conductance which is equal to the characteristic impedance of the line, i.e. the main length of the HF transmission line will be matched.

54. Advantages &Demerits of Single Stub Matching
Advantages of short circuited stub −
(i) Less power radiation and
(ii) Effective length variation is possible by shorting bar, thus, a short circuited stub is invariably used. For lossless short circuited stub VR = 0.
Demerits of Single Stub Matching
•The single stub matching suffers from the two main disadvantages as follows:
(i)The range of terminating impedances which can be transferred is limited.
(ii)It is useful only for a fixed frequency because as the frequency varies, the position of stub has to be varied.

55. Double Stub Matching
The disadvantages of single stub matching are overcome by using double stub matching as shown in Fig.
Fig. Double Stub Matching

56. Balun
A Balun or a balance to unbalance transformer, is a circuit element used to connect a balanced line to unbalanced line. i.e. it is used to connect an unbalanced (coaxial) line to a balance antenna such as a dipole.
• As shown in Fig here the windings associated with the balanced system is symmetrically arranged with respect to a grounded electrostatic shield so that stray capacitances enevitably present will not introduce unbalance.

57. Continued…
Fig. Balanced to Unbalanced Transformation With The Help of Tuned Transformer

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