Transmission Line by YEASIN NEWAJ
- 1. Transmission Line (Microwave Engineering) Presented By Yeasin Newaj Bsc. In Electrical And Electronic Engineering
- 2. TRANSMISSION LINE A transmission line is a connector which transmits energy from one point to another. The study of transmission line theory is helpful in the effective usage of power and equipment. In radio-frequency engineering, a transmission line is a specialized cable or other structure designed to conduct alternating current of radio frequency, that is, currents with a frequency high enough that their wave nature must be taken into account. Transmission lines are used for purposes such as connecting radio transmitters and receivers with their antennas (they are then called feed lines or feeders), distributing cable television signals, trunklines routing calls between telephone switching centres, computer network connections and high speed computer data buses. While transmitting or while receiving, the energy transfer has to be done effectively, without the wastage of power. To achieve this, there are certain important parameters which has to be considered.
- 3. OVERVIEW Ordinary electrical cables suffice to carry low frequency alternating current (AC), such as mains power, which reverses direction 100 to 120 times per second, and audio signals. However, they cannot be used to carry currents in the radio frequency range, above about 30 kHz, because the energy tends to radiate off the cable as radio waves, causing power losses. Radio frequency currents also tend to reflect from discontinuities in the cable such as connectors and joints, and travel back down the cable toward the source. These reflections act as bottlenecks, preventing the signal power from reaching the destination. Transmission lines use specialized construction, and impedance matching, to carry electromagnetic signals with minimal reflections and power losses. The distinguishing feature of most transmission lines is that they have uniform cross sectional dimensions along their length, giving them a uniform impedance, called the characteristic impedance to prevent reflections. The higher the frequency of electromagnetic waves moving through a given cable or medium, the shorter the wavelength of the waves. Transmission lines become necessary when the transmitted frequency's wavelength is sufficiently short that the length of the cable becomes a significant part of a wavelength. At microwave frequencies and above, power losses in transmission lines become excessive, and waveguides are used instead, which function as "pipes" to confine and guide the electromagnetic waves. Some sources define waveguides as a type of transmission line; however, this article will not include them. At even higher frequencies, in the terahertz, infrared and visible ranges, waveguides in turn become lossy, and optical methods, (such as lenses and mirrors), are used to guide electromagnetic waves.
- 4. TRANSMISSION LINE THEORY The key difference between circuit theory and transmission line theory is electrical size. Circuit analysis assumes that the physical dimensions of the network are much smaller than the electrical wavelength, while transmission lines may be a considerable fraction of a wavelength, or many wavelengths, in size. Thus a transmission line is a distributed parameter network, where voltages and currents can vary in magnitude and phase over its length, while ordinary circuit analysis deals with lumped elements, where voltage and current do not vary appreciably over the physical dimension of the elements.
- 6. TYPES OF TRANSMISSION LINE There are basically four types of transmission lines − Two-wire parallel transmission lines Coaxial lines Strip type substrate transmission lines Waveguides
- 7. TWO-WIRE PARALLEL TRANSMISSION LINES In this type of construction for two wire transmission lines the insulated spacers are used in order to maintain the distance between the transmission lines or between the two conducting wire equally throughout. In this type of transmission line the two conducting wires are kept parallel to each other with the help of plastic material. This is used throughout between the conducting wires. In this type of transmission line the rubber piping is used in circular rectangular or square shape. The two conducting wires are kept inside the rubber at opposite sides of the piping. These conducting wires urn throughout the construction and remains parallel to each other.
- 8. COAXIAL LINES It consists of an inner conducting wire which is made of the copper material. Over this conducting wire of copper, there is a coating of polyethylene or there is a carrying of ethylene material. Then after that, there is an enclosure in a braded wire which is in the form of a mesh. The outer part is having an enclosure of the surface jacket. As shown in the given diagram the co-axial cable consists of inner conducting wire made of copper, over this conducting wire the coating of polyethylene or taplon material is carried out. Then it is enclosed in the braded wire in the shape of mash. The outer surface of this wire is enclosed in a plastic jacket.
- 9. STRIP TYPE SUBSTRATE TRANSMISSION LINES A microstrip circuit uses a thin flat conductor which is parallel to a ground plane. Microstrip can be made by having a strip of copper on one side of a printed circuit board (PCB) or ceramic substrate while the other side is a continuous ground plane. The width of the strip, the thickness of the insulating layer (PCB or ceramic) and the dielectric constant of the insulating layer determine the characteristic impedance. Microstrip is an open structure whereas coaxial cable is a closed structure. Microwave components such as antennas, couplers, filters, power dividers etc. can be formed from microstrip, with the entire device existing as the pattern of metallization on the substrate. Microstrip is thus much less expensive than traditional waveguide technology.
- 10. WAVEGUIDES A waveguide is an electromagnetic feed line used in microwave communications, broadcasting, and radar installations. A waveguide consists of a rectangular or cylindrical metal tube or pipe. The electromagnetic field propagates lengthwise. Waveguides are most often used with horn antennas and dish antennas. They are practical only for signals of extremely high frequency, where the signal wavelength approaches the cross-sectional dimensions of the waveguide.
- 11. MAIN PARAMETERS OF A TRANSMISSION LINE The important parameters of a transmission line are resistance, inductance, capacitance and conductance. Resistance and inductance together are called as transmission line impedance. Capacitance and conductance together are called as admittance.
- 12. RESISTANCE The resistance offered by the material out of which the transmission lines are made, will be of considerable amount, especially for shorter lines. As the line current increases, the ohmic loss (I2Rloss) also increases. The resistance R of a conductor of length "l" and cross-section "a" is represented as Where ρ = resistivity of the conductor material, which is constant. Temperature and the frequency of the current are the main factors that affect the resistance of a line. The resistance of a conductor varies linearly with the change in temperature. Whereas, if the frequency of the current increases, the current density towards the surface of the conductor also increases. Otherwise, the current density towards the center of the conductor increases. This means, more the current flows towards the surface of the conductor, it flows less towards the center, which is known as the Skin Effect.
- 13. INDUCTANCE In an AC transmission line, the current flows sinusoidally. This current induces a magnetic field perpendicular to the electric field, which also varies sinusoidally. This is well known as Faraday's law. The fields are depicted in the following figure. This varying magnetic field induces some EMF into the conductor. Now this induced voltage or EMF flows in the opposite direction to the current flowing initially. This EMF flowing in the opposite direction is equivalently shown by a parameter known as Inductance, which is the property to oppose the shift in the current. It is denoted by "L". The unit of measurement is "Henry H". Inductive reactance, which is the Ohmic result of inductance, increases with frequency and can cause problems for high frequency circuits. Thus, the inductance should generally be kept low for efficient operation.
- 14. CONDUCTANCE There will be a leakage current between the transmission line and the ground, and also between the phase conductors. There is always a certain amount of conductance, because there is no such thing as a perfect dielectric. That means a certain amount of energy passing down the transmission line appears at the other conductor. This small amount of leakage current generally flows through the surface of the insulator. Inverse of this leakage current is termed as Conductance. It is denoted by "G" It usually is a very small quantity, because many dielectrics are very good insulators in transmission line applications. Conductance is represented by a shunt resistor between the signal wire and the return wire (ground).
- 15. CAPACITANCE The voltage difference between the Phase conductors gives rise to an electric field between the conductors. The two conductors are just like parallel plates and the air in between them becomes dielectric. This pattern gives rise to the capacitance effect between the conductors. Capacitive reactance, which is a result of the line capacitance, decreases with an increase in frequency and causes the propagating signals to be shorted to ground at certain frequencies. So, the distributed capacitance, as well as the distributed inductance and resistance of transmission lines should, in general, be minimized. The flow of line current is associated with inductance and the voltage difference between the two points is associated with capacitance. Inductance is associated with the magnetic field, while capacitance is associated with the electric field.
- 16. EQUIVALENT CIRCUIT DIAGRAM OF A TRANSMISSION LINE
- 17. KVL and KCL: Derivation of the Telegrapher Equation
- 19. Wave Propagation on a Transmission line
- 20. Characteristic Impedance If a uniform transmission line is considered, for a wave travelling in one direction, the ratio of the amplitudes of voltage and current along that line, which has no reflections, is called as Characteristic impedance.
- 21. Mathematical Problem from Liao
- 23. VOLTAGE AND CURRENT EQUATION FOR LOSS-LESS TRANSMISSION LINE
- 24. TRANSMISSION LINE PARAMETERS FOR SOME COMMON LINES
- 25. CHARACTERISTIC IMPEDANCE FOR A COAXIAL LINE
- 26. THE TERMINATED LOSSLESS TRANSMISSION LINE
- 27. THE TERMINATED LOSSLESS TRANSMISSION LINE
- 28. IMPEDANCE MATCHING To achieve maximum power transfer to the load, impedance matching has to be done. To achieve this impedance matching, the following conditions are to be met. The resistance of the load should be equal to that of the source. RL=RS The reactance of the load should be equal to that of the source but opposite in sign. XL=−XS Which means, if the source is inductive, the load should be capacitive and vice versa.
- 29. REFLECTION CO-EFFICIENT The parameter that expresses the amount of reflected energy due to impedance mismatch in a transmission line is called as Reflection coefficient. If the impedance between the device and the transmission line don't match with each other, then the energy gets reflected. The higher the energy gets reflected, the greater will be the value of reflection coefficient.
- 30. MATCHING AND TOTAL REFLECTION
- 31. MISMATCHED LINE - STANDING WAVE
- 32. MISMATCHED LINE - STANDING WAVE
- 33. STANDING WAVE RATIO VSWR The standing wave is formed when the incident wave gets reflected. The standing wave which is formed, contains some voltage. The magnitude of standing waves can be measured in terms of standing wave ratios. The ratio of maximum voltage to the minimum voltage in a standing wave can be defined as Voltage Standing Wave Ratio VSWR. VSWR describes the voltage standing wave pattern that is present in the transmission line due to phase addition and subtraction of the incident and reflected waves. Hence, it can also be written as The larger the impedance mismatch, the higher will be the amplitude of the standing wave. Therefore, if the impedance is matched perfectly, Vmax:Vmin=1:1 Hence, the value for VSWR is unity, which means the transmission is perfect.
- 34. STANDING WAVE RATIO VSWR
- 35. TRANSMISSION LINE IMPEDANCE EQUATION
- 36. CASE 1: SHORT CIRCUIT
- 37. CASE 1: SHORT CIRCUIT
- 38. SPECIAL CASE 2: OPEN CIRCUIT
- 39. SPECIAL CASE 2: OPEN CIRCUIT
- 40. CASE- 3:
- 41. CASE- 3:
- 42. MATHEMATICAL PROBLEM ON TRANSMISSION COEFFICIENT
- 44. EFFICIENCY OF TRANSMISSION LINES The efficiency of transmission lines is defined as the ratio of the output power to the input power.
- 45. VOLTAGE REGULATION The efficiency of transmission lines is defined as the ratio of the output power to the input power.
- 46. LOSSES DUE TO IMPEDANCE MISMATCH The transmission line, if not terminated with a matched load, occurs in losses. These losses are many types such as attenuation loss, reflection loss, transmission loss, return loss, insertion loss, etc Attenuation Loss The loss that occurs due to the absorption of the signal in the transmission line is termed as Attenuation loss, which is represented as
- 47. LOSSES DUE TO IMPEDANCE MISMATCH Reflection Loss The loss that occurs due to the reflection of the signal due to impedance mismatch of the transmission line is termed as Reflection loss, which is represented as Transmission Loss The loss that occurs while transmission through the transmission line is termed as Transmission loss, which is represented as
- 48. LOSSES DUE TO IMPEDANCE MISMATCH Return Loss The measure of the power reflected by the transmission line is termed as Return loss, which is represented as Insertion Loss The loss that occurs due to the energy transfer using a transmission line compared to energy transfer without a transmission line is termed as Insertion loss, which is represented as
- 49. LOSSES DUE TO IMPEDANCE MISMATCH Return Loss The measure of the power reflected by the transmission line is termed as Return loss, which is represented as Insertion Loss The loss that occurs due to the energy transfer using a transmission line compared to energy transfer without a transmission line is termed as Insertion loss, which is represented as
- 50. STUB MATCHING If the load impedance mismatches the source impedance, a method called "Stub Matching" is sometimes used to achieve matching. The process of connecting the sections of open or short circuit lines called stubs in the shunt with the main line at some point or points, can be termed as Stub Matching. At higher microwave frequencies, basically two stub matching techniques are employed.
- 51. STUB MATCHING Single Stub Matching In Single stub matching, a stub of certain fixed length is placed at some distance from the load. It is used only for a fixed frequency, because for any change in frequency, the location of the stub has to be changed, which is not done. This method is not suitable for coaxial lines. Double Stub Matching In double stud matching, two stubs of variable length are fixed at certain positions. As the load changes, only the lengths of the stubs are adjusted to achieve matching. This is widely used in laboratory practice as a single frequency matching device.
- 52. STUB MATCHING
- 53. MODES OF PROPAGATION A wave has both electric and magnetic fields. All transverse components of electric and magnetic fields are determined from the axial components of electric and magnetic field, in the z direction. This allows mode formations, such as TE, TM, TEM and Hybrid in microwaves. The direction of the electric and the magnetic field components along three mutually perpendicular directions x, y, and z are as shown in the following figure.
- 54. MODES OF PROPAGATION TEM (Transverse Electromagnetic Wave) This method is not suitable for coaxial lines. In this mode, both the electric and magnetic fields are purely transverse to the direction of propagation. There are no components in ′Z′ direction. TE (Transverse Electric Wave) In this mode, the electric field is purely transverse to the direction of propagation, whereas the magnetic field is not.
- 55. MODES OF PROPAGATION TM (Transverse Magnetic Wave) In this mode, the magnetic field is purely transverse to the direction of propagation, whereas the electric field is not. HE (Hybrid Wave) In this mode, neither the electric nor the magnetic field is purely transverse to the direction of propagation
- 56. MODES OF PROPAGATION Multi conductor lines normally support TEM mode of propagation, as the theory of transmission lines is applicable to only those system of conductors that have a go and return path, i.e., those which can support a TEM wave. Waveguides are single conductor lines that allow TE and TM modes but not TEM mode. Open conductor guides support Hybrid waves.