Transmission Lines Experiment - Lab Report Example

Name Course Institution Instructor DATE Abstract This report describes a transmission line experiment. A transmission line is a means of carrying electromagnetic signals in the wave –guided wave systems. It is generally distinguished from other guided-wave systems by having two conductors. The objective of the experiment was to be familiar with the apparatus for generating and measuring the properties of ultra-high frequency (UHF) electromagnetic waves, to verify the basic properties of transmission lines as predicted by the telegrapher’s equations. Measurement of the speed of a TEM wave in a coaxial cable and exploration of standing wave patterns as a function terminating impedance was carried out. It also describes the setup of the experiment; the results were recorded, discussed and analyzed. Moreover, the errors were analyzed and discussed. The experiment was based around the HP85 slotted transmission lines. The device has a travelling probe which carries a diode; called a crystal detector that generates a DC current that depend non-linearly on the intensity of the electromagnetic field around it. Introduction A transmission line is a device that is designed to guide electrical energy from one point to another. For example, to transfer the output radio frequency energy of a transmitter to an antenna with the least possible power loss. This will depend on the special physical and electrical characteristics like impedance and resistance of the transmission line. The electrical features of a two-wire transmission line depend primarily on the construction of the line. In that the change of its capacitance reactance is recognized as the frequency applied to it is changed. Transmission line in electromagnetic is commonly used in structures which are able of guiding transverse electric and magnetic waves (TEM) (Jackson, 1975). TEM waves exist in structures that contain two or more separate conductors. Coaxial waves, parallel plates and two-wire lines are examples of practical transmission lines. Transmission lines are generally characterized by the following properties; balance –to-ground, characteristic impedance, attenuation per unit length, velocity factor and electrical length. Balance-to-ground is a measure of electrical symmetry of a transmission line with respect to ground potential. The combination of a series inductance and shunt capacitance in the two conductors gives transitional line characteristic impedance (Ramo,Whinnery, Duzer,1965). Aerials and transmission lines differ from simple electrical networks in that their inductance, capacitance and resistance are not lumped but are distributed over distances whereby the time travels is taken into consideration. It consists of an arrangement of electrical conductors by means of electromagnetic waves from one place to another (Jackson, 1975). The theory of transmission lines provides a link between circuit theory and field theory of electromagnetic waves (Ramo,Whinnery, Duzer,1965). If the series inductance per unit length of line LS and the parallel capacitance per unit length CP are known, and the loss resistance can be neglected. The characteristic impedance of transmission line will be; The attenuation per unit length measures how much of the radio frequency (RF) signal is lost per unit length of transmission line due to radiation leakages, dielectric and skin effect losses. Radiation losses occur in two wires because the fields from one line do not completely cancel out those from the other line. Radiation occurs in braided coaxial lines since the braid does not provide 100% shielding (Ramo, Whinnery, Duzer, 1965). The conductors are separated from one another by an insulating material known as a dielectric. It exhibit losses that increases as the voltage and frequency on the conductors increases. The total losses in transmission line are approximately proportional to the square root of the frequency. The radio frequency current flowing along a transmission line creates radio wave that is guided by the transmission line. The velocity will be given by the equation: Where V = the wave velocity Ls = Series inductance per unit length Cp = Parallel capacitance per unit length The wave propagation velocity of the guided wave will always be less than the speed of light in a vacuum, 300,000,000M/sec The electrical length of a cable is its length measured in wavelengths (λ) and is related to the frequency of the wave and the velocity with which it propagates along the transmission line. Transmission line constants called distributed constants are spread along the entire length of the transmission line and cannot be distinguished separately (Jackson, 1975). The amount of inductance, capacitance and resistance depends on the length of the line, the size of the conducting wires, the spacing between the wires and the dielectric between the wires. The energy produced by the magnetic lines of force collapsing back into the wire tends to keep the current flowing in the same direction. This will represent a certain amount of inductance which is expressed in microhenrys per unit length. The two parallel plates will act as plates of a capacitor and the air between acts as dielectric. It is expressed in picofarads per unit length (Ramo, Whinnery, Duzer, 1965). Conductance in transmission lines is expressed as the reciprocal of resistance and is usually expressed in micromhos per unit length. The maximum transfer of electrical energy takes place when the source impedance is matched to the load impedance (Jackson, 1975). Induction losses occur when the electromagnetic field about a conductor cuts through any nearby metallic object and the current is induced in that object, as a result power is dissipated in the object and is lost. The measurement of standing waves on a transmission line yields information about equipment operating conditions. Maximum power is absorbed by the load when Z l=Z0. (Ramo, Whinnery, Duzer, 1965). The ratio of the maximum to the minimum is a measure of the perfection of the termination of a line known as standing wave ratio (swr). The ratio of maximum voltage to minimum voltage on a line is known as voltage standing wave ratio (vswr). Therefore the equation represented as; The rigid coaxial line consists of a central, insulated wire mounted inside a tubular outer conductor. The inner conductor is insulated from the outer conductor by insulating spacers or beads at regular intervals, the spacers are made of Pyrex, polystyrene which have good insulating characteristics and low dielectric losses at high frequencies. Coaxial lines are more efficient than two wire lines for transferring electromagnetic energy because the fields are completely confined by the conductors. Standing waves are stationary and occur when part of the energy travelling down the line is reflected by an impedance mismatch with the load (Ramo,Whinnery, Duzer,1965). It is an inter-connect, which consist of two conductors and a dielectric , characterized by the distributed series resistances and inductances along with distributed parallel capacitances between them is known as transmission line. These lines exhibit characteristic impedance over any length for which the distributed parameters are constant. A characteristic impedance of a line is dynamic quantity which represents the ratio of the transient voltage to the transient current passing through a point on the lines. (Jackson, 1975) Where L0= Inductance per unit length (H), C0= Capacitance per unit length (F) If the line characteristic impedance and termination resistance match (i.e. ZO=RT), the travelling wave does not encounter a discontinuity at the line-load interface thus the total voltage across the termination resistance is the incident voltage VS. However, if mismatches between the line characteristic impedance and the termination resistance occur, a reflected wave must be set up to ensure Ohm’s law is obeyed at the line –load interface (Jackson, 1975). The telegrapher’s equations The reflection Coefficient τ is defined as The voltage and the current at any position z are By considering a section of the co-axial line of length dz, the space between the conductors is filled with the insulator with permittivity ɛ. Applying Gauss’ Law, the electric field between the conductors is Answers to questions Answer to question 1 If a current I1 A is flowing along the z-axis, sheets of the H1-form will extend out radially from the current, as shown below. These are the planes of dϕ in the cylindrical coordinate system. We know that H is Where Ho is a constant we need to find using Ampere’s law. We choose the Amperian contour P to be a circle around the z-axis. Since we assume that D=0, the right–hand side of Ampere’s law becomes Since Il A of current flows through the disk A that lies inside the circle P. The left-hand side is the integral of H over the circle Solving for Ho shows that So that Is the current field due to the line circuit. Experimental Details The experiment was based on the HP805C slotted transmission line, which has a traveling probe which carries diode named, a crystal detector which generate a DC current. The principle was to set up a standing wave pattern that involved reflections and moves the probe along the line to locate the maxima and minima in the field intensity. A slotted transmission line was set up and the wavelength of the electromagnetic wave of the slotted line was determined and comparison to the wavelength in air at the same frequency was carried out. In addition the wavelength in a coaxial cable was measured with the speed of the TEM wave in the cable calculated and compare to the speed of light in air. Finally the standing wave pattern as a function of terminating impedance was explored. Result Task 2 Voltage (mV) Attenuation(dB) 80.225 3 43.95 6 20.995 9 15.700 10 7.410 12 6.255 13 2.961 15 2.065 16 0.827 19 0.595 20 0.009 35 SHORT CIRCUIT 208 mm –maximum, 126.5 mm - minimum Voltage (mV) Attenuation(dB) 106.5 11.172 116.5 0.44 126.5 -0.094 136.5 2.465 146.5 10.483 188 61.545 198 75.391 208 81.161 210 72.088 228 59.942 Open circuit 215 mm – Maximum, 290 mm - minimum Voltage (mV) Attenuation(dB) 195 2.636 205 5.29 215 -2.68 225 -2.00 235 3.284 270 82.78 280 102.66 290 115.15 300 116.21 300 106.10 Results Voltage (mV) Attenuation(dB) 80.225 3 43.95 6 20.995 9 15.700 10 7.410 12 6.255 13 2.961 15 2.065 16 0.827 19 0.595 20 0.009 35 Task two Resistor (Ω) d-max d-min d-max d-min VSWR 47 297 -0.886 378 -2.26 42.29 100 282 81.75 377 -1.643 49.76 150 304 81.139 381 -1.222 66.90 195 306 88.226 388 -4.476 19.71 ERROR ANALYSIS AND DISCUSSION OF ERRORS Some errors are due to calibration. Path loss is the loss of power of an RF signal travelling (propagating) through space. It is expressed in dB. Path loss depends on: The distance between transmitting and receiving antennas. Line of sight clearance between the receiving and transmitting antennas. Antenna height. Discussion A VSWR of 1:1 means that there is no power being reflected back to the source. This is an ideal situation that rarely, if ever, is seen. In the real world, a VSWR of 1.2:1 (or simply 1.2) is considered excellent in The graph below shows minimum position distance (mm) versus Off-cut length (mm) Conclusions In conclusion, the received signal power is above the sensitivity threshold, which made the link to work. The problem is that there is only small dB difference between received signal power and sensitivity. Normally, a higher margin is desirable due to fluctuation in received power as a result of signal fading. There are ways to improve the VSWR of a system. One way is to use impedance matching devices where a change in impedance occurs. Any cable loss, or attenuation, will make the VSWR at the input of the cable appear much better than at the load or termination. The reason is that the cable loss or attenuation increases the return loss. References Simón Ramo, John R. Whinnery, Theodore Van Duzer,(1965).Fields and waves in communication electronics, J. Wiley. John David Jackson, (1975).Classical electrodynamicsAuthorEdition2,Wiley. Read More

The characteristic impedance of transmission line will be; The attenuation per unit length measures how much of the radio frequency (RF) signal is lost per unit length of transmission line due to radiation leakages, dielectric and skin effect losses. Radiation losses occur in two wires because the fields from one line do not completely cancel out those from the other line. Radiation occurs in braided coaxial lines since the braid does not provide 100% shielding (Ramo, Whinnery, Duzer, 1965).

The conductors are separated from one another by an insulating material known as a dielectric. It exhibit losses that increases as the voltage and frequency on the conductors increases. The total losses in transmission line are approximately proportional to the square root of the frequency. The radio frequency current flowing along a transmission line creates radio wave that is guided by the transmission line. The velocity will be given by the equation: Where V = the wave velocity Ls = Series inductance per unit length Cp = Parallel capacitance per unit length The wave propagation velocity of the guided wave will always be less than the speed of light in a vacuum, 300,000,000M/sec The electrical length of a cable is its length measured in wavelengths (λ) and is related to the frequency of the wave and the velocity with which it propagates along the transmission line.

Transmission line constants called distributed constants are spread along the entire length of the transmission line and cannot be distinguished separately (Jackson, 1975). The amount of inductance, capacitance and resistance depends on the length of the line, the size of the conducting wires, the spacing between the wires and the dielectric between the wires. The energy produced by the magnetic lines of force collapsing back into the wire tends to keep the current flowing in the same direction.

This will represent a certain amount of inductance which is expressed in microhenrys per unit length. The two parallel plates will act as plates of a capacitor and the air between acts as dielectric. It is expressed in picofarads per unit length (Ramo, Whinnery, Duzer, 1965). Conductance in transmission lines is expressed as the reciprocal of resistance and is usually expressed in micromhos per unit length. The maximum transfer of electrical energy takes place when the source impedance is matched to the load impedance (Jackson, 1975).

Induction losses occur when the electromagnetic field about a conductor cuts through any nearby metallic object and the current is induced in that object, as a result power is dissipated in the object and is lost. The measurement of standing waves on a transmission line yields information about equipment operating conditions. Maximum power is absorbed by the load when Z l=Z0. (Ramo, Whinnery, Duzer, 1965). The ratio of the maximum to the minimum is a measure of the perfection of the termination of a line known as standing wave ratio (swr).

The ratio of maximum voltage to minimum voltage on a line is known as voltage standing wave ratio (vswr). Therefore the equation represented as; The rigid coaxial line consists of a central, insulated wire mounted inside a tubular outer conductor. The inner conductor is insulated from the outer conductor by insulating spacers or beads at regular intervals, the spacers are made of Pyrex, polystyrene which have good insulating characteristics and low dielectric losses at high frequencies. Coaxial lines are more efficient than two wire lines for transferring electromagnetic energy because the fields are completely confined by the conductors.

Standing waves are stationary and occur when part of the energy travelling down the line is reflected by an impedance mismatch with the load (Ramo,Whinnery, Duzer,1965). It is an inter-connect, which consist of two conductors and a dielectric , characterized by the distributed series resistances and inductances along with distributed parallel capacitances between them is known as transmission line.

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