# Exercise 1. Power Gain and Antenna Parameters EXERCISE OBJECTIVE DISCUSSION OUTLINE. Power gain DISCUSSION

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1 Exercise 1 Power Gain and Antenna Parameters EXERCISE OBJECTIVE When you have completed this exercise, you will be familiar with the concept of power gain as it applies to electrical circuits and to antennas. You will also be familiar with the other parameters that are used to characterize antennas. DISCUSSION OUTLINE The Discussion of this exercise covers the following points: Power gain Antennas Field regions. Solid angles. Radiation intensity. Directive gain and directivity Power density and the inverse-square law Radiation pattern and beamwidth Beam solid angle. Shortcut for calculating the beam solid angle. Efficiency Effective aperture Antenna gain Gain of a pyramidal horn antenna. Electrical size. Gain of a parabolic antenna. Shortcut for calculating the gain of a dish antenna from the frequency and the diameter. The relationship between gain and beamwidth. Shortcut for calculating the beamwidth of a dish antenna. Shortcut for calculating the gain of a dish antenna from the beamwidth. General rules for aperture antennas. Measuring antenna gain. Polarization The Satellite Communications Training System Horn antenna polarization. Frequencies used in the system. Power Sensors. Power measurements. DISCUSSION Power gain A communications system, whether it be a terrestrial or satellite system, is composed of a number of different elements. These elements include transmitters, receivers, amplifiers, antennas, antenna feeds (waveguides or cables), as well as the free space and the atmosphere between the antennas. Each of these elements affects the strength, or power, of the received signal, some increasing it and others decreasing it. The term gain can refer to the ratio of the output to input voltage (voltage gain), current (current gain), or power (power gain). In communications systems, it usually refers to the power gain. A power amplifier increases the power of the signal by adding energy to the signal. The added energy comes from the power supply of the equipment. The gain is the ratio of the output power to the input power and can be expressed as a dimensionless ratio or in decibels, as shown in Equation (1). Festo Didactic

2 Exercise 1 Power Gain and Antenna Parameters Discussion (1) where is the power gain [as a ratio or in decibels] is the output power [W] is the input power [W] a All logarithms in this manual are base 10 logarithms. A device that does not change the power level has a gain of one (0 db). A device that increases the power level has a gain greater than one (> 0 db). A device that decreases the power level has a gain less than one (< 0 db). A gain that is less than one is can be expressed as a loss greater than one: (2) Cascaded elements increase or decrease the overall gain of a system. The total gain of a cascade is equal to the product of the individual gains divided by the losses (or to the sum of the gains minus the losses in decibels). (3) Examples of devices in a communication systems that have positive power gain are high-power amplifiers (HPAs) used in the output stages of transmitters and repeaters, low-noise amplifiers (LNAs) used in the input stages of repeaters and receivers, and IF (intermediate frequency) amplifiers. Antennas used in communications systems also have positive power gains. Unlike amplifiers, however, antennas do not add power to the signal. Instead, they focus or collimate the radiated power into a relatively narrow beam. The higher the gain of a transmitting antenna, the more the radiated power is focused and the more power a receiving antenna located in the direction of maximum radiation can collect from the radiated beam. 4 Festo Didactic

3 Exercise 1 Power Gain and Antenna Parameters Discussion Antennas An antenna is electrical device that can radiate or receive energy in the form of radio waves. An antenna is a transition device, or transducer, between guided waves and free-space waves. When transmitting, an antenna acts as a transducer that converts the electrical energy fed to it into a radiating electromagnetic field. When receiving, it converts the incident electromagnetic field into electrical energy. Electromagnetic radiation is produced by accelerated charges in the antenna. In transmission, the transmitter generates an oscillating current of electrons which is sent to the antenna through a feed line. Since the electrons are accelerated in one direction and then in the other, an oscillating magnetic field is created around the antenna elements. Electrical charges create an electric field around them, but because the charges are moving back and forth, the electric field is also oscillating. Together, these time-varying electric and magnetic fields propagate away from the antenna through space as electromagnetic radiation. In reception, the antenna captures incident electromagnetic radiation. This produces an oscillating current in the antenna and creates a tiny oscillating voltage at its terminals that is fed to the receiver through the feed line. An antenna can be almost any shape or size and there are several different types of antennas. Two basic types of antennas are the wire antenna and the aperture antenna. A wire antenna is an antenna made of conductive wire or metal rods, as shown in Figure 1. Figure 1. Setting up a VHF Yagi satellite communications antenna (U.S. Marine Corps photo). Festo Didactic

4 Exercise 1 Power Gain and Antenna Parameters Discussion An aperture antenna is an antenna that has an aperture, or opening, through which the electromagnetic field passes (see Figure 2 and Figure 3). The aperture of a unidirectional antenna is that portion of the plane surface which is perpendicular to the direction of maximum radiation and through which the major part of the radiation passes. In transmission, the electromagnetic field is usually generated by a small transducer or probe, similar to a wire antenna, which is connected to the transmitter through a transmission line. The generated electromagnetic field is guided by a waveguide towards the aperture. In reception, the aperture collects electromagnetic radiation which is then guided towards a transducer. Probe in waveguide Waveguide Horn Aperture Figure 2. Aperture antenna (pyramidal horn antenna). Aperture antennas are frequently used in microwave and satellite communications as they produce narrow beams. The pyramidal horn antenna and the circular horn antenna are common aperture antennas. These horn antennas are frequently used as feeds for parabolic dish antennas, which are also classified as aperture antennas. 6 Festo Didactic

5 Exercise 1 Power Gain and Antenna Parameters Discussion Figure 3. Aperture antenna (Cassegrain dish antenna). In antenna theory, a hypothetical antenna that transmits and receives uniformly in all directions is called an isotropic antenna (see Figure 4). Although an isotropic antenna is a theoretical concept and cannot actually be built, the concept is useful in studying the parameters of practical antennas. Figure 4. Representation of an isotropic antenna radiating uniformly in all directions. In practice, all antennas are directional to some extent, that is, they transmit and receive more effectively in some directions than in others. Some antennas are designed to be omni-directional, that is, they transmit and receive more or less uniformly in all directions in a single plane, usually the horizontal plane. Festo Didactic

7 Exercise 1 Power Gain and Antenna Parameters Discussion (a) Vertex (b) Vertex Figure 5. Solid angles. Solid angles can also be expressed in square degrees: (4) The total solid angle of a sphere, expressed in square degrees, is therefore equal to. Festo Didactic

9 Exercise 1 Power Gain and Antenna Parameters Discussion Directive gain and directivity The directive gain of an antenna is a function of direction and compares the radiation intensity in a particular direction to the average radiation intensity: (6) where is the radiation intensity as a function of direction is the average radiation intensity The term directivity is often used in place of directive gain. The context will indicate whether the author is referring to the property as a function of direction or to the maximum value. The principal axis or boresight of an antenna corresponds to the direction of greatest directive gain (greatest radiation intensity). Directivity is a measure of the degree to which the radiated energy is concentrated in the direction of maximum radiation. Directivity, unlike gain, does not take into account power losses in the antenna. The directivity is defined as: (7) where is the directivity is the directive gain is the maximum radiation intensity is the average radiation intensity is the transmitted (radiated) power For an isotropic antenna,. Therefore, its directivity. Festo Didactic

10 Exercise 1 Power Gain and Antenna Parameters Discussion Power density and the inverse-square law The power density also called flux density or power flux density of radiation is the amount of power passing through a unit area. Consider an isotropic antenna transmitting a power located at the center of two concentric spheres, as in Figure 7. For clarity, only the bottom halves of the spheres are shown. If the radius of the smaller sphere is, then its surface area is. For the larger sphere with radius, the surface area is. Sphere 2 Sphere 1 A A A A A Figure 7. Inverse-square law. Since the power is radiated uniformly in all directions, the power density at a distance from the source is uniform over the entire surface of sphere 1 and is equal to the amount of power radiated divided by the surface area of the sphere: (8) where is the transmitted power (radiated isotropically) is the power density (the power passing through a unit area) at the surface of a sphere of radius is the surface area of sphere 1 is the radius of sphere 1 The power intercepted by a surface perpendicular to the direction of radiation is equal to the area of the surface multiplied by the power density. At the surface of sphere 1, the power intercepted by the colored area is. 12 Festo Didactic

11 Exercise 1 Power Gain and Antenna Parameters Discussion The power spreads as it propagates away from the source. The power intercepted by a surface on sphere 1 spreads to cover a surface equal to on sphere 2 where the distance from the source is twice as great. The power density at a distance from the source of radiation is: (9) At the surface of sphere 2, the power intercepted by each colored area is. Since all areas in the figure are equal: (10) where is the power density at radius is the power density at radius is the power intercepted by area at distance is the power intercepted by area at distance Equation (10) shows that the power intercepted per unit area is inversely proportional to the square of the distance from the source. This fundamental principle in radio wave propagation is known as the inverse square law. For an isotropic antenna, the power density is uniform in every direction. For directional antennas, the power density will be greatest in one direction. The units of power density are watts square meter or dbm per square meter. Festo Didactic

13 Exercise 1 Power Gain and Antenna Parameters Discussion Figure 9 shows the radiation pattern of a directional antenna. The distance from the origin of each point in the graph corresponds to the directive gain in that direction. The greater the directive gain in a particular direction, the further the corresponding point in the radiation pattern is removed from the origin. In addition, a color map maps the relative values to different colors. Boresight Directive gain 6 Main lobe or main beam Side lobes Back lobe Figure 9. Polar 3D radiation pattern of a directional antenna. The radiation pattern of a directional antenna has a number of different lobes. The main lobe or main beam is centered on the boresight and corresponds to the direction of maximum radiation. Smaller lobes in other directions are called side lobes, and sometimes back lobes. These are generally undesirable as they waste radiated power or pick up unwanted power (noise or interference). Although side lobes can be minimized by careful design, they can never be completely eliminated. The side lobe level is the maximum value of the side lobes. Since this radiation pattern is symmetric about the boresight, it can be completely represented as a two-dimensional graph in either polar coordinates, as shown in Figure 10, or in Cartesian coordinates, as in Figure 11. Festo Didactic

14 Exercise 1 Power Gain and Antenna Parameters Discussion Null-to-null beamwidth Half-power beamwidth Figure 10. Two-dimensional radiation pattern using polar coordinates Figure 11. Radiation pattern using Cartesian coordinates. 16 Festo Didactic

16 Exercise 1 Power Gain and Antenna Parameters Discussion H-plane E-plane Figure 13. E-plane and H-plane radiation pattern of a horn antenna (in db). One way of measuring the radiation pattern in a plane is to rotate the antenna in that plane while measuring the level of received power as a function of the antenna orientation. To obtain a valid pattern, the surrounding environment should be free from objects which could reflect the transmitted signal towards the antenna being tested and cause errors in the results. Radiation pattern measurements are often performed in an anechoic chamber, as shown in Figure Festo Didactic

17 Exercise 1 Power Gain and Antenna Parameters Discussion Figure 14. An antenna in an RF anechoic chamber (photo by Adamantios, from the Wikimedia Commons, reproduced under the GNU Free Documentation License). Beam solid angle The beam solid angle or beam area is the solid angle that would be required to pass all of the power radiated by the antenna if the radiation intensity over this solid angle was uniform and equal to its maximum radiation intensity and was zero elsewhere. (11) The total power radiated by the antenna is therefore: (12) Festo Didactic

18 Exercise 1 Power Gain and Antenna Parameters Discussion An alternate definition of directivity is therefore: (13) where is the directivity is the transmitted (radiated) power is the maximum radiation intensity is the beam solid angle Shortcut for calculating the beam solid angle The beam solid angle is approximately equal to the product of the two half power beam widths: Efficiency Practical antennas are never 100% efficient. There are always some losses associated with the antenna. The antenna efficiency is the ratio of the radiated power to the input power of the antenna. The efficiency of a practical antenna is always less than one. Efficiency can be expressed as a fraction, as a percentage, or in decibels. (14) where is the power radiated by the antenna is the power input to the antenna is the antenna efficiency is the illumination efficiency is the spill-over efficiency is the surface finish efficiency The antenna efficiency is the product of a number of different efficiency factors. When the reflector of a dish antenna is illuminated uniformly, the illumination efficiency. In most cases however the illumination is attenuated (tapered) towards the reflector boundaries. This is a natural result of the radiation pattern of the feed and has the advantage of reducing the level of side lobes in the radiation pattern. With tapered illumination, the illumination efficiency. The 20 Festo Didactic

19 Exercise 1 Power Gain and Antenna Parameters Discussion Cassegrain antenna, for example, has an illumination efficiency of approximately. When the reflector intercepts less than the total energy radiated by the feed, some energy is lost. The spill-over efficiency is the ratio of the energy radiated by the primary source that is intercepted by the reflector. A common value is. The surface finish efficiency represents the effect of surface roughness on the gain of a reflector antenna. The surface finish efficiency of some antennas is approximately. Other losses are generally of less importance. The product of all of the efficiencies is typically between 0.55 and The efficiency may or may not include losses due to impedance mismatch, since these losses can be reduced by careful design. The term radiation efficiency is sometimes used to include all losses except mismatch losses and the term total efficiency includes mismatch losses. a An isotropic antenna, which is a hypothetical antenna, is assumed to be lossless, that is, its efficiency. Effective aperture An antenna exposed to electromagnetic radiation will collect a quantity of power proportional to the physical area or physical aperture of the antenna as seen from the source of the radiation. The greater the area, the more power is collected. Because of losses however, the power collected by an antenna is always less than what you would expect for a given physical area. For this reason, the concept of effective area is used. The effective area or effective aperture or of an antenna is defined as the area, oriented perpendicular to the direction of the incident radiation, which would intercept the same amount of power as is produced by the antenna at its output. The larger the effective aperture, the more power it produces. Used alone, the term aperture often designates the effective aperture. For a lossless aperture antenna, the aperture would be equal to the physical area that intercepts the radiation. For a practical antenna, the effective aperture is always less than its physical aperture. For wire antennas, there is no simple relation between the size of the antenna and its effective aperture. Generally speaking, however, the larger the physical size of the antenna, the greater its effective aperture. Festo Didactic

20 Exercise 1 Power Gain and Antenna Parameters Discussion Since there is not necessarily a clear correspondence between the physical size of an antenna and its effective aperture, the formal definition of aperture does not mention the physical size. For any antenna, the effective aperture or effective area is: (15) where is the effective aperture (effective area) of the antenna is the power at the output of the antenna is the power density of the incident radiation The above equation assumes that the antenna is oriented to receive the maximum power, that it is correctly polarized with respect to the radiation, and that there are no losses due to impedance mismatch. The calculations giving the effective area of an isotropic antenna are beyond the scope of this manual. For an isotropic antenna, which by definition has unit directivity, it can be shown that the effective aperture is (16) where is the wavelength of the radiation For an aperture antenna, which has a physical aperture perpendicular to the radiation, there is a simple relationship between the effective aperture and the physical aperture of the antenna: (17) where is the effective aperture of the antenna is the physical aperture of the antenna is the antenna efficiency Although it is easier to imagine the concept of effective aperture when considering a receiving antenna, the effective aperture is the same whether the antenna is receiving or transmitting. Antenna gain The concept of directivity and directive gain do not include losses which are present in every practical antenna. The gain is similar to the directive gain except that gain takes into consideration the antenna efficiency and is therefore a practical figure of merit for quantifying antenna performance. It is sometimes easier to imagine the concept of gain when considering a transmitting antenna. Like directivity however, the gain is the same whether the antenna is transmitting or receiving. The gain of an antenna is defined as the ratio of the radiation intensity (power radiated per solid angle) in a given direction, to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically. 22 Festo Didactic

21 Exercise 1 Power Gain and Antenna Parameters Discussion An alternate definition of gain uses a dipole antenna as a reference, rather than a hypothetical isotropic antenna. To distinguish between the two, the units dbd (decibels over dipole) and dbi (decibels over isotropic) are sometimes used. In this manual, units of dbi are assumed. The gain can be expressed as a dimensionless value or in decibels. The gain of an isotropic antenna is equal to one. When expressed in decibels, the unit used is often dbi, to show that an isotropic antenna is used as a reference. By definition, the gain of an isotropic antenna or 0 dbi. Gain is a function of direction and is often written. In most cases however the value of interest is the maximum gain of the antenna, that is, the gain along the boresight. Unless specifically stated, the gain of an antenna is considered to be the maximum gain of the antenna. For a lossless antenna, the gain would be the same as the directivity. When the antenna efficiency is less than one, the gain is: (18) where is the gain is the antenna efficiency is the directivity Antenna gain is different from amplifier gain, since antennas are passive devices and cannot amplify the signal. Antennas can only focus power. This has the same effect as amplifying the signal since doubling the gain of either the transmitting or receiving antenna doubles the amount of power at the input of the receiver. With the wavelength and the effective aperture in the same units, the gain of an antenna is related to the effective aperture by: (19) where is the (maximum) gain of the antenna is the effective aperture of the antenna is the effective aperture of an isotropic antenna is the wavelength of the electromagnetic radiation is the frequency of the electromagnetic radiation is the speed of light Gain of a pyramidal horn antenna The pyramidal horn antenna is one of the most popular antenna forms. This antenna has a waveguide that guides the wave towards the horn. The geometry is illustrated in Figure 15. Since the aperture sizes in each of the principal planes are and, the physical aperture or area of the horn is. Festo Didactic

22 Exercise 1 Power Gain and Antenna Parameters Discussion Y X (a) Geometry Z X (b) Cross section through H-plane Z Y (c) Cross section through E-plane Z Figure 15. Pyramidal horn antenna. A waveguide can propagate an infinite number of different types or modes of electromagnetic waves. Each mode has its own electrical and magnetic field configurations. If the opening angle of the flare of a pyramidal horn antenna is small enough, only the dominant mode of the waveguide will be significant. The field lines of the dominant mode will expand into a spherical form for a pyramidal horn antenna. This is shown in Figure 16. Phase error Figure 16. Phase error in pyramidal horn antenna. 24 Festo Didactic

23 Exercise 1 Power Gain and Antenna Parameters Discussion The approximate gain of the pyramidal horn antenna can be calculated using Equation (20). (20) All lengths in Equation (20) are expressed in the same units. Determining the gain reduction factors is beyond the scope of this manual. where and are the aperture sizes of the horn, as shown in Figure 15. is the wavelength is the frequency is the speed of light and are the gain reduction factors in the E and H planes The gain reduction factors, or loss factors, and are due to the phase errors caused by the flair. These factors are less than one and vary with frequency. In decibels, the approximate gain of the pyramidal horn antenna is: (21) a Since the gain reduction factors and are less than one, their values in db are negative. Adding their values in db reduces the gain. Sometimes Equation (21) is written as: In this case, the decibel values are positive and subtracting them reduces the gain. Electrical size Equation (20) shown that the gain of a pyramidal horn antenna is proportional to the physical aperture. Neglecting the effect of the gain reduction factors, it would also be inversely proportional to the square of the wavelength, that is, proportional to the square of the frequency. The aperture of an antenna can be measured in square centimeters or in square wavelengths. An antenna whose aperture is greater than one square wavelength is considered to be electrically large. Otherwise, it is said to be electrically small. Increasing the electrical size of the antenna by increasing its physical aperture or decreasing the wavelength (increasing the frequency) increases the gain. When the horn antenna is designed for a given gain, the optimal geometry in terms of length and aperture size can be calculated. This optimal geometry, however, is only valid at a single frequency. Since horn antennas are often used over a wide frequency band, they are often designed to have optimal gain at the lowest frequency in this band. At higher frequencies, the gain reduction factors become greater. This may be more than compensated for, however, by the increase in electrical size of the antenna. As a result, the measured gain of a horn antenna may increase as the frequency increases. Festo Didactic

24 Exercise 1 Power Gain and Antenna Parameters Discussion Gain of a parabolic antenna For a parabolic dish antenna with the reflector diameter, the physical aperture of the antenna is. The effective aperture is. The gain of the antenna is related to the diameter of the antenna by: (22) where is the effective aperture of the antenna is the physical aperture of the antenna is the diameter of the antenna is the antenna efficiency The gain of a parabolic dish antenna is proportional to the square of the physical aperture and to the square of the frequency. It is inversely proportional to the square of the wavelength. Shortcut for calculating the gain of a dish antenna from the frequency and the diameter The gain of a circular parabolic dish antenna with efficiency is approximately equal to: For example, the gain of a 2 m antenna operating at 12 GHz would be approximately, as shown by the graph in Figure 17. Figure 17 and Figure 18 show typical relationships between antenna gain and dish size for different frequencies. Figure 17 has a logarithmic horizontal axis and shows that a 1 m dish operating at 4 GHz provides a gain of approximately 30 db. Doubling the diameter of the dish, or doubling the frequency, increases the gain by 6 db, that is, by a factor four. 26 Festo Didactic

25 Exercise 1 Power Gain and Antenna Parameters Discussion 70 Gain (db) GHz 12 GHz 8 GHz 4 GHz Dish diameter (m) Figure 17. Typical antenna gain versus dish size (0.5 m to 32 m, efficiency factor = 0.6) Gain (db) GHz 12 GHz 8 GHz 4 GHz Dish diameter (cm) Figure 18. Typical antenna gain versus dish size (up to 2 m, efficiency factor = 0.6). As the dish size, and the gain, increase, the 3 db beamwidth of the antenna decreases, as shown in Figure db Beamwidth ( ) GHz 8 GHz 12 GHz 16 GHz Dish diameter (m) Figure db (half-power) beamwidth versus dish size (efficiency factor = 0.6). Festo Didactic

26 Exercise 1 Power Gain and Antenna Parameters Discussion The relationship between gain and beamwidth For a parabolic antenna of diameter, the 3 db beamwidth is related to the ratio by a coefficient whose value depends on the illumination law. For nonuniform illumination, as with most parabolic antennas, the value commonly used is 70. (23) where is the 3 db beamwidth in degrees is the diameter in meters is the wavelength in meters is the frequency in Hz Shortcut for calculating the beamwidth of a dish antenna For a circular parabolic dish antenna, the 3 db beamwidth is approximately related to the diameter and the frequency by: Combining Equation (22) and Equation (23) shows that the gain of an antenna is a function of its 3 db beamwidth. This relation is independent of frequency: (24) Shortcut for calculating the gain of a dish antenna from the beamwidth If the antenna efficiency, then 3 db General rules for aperture antennas Doubling the frequency: quadruples the gain (increases by 6 db): and halves the beamwidth: Doubling the physical area: quadruples the gain (increases by 6 db): and halves the beamwidth: The beam width of an antenna gives an indication of how accurately the antenna must be pointed. Narrow-beam antennas on masts must resist wind forces that tend to affect the antenna direction. Small dish antennas pointed at geostationary satellites can be fixed, even though geostationary satellites are allowed to wander approximately ±0.15 in each direction, as the antenna beam width is 28 Festo Didactic

27 Exercise 1 Power Gain and Antenna Parameters Discussion large enough so that the satellite stays in the beam. With large, high-gain dish antennas, however, the beam is extremely narrow and a tracking mechanism may be required to keep the antenna accurately pointed at the satellite. Measuring antenna gain There are various ways of measuring the gain of an antenna. These methods involve transmitting from one antenna and measuring the power received by another antenna. One method uses three antennas, a transmitting antenna, a receiving reference antenna of known gain, and a receiving antenna under test (AUT) of unknown gain. The transmitting antenna and the reference antenna are set up a certain distance apart and correctly aligned. The power received by the reference antenna is measured. Then the antenna under test is set up in place of the reference antenna, at exactly the same distance from the transmitting antenna, and the antennas are correctly aligned. The power received by the antenna under test is measured. The gain of the antenna under test is given by: (25) A second method uses two identical antennas of unknown gain, one antenna transmitting and the other receiving. The radiated power and received power as well as the distance between the two antennas are measured. The gain of the antennas is given by: (26) The second method is used in this exercise. Polarization An electromagnetic wave is a combination of an electric field (E-field) and a magnetic field (H-field). The two fields always appear simultaneously. The plane of the electric field is orthogonal to the plane of the magnetic field and both planes are perpendicular to the direction of propagation. By convention, the polarization of an electromagnetic wave is defined as the orientation of the plane of the electric field. Polarization can be linear, where the electric field is always oriented at the same angle with respect to a reference plane. For earth-station antennas, the reference Festo Didactic

28 Exercise 1 Power Gain and Antenna Parameters Discussion plane is the local horizontal plane. For antennas on a satellite, the reference plane is usually the equatorial plane. Because of the curvature of the earth, these two reference planes are not parallel, unless the earth station and the satellite have the same longitude. The angle between these reference planes is called the polarization angle or skew. It is the difference between the polarization of the signal transmitted by the satellite and the apparent polarization of the received signal at the earth station. An adjustment for the polarization angle must be made when pointing a linearly polarized earth-station antenna to a satellite, in order to maximize the signal. Polarization can also be elliptical, where the plane of the electric field rotates with time making one complete revolution during one period of the wave. An elliptically polarized wave radiates energy in all planes perpendicular to the direction of propagation. The ratio between the maximum and minimum peaks of the electric field during the rotation is called the axial ratio and is usually specified in decibels. When the axial ratio is near 0 db, the polarization is said to be circular. If the axial ratio is infinite, the electric field maintains a fixed direction and the polarization is linear. If the rotation is clockwise, looking in the direction of propagation, the polarization is called right-hand. If it is counterclockwise, the polarization is called left-hand. The polarization of an antenna depends on the shape and the orientation of the waveguide in the feed. The polarization of each antenna in a communications system should be of the same type and, if linear, should be properly aligned. Maximum signal strength at the receiver input occurs when the polarization of the receiving antenna matches the polarization of the incident wave. The Satellite Communications Training System Horn antenna polarization The horn antennas in the Satellite Communications Training System can be mounted for either horizontal or vertical polarization. The waveguide of the antenna is energized by a small probe, or antenna element, protruding through the broad side of the waveguide. It is the orientation of this probe that determines the polarization of the antenna (see Figure 20). Vertical polarization Horizontal polarization Figure 20. Vertically and horizontally polarized waveguides. For vertical polarization, the probe is vertical (at the top or the bottom of the waveguide). For horizontal polarization, it is horizontal (at the left side or the right side of the waveguide). 30 Festo Didactic

29 Exercise 1 Power Gain and Antenna Parameters Discussion The waveguide holder has two metal pins that allow the antenna to be mounted on the mast for either vertical or horizontal polarization (see Figure 21). Waveguide Metal pin Waveguide holder Figure 21. Assembled horn antenna. Figure 22 shows how to mount the antennas for vertical and for horizontal polarization. Vertical polarization Horizontal polarization Figure 22. Vertical and horizontal polarization. In both the uplink and in the downlink, the polarization of the transmitting and receiving antennas should be of the same. Maximum signal strength at the Festo Didactic

31 Exercise 1 Power Gain and Antenna Parameters Discussion a The Power Sensors and the spectrum analyzer indicate power differently. A spectrum analyzer shows the power of each individual frequency component present in the signal whereas the Power Sensor produces a dc voltage proportional to the sum of the powers of all frequency components in its range. Since the spectrum analyzer displays only a limited range of frequencies at a time, some significant frequency components, including parasitic frequency components, may not be visible on the spectrum analyzer display. They will, however, be included in the Power Sensor reading. For this reason, and because of non-linearities in the two instruments, they may not indicate exactly the same power. In addition, the Power Sensors are calibrated for the Channel D frequencies. When using other channels, the Power Sensors may give less accurate results. For measuring the power of a single frequency component (e.g. the power of an unmodulated carrier signal), the spectrum analyzer will give more accurate results the Power Sensor generally indicates a higher power than the spectrum analyzer does. For measuring the total power of a complex signal, however, the Power Sensor is much easier to use. On the Satellite Repeater, the three Power Sensor Level LEDs provide a rough indication of the power at the RF OUTPUT, which is proportional to the power at the RF INPUT. The greater the power, the more LEDs are lit. On the Earth Station Receiver, the three Power Sensor Level LEDs provide a rough indication of the power at the IF OUTPUT of Down Converter 1, which is proportional to the power at the RF INPUT and to the Gain adjustment. During normal operation, the Gain should be adjusted so the green LED is lit. The red LED and LED indicate that the power level is too low or too high, respectively. Power measurements Power measurements are made in each of the exercises of this manual and there are different ways to perform these measurements. Power measurements can be made using the power sensors built into the RF modules in the system. It may be necessary, in some cases, to take into consideration the loss in the cable that connects the antenna. Cable loss, also referred to as feed-line loss, is measured at the beginning of this exercise If you are using conventional instruments, you can use the spectrum analyzer to measure the power of an unmodulated carrier. a Although this manual makes frequent reference to the use of the spectrum analyzer for measuring power, a conventional power meter can also be used to measure power. In the exercises in this manual, the spectrum analyzer should always be connected using a long (120 cm) microwave cable. In many cases, you ll need to take into consideration the loss in this cable. Festo Didactic

32 Exercise 1 Power Gain and Antenna Parameters Procedure Outline PROCEDURE OUTLINE The Procedure is divided into the following sections: System startup Connection Diagrams. Power gain Aligning the antennas. Feed-line loss. Gain of the repeater. Gain of Down Converter 2. Antenna gain Gain of the large-aperture horn antenna at the uplink frequency. Gain of the small-aperture horn antenna versus downlink frequency. Gain of the large-aperture horn antenna versus downlink frequency. Effective aperture and efficiency. Beamwidth and radiation pattern 3 db beamwidth. Radiation pattern. Polarization isolation PROCEDURE System startup 1. If not already done, set up the system and align the antennas visually as shown in Appendix B. 2. Make sure that no hardware faults have been activated in the Earth Station Transmitter or the Earth Station Receiver. b Faults in these modules are activated for troubleshooting exercises using DIP switches located behind a removable panel on the back of these modules. For normal operation, all fault DIP switches should be in the O position. 3. Turn on each module that has a front panel Power switch (push the switch into the I position). After a few seconds, the Power LED should light. 4. If you are using the optional Telemetry and Instrumentation Add-On: Make sure there is a USB connection between the Data Generation/Acquisition Interface, the Virtual Instrument, and the host computer, as described in Appendix B. Turn on the Virtual Instrument using the rear panel power switch. b If the TiePieSCOPE drivers need to be installed, this will be done automatically in Windows 7 and 8. In Windows XP, the Found New Hardware Wizard will appear (it may appear twice). In this case, do not connect to Windows Update (select No, not this time and click Next). Then select Install the software automatically and click Next. Start the Telemetry and Instrumentation application. In the Application Selector, do not select Work in stand-alone mode. b If the Telemetry and Instrumentation application is already running, exit and restart it. This will ensure that no faults are active in the Satellite Repeater. 34 Festo Didactic

33 Exercise 1 Power Gain and Antenna Parameters Procedure Connection Diagrams Connections are shown in this manual using diagrams that contain colored blocks. These blocks correspond to functional blocks or sections shown on the front panels of the modules. Color is used to identify the module, as shown in the examples below: Earth Station Transmitter Satellite Repeater Up Converter Up Converter 2 Satellite Repeater Down Converter 2 Other colors are used to identify the modules of the optional Telemetry and Instrumentation Add-On. The type of cable required for each connection depends on the type of connectors used on the modules. Microwave cables have SMA connectors whereas low-frequency cables have BNC connectors. Long microwave cables are usually used to connect the antennas, for flexibility in placing the antennas, although short microwave cables can be used if desired. Small-Aperture Horn Antennas are usually connected to the Satellite Repeater. Large-Aperture Horn Antennas are usually connected to the Earth Station Transmitter RF OUTPUT and the Earth Station Receiver RF INPUT. Small-Aperture Horn Antenna (Uplink) Satellite Repeater RF OUTPUT Small-Aperture Horn Antenna (Downlink) Grey blocks are instruments. These can be either conventional instruments provided by the user or virtual instruments included in the optional Telemetry and Instrumentation Add-On. Waveform Generator Pre-Emphasis Earth Station Transmitter BNC T-connector CH1 Oscilloscope CH2 In these connection diagrams, the names of the inputs and outputs of the blocks are given where necessary for clarity or in order to prevent ambiguity. For example, since the Pre-Emphasis block on the Earth Station Transmitter has only one input and one output, these outputs may not be named. As the Satellite Repeater has two outputs, however, the output to be used is always named. Festo Didactic

34 Exercise 1 Power Gain and Antenna Parameters Procedure Power gain In this section, you will measure the power gain of the repeater as well as the power gain of the first stage of the receiver. To facilitate these measurements, you will first measure the antenna feed-line loss (cable loss) at several different frequencies used in the system. The feed-lines included with the system are coaxial microwave cables approximately 120 cm in length. Although the shorter microwave cables included with the system can be used to connect the antennas when necessary, the longer cables should be used when feed-line loss is considered. 5. Position the Earth Station Receiver, the spectrum analyzer, and the receiving antenna so that you can easily connect this antenna to either to the RF INPUT of the Earth Station Receiver or to the input of the spectrum analyzer without putting tension on the antenna cable. 6. Make the connections shown in Figure 23 connecting the antennas as follows: a Connect a large-aperture horn antenna to the RF OUTPUT of the transmitter and to the RF INPUT of the receiver. Connect the two small-aperture horn antennas to the RF INPUT and RF OUTPUT of the repeater. Always use the long (120 cm) microwave cables to connect the antennas, unless otherwise specified. 36 Festo Didactic

35 Exercise 1 Power Gain and Antenna Parameters Procedure I OUTPUT to I INPUT Digital Modulator I Q I Q Q OUTPUT to Q INPUT Up Converter 1 Earth Station Transmitter Up Converter 2 RF OUTPUT Satellite Repeater RF OUTPUT Earth Station Receiver Down Converter 2 I OUTPUT to I INPUT Digital Modulator I Q I Q Q OUTPUT to Q INPUT Down Converter 1 Up Converter 1 Earth Station Transmitter Up Converter 2 Satellite Repeater Down Converter 2 Earth Station Receiver Down Converter 1 Figure 23. Initial connections. 7. On the Earth Station Transmitter, make the following adjustments: Data Source... any Scrambler... Off Clock & Frame Encoder... Off This will cause the transmitter to transmit an unmodulated carrier. On the transmitter and the receiver, select Channel D. This sets the downlink frequency to 9 GHz. b If another system in the same laboratory is using Channel D, select a different channel. Using a different channel will have a negligible effect on the measurements. Festo Didactic

38 Exercise 1 Power Gain and Antenna Parameters Procedure Taking care not to change the orientation of the antenna, connect the antenna to the spectrum analyzer using two long cables joined together with a female SMA-SMA adapter (see Figure 24) and measure the power. b Figure 24. Female SMA-SMA adapter. To avoid moving the antenna, add the second cable at the input of the spectrum analyzer. Calculate the feed-line loss in one long cable at the downlink frequency and enter this value in Table Connect the antenna to the RF INPUT of the receiver using one short microwave cable. Align the antennas for maximum power. 11. Adjust the input range and/or attenuation of the spectrum analyzer to measure a signal of roughly -20 dbm. Connect the IF 2 OUTPUT of the Earth Station Receiver to the spectrum analyzer using one long (120 cm) microwave cable and measure the power. Enter this value in Table 3. Then do the same using two long cables joined together with an SMA-SMA adapter, and measure the power. Calculate the loss in one long cable at the IF 2 frequency. Table 3. Cable loss (long cable) at IF 2. IF 2 frequency Power with one long cable Power with two long cables 1.56 GHz dbm dbm Cable loss (long cable) at db 40 Festo Didactic

39 Exercise 1 Power Gain and Antenna Parameters Procedure 12. On the receiver, reconnect the IF 2 OUTPUT to the IF 2 INPUT. Adjust the input range and/or attenuation of the spectrum analyzer to measure a signal of roughly 0 dbm. Using the Telemetry and Instrumentation Add-On The maximum input level of the Frequency Converter on the Telemetry and Instrumentation Add-On is 10 dbm. You will need to use one of the built-in attenuators. When using an attenuator with the Spectrum Analyzer, you must add the value of the external attenuation to the level indicated by the Spectrum Analyzer in order to obtain the measured carrier level. Connect the IF 1 OUTPUT of the Earth Station Receiver to the spectrum analyzer using one long (120 cm) microwave cable and measure the power. Enter this value in Table 4. Then do the same using two long cables joined together with an SMA-SMA adapter, and measure the power. Table 4. Cable loss (long cable) at IF 1 of the receiver. IF 1 frequency Power with one long cable Power with two long cables 280 MHz dbm dbm Feed-line loss (long cable) at db Calculate the loss in one long cable at the IF 1 frequency. Is the cable loss at this frequency significant? b A measured loss that is comparable to the level of fluctuation on the measuring instrument is not significant. 13. Connect the RF OUTPUT of the transmitter to the spectrum analyzer using one long (120 cm) microwave cable and measure the power. Enter this value in Table 5. Festo Didactic

40 Exercise 1 Power Gain and Antenna Parameters Procedure Then do the same using two long cables joined together with an SMA-SMA adapter, and measure the power. Calculate the feed-line loss in one long cable at the uplink frequency. Table 5. Feed-line loss (long cable) at the uplink frequency. Uplink frequency Power with one long cable Power with two long cables Feed-line loss (long cable) at uplink frequency GHz dbm dbm db Gain of the repeater The steps in this section serve to measure the gain of the repeater at different frequencies. Later in this exercise, you will need to know the power at the RF input of the repeater. If you know the gain of the repeater, you can measure the power at the RF output using the Power Sensor, and then subtract the gain of the repeater. 14. In order to measure the RF INPUT and RF OUTPUT power of the repeater using the spectrum analyzer, the repeater and the spectrum analyzer must be set up close to each other. There are two ways to arrange this: A. If you are using conventional instruments, you can simply set up your spectrum analyzer near the repeater. B. Alternatively, you can exchange the repeater and the transmitter, as shown in Figure 25. a If you are using the Telemetry and Instrumentation Add-On, it is preferable to make all repeater gain measurements using the same level of external attenuation (preferably none). It may be necessary to move the tables further apart in order to obtain the appropriate signal level. 42 Festo Didactic

41 Exercise 1 Power Gain and Antenna Parameters Procedure Earth Station Receiver Add-On Satellite Repeater Uplink Earth Station Transmitter Figure 25. Setup to observe the spectrum at the input and output of the Satellite Repeater using the Telemetry and Instrumentation Add-On. Festo Didactic

42 Exercise 1 Power Gain and Antenna Parameters Procedure 15. Turn on both the transmitter and the repeater. On the Earth Station Transmitter, make the following adjustments: Data Source... any Scrambler... Off Clock & Frame Encoder... Off The transmitter will transmit an unmodulated carrier to the repeater. 16. Optimize the antenna alignment of the two uplink antennas. 17. Connect the RF OUTPUT of the Satellite Repeater to the input of the spectrum analyzer using one long (120 cm) cable. Digital Modulator I Q I Q Up Converter 1 Up Converter 2 RF OUTPUT I OUTPUT to I INPUT Q OUTPUT to Q INPUT Earth Station Transmitter RF INPUT Satellite Repeater RF OUTPUT Spectrum Analyzer a Figure 26. Measuring repeater RF OUTPUT level. If you are using the Telemetry and Instrumentation Add-On, connect the RF OUTPUT of the Satellite Repeater directly to the Frequency Converter INPUT of the Data Generation/Acquisition Interface. The maximum input level of the Frequency Converter is 10 dbm. On the transmitter, select each Channel in turn and observe the approximate power level at the RF OUTPUT of the Satellite Repeater. Make sure that the power is always below the maximum input level of the spectrum analyzer. If the power exceeds this maximum level for any Channel, increase the distance between the two antennas (you may have to move one of the tables) or make the appropriate adjustment on the spectrum analyzer. Record the serial number (S/N) of the Satellite Repeater below (the serial number is on the back of the module): b Satellite Repeater S/N: You should try to use the same repeater and the receiver for all subsequent exercises in this manual. If this is not possible, you can obtain the gain values for these modules from another student when you perform further exercises. 44 Festo Didactic

43 Exercise 1 Power Gain and Antenna Parameters Procedure Fill in the and columns of Table 6. (refer to Table 1 on page 32 for the frequency corresponding to each Channel). Table 6. Gain of Satellite Repeater. Channel (GHz) (GHz) (dbm) (dbm) (db) A B C D E F For each Channel, observe the spectrum of the RF OUTPUT signal of the Satellite Repeater. Record the power of the unmodulated carrier in Table Taking care to avoid moving the antenna, disconnect the cables at the RF INPUT and at the RF OUTPUT of the Satellite Repeater. Connect these two cables together using an SMA-SMA adapter. This will allow you to observe the spectrum normally present at the RF INPUT of the Satellite Repeater. Wideband FM Modulator Up Converter 1 Up Converter 2 RF OUTPUT Earth Station Transmitter Satellite Repeater SMA-SMA adapter Spectrum Analyzer a Figure 27. Measuring the RF INPUT level. Since the microwave cables attenuate the signal, it is important that the total cable length be the same in Figure 26 and Figure 27. If you accidently change the orientation of the antenna, you should repeat Step 17 before continuing. Observe the spectrum. For each Channel, record the power in Table 6. Calculate the gain of the Satellite Repeater for each Channel and enter your results in Table 6. The approximate gain in db of the repeater can be calculated as. However, this ignores the difference in feed- Festo Didactic

44 Exercise 1 Power Gain and Antenna Parameters Procedure line loss at the uplink and downlink frequencies. For more precise results you can use the following formula: a Because there is not a great difference between the uplink and downlink frequencies, the value is small and can be ignored. 19. If you have exchanged the repeater and the transmitter, move them back to their normal positions. Gain of Down Converter 2 In this section, you will measure the gain of the receiver Down Converter 2. Because the down converter causes a large change in frequency, the cable loss at the input frequency and at the output frequency is not the same. 20. Align the antennas. Record the serial number (S/N) of the Earth Station Receiver. Receiver SN: Use the spectrometer to measure the gain of Down Converter 2 on the Earth Station Receiver, as follows: a Using one long cable, connect the receiving antenna to the input of the spectrum analyzer and measure. Taking care to avoid changing the orientation of the antenna, connect it to the RF INPUT of the receiver using one long cable. Connect the IF 2 OUTPUT to the input of the spectrum analyzer using one long cable and measure. Calculate the gain of Down Converter 2, taking into consideration the cable loss at the IF 2 frequency. It is not necessary to take into consideration the cable loss at 9 GHz because the power at the RF INPUT of the receiver is important here, not the power at the antenna. 46 Festo Didactic

45 Exercise 1 Power Gain and Antenna Parameters Procedure Table 7. Gain of down converter 2. Power at RF INPUT Power at IF 2 OUTPUT (1 long cable) dbm dbm Cable loss at (from Table 3) db Gain of Down Converter 2 db Antenna gain 21. Connect a small-aperture horn antenna to the input of the receiver and connect a large-aperture horn antenna to the input of the repeater. With this setup, both downlink antennas are small-aperture antennas and both the uplink antennas are large-aperture antennas. Make sure that all antennas are connected using cables of the same length (120 cm). 22. On the Earth Station Transmitter, make the following adjustments: Channel... any Data Source... any Scrambler... Of Clock & Frame Encoder... Off On the Earth Station Receiver, make the following adjustments: Channel... same as transmitter Festo Didactic

46 Exercise 1 Power Gain and Antenna Parameters Procedure You will need to measure the power at the satellite repeater. If you intend to use the Power Sensor on the repeater, adjust the distance between the two tables so the Power Sensor on the Satellite Repeater does not saturate. a The maximum displayed level of the Power Sensor on the Satellite Repeater is approximately -6.7 dbm. While observing the power (or the voltage) at the repeater Power Sensor OUTPUT, move the table of the Satellite Repeater slightly toward or away from the transmitter. If the displayed power changes, the Power Sensor is not saturated. If the displayed power does not change, and the three LEDs on the repeater are lit, then move the table away from the transmitter until the Power Sensor is no longer saturated, or slightly de-align one of the uplink antennas in order to reduce the power. Optimize the alignment of the downlink antennas. Gain of the large-aperture horn antenna at the uplink frequency 23. Measure the distance between the front faces of the large-aperture horn antennas in the uplink, as shown in Figure 28, and record this value in Table 8. Figure 28. Distance between antennas. Record the uplink frequency of the selected channel in Table 8. In this step, the repeater will be the receiver. To measure the gain of the antenna, you will need to determine the ratio of the power received by the repeater antenna to the power radiated by the transmitter antenna. Depending on how you measure the power (using the Power Sensors or an instrument), you will have to take into consideration the cable loss at the uplink frequency and perhaps the gain of the repeater. 48 Festo Didactic

48 Exercise 1 Power Gain and Antenna Parameters Procedure Table 8. Gain of large-aperture horn antenna (uplink frequency). Distance Frequency Cable loss Measured transmit power m GHz db dbm Transmitted power dbm Repeater gain 1 Measured receive power db dbm Received power dbm Gain dbi 1 if using the Power Sensors Calculate the gain of the antenna using: Gain of the small-aperture horn antenna versus downlink frequency 24. Make sure the two small-aperture horn antennas are on the downlink and the two large-aperture horn antennas are on the uplink. Align the antennas. Measure the distance between the front faces of the downlink antennas and record it in Table Festo Didactic

49 Exercise 1 Power Gain and Antenna Parameters Procedure Enter the cable loss at the downlink frequency and the gain of Down Converter 2 using the values already measured. Table 9. Initial values for the gain measurement of the small-aperture horn antenna. Distance Cable loss Down Converter 2 Gain m db db 25. Depending on how you will measure the transmitted and received powers, enter the appropriate formula for these two values in Table 10. On the transmitter and the receiver, select each channel in turn to obtain the downlink frequencies shown in Table 10. For each frequency, determine the gain of the large-aperture horn antennas presently connected in the downlink. Then plot the measured gain versus the frequency in Figure 30. Table 10. Gain of small-aperture horn antenna (downlink frequencies). Channel A B C D E F Downlink frequency Measured transmit power GHz dbm Transmitted power dbm IF 2 OUTPUT power 1 dbm Received power dbm db Antenna gain dbi 1 if using the Power Sensor Festo Didactic

50 Exercise 1 Power Gain and Antenna Parameters Procedure Gain [dbi] Downlink frequency [GHz] Figure 30. Gain of small and large aperture horn antenna vs frequency. Gain of the large-aperture horn antenna versus downlink frequency 26. Install the two large-aperture horn antennas on the downlink and the two small-aperture horn antennas on the uplink. Align the antennas. Measure the distance between the front faces of the downlink antennas and record it in Table 11. Enter the other values in the table using the values already measured. Table 11. Initial values for the gain measurement of the large-aperture horn antenna. Distance Cable loss Down Converter 2 Gain m db db 27. Depending on how you will measure the transmitted and received powers, enter the appropriate formula for these two values in Table 12. On the transmitter and the receiver, select each channel in turn to obtain the downlink frequencies shown in Table 12. For each frequency, determine the gain of the large-aperture horn antennas presently connected in the downlink. Then plot the measured gain versus the frequency in Figure Festo Didactic

51 Exercise 1 Power Gain and Antenna Parameters Procedure Table 12. Gain of large-aperture horn antenna (downlink frequencies). Channel A B C D E F Downlink frequency Measured transmit power GHz dbm Transmitted power dbm IF 2 OUTPUT power 1 dbm Received power dbm dbm Antenna gain dbi 1 if using the Power Sensor 28. Using Table 13, calculate the theoretical gains of the large aperture horn antenna at each of the downlink frequencies using the following information: Plot the calculated gain versus frequency in Figure 30. Festo Didactic

52 Exercise 1 Power Gain and Antenna Parameters Procedure Table 13. Theoretical gain vs frequency of the large-aperture horn antenna. Channel A B C D E F Downlink frequency Downlink wavelength Antenna gain GHz cm dbi Effective aperture and efficiency 29. For one of the Channels, calculate the effective aperture of the antenna using Equation (19) rearranged as follows: Then calculate the efficiency using Equation (17) rearranged as follows: Beamwidth and radiation pattern In this section, you will determine the beam width of a horn antenna and plot the radiation pattern. Since the radiation pattern of an antenna is the same whether the antenna is transmitting or receiving, the antenna used to plot the pattern can be at any one of the four antenna positions (transmitter, repeater input, repeater output, or receiver) in the system. 54 Festo Didactic

53 Exercise 1 Power Gain and Antenna Parameters Procedure However, because the radiation pattern will be affected by reflections from metallic objects, it is preferable to choose the antenna position that is furthest away from reflecting objects. Since the transmitter and receiver housings are reflecting objects, one of the antennas is connected to the repeater may be the best choice. If you have microwave absorbing panels, you may wish to install these in order to minimize reflections from other objects. 30. Choose one of the four antenna positions in the system (transmitter, repeater input, repeater output, or receiver) that is furthest from reflecting objects. Install the Antenna Azimuth Indicator on the mast (see Figure 31) at that location and install a small aperture horn antenna on the Antenna Positioner. Figure 31. Antenna azimuth indicator on mast. Connect this antenna to the module using two long microwave cables connected together using an SMA-SMA adapter. This will allow you to turn the antenna to any angle without putting strain on the cable. Connect the other antennas and align all antennas to obtain the maximum power at the receiver. Adjust the antenna positioner so that 0 corresponds to the principal axis of the antenna, that is, the position that gives the maximum power (see Figure 32). Then tighten the knob on the mast. The antenna should turn freely through 360. Festo Didactic

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