Download presentation

Presentation is loading. Please wait.

1
**Amateur Extra License Class**

Chapter 9 Antennas and Feedlines

2
**Basics of Antennas Antenna Radiation Patterns.**

Graphical representation of spatial distribution of energy around an antenna. 3D = Full representation. 2D = “Slice” through pattern.

3
**Basics of Antennas Antenna Radiation Patterns.**

Represent radiation pattern in “far field” of the antenna. Radiation pattern does not change with distance. 10 wavelengths or more from the antenna.

4
**Basics of Antennas Antenna Gain. Antennas are passive devices.**

POut ≤ PIn. Gain comes from increasing power in one direction at the expense of another direction. Gain is defined as the ratio of the signal strength in the direction of maximum radiation to the signal strength of a reference antenna.

5
**Basics of Antennas Antenna Gain. Isotropic antenna.**

Theoretical point radiator. Impossible to build. Radiates equally in ALL directions. No gain in any direction. Used as a reference for antenna gain. Gain referenced to an isotropic radiator expressed as dBi.

6
**Basics of Antennas Antenna Gain. Half-wave dipole antenna.**

Most basic real-world antenna. Most other antenna designs are based on the half-wave dipole. Easily constructed. Also used as a reference for antenna gain. Gain referenced to a dipole is expressed as dBd. 0 dBd = 2.15 dBi

7
**Basics of Antennas Antenna Gain. Directional antennas.**

ALL real-world antennas are directional in one or more planes. “Omni-directional” antennas are omni-directional in the horizontal plane, but directional in the vertical plane.

8
**Basics of Antennas Antenna Gain. Directional antennas.**

Major lobe = Direction of most energy. a.k.a. – Main lobe or forward direction. Minor lobes = Additional lobes to side or rear of main lobe.

9
**E9A01 -- Which of the following describes an isotropic antenna?**

A grounded antenna used to measure earth conductivity A horizontally polarized antenna used to compare Yagi antennas A theoretical antenna used as a reference for antenna gain A spacecraft antenna used to direct signals toward the earth

10
E9A02 -- How much gain does a 1/2-wavelength dipole in free space have compared to an isotropic antenna? 1.55 dB 2.15 dB 3.05 dB 4.30 dB

11
**E9A03 -- Which of the following antennas has no gain in any direction?**

Quarter-wave vertical Yagi Half-wave dipole Isotropic antenna

12
**E9A08 -- What is meant by antenna gain?**

The ratio relating the radiated signal strength of an antenna in the direction of maximum radiation to that of a reference antenna The ratio of the signal in the forward direction to that in the opposite direction The ratio of the amount of power radiated by an antenna compared to the transmitter output power The final amplifier gain minus the transmission-line losses, including any phasing lines present

13
E9A13 -- How much gain does an antenna have compared to a 1/2-wavelength dipole when it has 6 dB gain over an isotropic antenna? 3.85 dB 6.0 dB 8.15 dB 2.79 dB

14
E9A14 -- How much gain does an antenna have compared to a 1/2-wavelength dipole when it has 12 dB gain over an isotropic antenna? 6.17 dB 9.85 dB 12.5 dB 14.15 dB

15
E9B07 -- How does the total amount of radiation emitted by a directional gain antenna compare with the total amount of radiation emitted from an isotropic antenna, assuming each is driven by the same amount of power? The total amount of radiation from the directional antenna is increased by the gain of the antenna The total amount of radiation from the directional antenna is stronger by its front to back ratio They are the same The radiation from the isotropic antenna is 2.15 dB stronger than that from the directional antenna

16
**E9B12 -- What is the far-field of an antenna?**

The region of the ionosphere where radiated power is not refracted The region where radiated power dissipates over a specified time period The region where radiated field strengths are obstructed by objects of reflection The region where the shape of the antenna pattern is independent of distance

17
**Basics of Antennas Beamwidth and Pattern Ratios. Beamwidth.**

Angle between the half-power (-3 dB) points. Higher gain ↔ narrower beamwidth. Front-to-Back ratio. Ratio of power in forward direction to power in reverse direction. Front-to-Side ratio. Ratio of power in forward direction to power 90º from forward direction. Assumes a symmetrical pattern.

18
**Basics of Antennas Beamwidth and Pattern Ratios. Beamwidth?**

50°. Front-to-Back Ratio? 18 dB. Front-to-Side Ratio? 14 dB.

19
**E9B01 -- In the antenna radiation pattern shown in Figure E9-1, what is the 3-dB beamwidth?**

75 degrees 50 degrees 25 degrees 30 degrees

20
**E9B02 -- In the antenna radiation pattern shown in Figure E9-1, what is the front-to-back ratio?**

36 dB 18 dB 24 dB 14 dB

21
**E9B03 -- In the antenna radiation pattern shown in Figure E9-1, what is the front-to-side ratio?**

12 dB 14 dB 18 dB 24 dB

22
**E9B08 -- How can the approximate beamwidth in a given plane of a directional antenna be determined?**

Note the two points where the signal strength of the antenna is 3 dB less than maximum and compute the angular difference Measure the ratio of the signal strengths of the radiated power lobes from the front and rear of the antenna Draw two imaginary lines through the ends of the elements and measure the angle between the lines Measure the ratio of the signal strengths of the radiated power lobes from the front and side of the antenna

23
**E9D03 -- How does the beamwidth of an antenna vary as the gain is increased?**

It increases geometrically It increases arithmetically It is essentially unaffected It decreases

24
**Basics of Antennas Radiation and Ohmic Resistance Power in antenna is:**

Radiated into space. Dissipated as heat (ohmic losses). Want more power radiated into space. Want less power dissipated as heat.

25
**Basics of Antennas Radiation and Ohmic Resistance**

Radiation Resistance. Resistance that would dissipate power equal to that radiated by the antenna. Affected by earth & other nearby conductive objects. Closer to earth or other objects lowers radiation resistance. Affected by length/diameter ratio of conductors. Larger diameter lowers radiation resistance.

26
**Basics of Antennas Radiation and Ohmic Resistance Ohmic Resistance.**

Resistance of materials used in construction of the antenna. Power lost as heat. Total resistance. Sum of radiation resistance and ohmic resistance.

27
**Basics of Antennas Feedpoint Impedance**

Ratio of RF voltage to RF current at point feedline is connected to antenna. If voltage and current are in phase: Antenna is resonant. Impedance is purely resistive. If voltage and current are not in phase: Impedance will include either inductive or capacitive reactance.

28
**Basics of Antennas Feedpoint Impedance Impedance changes with:**

Frequency. Position of feedpoint along antenna. Length/diameter ratio of conductor. Height above ground. Nearby objects. Other antennas. Buildings. Power lines.

29
**Basics of Antennas Radiation and Ohmic Resistance Antenna Efficiency.**

RT = RR + R Efficiency = 100% x RR / (RR + R) Efficiency = 100% x RR / RT RT = Total Resistance RR = Radiation Resistance R = Real (ohmic) Resistance

30
**Basics of Antennas Radiation and Ohmic Resistance Antenna Efficiency.**

A 1/2 λ dipole has high efficiency because conductor resistance is very low compared to radiation resistance. A shortened antenna with a loading coil may have low efficiency because resistance of loading coil may be significant. A ground-mounted 1/4 λ vertical requires a good ground radial system to achieve high efficiency. Otherwise, ground resistance increases ohmic resistance.

31
**E9A05 -- Which of the following factors may affect the feed point impedance of an antenna?**

Transmission-line length Antenna height, conductor length/diameter ratio and location of nearby conductive objects Constant feed point impedance Sunspot activity and time of day

32
**E9A06 -- What is included in the total resistance of an antenna system?**

Radiation resistance plus space impedance Radiation resistance plus transmission resistance Transmission-line resistance plus radiation resistance Radiation resistance plus ohmic resistance

33
**E9A10 -- How is antenna efficiency calculated?**

(radiation resistance / transmission resistance) x 100% (radiation resistance / total resistance) x 100% (total resistance / radiation resistance) x 100% (effective radiated power / transmitter output) x 100%

34
E9A11 -- Which of the following choices is a way to improve the efficiency of a ground-mounted quarter-wave vertical antenna? Install a good radial system Isolate the coax shield from ground Shorten the radiating element Reduce the diameter of the radiating element

35
**E9A15 -- What is meant by the radiation resistance of an antenna?**

The combined losses of the antenna elements and feed line The specific impedance of the antenna The value of a resistance that would dissipate the same amount of power as that radiated from an antenna The resistance in the atmosphere that an antenna must overcome to be able to radiate a signal

36
**Basics of Antennas Antenna Polarization.**

Orientation of electric field with respect to the ground. Electric field is in same plane as the antenna elements. If elements are parallel to the ground, antenna is horizontally polarized. If elements are perpendicular to the ground, antenna is vertically polarized.

37
**Basics of Antennas Azimuthal and Elevation Patterns.**

Azimuthal pattern shows radiation around the antenna. Elevation pattern shows radiation at various angles above horizontal. Take-off angle.

38
**E9C07 -- What type of antenna pattern over real ground is shown in Figure E9-2?**

Elevation Azimuth Radiation resistance Polarization

39
E9C08 -- What is the elevation angle of peak response in the antenna radiation pattern shown in Figure E9-2? 45 degrees 75 degrees 7.5 degrees 25 degrees

40
**E9C09 -- What is the front-to-back ratio of the radiation pattern shown in Figure E9-2?**

15 dB 28 dB 3 dB 24 dB

41
E9C10 -- How many elevation lobes appear in the forward direction of the antenna radiation pattern shown in Figure E9-2? 4 3 1 7

42
**Basics of Antennas Bandwidth.**

As frequency changes, feedpoint impedance, radiation pattern, & gain all change.

43
**Basics of Antennas Bandwidth.**

Bandwidth defined as the range of frequencies over which an antenna meets a published performance requirement. Often stated as 2:1 SWR bandwidth.

44
**E9A09 -- What is meant by antenna bandwidth?**

Antenna length divided by the number of elements The frequency range over which an antenna satisfies a performance requirement The angle between the half-power radiation points The angle formed between two imaginary lines drawn through the element ends

45
**Practical Antennas Effects of Ground and Ground Systems.**

Biggest effect on antenna system efficiency is losses in nearby ground, grounded structures, or the antenna ground system. At HF, soil conductivity determines ground losses. Radiation pattern of an antenna over real ground is ALWAYS affected by the conductivity and dielectric constant of the soil. Especially true for ground-mounted vertical antennas. Poor ground raises radiation angle.

46
**Practical Antennas Effects of Ground and Ground Systems.**

Height above ground. Also affects radiation pattern. The higher the better. Up to 1/2λ. Fewer ground losses. Lower angle of radiation.

47
**Practical Antennas Effects of Ground and Ground Systems. Terrain.**

Radiation patterns approach published values on flat open terrain. Add hills and/or buildings & all bets are off! If antenna is mounted on a slope or hillside, the radiation pattern is tilted. Higher take-off angle in uphill direction. Lower take-off angle in downhill direction. Hilltops are good, but NOT because of elevation. All directions are downhill – therefore lower take-off angle.

48
**Practical Antennas Effects of Ground and Ground Systems.**

Connection must be short compared to a wavelength. > 0.1λ acts like antenna or transmission line. Object is to create a path to ground with as low an impedance as possible. Inductance of 1 foot of #10 wire > 0.1 μH. Skin effect. Use wide, flat copper strap. 3 or 4 inter-connected ground rods. For RF grounding, 4-ft rods work just as well as 8-ft rods.

49
E3C07 -- How does the radiation pattern of a horizontally polarized 3-element beam antenna vary with its height above ground? The main lobe takeoff angle increases with increasing height The main lobe takeoff angle decreases with increasing height The horizontal beam width increases with height The horizontal beam width decreases with height

50
E3C10 -- How does the performance of a horizontally polarized antenna mounted on the side of a hill compare with the same antenna mounted on flat ground? The main lobe takeoff angle increases in the downhill direction The main lobe takeoff angle decreases in the downhill direction The horizontal beam width decreases in the downhill direction The horizontal beam width increases in the uphill direction

51
E9A12 -- Which of the following factors determines ground losses for a ground-mounted vertical antenna operating in the 3-30 MHz range? The standing-wave ratio Distance from the transmitter Soil conductivity Take-off angle

52
E9C11 -- How is the far-field elevation pattern of a vertically polarized antenna affected by being mounted over seawater versus rocky ground? The low-angle radiation decreases The high-angle radiation increases Both the high- and low-angle radiation decrease The low-angle radiation increases

53
**E9C13 -- What is the main effect of placing a vertical antenna over an imperfect ground?**

It causes increased SWR It changes the impedance angle of the matching network It reduces low-angle radiation It reduces losses in the radiating portion of the antenna

54
E9D14 -- Which of the following types of conductor would be best for minimizing losses in a station's RF ground system? A resistive wire, such as a spark plug wire A wide flat copper strap A cable with 6 or 7 18-gauge conductors in parallel A single 12 or 10-gauge stainless steel wire

55
**E9D15 -- Which of the following would provide the best RF ground for your station?**

A 50-ohm resistor connected to ground An electrically-short connection to a metal water pipe An electrically-short connection to 3 or 4 interconnected ground rods driven into the Earth An electrically-short connection to 3 or 4 interconnected ground rods via a series RF choke

56
**Practical Antennas Shortened and Multi-Band Antennas. Loaded whips.**

Except for 12m & 10m, full-sized 1/4λ verticals not practical for mobile operation. Radiation resistance of a full-sized 1/4λ vertical is about 36Ω. At less than 1/4λ, radiation resistance decreases & capacitive reactance is added. Need some way to cancel capacitive reactance.

57
**Practical Antennas Shortened and Multi-Band Antennas. Loaded whips.**

Loading coil. Inductance cancels capacitive reactance of short antenna. Narrows bandwidth & adds loss. Base loading. Coil at bottom of whip. Lowest inductance for given whip length. Center loading. Coil part way up the whip. Increases radiation resistance, increasing efficiency. Higher inductance → higher losses. More difficult to construct mechanically.

58
**Practical Antennas Shortened and Multi-Band Antennas. Loaded whips.**

Hamstick® antennas. Base loaded whip with long loading coil. Loading coil wound on fiberglass tube about 3-4 feet long. Turns on loading coil are widely spaced. More efficient than conventional base-loaded whip. Low cost. Single band. Must change antenna to change bands.

59
**Practical Antennas Shortened and Multi-Band Antennas. Loaded whips.**

Screwdriver antennas. Base loaded whip with remotely adjustable inductor. High cost. Multi-band. Convenient to change bands. Shortened and Multi-Band Antennas.

60
**Practical Antennas Shortened and Multi-Band Antennas. Capacity hat.**

a.k.a. – Top loading. Adds capacitance. Lowers capacitive reactance. Less inductance required. Improves radiation efficiency.

61
**Practical Antennas Shortened and Multi-Band Antennas. Trap Antennas.**

Most common design method for multi-band antenna. Traps are parallel L-C circuits resonant on a particular band. Below fR trap acts as a loading coil. At fR trap acts as an open circuit. Antenna efficiency depends on Q of trap.

62
**Practical Antennas Shortened and Multi-Band Antennas. Trap Antennas.**

Disadvantages: Will not reject harmonics. Traps narrow bandwidth. Traps add loss. Higher Q → Lower loss.

63
E9D05 -- Where should a high-Q loading coil be placed to minimize losses in a shortened vertical antenna? Near the center of the vertical radiator As low as possible on the vertical radiator As close to the transmitter as possible At a voltage node

64
**E9D06 -- Why should an HF mobile antenna loading coil have a high ratio of reactance to resistance?**

To swamp out harmonics To maximize losses To minimize losses To minimize the Q

65
**E9D07 -- What is a disadvantage of using a multiband trapped antenna?**

It might radiate harmonics It radiates the harmonics and fundamental equally well It is too sharply directional at lower frequencies It must be neutralized

66
E9D08 -- What happens to the bandwidth of an antenna as it is shortened through the use of loading coils? It is increased It is decreased No change occurs It becomes flat

67
**E9D09 -- What is an advantage of using top loading in a shortened HF vertical antenna?**

Lower Q Greater structural strength Higher losses Improved radiation efficiency

68
**E9D11 -- What is the function of a loading coil as used with an HF mobile antenna?**

To increase the SWR bandwidth To lower the losses To lower the Q To cancel capacitive reactance

69
**E9D12 -- What is one advantage of using a trapped antenna?**

It has high directivity in the higher-frequency bands It has high gain It minimizes harmonic radiation It may be used for multiband operation

70
E9D13 -- What happens to feed point impedance at the base of a fixed-length HF mobile antenna as the frequency of operation is lowered? The radiation resistance decreases and the capacitive reactance decreases The radiation resistance decreases and the capacitive reactance increases The radiation resistance increases and the capacitive reactance decreases The radiation resistance increases and the capacitive reactance increases

71
**Practical Antennas Folded Dipole.**

1λ of wire formed into a long, narrow loop. Feedpoint impedance approximately 300Ω. SWR bandwidth greater than standard dipole.

72
Practical Antennas Folded Dipole.

73
**E9A07 -- What is a folded dipole antenna?**

A dipole one-quarter wavelength long A type of ground-plane antenna A dipole constructed from one wavelength of wire forming a very thin loop A dipole configured to provide forward gain

74
E9D10 -- What is the approximate feed point impedance at the center of a two-wire folded dipole antenna? 300 ohms 72 ohms 50 ohms 450 ohms

75
**Practical Antennas Traveling Wave Antennas. Long-wire antenna.**

1λ long or more. Typically fed 1/4λ from one end. Dipole with one leg extended. 4 major lobes & many minor lobes. The longer the wire, the closer the major lobes are to the wire.

76
**Practical Antennas Traveling Wave Antennas. “V” Beam.**

2 long-wires fed 180° out of phase. 2 major lobes.

77
**Practical Antennas Traveling Wave Antennas.**

Resonant (unterminated) rhombic antenna. 2 V-beams placed end-to-end. Bi-directional. Not widely used.

78
**Practical Antennas Traveling Wave Antennas.**

Non-resonant rhombic antenna. Termination resistor. Uni-directional. Resistive load over wide frequency range. Very large area. 4 tall supports needed.

79
**Practical Antennas Traveling Wave Antennas. Beverage antenna.**

1λ or more long. Uni-directional. Receive only. Mostly used on 160m & 80m.

80
**E9C04 -- Which of the following describes a basic unterminated rhombic antenna?**

Unidirectional; four-sides, each side one quarter-wavelength long; terminated in a resistance equal to its characteristic impedance Bidirectional; four-sides, each side one or more wavelengths long; open at the end opposite the transmission line connection Four-sides; an LC network at each corner except for the transmission connection; Four-sides, each of a different physical length

81
**E9C05 -- What are the disadvantages of a terminated rhombic antenna for the HF bands?**

The antenna has a very narrow operating bandwidth The antenna produces a circularly polarized signal The antenna requires a large physical area and 4 separate supports The antenna is more sensitive to man-made static than any other type

82
**E9C06 -- What is the effect of a terminating resistor on a rhombic antenna?**

It reflects the standing waves on the antenna elements back to the transmitter It changes the radiation pattern from bidirectional to unidirectional It changes the radiation pattern from horizontal to vertical polarization It decreases the ground loss

83
E9C12 -- When constructing a Beverage antenna, which of the following factors should be included in the design to achieve good performance at the desired frequency? Its overall length must not exceed 1/4 wavelength It must be mounted more than 1 wavelength above ground It should be configured as a four-sided loop It should be one or more wavelengths long

84
**Practical Antennas Phased Arrays.**

2 (or more) vertical antennas fed with specific phase relationships. If fed in-phase, a pattern broadside to the elements results. If 1/2λ apart, figure-8 pattern broadside to the array. If fed 180° out-of-phase, a pattern in line with the elements results. If 1/2λ apart, figure-8 pattern in line with the array.

85
**Practical Antennas Phased Arrays.**

If 1/4λ apart & fed 90° out-of phase, a cardioid pattern results.

86
**Practical Antennas Phased Arrays. Phasing lines. Wilkinson divider.**

Transmission lines with specific electrical length. Ensure that signals from each driven element combine to produce the desired radiation pattern. Wilkinson divider. Divides power into 2 or more equal portions. Provides load isolation.

87
Practical Antennas Phased Arrays. Phasing harness.

88
E9C01 -- What is the radiation pattern of two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed 180 degrees out of phase? A cardioid Omnidirectional A figure-8 broadside to the axis of the array A figure-8 oriented along the axis of the array

89
E9C02 -- What is the radiation pattern of two 1/4-wavelength vertical antennas spaced 1/4-wavelength apart and fed 90 degrees out of phase? A cardioid A figure-8 end-fire along the axis of the array A figure-8 broadside to the axis of the array Omnidirectional

90
E9C03 -- What is the radiation pattern of two 1/4-wavelength vertical antennas spaced 1/2-wavelength apart and fed in phase? Omnidirectional A cardioid A Figure-8 broadside to the axis of the array A Figure-8 end-fire along the axis of the array

91
E9E12 -- What is the primary purpose of a phasing line when used with an antenna having multiple driven elements? It ensures that each driven element operates in concert with the others to create the desired antenna pattern It prevents reflected power from traveling back down the feed line and causing harmonic radiation from the transmitter It allows single-band antennas to operate on other bands It makes sure the antenna has a low-angle radiation pattern

92
**E9E13 -- What is the purpose of a Wilkinson divider?**

It divides the operating frequency of a transmitter signal so it can be used on a lower frequency band It is used to feed high-impedance antennas from a low-impedance source It divides power equally among multiple loads while preventing changes in one load from disturbing power flow to the others It is used to feed low-impedance loads from a high-impedance source

93
**Practical Antennas Effective Radiated Power.**

Equivalent power if antenna was a reference antenna. Dipole (dBd). Used for most calculations. Isotropic (dBi). Used for space communications calculations. Includes feedline & other losses. ERP = Power Output – System Losses + Antenna Gain

94
E9H01 -- What is the effective radiated power relative to a dipole of a repeater station with 150 watts transmitter power output, 2-dB feed line loss, 2.2-dB duplexer loss and 7-dBd antenna gain? 1977 watts 78.7 watts 420 watts 286 watts

95
E9H02 -- What is the effective radiated power relative to a dipole of a repeater station with 200 watts transmitter power output, 4-dB feed line loss, 3.2-dB duplexer loss, 0.8-dB circulator loss and 10-dBd antenna gain? 317 watts 2000 watts 126 watts 300 watts

96
E9H03 -- What is the effective isotropic radiated power of a repeater station with 200 watts transmitter power output, 2-dB feed line loss, 2.8-dB duplexer loss, 1.2-dB circulator loss and 7-dBi antenna gain? 159 watts 252 watts 632 watts 63.2 watts

97
E9H04 -- What term describes station output, including the transmitter, antenna and everything in between, when considering transmitter power and system gains and losses? Power factor Half-power bandwidth Effective radiated power Apparent power

98
**Practical Antennas Satellite Antenna Systems Gain and antenna size.**

Rule-of-thumb: The bigger the antenna (in wavelengths) the more gain. Yagi with a longer boom = more gain. Dish with twice the diameter = 4x gain (6dB).

99
**Practical Antennas Satellite Antenna Systems**

How much gain is required? The more the better – NOT! Higher gain → narrower beamwidth. Narrower beamwidth → harder to aim antenna. At VHF/UHF, Yagi antennas are usually sufficient.

100
**Practical Antennas Satellite Antenna Systems Pointing the antenna.**

Directional antennas for terrestrial communications use a single rotator. Azimuth. Directional antennas for satellite communications often use 2 rotators to more accurately point antenna at satellite. Elevation.

101
**Practical Antennas Satellite Antenna Systems What about polarization?**

Circular polarization gives best results. Can get circular polarization by constructing 2 Yagis on same boom fed 90° out-of-phase.

102
E9D01 -- How does the gain of an ideal parabolic dish antenna change when the operating frequency is doubled? Gain does not change Gain is multiplied by 0.707 Gain increases by 6 dB Gain increases by 3 dB

103
**E9D02 -- How can linearly polarized Yagi antennas be used to produce circular polarization?**

Stack two Yagis, fed 90 degrees out of phase, to form an array with the respective elements in parallel planes Stack two Yagis, fed in phase, to form an array with the respective elements in parallel planes Arrange two Yagis perpendicular to each other with the driven elements at the same point on the boom and fed 90 degrees out of phase Arrange two Yagis collinear to each other, with the driven elements fed 180 degrees out of phase

104
E9D04 -- Why is it desirable for a ground-mounted satellite communications antenna system to be able to move in both azimuth and elevation? In order to track the satellite as it orbits the Earth So the antenna can be pointed away from interfering signals So the antenna can be positioned to cancel the effects of Faraday rotation To rotate antenna polarization to match that of the satellite

105
**Practical Antennas Receiving Loop Antennas.**

One or more turns of wire in a large open loop. Add gain by adding turns or making loop bigger.

106
**E9H09 -- Which of the following describes the construction of a receiving loop antenna?**

A large circularly-polarized antenna A small coil of wire tightly wound around a toroidal ferrite core One or more turns of wire wound in the shape of a large open coil A vertical antenna coupled to a feed line through an inductive loop of wire

107
**E9H10 -- How can the output voltage of a multi-turn receiving loop antenna be increased?**

By reducing the permeability of the loop shield By increasing the number of wire turns in the loop and reducing the area of the loop structure By winding adjacent turns in opposing directions By increasing either the number of wire turns in the loop or the area of the loop structure or both

108
**Practical Antennas Direction-Finding and DF Antennas**

Finding the direction of a transmitted signal. Directional antenna. Signal detector (receiver).

109
**Practical Antennas Direction-Finding and DF Antennas Antenna.**

Lobes may be broad, but nulls are usually sharp. Loops are easy to construct, but are bi-directional. Shielded loops are electrostatically balanced against ground & have deeper, sharper nulls. Adding a sense antenna to a loop makes the antenna have a single null. Sense antenna is an omni-directional antenna fed 90° out-of-phase yielding a cardioid pattern.

110
**Practical Antennas Direction-Finding and DF Antennas Signal detector.**

Receiver for desired frequency. Variable RF gain and/or an attenuator useful for close-in work. Prevents overload. Active attenuator.

111
**Practical Antennas Direction-Finding and DF Antennas Terrain effects.**

Physical surroundings can cause false bearings. Terrain. Buildings, water towers, radio towers, etc. Overhead power/utility lines.

112
**Practical Antennas Direction-Finding and DF Antennas Triangulation.**

Several stations in different locations take headings. Or same station from different locations. Results are plotted on a map to determine approximate location.

113
**E9H05 -- What is the main drawback of a wire-loop antenna for direction finding?**

It has a bidirectional pattern It is non-rotatable It receives equally well in all directions It is practical for use only on VHF bands

114
**E9H06 -- What is the triangulation method of direction finding?**

The geometric angle of sky waves from the source are used to determine its position A fixed receiving station plots three headings from the signal source on a map Antenna headings from several different receiving locations are used to locate the signal source A fixed receiving station uses three different antennas to plot the location of the signal source

115
**E9H07 -- Why is it advisable to use an RF attenuator on a receiver being used for direction finding?**

It narrows the bandwidth of the received signal to improve signal to noise ratio It compensates for the effects of an isotropic antenna, thereby improving directivity It reduces loss of received signals caused by antenna pattern nulls, thereby increasing sensitivity It prevents receiver overload which could make it difficult to determine peaks or nulls

116
**E9H08 -- What is the function of a sense antenna?**

It modifies the pattern of a DF antenna array to provide a null in one direction It increases the sensitivity of a DF antenna array It allows DF antennas to receive signals at different vertical angles It provides diversity reception that cancels multipath signals

117
**E9H11 -- What characteristic of a cardioid-pattern antenna is useful for direction finding?**

A very sharp peak A very sharp single null Broad band response High-radiation angle

118
**E9H12 -- What is an advantage of using a shielded loop antenna for direction finding?**

It automatically cancels ignition noise pickup in mobile installations It is electro-statically balanced against ground, giving better nulls It eliminates tracking errors caused by strong out-of-band signals It allows stations to communicate without giving away their position

119
Break

120
Antenna Systems The antenna system is more than just the antenna itself. Antenna. Supports. Feedline. Matching devices. Metering devices.

121
**Antenna Systems Impedance matching.**

Impedance matching done at transmitter . Convenient. Lazy man’s method. Probably more expensive. Antenna tuner required. Higher transmission line losses. SWR on transmission line is still high.

122
**Antenna Systems Impedance matching.**

Impedance matching done at antenna feedpoint. Not as convenient. Have to make adjustments at antenna instead of from operating position. Must know feedpoint impedance of antenna. Probably less expensive. Simple L-C network can be used. Lower transmission line losses. SWR on transmission line is low. Discuss ATU at antenna.

123
**Antenna Systems Impedance matching. Delta match.**

Matches higher impedance transmission line to lower impedance antenna. Balanced. Some radiation from delta. Difficult to adjust. No center insulator.

124
**Antenna Systems Impedance matching. Gamma match.**

Common matching method for beams. Used to load towers for use as vertical antennas. Can match wide range of impedances. Inherently unbalanced so no balun needed.

125
**Antenna Systems Impedance matching.**

Hairpin match (a.k.a. – Beta match). Common matching method for beams. Driven element must have capacitive reactance. Equivalent to an L-network.

126
**Antenna Systems Impedance matching. Stub match.**

Can match highly reactive loads. Can be made from a piece of coax. “Universal stub system” often used at VHF & UHF when impedances to be matched are unknown & coax lengths are manageable.

127
**E9A04 -- Why would one need to know the feed point impedance of an antenna?**

To match impedances in order to minimize standing wave ratio on the transmission line To measure the near-field radiation density from a transmitting antenna To calculate the front-to-side ratio of the antenna To calculate the front-to-back ratio of the antenna

128
**The gamma matching system The delta matching system **

E9E01 -- What system matches a high-impedance transmission line to a lower impedance antenna by connecting the line to the driven element in two places spaced a fraction of a wavelength each side of element center? The gamma matching system The delta matching system The omega matching system The stub matching system

129
**The gamma match The delta match The epsilon match The stub match**

E9E02 -- What is the name of an antenna matching system that matches an unbalanced feed line to an antenna by feeding the driven element both at the center of the element and at a fraction of a wavelength to one side of center? The gamma match The delta match The epsilon match The stub match

130
E9E03 -- What is the name of the matching system that uses a section of transmission line connected in parallel with the feed line at or near the feed point? The gamma match The delta match The omega match The stub match

131
**E9E04 -- What is the purpose of the series capacitor in a gamma-type antenna matching network?**

To provide DC isolation between the feed line and the antenna To cancel the inductive reactance of the matching network To provide a rejection notch to prevent the radiation of harmonics To transform the antenna impedance to a higher value

132
**E9E05 -- How must the driven element in a 3-element Yagi be tuned to use a hairpin matching system?**

The driven element reactance must be capacitive The driven element reactance must be inductive The driven element resonance must be lower than the operating frequency The driven element radiation resistance must be higher than the characteristic impedance of the transmission line

133
E9E06 -- What is the equivalent lumped-constant network for a hairpin matching system on a 3-element Yagi? Pi network Pi-L network L network Parallel-resonant tank

134
E9E09 -- Which of these matching systems is an effective method of connecting a 50-ohm coaxial cable feed line to a grounded tower so it can be used as a vertical antenna? Double-bazooka match Hairpin match Gamma match All of these choices are correct

135
E9E11 -- What is an effective way of matching a feed line to a VHF or UHF antenna when the impedances of both the antenna and feed line are unknown? Use a 50-ohm 1:1 balun between the antenna and feed line Use the universal stub matching technique Connect a series-resonant LC network across the antenna feed terminals Connect a parallel-resonant LC network across the antenna feed terminals

136
**Antenna Systems Transmission Line Mechanics. Wavelength in a wire.**

Current in a wire travels at some finite speed. Therefore length of a wire can be expressed in wavelengths.

137
**Antenna Systems Transmission Line Mechanics.**

Velocity of propagation (VP). Speed at which wave travels down a wire. Always less than speed of light (C). Velocity factor (VF) = VP / C. Velocity factor determined by dielectric constant of insulator. VF = 1 / ε is close to 1 for parallel-wire feed lines. ε

138
**Antenna Systems Transmission Line Mechanics. Electrical length.**

Length of a wire in wavelengths. (Electrical Length) = (Physical Length) / (Velocity Factor) or (Physical Length) = (Electrical Length) x (Velocity Factor)

139
**Antenna Systems Transmission Line Mechanics. Feed line loss.**

All physical feed lines have some loss. Parallel-conductor feedlines have lowest loss. Loss increases as frequency increases. Larger diameter cables tend to have lower loss. Foam dielectric cables have lower loss than solid dielectric cables of the same diameter. Foam dielectric cables have a lower maximum voltage than solid dielectric cables of the same diameter.

140
**Antenna Systems Transmission Line Mechanics. Feed line loss.**

Feed line loss is normally specified in dB for a 100-foot length at some frequency.

141
**Antenna Systems Cable Type Z0 VF (%) OD (in) Vmax (RMS)**

Loss (dB/100 ft) @ 100 MHz RG-8 (Foam) 50Ω 82 .405 600 1.5 RG-8 (Solid) 52Ω 66 3700 1.9 RG-8X .242 3.2 RG-58 (Solid) .195 1400 4.5 RG-58A Foam) 73 300 4.3 RG-174 .110 1100 8.6 Twin Lead 300Ω 80 n/a 8,000 1.1 Ladder Line 450Ω 91 10,000 0.3 Open-Wire Line 600Ω 95-99 12,000 0.2

142
**Antenna Systems Transmission Line Mechanics.**

Reflection Coefficient and SWR. Reflection coefficient. Ratio of reflected voltage at a given point on a feedline to the incident (forward) voltage at the same point on the feedline. Determined by feedline impedance and actual load impedance. ρ = (ZL – Z0) / (ZL + Z0) When ρ = 0, voltage distribution along length of line is constant (line is flat).

143
**Antenna Systems Transmission Line Mechanics.**

Reflection Coefficient and SWR. Standing wave ratio (SWR). If ρ < 0, then voltage distribution along line is not constant. Ratio of voltage peaks to voltage minimums is called the voltage standing wave ratio (VSWR or simply SWR). SWR = (1 + ρ) / (1 – ρ) SWR can also be computed from line & load impedances. If ZL > Z0 then SWR = ZL / Z0 If ZL < Z0 then SWR = Z0 / ZL

144
**Antenna Systems Transmission Line Mechanics. Power Measurement.**

Reading relative power output. Neon bulb. RF ammeter. SWR Meter. Reading actual power output. Directional RF Wattmeter.

145
**Antenna Systems Transmission Line Mechanics. Power Measurement.**

Can calculate reflection coefficient from forward & reflected power. ρ = PR/PF Power delivered to load is: PL = PF - PR

146
E4B06 -- How much power is being absorbed by the load when a directional power meter connected between a transmitter and a terminating load reads 100 watts forward power and 25 watts reflected power? 100 watts 125 watts 25 watts 75 watts

147
E4B09 -- What is indicated if the current reading on an RF ammeter placed in series with the antenna feed line of a transmitter increases as the transmitter is tuned to resonance? There is possibly a short to ground in the feed line The transmitter is not properly neutralized There is an impedance mismatch between the antenna and feed line There is more power going into the antenna

148
E9E07 -- What term best describes the interactions at the load end of a mismatched transmission line? Characteristic impedance Reflection coefficient Velocity factor Dielectric constant

149
**E9E08 -- Which of the following measurements is characteristic of a mismatched transmission line?**

An SWR less than 1:1 A reflection coefficient greater than 1 A dielectric constant greater than 1 An SWR greater than 1:1

150
**E9F01 -- What is the velocity factor of a transmission line?**

The ratio of the characteristic impedance of the line to the terminating impedance The index of shielding for coaxial cable The velocity of the wave in the transmission line multiplied by the velocity of light in a vacuum The velocity of the wave in the transmission line divided by the velocity of light in a vacuum

151
**E9F02 -- Which of the following determines the velocity factor of a transmission line?**

The termination impedance The line length Dielectric materials used in the line The center conductor resistivity

152
E9F03 -- Why is the physical length of a coaxial cable transmission line shorter than its electrical length? Skin effect is less pronounced in the coaxial cable The characteristic impedance is higher in a parallel feed line The surge impedance is higher in a parallel feed line Electrical signals move more slowly in a coaxial cable than in air

153
**E9F04 -- What is the typical velocity factor for a coaxial cable with solid polyethylene dielectric?**

2.70 0.66 0.30 0.10

154
E9F05 -- What is the approximate physical length of a solid polyethylene dielectric coaxial transmission line that is electrically one-quarter wavelength long at 14.1 MHz? 20 meters 2.3 meters 3.5 meters 0.2 meters

155
E9F06 -- What is the approximate physical length of an air-insulated, parallel conductor transmission line that is electrically one-half wavelength long at MHz? 15 meters 20 meters 10 meters 71 meters

156
**E9F07 -- How does ladder line compare to small-diameter coaxial cable such as RG-58 at 50 MHz?**

Lower loss Higher SWR Smaller reflection coefficient Lower velocity factor

157
E9F08 -- What is the term for the ratio of the actual speed at which a signal travels through a transmission line to the speed of light in a vacuum? Velocity factor Characteristic impedance Surge impedance Standing wave ratio

158
E9F09 -- What is the approximate physical length of a solid polyethylene dielectric coaxial transmission line that is electrically one-quarter wavelength long at 7.2 MHz? 10 meters 6.9 meters 24 meters 50 meters

159
E9F16 -- Which of the following is a significant difference between foam-dielectric coaxial cable and solid-dielectric cable, assuming all other parameters are the same? Reduced safe operating voltage limits Reduced losses per unit of length Higher velocity factor All of these choices are correct

160
**Antenna Systems Smith Chart. First a review.**

Impedances consist of a resistance and a reactance. All possible impedances can be plotted on a graph using rectangular coordinates. When a load (impedance) is connected to a transmission line & a signal source is connected to the other end of the line, energy is reflected back & forth along the line. Ratio of voltage to current (impedance) varies at different points along the line. At 1/2λ impedance equals the load impedance.

161
Antenna Systems Smith Chart.

162
**Antenna Systems Smith Chart. Outermost circle = pure reactance.**

Horizontal line = pure resistance. Circles = constant resistance. Arcs = constant reactance.

163
**Antenna Systems Smith Chart. Normalization.**

Scale all values to characteristic impedance of transmission line (Z0). If Z0 = 50Ω, then 50 + j0 1 + j0. The point 1 + j0 = prime center. Prime Center

164
**Antenna Systems Smith Chart.**

Circles centered on prime center = constant SWR circles.

165
**Antenna Systems Smith Chart. Wavelength scales.**

Additional scales around the outer edge of the chart. Calibrated in fractions of electrical wavelength in a transmission line.

166
**Antenna Systems Smith Chart. Wavelength scales.**

Ratio of voltage to current (impedance) varies at different points along the line. At 1/2λ impedance equals the load impedance. One trip around Smith Chart = 1/2λ (180°). Can be used to calculate impedance at different points along a transmission line.

167
**E9G01 -- Which of the following can be calculated using a Smith chart?**

Impedance along transmission lines Radiation resistance Antenna radiation pattern Radio propagation

168
**E9G02 -- What type of coordinate system is used in a Smith chart?**

Voltage circles and current arcs Resistance circles and reactance arcs Voltage lines and current chords Resistance lines and reactance chords

169
**E9G03 -- Which of the following is often determined using a Smith chart?**

Beam headings and radiation patterns Satellite azimuth and elevation bearings Impedance and SWR values in transmission lines Trigonometric functions

170
**E9G04 -- What are the two families of circles and arcs that make up a Smith chart?**

Resistance and voltage Reactance and voltage Resistance and reactance Voltage and impedance

171
**E9G05 -- What type of chart is shown in Figure E9-3?**

Smith chart Free-space radiation directivity chart Elevation angle radiation pattern chart Azimuth angle radiation pattern chart

172
E9G06 -- On the Smith chart shown in Figure E9-3, what is the name for the large outer circle on which the reactance arcs terminate? Prime axis Reactance axis Impedance axis Polar axis

173
**E9G07 -- On the Smith chart shown in Figure E9-3, what is the only straight line shown?**

The reactance axis The current axis The voltage axis The resistance axis

174
**E9G08 -- What is the process of normalization with regard to a Smith chart?**

Reassigning resistance values with regard to the reactance axis Reassigning reactance values with regard to the resistance axis Reassigning impedance values with regard to the prime center Reassigning prime center with regard to the reactance axis

175
E9G09 -- What third family of circles is often added to a Smith chart during the process of solving problems? Standing-wave ratio circles Antenna-length circles Coaxial-length circles Radiation-pattern circles

176
**E9G10 -- What do the arcs on a Smith chart represent?**

Frequency SWR Points with constant resistance Points with constant reactance

177
**E9G11 -- How are the wavelength scales on a Smith chart calibrated?**

In fractions of transmission line electrical frequency In fractions of transmission line electrical wavelength In fractions of antenna electrical wavelength In fractions of antenna electrical frequency

178
**Antenna Systems Transmission Line Stubs and Transformers.**

Impedance varies at different points along the line. Impedance values repeat every 1/2λ. Shorted transmission line: 0λ 1/2λ 1/4λ Z = Low Z = Low Z = High

179
**Antenna Systems Transmission Line Stubs and Transformers.**

Open transmission line: Z = High Z = Low Z = High 0λ 1/4λ 1/2λ

180
**Antenna Systems Transmission Line Stubs and Transformers.**

1/8λ lines not quite as easy to remember. Open line = capacitive reactance. Shorted line = inductive reactance.

181
**Antenna Systems Transmission Line Stubs and Transformers.**

Synchronous transformers. 1/4λ matching line: ZXfmr = ZLoad x Zin ZLoad = ZXfmr2 / Zin ZIn = ZXfmr2 / Zload Example: To match a 100Ω antenna to a 50Ω feedline, insert a 1/4λ long piece of 75Ω line between the antenna and the feedline.

182
**Antenna Systems Transmission Line Stubs and Transformers.**

Want to connect two 50Ω antennas in parallel & feed them with 50Ω transmission line. If using RG-6 or RG-11 cable for transformer, then ZXfmr = 75Ω. ZIn = ZXfmr2 / ZL ZIn = 752 / 50 = 112.5Ω 2 in parallel = 112.5/2 = 56.25Ω SWR = 56.25/50 = 1.125:1

183
E9E10 -- Which of these choices is an effective way to match an antenna with a 100-ohm feed point impedance to a 50-ohm coaxial cable feed line? Connect a 1/4-wavelength open stub of 300-ohm twin-lead in parallel with the coaxial feed line where it connects to the antenna Insert a 1/2 wavelength piece of 300-ohm twin-lead in series between the antenna terminals and the 50-ohm feed cable Insert a 1/4-wavelength piece of 75-ohm coaxial cable transmission line in series between the antenna terminals and the 50-ohm feed cable Connect 1/2 wavelength shorted stub of 75-ohm cable in parallel with the 50-ohm cable where it attaches to the antenna

184
E9F10 -- What impedance does a 1/8-wavelength transmission line present to a generator when the line is shorted at the far end? A capacitive reactance The same as the characteristic impedance of the line An inductive reactance The same as the input impedance to the final generator stage

185
E9F11 -- What impedance does a 1/8-wavelength transmission line present to a generator when the line is open at the far end? The same as the characteristic impedance of the line An inductive reactance A capacitive reactance The same as the input impedance of the final generator stage

186
E9F12 -- What impedance does a 1/4-wavelength transmission line present to a generator when the line is open at the far end? The same as the characteristic impedance of the line The same as the input impedance to the generator Very high impedance Very low impedance

187
E9F13 -- What impedance does a 1/4-wavelength transmission line present to a generator when the line is shorted at the far end? Very high impedance Very low impedance The same as the characteristic impedance of the transmission line The same as the generator output impedance

188
E9F14 -- What impedance does a 1/2-wavelength transmission line present to a generator when the line is shorted at the far end? Very high impedance Very low impedance The same as the characteristic impedance of the line The same as the output impedance of the generator

189
E9F15 -- What impedance does a 1/2-wavelength transmission line present to a generator when the line is open at the far end? Very high impedance Very low impedance The same as the characteristic impedance of the line The same as the output impedance of the generator

190
**Antenna Systems Antenna Analyzers.**

Available on amateur market since 1990’s. Microprocessor-controlled impedance bridge with tunable signal source & frequency counter.

191
**Antenna Systems Antenna Analyzers.**

Make measuring antenna impedance & SWR easy. Just connect analyzer to antenna feed line & go. No external signal source required. Many other functions available. Velocity factor. Line length.

192
E4A07 -- Which of the following is an advantage of using an antenna analyzer compared to an SWR bridge to measure antenna SWR? Antenna analyzers automatically tune your antenna for resonance Antenna analyzers do not need an external RF source Antenna analyzers display a time-varying representation of the modulation envelope All of these choices are correct

193
**E4A08 -- Which of the following instruments would be best for measuring the SWR of a beam antenna?**

A spectrum analyzer A Q meter An ohmmeter An antenna analyzer

194
E4B11 -- How should a portable antenna analyzer be connected when measuring antenna resonance and feed point impedance? Loosely couple the analyzer near the antenna base Connect the analyzer via a high-impedance transformer to the antenna Connect the antenna and a dummy load to the analyzer Connect the antenna feed line directly to the analyzer's connector

195
**Antenna Design Antenna Modeling and Design Far Field vs. Near Field.**

Radiation pattern is dependent on distance from antenna. Energy absorbed in near field changes load on transmitter. Far Field. Radiation pattern is not dependent on distance from antenna. Energy absorbed in far field does not change load on transmitter. Antenna modeling calculates for the far field.

196
**Antenna Design Antenna Modeling and Design Far Field vs. Near Field.**

Boundary between near & far fields is not well-defined but is several wavelengths from antenna. Typically, anything over 10λ from antenna is considered to be in the far field.

197
**Antenna Design Antenna Modeling and Design. Antenna modeling software.**

Most based on NEC. Numerical Electromagnetics Code.

198
**Antenna Design Antenna Modeling and Design. Antenna modeling software.**

Method of moments technique. Antenna broken down into segments. Current in each segment calculated. Field resulting from that current evaluated. More segments → more accurate results. More segments → greater processing time. Many programs set a limit to number of segments. Fewer than 10 segments per 1/2λ may produce incorrect value of feedpoint impedance.

199
**Antenna Design Antenna Modeling and Design. Antenna modeling software.**

All programs provide just about everything you wanted to know about the antenna. Gain. Beamwidth. Pattern ratios (front-to-back, front-to-side, etc.). Polar plots of far-field radiation patterns. Azimuth & elevation. Feed point impedance. SWR vs. frequency.

200
**E9B09 -- What type of computer program technique is commonly used for modeling antennas?**

Graphical analysis Method of Moments Mutual impedance analysis Calculus differentiation with respect to physical properties

201
**E9B10 -- What is the principle of a Method of Moments analysis?**

A wire is modeled as a series of segments, each having a uniform value of current A wire is modeled as a single sine-wave current generator A wire is modeled as a series of points, each having a distinct location in space A wire is modeled as a series of segments, each having a distinct value of voltage across it

202
E9B11 -- What is a disadvantage of decreasing the number of wire segments in an antenna model below the guideline of 10 segments per half-wavelength? Ground conductivity will not be accurately modeled The resulting design will favor radiation of harmonic energy The computed feed point impedance may be incorrect The antenna will become mechanically unstable

203
**E9B13 -- What does the abbreviation NEC stand for when applied to antenna modeling programs?**

Next Element Comparison Numerical Electromagnetics Code National Electrical Code Numeric Electrical Computation

204
E9B14 -- What type of information can be obtained by submitting the details of a proposed new antenna to a modeling program? SWR vs. frequency charts Polar plots of the far-field elevation and azimuth patterns Antenna gain All of these choices are correct

205
**Antenna Design Antenna Modeling and Design.**

Design Tradeoffs and Optimization. Any antenna design is a compromise. Gain may drop significantly as frequency moves away from the design center frequency. Gain of a Yagi can be increased by lengthening the boom.

206
**Antenna Design Antenna Modeling and Design.**

Design Tradeoffs and Optimization. If a Yagi is optimized for maximum gain, Front-to-back ratio will decrease, Feedpoint impedance will become very low, and SWR bandwidth will be reduced.

207
E9B04 -- What may occur when a directional antenna is operated at different frequencies within the band for which it was designed? Feed point impedance may become negative The E-field and H-field patterns may reverse Element spacing limits could be exceeded The gain may change depending on frequency

208
**E9B05 -- What usually occurs if a Yagi antenna is designed solely for maximum forward gain?**

The front-to-back ratio increases The front-to-back ratio decreases The frequency response is widened over the whole frequency band The SWR is reduced

209
E9B06 -- If the boom of a Yagi antenna is lengthened and the elements are properly retuned, what usually occurs? The gain increases The SWR decreases The front-to-back ratio increases The gain bandwidth decreases rapidly

210
Questions?

Similar presentations

OK

APRS ANTENNAS by ED LAWRENCE WA5SWD SIMPLIFIED & TRANSMISSION LINES.

APRS ANTENNAS by ED LAWRENCE WA5SWD SIMPLIFIED & TRANSMISSION LINES.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on environmental pollution in india Ppt on presentation tips Ppt on history of google Ppt on crash fire tender for sale Ppt on solar system with sound Ppt on wind power in india Ppt on polynomials and coordinate geometry pdf Ppt on natural and artificial satellites images Ppt on work and energy class 9 Ppt on duty roster