Overview 1 An EM wave is generated from an oscillating current in a conductor • an EM field in a waveguide with an opening to free space. • • We know that EM fields reflect, refract, transmit when the intrinsic impedance along the propagation path changes. • An antenna is a combination of current carrying conductors and insulators containing EM fields. 2 We must understand the properties of antennas … • To ensure good transfer of energy from a currently carrying conductor to the surrounding dielectric material. • To ensure effective radiation in a designated direction. • Remember: The main aim of this course is to ensure that you can engineer a radio link which ensures reliable communications. 3 Examples of Antennas 4 Antenna Properties 1. An antenna is a transducer that converts a guided wave propagating on a transmission line into an electromagnetic wave propagating in an unbounded medium (usually free space), or vice versa. 2. Most antennas are reciprocal devices, exhibiting the same radiation pattern for transmission as for reception. 3. Being a reciprocal device, an 5 Antenna Reciprocity • In a communications system if you change the antennas between transmit and receive, the same signal level received. • The radiation pattern of the transmit antenna is identical to the radiation pattern of the receive antenna. 6 Far-Field Approximation In close proximity to a • 1. radiating source, the wave is spherical in shape, but at a far distance, it becomes approximately a plane wave if the receiving antenna is small enough. • 2. The far-field approximation (plane wave approximation) simplifies the calculations. • 3. The distance beyond which the far-field approximation is 7 The Hertzian Dipole A Hertzian dipole is a thin, linear conductor whose length l is very short compared with the wavelength λ0; l should not exceed λ0/50. This restriction allows us to treat the current along the length of the conductor as constant, even though it has must be zero at the 8 Fields Radiated by Hertzian Dipole Current along dipole: Magnetic Vector Potential: With: s cross sectional area of the dipole R Range θ Zenith angle φ Azimuth angle Given A, we can determine E and H 9 Fields Radiated by Hertzian Dipole (cont.) R Range θ Zenith angle φ Azimuth angle Upon converting z to spherical coordinates: we have: 10 Fields Radiated by Hertzian Dipole (cont.) With: And application of: leads to: 11 Radiated Electric Field 12 Hertzian Dipole — Far-Field Approximation At any range R: At Spherical propagation factor Intrinsic free space impedance 13 Normalized Radiation Intensity Electric and Magnetic Fields Normalized Radiation Intensity Average Power Density / Time-average Poynting vector 14 Radiation Pattern of Hertzian Dipole 15 Concept Questions • Concept Question 9-1: What does it mean to say that most antennas are reciprocal devices? • Concept Question 9-2: What is the radiated wave like in the far field region of an antenna? • Concept Question 9-3: In a Hertzian dipole, what is the underlying assumption about the current flowing through the wire? • Concept Question 9-4: Outline the basic steps used to relate the current in a wire to the radiated power density? 16 17 End Lecture 11 Antenna Radiation Characteristics 1. By virtue of reciprocity, a receiving antenna has the same directional antenna pattern as the pattern that it exhibits when operated in the transmission mode. 2. Total Radiated Power Differential area Solid Angle Power radiated through dA 19 Example of 3-D Pattern F (dB) = 10 log F Principal planes: 1. Elevation plane (x-z and y-z planes) 2. Azimuth plane (x-y plane) 20 Polar and Rectangular Plots 21 Beam Dimensions 1. Pattern solid angle 2. Half-power beamwidth Since 0.5 corresponds to ‒3 dB, the half power beamwidth is also called the 3dB beamwidth. 22 Antenna Directivity D Antenna pattern solid angle Directivity 23 Antennas with Single Main Lobe Equivalent Solid Angle 24 Half-Wave Dipole 1. Current in half-wave dipole 2. For Hertzian dipole of length l, E field is: 3. Each length element dz of halfwave dipole is like a Hertzian dipole, radiating a field 4. For the entire dipole, the total radiated field is 25 Half-Wave Dipole (cont.) Integration leads to: 26 Radiation Pattern of Half-Wave Dipole Radiation pattern resembles that of the Hertzian dipole. Its beamwidth is slightly narrower, 78 degrees compared with 90 degrees for the Hertzian dipole. 27 Other Half-Wave Dipole Properties 1. Directivity Numerical integration gives: 2. Radiation Resistance This is very important, because it makes it easy to match the antenna to a 75-Ω transmission line. In contrast, the radiation resistance of a dipole whose length is much shorter than a wavelength is on the order of 1 Ω or less. 28 Dipole of Arbitrary Length 29 Wire Dipoles with various lengths 30 Quarter-Wave Monopole When placed over a conducting ground plane, a quarter-wave monopole antenna excited by a source at its base [Fig.9-15(a)] exhibits the same radiation pattern in the region above the ground plane as a half-wave dipole in free space. However, its radiation resistance if only half of that of a half-wave dipole, namely 36.5 Ω. 31 End Lecture 12 Thanks for the Mid-trimester feedback Summary • Clear learning aims • Engaging to learn • Testing knowledge & giving feedback • Organisation of Learning • Prepared for this course? • Keeping on track • Relevance to career • Textbook is useful • Confident to do well in assignments • Recommend this course? 4.25 + 1.0 4.0 + 1.4 3.0 + 1.8 3.75 + 0.5 3.12 + 0.6 4.0 + 0 4.5 + 0.58 4.0 + 0.82 2.38 + 1.1 3.25 + 1.7 33 What is working well • Replies to emails and answers to questions (4) • Online labs and 1 hr lectures • Quizzes in class (2) • Applications to daily life • Q & A in class 34 What is not working well • Not enough example questions (2) • Improved lab videos • Labs before lecture material in an online world (2) 35 Return to the Laboratory • We are now scheduled to use N44 3.05 (Communications Lab) for the rest of the semester. • Please check your experiment schedule for which experiment you should do tomorrow or next week. • If you have any mild illness or have been in Victoria or NSW in the last two weeks prior to Tuesday, please let me know. • If you show signs of illness during the class I may send you out of the laboratory. • Each student will work on one experiment space and must remain there. • If you can not come to the lab class you must let me know by email before the class. Radiation Resistance (Ulaby Section 9-2.5) • When calculating the antenna directivity, we calculated the total radiated field Prad • The power delivered to the antenna Pt is partly radiated, but some is lost in the conductor and dielectric materials of the antenna. • The radiation efficiency 𝜉 is defined as the ratio Prad /Pt • The energy lost from the transmission circuit is a resistive load which consumes the power: the radiation resistance Rrad • The total resistance of the antenna Rin = Rrad + Rloss and Rloss is the loss in the conductors and insulators in the antenna Antenna input impedance • There is a reactive load in the antenna so the total input impedance Zin = Rin + jXin Ω • The efficiency is given by 𝑅𝑟𝑎𝑑 𝜉= 𝑅𝑟𝑎𝑑 + 𝑅𝑙𝑜𝑠𝑠 • There is maximum radiated power when • Xin = 0, and • Rloss = 0 Radiation Resistance of a Hertzian Dipole 4𝜋𝑅 2 𝑆𝑚𝑎𝑥 • From the radiated power Prad we have 𝑃𝑟𝑎𝑑 = 𝐷 15𝜋𝐼𝑜2 𝑙 2 For Hertzian dipole we calculated D = 1.5 and 𝑆𝑚𝑎𝑥 = • 𝑅2 ( 𝜆 ) 2 2 𝑙 So 𝑃𝑟𝑎𝑑 = 40𝜋 𝐼𝑜 • (𝜆) 2 𝑙 2 and 𝑅𝑟𝑎𝑑 = 80𝜋 • (𝜆) 2 • If l/λ = 0.01, then Rrad = 0.08 Ω • This is effectively a short circuit so very little power is radiated. Radiation Resistance of a Half wave Dipole 4𝜋𝑅 2 • From the radiated power Prad we have 𝑃𝑟𝑎𝑑 = 𝐷 𝑆𝑚𝑎𝑥 • For Half wave dipole we calculated 𝐷 = 36.6𝐼2𝑜 ( 4𝜋𝑅 2 15𝐼𝑜2 𝜋𝑅 ) 2 = 1.64 • D = 2.15 dB • and 𝑅𝑟𝑎𝑑 = 2𝑃𝑟𝑎𝑑 ≅ 73 Ω 2 𝐼𝑜 • This is easily matched to a coaxial cable so most power is radiated. • This type of antenna is in common use. Various forms of a half wave dipole/monopole λ/2 Conducting ground plane Coaxial cable feed line Small Loop Antennas (magnetic dipole antenna) • We can make and use very small loop antennas. • The field calculation is performed on a square of 4 Hertzian dipoles but the result is correct of any shape. • The circumference of the loop should be less than 0.01λ0 z • The current is uniform in all 4 sides. • Angle φ measured from the X axis in the horizontal plane • Angle θ measured from Z axis, y I0 x Equations become: ⎡ 1 jωµ 0 m 2 1 ⎤ − jβ R Eφ = β sin θ ⎢ + e 2 ⎥ 4π ⎣ jβ R ( jβ R ) ⎦ ⎡ 1 jωµ 0 m 2 1 ⎤ − jβ R HR = − β 2 cos θ ⎢ + e 2 3⎥ 4πη 0 ⎣ ( jβ R ) ( jβ R ) ⎦ ⎡ 1 jωµ 0 m 2 1 1 ⎤ − jβ R Hθ = − β sin θ ⎢ + + e 2 3⎥ 4πη 0 ⎣ jβ R ( jβ R ) ( jβ R ) ⎦ where the magnetic moment m = I0A and the area A = a2 for a square of length a. If the loop is a circle, then A = πr2 where r is the radius of the circle. Radiation pattern is symmetrical about the Z axis and identical to the Hertzian dipole, but the polarization is rotated through 90 degrees. E H k H k E Antenna Effective Area (short Dipole: D=1.5) 45 Isotropic Radiator 𝑃𝑡 Isotropic radiator (hypothetical, unrealizable) is used as a reference: 𝑆𝑖𝑠𝑜 = 4𝜋𝑅 2 Radiates equally in all directions. Power density Siso at a distance R is equal to the transmitted power Pt divided by the surface area of a sphere with radius R: 46 Power Density from an Antenna Isotropic radiator 𝑃𝑡 𝑆𝑖𝑠𝑜 = 4𝜋𝑅 2 Real antenna 𝑆𝑡 = 𝐺𝑡𝑆𝑖𝑠𝑜 = 𝜉𝑡𝐺𝑡𝑃 𝑡 𝐺𝑡𝑃𝑡 4𝜋𝑅 2 = 47 Power Transfer Ratio If the antennas are not oriented in the direction of maximum power transfer: 48 Friis Transmission Formula 49 Power Transfer Ratio If the antennas are not oriented in the direction of maximum power transfer: 50 End of Lecture 13 Classes: • No class this Thursday morning (and no more Thursday classes) • Next Monday’s class will be a review of Assignment 1. Power Density from an Antenna Isotropic radiator 𝑃𝑡 𝑆𝑖𝑠𝑜 = 4𝜋𝑅 2 Real antenna 𝑆𝑡 = 𝐺𝑡𝑆𝑖𝑠𝑜 = 𝜉𝑡𝐺𝑡𝑃 𝑡 𝐺𝑡𝑃𝑡 4𝜋𝑅 2 = 53 The effective area of a half-wave dipole • D = 1.65 𝜆2 𝐴 = 1.65 • 𝑒 4𝜋 • But the antenna has zero physical area!! • For a linear polarised EM wave incident on the halfwave dipole the effective area varies from 0 to maximum. • So a wire antenna with little physical area can have a significant effective area. Power Transfer Ratio If the antennas are not oriented in the direction of maximum power transfer: 55 Convert the Friis formula to dB • 56 Link Budget Plot (dB calculation) 57 The efficiency of an antenna is….. 1. The ratio of the radiation resistance to the total real part of the antenna impedance. 2. The S11 of the antenna. 3. The speed at which the radiation pattern of the antenna can be controlled. 4. The conduction loss in the metallic parts of the antenna 58 The directivity of an antenna is .. 1. The beamwidth of the main beam 2. The ratio of the main beam power to the total power applied to the antenna and is always greater than 1 3. The gain of the antenna divided by the antenna efficiency. 4. The overall physical size of the antenna 59 A half-wave dipole antenna has a length … 1. Less than λ0/10 2. Equal to λ0/4 3. Equal to λ0/2 4. Equal to λ0 60 A half-wave dipole antenna is a practical antenna because … 1. 2. 3. 4. 5. 6. 7. It is omnidirectional radiation pattern It has low gain It has an impedance close to 50Ω at resonance It can easily be driven by a coaxial cable It has no reactive part to the input impedance. It can function as a receiver and a transmitter simultaneously. It is small but has a very high gain. 61 At resonance the imaginary part of an antenna input impedance is preferably … 1. 0 Ω 2. 50 Ω 3. Capacitive 4. Inductive 5. Resistive 6. None of the above 62 The effective area of an antenna is … 1. The maximum dimension of the antenna in one direction 2. The area of the aperture of a horn antenna 3. The effective power trapping ability of an antenna regardless of its size 4. The size of the antenna in wavelengths 63 The Friis transmission formula is Prec ⎛ λ ⎞ = Gt G r ⎜ ⎟ Pt ⎝ 4πR ⎠ 2 1. A statement of the inverse square law 2. The relationship between the input power and the received power in a radio link 3. The relationship between the noise temperature and the receiver bandwidth 4. An expression for the gain and efficiency of an antenna 64 The effective area of an antenna depends on … 1. 2. 3. 4. 5. 6. The attenuation in the propagation path The physical size of the antenna The power into the transmitter The orientation of the antenna structure The antenna efficiency All of the above 65 A linearly polarised antenna with an effective area Ae is used to receive a circularly polarised wave. G 4πAe 4π D= = 2 ≅ ξ β xz β yz λ 1. 2. 3. 4. 5. Prec ⎛ λ ⎞ = Gt G r ⎜ ⎟ Pt ⎝ 4πR ⎠ 2 No power is received 25% of the available power is received 50% of the available power is received 100% of the available power is received 200% of the available power is received 66 What is the effective area of a half wave dipole? 1. 0 2. Wire diameter * λ0/4 3. Wire diameter * λ0/2 4. Wire diameter * λ0 5. None of the above 67 If the antenna input impedance is 25+7jΩ what is the impedance of the transmission line matching unit required for maximum power reception? 1. 2. 3. 4. 5. 6. 7. 25Ω 25-7j Ω 0j Ω ∞Ω 50 Ω 25+7j Ω Depends on the transmission line impedance 68 Radiation Efficiency and Gain Radiation efficiency Antenna gain G 69 Antenna Radiation and Loss Resistances 70 Antenna Effective Area (short Dipole: D=1.5) 71 Friis Transmission Formula 72 Power Transfer Ratio If the antennas are not oriented in the direction of maximum power transfer: 73 Aperture Antennas Source of radiation is the electric-field distribution Ea(xa,ya) across the aperture. Every point of its wavefront serves as a source of spherical secondary wavelets. The aperture may then be represented as a distribution of isotropic radiators. Aperture must be at least several wavelengths long along each of its principal dimensions. 74 Relating Radiated Field to Aperture Distribution Far Field Condition where Accounting for difference between R and s 75 Rectangular Aperture with Uniform Distribution Uniform distribution across aperture Scalar formulation leads to: Ap = lx ly The sinc function is maximum when its argument is zero; Uniform aperture distribution provides narrowest possible far-field pattern 76 Examples of Radiation Patterns Circular aperture has circular beam In each principal plane, beamwidth is inversely proportional to antenna dimension in that plane Cylindrical reflector has narrow beam along length direction and wide beam along its width direction 77 Directivity & Effective Area (9.26) / 78 79 Antenna Arrays 80 Antenna Arrays An antenna array to a continuous aperture is analogous to digital data to analog. By controlling the signals fed into individual array elements, the pattern can be shaped to suit the desired application. Also, through the use of electronically controlled solid-state phase shifters, the beam direction of the antenna array can be steered electronically by controlling the relative phases of the array elements. This flexibility of the array antenna has led to numerous applications, including electronic steering and multiple-beam generation. 81 Array Pattern Power density radiated by the entire array Power density radiated by an individual element Array Factor The array factor represents the far-field radiation intensity of the N elements, had the elements been isotropic radiators. 82 Cont. 83 Example 9-5 (cont.) 84 Example 9-5 (cont.) Se 4Se 85 86 Array Pattern for Uniform Phase Distribution Any array with identical elements and equal spacing d with 87 Array Pattern for Uniform Phase Distribution Any array with identical elements and equal spacing d with Maximum for γ = 0 → θ = 90° 88 89 90 9. Radiation & Antennas 7e Applied EM by Ulaby and Ravaioli 1 Overview 2 An EM wave is generated from an oscillating current in a conductor • an EM field in a waveguide with an opening to free space. • • We know that EM fields reflect, refract, transmit when the intrinsic impedance along the propagation path changes. • An antenna is a combination of current carrying conductors and insulators containing EM fields. We must understand the properties of antennas … • To ensure good transfer of energy from a currently carrying conductor to the surrounding dielectric material. • To ensure effective radiation in a designated direction. • Remember: The main aim of this course is to ensure that you can engineer a radio link which ensures reliable communications. Examples of Antennas 5 Antenna Properties 1. An antenna is a transducer that converts a guided wave propagating on a transmission line into an electromagnetic wave propagating in an unbounded medium (usually free space), or vice versa. 2. Most antennas are reciprocal devices, exhibiting the same radiation pattern for transmission as for reception. 3. Being a reciprocal device, an antenna, when operating in the receiving mode, can extract from an incident wave only that component of the wave whose electric field matches the antenna polarization 6 Antenna Reciprocity • In a communications system if you change the antennas between transmit and receive, the same signal level received. • The radiation pattern of the transmit antenna is identical to the radiation pattern of the receive antenna. 7 Far-Field Approximation • 1. In close proximity to a radiating source, the wave is spherical in shape, but at a far distance, it becomes approximately a plane wave if the receiving antenna is small enough. • 2. The far-field approximation (plane wave approximation) simplifies the calculations. • 3. The distance beyond which the far-field approximation is valid is called the far-field range (will be defined later). 8 The Hertzian Dipole A Hertzian dipole is a thin, linear conductor whose length l is very short compared with the wavelength λ0; l should not exceed λ0/50. This restriction allows us to treat the current along the length of the conductor as constant, even though it has must be zero at the ends of the open circuit wire. 9 Fields Radiated by Hertzian Dipole Current along dipole: Magnetic Vector Potential: With: s cross sectional area of the dipole R Range q Zenith angle f Azimuth angle Given A, we can determine E and H 10 Fields Radiated by Hertzian Dipole (cont.) R Range q Zenith angle f Azimuth angle Upon converting z to spherical coordinates: we have: 11 Fields Radiated by Hertzian Dipole (cont.) With: And application of: leads to: 12 Radiated Electric Field 13 Hertzian Dipole — Far-Field Approximation At any range R: At Spherical propagation factor Intrinsic free space impedance 14 Normalized Radiation Intensity Electric and Magnetic Fields Normalized Radiation Intensity Average Power Density / Time-average Poynting vector 15 Radiation Pattern of Hertzian Dipole 16 Concept Questions • Concept Question 9-1: What does it mean to say that most antennas are reciprocal devices? • Concept Question 9-2: What is the radiated wave like in the far field region of an antenna? • Concept Question 9-3: In a Hertzian dipole, what is the underlying assumption about the current flowing through the wire? • Concept Question 9-4: Outline the basic steps used to relate the current in a wire to the radiated power density? 17 18 End Lecture 11 Antenna Radiation Characteristics 1. By virtue of reciprocity, a receiving antenna has the same directional antenna pattern as the pattern that it exhibits when operated in the transmission mode. 2. Total Radiated Power Differential area Solid Angle Power radiated through dA 20 Example of 3-D Pattern F (dB) = 10 log F Principal planes: 1. Elevation plane (x-z and y-z planes) 2. Azimuth plane (x-y plane) 21 Polar and Rectangular Plots 22 Beam Dimensions 1. Pattern solid angle 2. Half-power beamwidth Since 0.5 corresponds to ‒3 dB, the half power beamwidth is also called the 3dB beamwidth. 23 Antenna Directivity D Antenna pattern solid angle Directivity 24 Antennas with Single Main Lobe Equivalent Solid Angle 25 Half-Wave Dipole 1. Current in half-wave dipole 2. For Hertzian dipole of length l, E field is: 3. Each length element dz of half-wave dipole is like a Hertzian dipole, radiating a field 4. For the entire dipole, the total radiated field is 26 Half-Wave Dipole (cont.) Integration leads to: 27 Radiation Pattern of Half-Wave Dipole Radiation pattern resembles that of the Hertzian dipole. Its beamwidth is slightly narrower, 78 degrees compared with 90 degrees for the Hertzian dipole. 28 Other Half-Wave Dipole Properties 1. Directivity Numerical integration gives: 2. Radiation Resistance This is very important, because it makes it easy to match the antenna to a 75-Ω transmission line. In contrast, the radiation resistance of a dipole whose length is much shorter than a wavelength is on the order of 1 Ω or less. 29 Dipole of Arbitrary Length 30 Wire Dipoles with various lengths 31 Quarter-Wave Monopole When placed over a conducting ground plane, a quarter-wave monopole antenna excited by a source at its base [Fig.9-15(a)] exhibits the same radiation pattern in the region above the ground plane as a halfwave dipole in free space. However, its radiation resistance if only half of that of a half-wave dipole, namely 36.5 Ω. 32 End Lecture 12 Thanks for the Mid-trimester feedback Summary • Clear learning aims • Engaging to learn • Testing knowledge & giving feedback • Organisation of Learning • Prepared for this course? • Keeping on track • Relevance to career • Textbook is useful • Confident to do well in assignments • Recommend this course? 4.25 + 1.0 4.0 + 1.4 3.0 + 1.8 3.75 + 0.5 3.12 + 0.6 4.0 + 0 4.5 + 0.58 4.0 + 0.82 2.38 + 1.1 3.25 + 1.7 34 What is working well • Replies to emails and answers to questions (4) • • • • Online labs and 1 hr lectures Quizzes in class (2) Applications to daily life Q & A in class 35 What is not working well • Not enough example questions (2) • Improved lab videos • Labs before lecture material in an online world (2) 36 Return to the Laboratory • We are now scheduled to use N44 3.05 (Communications Lab) for the rest of the semester. • Please check your experiment schedule for which experiment you should do tomorrow or next week. • If you have any mild illness or have been in Victoria or NSW in the last two weeks prior to Tuesday, please let me know. • If you show signs of illness during the class I may send you out of the laboratory. • Each student will work on one experiment space and must remain there. • If you can not come to the lab class you must let me know by email before the class. Radiation Resistance (Ulaby Section 9-2.5) • When calculating the antenna directivity, we calculated the total radiated field Prad • The power delivered to the antenna Pt is partly radiated, but some is lost in the conductor and dielectric materials of the antenna. • The radiation efficiency 𝜉 is defined as the ratio Prad /Pt • The energy lost from the transmission circuit is a resistive load which consumes the power: the radiation resistance Rrad • The total resistance of the antenna Rin = Rrad + Rloss and Rloss is the loss in the conductors and insulators in the antenna Antenna input impedance • There is a reactive load in the antenna so the total input impedance Zin = Rin + jXin W • The efficiency is given by 𝜉 = 𝑅𝑟𝑎𝑑 𝑅𝑟𝑎𝑑 +𝑅𝑙𝑜𝑠𝑠 • There is maximum radiated power when • Xin = 0, and • Rloss = 0 Radiation Resistance of a Hertzian Dipole • • • • 4𝜋𝑅 2 From the radiated power Prad we have 𝑃𝑟𝑎𝑑 = 𝑆𝑚𝑎𝑥 𝐷 15𝜋𝐼𝑜2 𝑙 2 For Hertzian dipole we calculated D = 1.5 and 𝑆𝑚𝑎𝑥 = 2 𝑅 𝜆 2 𝑙 So 𝑃𝑟𝑎𝑑 = 40𝜋 2 𝐼𝑜2 𝜆 𝑙 2 2 and 𝑅𝑟𝑎𝑑 = 80𝜋 𝜆 • If l/l = 0.01, then Rrad = 0.08 W • This is effectively a short circuit so very little power is radiated. Radiation Resistance of a Half wave Dipole • • 4𝜋𝑅2 From the radiated power Prad we have 𝑃𝑟𝑎𝑑 = 𝑆𝑚𝑎𝑥 𝐷 4𝜋𝑅2 15𝐼𝑜2 For Half wave dipole we calculated 𝐷 = = 1.64 36.6𝐼𝑜2 𝜋𝑅2 • D = 2.15 dB • and 𝑅𝑟𝑎𝑑 = 2𝑃𝑟𝑎𝑑 𝐼𝑜2 73 W • This is easily matched to a coaxial cable so most power is radiated. • This type of antenna is in common use. Various forms of a half wave dipole/monopole l/2 Conducting ground plane Coaxial cable feed line Small Loop Antennas (magnetic dipole antenna) • We can make and use very small loop antennas. • The field calculation is performed on a square of 4 Hertzian dipoles but the result is correct of any shape. • The circumference of the loop should be less than 0.01l0 z • The current is uniform in all 4 sides. • Angle f measured from the X axis in the horizontal plane • Angle q measured from Z axis, I0 x y Equations become: 1 j 0 m 2 1 − j R Ef = sin q + e 2 4 j R ( j R ) 1 j 0 m 2 1 − j R HR = − 2 cos q + e 2 3 40 ( j R ) ( j R ) 1 j 0 m 2 1 1 − j R Hq = − sin q + + e 2 3 40 ( j R ) j R ( j R ) where the magnetic moment m = I0A and the area A = a2 for a square of length a. If the loop is a circle, then A = r2 where r is the radius of the circle. Radiation pattern is symmetrical about the Z axis and identical to the Hertzian dipole, but the polarization is rotated through 90 degrees. E H k H k E Antenna Effective Area (short Dipole: D=1.5) 46 Isotropic Radiator Isotropic radiator (hypothetical, unrealizable) is used as a reference: 𝑆𝑖𝑠𝑜 = 𝑃𝑡 4𝜋𝑅2 Radiates equally in all directions. Power density Siso at a distance R is equal to the transmitted power Pt divided by the surface area of a sphere with radius R: 47 Power Density from an Antenna Isotropic radiator 𝑆𝑖𝑠𝑜 𝑃𝑡 = 4𝜋𝑅 2 Real antenna 𝑆𝑡 = 𝐺𝑡 𝑆𝑖𝑠𝑜 = 𝐺𝑡 𝑃𝑡 𝜉𝑡 𝐺𝑡 𝑃𝑡 = 2 4𝜋𝑅 4𝜋𝑅 2 48 Power Transfer Ratio If the antennas are not oriented in the direction of maximum power transfer: 49 Friis Transmission Formula 50 Power Transfer Ratio If the antennas are not oriented in the direction of maximum power transfer: 51 End of Lecture 13 Classes: No class this Thursday morning (and no more Thursday classes) Next Monday’s class will be a review of Assignment 1. Power Density from an Antenna Isotropic radiator 𝑆𝑖𝑠𝑜 𝑃𝑡 = 4𝜋𝑅 2 Real antenna 𝑆𝑡 = 𝐺𝑡 𝑆𝑖𝑠𝑜 = 𝐺𝑡 𝑃𝑡 𝜉𝑡 𝐺𝑡 𝑃𝑡 = 2 4𝜋𝑅 4𝜋𝑅 2 54 • D = 1.65 The effective area of a half-wave dipole • 𝐴𝑒 = 𝜆2 1.65 4𝜋 • But the antenna has zero physical area!! • For a linear polarised EM wave incident on the halfwave dipole the effective area varies from 0 to maximum. • So a wire antenna with little physical area can have a significant effective area. Power Transfer Ratio If the antennas are not oriented in the direction of maximum power transfer: 56 Convert the Friis formula to dB 57 Link Budget Plot (dB calculation) 58 The efficiency of an antenna is….. 1. The ratio of the radiation resistance to the total real part of the antenna impedance. 2. The S11 of the antenna. 3. The speed at which the radiation pattern of the antenna can be controlled. 4. The conduction loss in the metallic parts of the antenna 59 The directivity of an antenna is .. 1. The beamwidth of the main beam 2. The ratio of the main beam power to the total power applied to the antenna and is always greater than 1 3. The gain of the antenna divided by the antenna efficiency. 4. The overall physical size of the antenna 60 A half-wave dipole antenna has a length … 1. 2. 3. 4. Less than l0/10 Equal to l0/4 Equal to l0/2 Equal to l0 61 A half-wave dipole antenna is a practical antenna because … 1. 2. 3. 4. 5. 6. 7. It is omnidirectional radiation pattern It has low gain It has an impedance close to 50W at resonance It can easily be driven by a coaxial cable It has no reactive part to the input impedance. It can function as a receiver and a transmitter simultaneously. It is small but has a very high gain. 62 At resonance the imaginary part of an antenna input impedance is preferably … 1. 0 W 2. 50 W 3. Capacitive 4. Inductive 5. Resistive 6. None of the above 63 The effective area of an antenna is … 1. The maximum dimension of the antenna in one direction 2. The area of the aperture of a horn antenna 3. The effective power trapping ability of an antenna regardless of its size 4. The size of the antenna in wavelengths 64 The Friis transmission formula is Prec l = Gt Gr Pt 4R 2 1. A statement of the inverse square law 2. The relationship between the input power and the received power in a radio link 3. The relationship between the noise temperature and the receiver bandwidth 4. An expression for the gain and efficiency of an antenna 65 The effective area of an antenna depends on … 1. 2. 3. 4. 5. 6. The attenuation in the propagation path The physical size of the antenna The power into the transmitter The orientation of the antenna structure The antenna efficiency All of the above 66 A linearly polarised antenna with an effective area Ae is used to receive a circularly polarised wave. D= G 1. 2. 3. 4. 5. = 4Ae l 2 4 xz yz Prec l = Gt Gr Pt 4R 2 No power is received 25% of the available power is received 50% of the available power is received 100% of the available power is received 200% of the available power is received 67 What is the effective area of a half wave dipole? 1. 2. 3. 4. 5. 0 Wire diameter * l0/4 Wire diameter * l0/2 Wire diameter * l0 None of the above 68 If the antenna input impedance is 25+7jW what is the impedance of the transmission line matching unit required for maximum power reception? 1. 2. 3. 4. 5. 6. 7. 25W 25-7j W 0j W ∞W 50 W 25+7j W Depends on the transmission line impedance 69 Radiation Efficiency and Gain Radiation efficiency Antenna gain G 70 Antenna Radiation and Loss Resistances 71 Antenna Effective Area (short Dipole: D=1.5) 72 Friis Transmission Formula 73 Power Transfer Ratio If the antennas are not oriented in the direction of maximum power transfer: 74 Aperture Antennas Source of radiation is the electric-field distribution Ea(xa,ya) across the aperture. Every point of its wavefront serves as a source of spherical secondary wavelets. The aperture may then be represented as a distribution of isotropic radiators. Aperture must be at least several wavelengths long along each of its principal dimensions. 75 Relating Radiated Field to Aperture Distribution Far Field Condition where Accounting for difference between R and s 76 Rectangular Aperture with Uniform Distribution Uniform distribution across aperture Scalar formulation leads to: Ap = lx ly The sinc function is maximum when its argument is zero; Uniform aperture distribution provides narrowest possible far-field pattern 77 Examples of Radiation Patterns Circular aperture has circular beam In each principal plane, beamwidth is inversely proportional to antenna dimension in that plane Cylindrical reflector has narrow beam along length direction and wide beam along its width direction 78 Directivity & Effective Area (9.26) / 79 80 Antenna Arrays 81 Antenna Arrays An antenna array to a continuous aperture is analogous to digital data to analog. By controlling the signals fed into individual array elements, the pattern can be shaped to suit the desired application. Also, through the use of electronically controlled solid-state phase shifters, the beam direction of the antenna array can be steered electronically by controlling the relative phases of the array elements. This flexibility of the array antenna has led to numerous applications, including electronic steering and multiple-beam generation. 82 Array Pattern Power density radiated by the entire array Power density radiated by an individual element Array Factor The array factor represents the far-field radiation intensity of the N elements, had the elements been isotropic radiators. 83 Cont. 84 Example 9-5 (cont.) 85 Example 9-5 (cont.) Se 4Se 86 87 Array Pattern for Uniform Phase Distribution Any array with identical elements and equal spacing d with 88 Array Pattern for Uniform Phase Distribution Any array with identical elements and equal spacing d with Maximum for = 0 → q = 90° 89 90 91 Link budget details Your path distance is given by R=(f*10+c) x10(e+d) m. Your frequency is: f=(e*10+d) GHz. Your transmitting antenna diameter is: D = (0.5+g/10) m 4. Calculate the free space path loss (in dB) for your microwave link. 5. Calculate the directivity of your transmitting antenna in dB and an approximate value for the beam width. 6. Calculate the link budget (PredP:) in dB if the transmit and receive antennas are identical. Assume the propagation medium has is loss-less. 7. If the receiver sensitivity is 10-11 watts, and the transmitter power is 20 watts, calculate the minimum radius of a receiving antenna capable of achieving a signal to noise ratio of 5 dB. The aim of this assignment is to re-enforce the learning from Chapter 9 of Ulaby. It is important that you can apply the appropriate equations to solving these problems and gain an understanding of what values you should expect. Rectangular waveguide dimensions (d+e) mm x (d+g) mm 1. Calculate the lowest cutoff frequency of your waveguide. 2. If your applied frequency is 4 times the cut-off frequency in your waveguide, calculate the impedance and the wavelength in your waveguide. 3. If your waveguide is terminated and the VSWR = 1 + (d+e)/10, calculate the impedance of your termination. = Link budget details Your path distance is given by R=(f*10+c) x10le+d) m. Your frequency is: f= (e*10+d) GHz. Your transmitting antenna diameter is: D: = (0.5+g/10) m = 4. Calculate the free space path loss (in dB) for your microwave link. 5. Calculate the directivity of your transmitting antenna in dB and an approximate value for the beam width. 6. Calculate the link budget (Pred Pt) in dB if the transmit and receive antennas are identical. Assume the propagation medium has is loss-less. 7. If the receiver sensitivity is 10-11 watts, and the transmitter power is 20 watts, calculate the minimum radius of a receiving antenna capable of achieving a signal to noise ratio of 5 dB. The aim of this assignment is to re-enforce the learning from Chapter 9 of Ulaby. It is important that you can apply the appropriate equations to solving these problems and gain an understanding of what values you should expect.
