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- Antenna and wave Propagation - AWP
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**Amity University - AMITY**- Electronics and Communication Engineering
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related to the temperature of distant objects that the antenna is looking at. Rr may be thought of as virtual resistance that does not exist physically but is a quantity coupling the antenna to distant regions of space via a virtual transmission .line Reciprocity-An antenna exhibits identical impedance during Transmission or Reception, same directional patterns during Transmission or Reception, same effective height while transmitting or receiving . Transmission and reception antennas can be used interchangeably. Medium must be linear, passive and isotropic(physical properties are the same in different directions.) Antennas are usually optimised for reception or transmission, not both. Patterns The radiation pattern or antenna pattern is the graphical representation of the radiation properties of the antenna as a function of space. That is, the antenna's pattern describes how the antenna radiates energy out into space (or how it receives energy. It is important to state that an antenna can radiate energy in all directions, so the antenna pattern is actually three-dimensional. It is common, however, to describe this 3D pattern with two planar patterns, called the principal plane patterns. These principal plane patterns can be obtained by making two slices through the 3D pattern ,through the maximum value of the pattern . It is these principal plane patterns that are commonly referred to as the antenna patterns 3 ANTENNA & PROPAGATION(06EC64)-Unit 1

Radiation pattern or Antenna pattern is defined as the spatial distribution of a ‘quantity’ that characterizes the EM field generated by an antenna. The ‘quantity’ may be Power, Radiation Intensity, Field amplitude, Relative Phase etc. Normalized patterns It is customary to divide the field or power component by it’s maximum value and θ φ plot the normalized function.Normalized quantities are φ dimensionless and are quantities with maximum value of unity Eθ (θ , ) n = Normalized Field Pattern = Eθ ( , ) Eθ (θ , φ ) max Half power level occurs at those angles (θ,Φ)for which Eθ(θ,Φ)n =0.707 At distance d>>λ and d>> size of the antenna, the shape of the field pattern is independent of the distance S (θ , φ ) Normalized Power Pattern = Pn (θ , φ ) n = S (θ , φ ) max where S (θ , φ ) = Eθ2 (θ , φ ) + Eφ2 (θ , φ ) Z0 [ W m2 ] is the poynting vector. Half power level occurs at those angles (θ,Φ)for which P(θ,Φ)n =0.5 Pattern lobes and beam widths 4 ANTENNA & PROPAGATION(06EC64)-Unit 1

Pattern in spherical co-ordinate system Beamwidth is associated with the lobes in the antenna pattern. It is defined as the angular separation between two identical points on the opposite sides of the main lobe. The most common type of beamwidth is the half-power (3 dB) beamwidth (HPBW). To find HPBW, in the equation, defining the radiation pattern, we set power equal to 0.5 and solve it for angles. Another frequently used measure of beamwidth is the first-null beamwidth (FNBW), which is the angular separation between the first nulls on either sides of the main lobe. Pattern in Cartesian co-ordinate system Beamwidth defines the resolution capability of the antenna: i.e., the ability of the system to separate two adjacent targets 5 ANTENNA & PROPAGATION(06EC64)-Unit 1

Examples : 1.An antenna has a field pattern given by E(θ)=cos2θ for 0o ≤ θ ≤ 90o . Find the Half power beamwidth(HPBW) E(θ) at half power=0.707 Therefore, cos2θ= 0.707 at Halfpower point i.e., θ =cos-1[(0.707)1/2]=33o HPBW=2θ=66o 2.Calculate the beamwidths in x-y and y-z planes of an antenna, the power 2 pattern of which is given by sin θ sin φ ;0 ≤ θ ≤ π ,0 ≤ φ ≤ π U (θ , φ ) = 0; π ≤ θ ≤ 2π , π ≤ φ ≤ 2π soln: In the x-y plane,θ=π/2 and power pattern is given by U(π/2,Φ)=sinΦ • Therefore half power points are at sinΦ=0.5, i.e., at Φ=30o and Φ= 150o • Hence 3dB beamwidth in x-y plane is (150-30)=120o • In the y-z plane,Φ =π/2 and power pattern is given by U(θ,π/2)=sin2θ • Therefore half power points are at sin2θ =0.5, i.e., at θ =45o and θ =135o • Hence 3dB beamwidth in y-z plane is (135-45)= 90o Beam area or Beam solid angle ΩA Radian and Steradian:Radian is plane angle with it’s vertex a the centre of a circle of radius r and is subtended by an arc whose length is equal to r. Circumference of the circle is 2πr Therefore total angle of the circle is 2π radians. Steradian is solid angle with it’s vertex at the centre of a sphere of radius r, which is subtended by a spherical surface area equal to the area of a square with side length r Area of the sphere is 4πr2. Therefore the total solid angle of the sphere is 4π steradians 6 ANTENNA & PROPAGATION(06EC64)-Unit 1

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