1. Antenna Engineering EC 544 Lecture#9

2. Chapter 9 Horn Antenna Horn Antenna

3. The horn is widely used as a feed element for large radio astronomy, satellite tracking, and communication dishes found installed throughout the world. In addition to its utility as a feed for reflectors and lenses, it is a common element of phased arrays and serves as a universal standard for calibration and gain measurements of other high-gain antennas. Its widespread applicability stems from its simplicity in construction, ease of excitation, versatility, large gain, and preferred overall performance. The horn is widely used as a feed element for large radio astronomy, satellite tracking, and communication dishes found installed throughout the world. In addition to its utility as a feed for reflectors and lenses, it is a common element of phased arrays and serves as a universal standard for calibration and gain measurements of other high-gain antennas. Its widespread applicability stems from its simplicity in construction, ease of excitation, versatility, large gain, and preferred overall performance. The horn is nothing more than a hollow pipe of different cross sections, which has been tapered (flared) to a larger opening. An electromagnetic horn can take many different forms, four of which The horn is nothing more than a hollow pipe of different cross sections, which has been tapered (flared) to a larger opening. An electromagnetic horn can take many different forms, four of which The horn is widely used as a feed element for large radio astronomy, satellite tracking, and communication dishes found installed throughout the world. In addition to its utility as a feed for reflectors and lenses, it is a common element of phased arrays and serves as a universal standard for calibration and gain measurements of other high-gain antennas. Its widespread applicability stems from its simplicity in construction, ease of excitation, versatility, large gain, and preferred overall performance. The horn is widely used as a feed element for large radio astronomy, satellite tracking, and communication dishes found installed throughout the world. In addition to its utility as a feed for reflectors and lenses, it is a common element of phased arrays and serves as a universal standard for calibration and gain measurements of other high-gain antennas. Its widespread applicability stems from its simplicity in construction, ease of excitation, versatility, large gain, and preferred overall performance. The horn is nothing more than a hollow pipe of different cross sections, which has been tapered (flared) to a larger opening. An electromagnetic horn can take many different forms, four of which The horn is nothing more than a hollow pipe of different cross sections, which has been tapered (flared) to a larger opening. An electromagnetic horn can take many different forms, four of which

4. Horn Antenna Horn Antenna The horn is nothing more than a hollow pipe of different cross sections, which has been tapered (flared) to a larger opening. The type, direction, and amount of taper (flare) can have a profound effect on the overall performance of the element as a radiator. The horn is nothing more than a hollow pipe of different cross sections, which has been tapered (flared) to a larger opening. The type, direction, and amount of taper (flare) can have a profound effect on the overall performance of the element as a radiator. An electromagnetic horn can take many different forms, four of which are An electromagnetic horn can take many different forms, four of which are (a) E-plane (b) H-plane (a) E-plane (b) H-plane (c) Pyramidal (d) Conical (c) Pyramidal (d) Conical The horn is nothing more than a hollow pipe of different cross sections, which has been tapered (flared) to a larger opening. The type, direction, and amount of taper (flare) can have a profound effect on the overall performance of the element as a radiator. The horn is nothing more than a hollow pipe of different cross sections, which has been tapered (flared) to a larger opening. The type, direction, and amount of taper (flare) can have a profound effect on the overall performance of the element as a radiator. An electromagnetic horn can take many different forms, four of which are An electromagnetic horn can take many different forms, four of which are (a) E-plane (b) H-plane (a) E-plane (b) H-plane (c) Pyramidal (d) Conical (c) Pyramidal (d) Conical

5. Horn Antenna Horn Antenna

6. E Plane Horn

7. E-Plane Horn E-Plane Horn The E-plane sectoral horn is one whose opening is flared in the direction of the E-field.

8. E-Plane Horn E-Plane Horn The horn can be treated as an aperture antenna. To find its radiation characteristics, the equivalent principle techniques can be utilized. The horn can be treated as an aperture antenna. To find its radiation characteristics, the equivalent principle techniques can be utilized. To develop an exact equivalent of it, it is necessary that the tangential electric and magnetic field components over a closed surface are known. The closed that is usually selected is an infinite plane that coincides with the aperture of the horn. To develop an exact equivalent of it, it is necessary that the tangential electric and magnetic field components over a closed surface are known. The closed that is usually selected is an infinite plane that coincides with the aperture of the horn. When the horn is not mounted on an infinite ground plane, the fields outside the aperture are not known and an exact equivalent cannot be formed. However, the usual approximation is to assume that the fields outside the aperture are zero. When the horn is not mounted on an infinite ground plane, the fields outside the aperture are not known and an exact equivalent cannot be formed. However, the usual approximation is to assume that the fields outside the aperture are zero. The horn can be treated as an aperture antenna. To find its radiation characteristics, the equivalent principle techniques can be utilized. The horn can be treated as an aperture antenna. To find its radiation characteristics, the equivalent principle techniques can be utilized. To develop an exact equivalent of it, it is necessary that the tangential electric and magnetic field components over a closed surface are known. The closed that is usually selected is an infinite plane that coincides with the aperture of the horn. To develop an exact equivalent of it, it is necessary that the tangential electric and magnetic field components over a closed surface are known. The closed that is usually selected is an infinite plane that coincides with the aperture of the horn. When the horn is not mounted on an infinite ground plane, the fields outside the aperture are not known and an exact equivalent cannot be formed. However, the usual approximation is to assume that the fields outside the aperture are zero. When the horn is not mounted on an infinite ground plane, the fields outside the aperture are not known and an exact equivalent cannot be formed. However, the usual approximation is to assume that the fields outside the aperture are zero.

9. Aperture Phase Distribution It is assumed that, there exist a line source radiating cylindrical waves at the imaginary apex of the horn. As waves travel in the outward radial direction, the constant phase fronts are cylindrical which do not coincide with aperture plane. It is assumed that, there exist a line source radiating cylindrical waves at the imaginary apex of the horn. As waves travel in the outward radial direction, the constant phase fronts are cylindrical which do not coincide with aperture plane. At any point y ’ at the aperture of the horn, the phase of the field will not be the same as that at the origin. At any point y ’ at the aperture of the horn, the phase of the field will not be the same as that at the origin. The phase difference because the wave travelled different distances from the apex to the aperture. The phase difference because the wave travelled different distances from the apex to the aperture. The difference in path of travel, designated as δ(y’), can be obtained as follows The difference in path of travel, designated as δ(y’), can be obtained as follows It is assumed that, there exist a line source radiating cylindrical waves at the imaginary apex of the horn. As waves travel in the outward radial direction, the constant phase fronts are cylindrical which do not coincide with aperture plane. It is assumed that, there exist a line source radiating cylindrical waves at the imaginary apex of the horn. As waves travel in the outward radial direction, the constant phase fronts are cylindrical which do not coincide with aperture plane. At any point y ’ at the aperture of the horn, the phase of the field will not be the same as that at the origin. At any point y ’ at the aperture of the horn, the phase of the field will not be the same as that at the origin. The phase difference because the wave travelled different distances from the apex to the aperture. The phase difference because the wave travelled different distances from the apex to the aperture. The difference in path of travel, designated as δ(y’), can be obtained as follows The difference in path of travel, designated as δ(y’), can be obtained as follows

10. E-Plane View E-Plane View

11. Aperture Phase Distribution Quadratic Distance Variation

12. Aperture Fields When δ(y’) is multiplied by the phase constant k, the result is a quadratic phase variation between the constant phase surface and the aperture plane. When δ(y’) is multiplied by the phase constant k, the result is a quadratic phase variation between the constant phase surface and the aperture plane. It can be shown that if :- (1) The fields of the feed waveguide are those of its (1) The fields of the feed waveguide are those of its dominant TE 10 – mode and neglecting the higher dominant TE 10 – mode and neglecting the higher order modes. order modes. (2) The horn length is large compared to the aperture (2) The horn length is large compared to the aperture dimensions, the lowest order mode fields at the dimensions, the lowest order mode fields at the aperture of the horn considering the quadratic phase aperture of the horn considering the quadratic phase variation are given by :- variation are given by :- When δ(y’) is multiplied by the phase constant k, the result is a quadratic phase variation between the constant phase surface and the aperture plane. When δ(y’) is multiplied by the phase constant k, the result is a quadratic phase variation between the constant phase surface and the aperture plane. It can be shown that if :- (1) The fields of the feed waveguide are those of its (1) The fields of the feed waveguide are those of its dominant TE 10 – mode and neglecting the higher dominant TE 10 – mode and neglecting the higher order modes. order modes. (2) The horn length is large compared to the aperture (2) The horn length is large compared to the aperture dimensions, the lowest order mode fields at the dimensions, the lowest order mode fields at the aperture of the horn considering the quadratic phase aperture of the horn considering the quadratic phase variation are given by :- variation are given by :-

13. Aperture Fields

14. So the aperture fields become….. So the aperture fields become….. Aperture Fields

15. Aperture Equivalent Currents To find the fields radiated by the horn, only the tangential components of the E - and / or H – fields over a closed surface must be known. The closed surface is chosen to coincide with an infinite plane passing through the mouth of the horn. To find the fields radiated by the horn, only the tangential components of the E - and / or H – fields over a closed surface must be known. The closed surface is chosen to coincide with an infinite plane passing through the mouth of the horn.

16. Aperture Equivalent Currents

17. Radiation Equations

22. Far Field Components

23. E Plane Φ =

24. H Plane Φ = 0

25. E-and H-plane patterns of an E- plane sectoral horn

26. E-plane patterns of E-plane sectoral horn for constant length

27. Universal Curves

28. E Plane Φ =

29. For a given value of s, the field E θn can be plotted as a function of b 1 / λ sinθ, as shown in the following figure for s = 1/64, 1/8, 1/4, 1/2, 3/4, and 1. For a given value of s, the field E θn can be plotted as a function of b 1 / λ sinθ, as shown in the following figure for s = 1/64, 1/8, 1/4, 1/2, 3/4, and 1. These plots are usually referred to as universal curves, because from them the normalized E-plane sectoral horn can be obtained. These plots are usually referred to as universal curves, because from them the normalized E-plane sectoral horn can be obtained. Finally the value of (1+cosθ), normalized to 0 dB and written as 20 log 10 ((1+cosθ)/2), is added to that number to arrive at the required field strength. Finally the value of (1+cosθ), normalized to 0 dB and written as 20 log 10 ((1+cosθ)/2), is added to that number to arrive at the required field strength. For a given value of s, the field E θn can be plotted as a function of b 1 / λ sinθ, as shown in the following figure for s = 1/64, 1/8, 1/4, 1/2, 3/4, and 1. For a given value of s, the field E θn can be plotted as a function of b 1 / λ sinθ, as shown in the following figure for s = 1/64, 1/8, 1/4, 1/2, 3/4, and 1. These plots are usually referred to as universal curves, because from them the normalized E-plane sectoral horn can be obtained. These plots are usually referred to as universal curves, because from them the normalized E-plane sectoral horn can be obtained. Finally the value of (1+cosθ), normalized to 0 dB and written as 20 log 10 ((1+cosθ)/2), is added to that number to arrive at the required field strength. Finally the value of (1+cosθ), normalized to 0 dB and written as 20 log 10 ((1+cosθ)/2), is added to that number to arrive at the required field strength.

30. E Plane Universal Patterns for E Plane Sectoral Horn

31. To find the directivity, the maximum radiation is formed. That is, U max = U(θ,Ф)| max = r 2 / 2 η |E| 2 max U max = U(θ,Ф)| max = r 2 / 2 η |E| 2 max For most horn antennas |E| max is directed nearly along the z-axis (θ = 0). Thus, |E| max = [ |E θ | 2 max + |E Ф | 2 max ] 1/2 |E| max = [ |E θ | 2 max + |E Ф | 2 max ] 1/2 = Directivity

32. F(t) = [ C(t) - j S(t) ] F(t) = [ C(t) - j S(t) ] Since k x = k y = 0 t 1 = - t & t 2 = t t 1 = - t & t 2 = t C(-t) = - C(t) C(-t) = - C(t) S(-t) = - S(t) S(-t) = - S(t) Directivity

33. U max = U(θ,Ф)| max = r 2 / 2 η |E| 2 max = |F(t)| 2 = [ C 2 ( ) + S 2 ( )] The total power radiated can be simply integrating the average power density over the aperture of the horn. η η Directivity

35. E Plane Horn HPBW E Plane Horn HPBW

36. E Plane Horn Normalized Directivity E Plane Horn Normalized Directivity

37. Directivity

38. Alternate Method for Directivity

39. G E as a Function of B

40. Example

41. Alternate solution