Seminar on Microwave and Optical Communication Wonhong Jeong 2014.12.9

CONTEXT 12.5.1 Uniform Distribution on an Infinite Ground Plane 12.5.2 Uniform Distribution in Space 12.5.3 TE10-Mode Distribution on an Infinite Ground Plane

Antennas & RF Devices Lab. 12.5.1 Uniform Distribution on an Infinite Ground Plane To reduce the mathematical complexities, assumed E-field over the opening region as below equation (12-17) and Figure 12.7 Antennas & RF Devices Lab.

A. Equivalent In this textbook, Used infinite closed surface xy-plane to form the equivalent.

B. Radiation Fields: Element and Space Factors In the far field, we can obtain the radiation fields using equation (12-10a) - (12-10f) & (12-12a) - (12-12d) Before substitute equations, we need to simplify Lθ and Lϕ. Space factor Element factor Using the integral characteristic equation (12-20), we can obtain Lθ and Lϕ.

Use equations (12-19), (12-21), and (12-22) for substituting radiated E-field and H-field.

Equation (12-23a) to (12-23f) represent the 3D distributions of the far field. We need to represent 2D radiated fields due to experimentally only 2D plots can be measured. Thus, substitute each angles, we can earn

Radiated field pattern characteristics Appear multiple lobes: Because The dimensions of the aperture are greater than 1λ H-plane is only a function of the dimension ‘a’ and E-plane is only influenced by ‘b’. If the aperture dimensions increase, additional lobes are formed.

Using 2D radiated pattern we can see the H-plane patterns along the ground plane vanished. (at infinite ground) However, The E-plane patterns do not vanish along the ground plane, unless dimension of the aperture in that plane is a multiple of a wavelength.

C. Beamwidths First null beamwidth (FNBW) To obtain beamwidth, using the null occurs in E-field equation (12-24b). If b >> nλ, equation (12-26a) reduces approximately to

The total beamwidth between null is given by If b >> nλ, beamwidth reduces to The first-null beamwidth (FNBW) is obtained by letting n=1.

Half power beamwidth (HPBW) First side lobes beamwidth (FSLBW) The half power point occurs when The maximum of the first side lobe occurs when Then, we can earn angle at half power point Then, we can earn angle at first side lobe point If b >> 1.43λ, equation (12-30a) reduces to If b >> 0.443λ, equation (12-28) reduces to The beamwidth between first side lobes beamwidth (FSLBW) is given by Thus the half power beamwidth (HPBW) is given by (When b >> 1.43λ) (When b >> 0.443λ)

D. Side Lobe Level Method 1. Method 2. The maximum of the first side lobe occurs when The maximum of the first side lobe occurs when numerator is maximum in equation (12-24b) Thus, using equation (12-24b), we can obtain maximum value of the first side lobe. That is, when Using bracket term, we can calculate maximum of first side lobe ratio. Thus, As a result, 13.26 dB down from the maximum of the main lobe.

E. Directivity The directivity can be found using equations (12-13), (12-23), (2-21), and (2-22). substitute Use fundamental directivity formula This method is so hard to compute integrals. So, the other method needs to solve.

We assumed that aperture is mounted on an infinite ground plane. In this situation, simpler method is exist to compute the radiated power. Considerations The average power density at the aperture. Integrate over the physical bounds of the opening. Consider these matters, we can simply obtain the radiated power. First, Find the H-field basis on E-field. Then, obtain the radiated power from radiated power formula

Using the fields of equations (12-23a) – (12-23b) and θ = 0° due to maximum radiation intensity occurs at this direction. Then, we can obtain Thus the directivity is

12.5.2 Uniform Distribution in Space The field distribution is given by A. Equivalent Compare with infinite ground situation, Js and Ms are not zero outside the opening and expressions for them are not known. Thus difficult to define the equivalent. So, Assumed both Ea, Ha, Js, and Ms exist over the opening but are zero outside it. This approximate equivalent expression is the best way to represent.

Comparison between aperture from infinite plane and free space B. Radiated Fields Similar to that of the previous, we can determine the radiated field of aperture antenna at free space. Comparison between aperture from infinite plane and free space The angular limits are extended to 180°  Compare with infinite plane, we can find additional minor lobes are formed.

C. Beamwidths and Side Lobe Levels Similar to that of the previous, we can determine the Beamwidths and side lobe level. Half power beamwidth (degree) First side lobe maximum (to main maximum) (dB) E-plane (b >> λ): E-plane: -13.26 H-plane: -13.26 (a >> λ) H-plane (a >> λ): First null beamwidth (degree) E-plane (b >> λ): H-plane (a >> λ): D. Directivity Although the physical geometry of the opening is same as section 12.5.1, their directivities are not same.  Because, outside the aperture along the xy-plane are not exactly same in the far field. However, if the patterns of the aperture especially main lobe is same, directivities are almost same.

12.5.3 TE10 Mode Distribution on an Infinite Ground Plane In practice, a commonly used rectangular waveguide aperture antenna mounted on infinite ground plane is used. At the opening, the field is usually approximated by the dominant TE10 mode. A. Equivalent, Radiated Fields, Beamwidths, and Side Lobe Levels Eqiuvalent Radiated fields

Half power beamwidth (degree) First side lobe maximum (to main maximum) (dB) E-plane (b >> λ): E-plane: -13.26 H-plane: -23 (a >> λ) H-plane (a >> λ): First null beamwidth (degree) E-plane (b >> λ): H-plane (a >> λ):

Comparison between uniform distribution and TE10 Aperture

B. Directivity and Aperture Efficiency Use E-field equation (12-39) and magnetic field related to the E-field by the intrinsic impedance η, the radiated power can be given by The maximum radiation intensity occurs at θ = 0°, thus Using maximum radiation intensity, we can obtain directivity. (Aem = The maximum effective area, Ap = Physical area, εap =aperture efficiency)

TE10 mode distribution on infinite ground Aperture efficiency The aperture efficiency is a figure of merit which indicates how efficiently the physical area of the antenna is utilized. TE10 mode distribution on infinite ground Aperture antenna Horn antenna (Optimum gain horns have εap = 0.5) Circular reflector antenna

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