Скачать или смотреть Antenna #19. How to Proof the Max Directivity & Effective Area Relationship (Derivation + Equation)

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An antenna's maximum directivity represents its ability to focus radiated power in a specific direction, while its maximum effective area represents the equivalent area it can capture electromagnetic energy from. These two concepts are related, with higher directivity generally leading to a larger effective area. 

Definition:
Directivity measures how much more concentrated the antenna's radiation is in one direction compared to an isotropic antenna (which radiates equally in all directions). 

Relationship to Radiation Pattern:
Directivity is a property of the antenna's radiation pattern, describing the power density in a particular direction.

Maximum Value:
The maximum directivity is the highest value of the radiation pattern, often expressed in decibels (dB). 

Factors Affecting Directivity:
Antenna size, frequency and shape all influence directivity.
 
Example:
A large parabolic dish antenna will have a higher directivity than a small dipole antenna. 

Definition:
Effective area, also known as effective aperture, quantifies the area an antenna presents to an incoming electromagnetic wave.
 
Capturing Electromagnetic Energy:
It's the area that determines how much power from the incoming wave is captured by the antenna. 

Relationship to Directivity:
The effective area is directly proportional to the directivity.

Maximum Effective Area:
The maximum effective area is the largest value of the antenna's effective area over all directions. 

Example:
A larger, high-gain antenna will have a larger effective area, enabling it to capture more incoming power. 

For any antenna, the maximum directivity (D0) and maximum effective area (Aem) are fundamentally related through the formula:

where λ is the wavelength of the electromagnetic wave.
This means higher directivity antennas generally have a larger effective area, but the relationship depends on wavelength.
In summary:
Directivity focuses on the concentration of radiated power.
Effective area focuses on the amount of incoming power captured.
These two concepts are interconnected, with higher directivity generally leading to a larger effective area.
Both directivity and effective area are important parameters for evaluating antenna performance.

Let's derive the relationship between directivity and maximum effective area based on the geometrical arrangement. Antenna 1 serves as the transmitter, while Antenna 2 functions as the receiver. The effective areas and directivities of each are represented by At, Ar, Dt, and Dr, respectively.