Calculating Dish Resolution at 4 GHz with 3m Diameter - Homework Problem

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In summary, the resolution of a dish operating at a frequency of 4 GHz and with a diameter of 3 m can be calculated using the equation x = 1.22(y GHz/ D), where y is the wavelength. This will give a resolution of 1.63 degrees. However, it is important to verify that "y GHz" refers to the wavelength before using this equation.
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wakejosh
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Homework Statement

A dish operates at a frequency of 4 GHz and has a diameter of 3 m. What is its resolution?



Homework Equations


my take home quiz referres me to a page number in my book for the equation, but I have an older book so I can't find it. i think it is the equation for the Limiting angle of resolution of a circular aperture, but I am not sure. something like:
x = 1.22(y GHz/ D) is this what I am looking for?


The Attempt at a Solution


If I try it with this equation I get: 1.63 degrees. any help is appreciated. thanks.
 
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  • #2
x = 1.22(y GHz/ D) is this what I am looking for?

As long as "y GHz" means the wavelength.
 
  • #3


Yes, you are correct. The equation you are looking for is the Limiting angle of resolution of a circular aperture, which is given by x = 1.22(y GHz/ D), where x is the resolution in degrees, y is the frequency in GHz, and D is the diameter of the dish in meters. Plugging in the values given in the problem, we get x = 1.22(4 GHz/ 3 m) = 1.63 degrees. This means that the dish has a resolution of 1.63 degrees at a frequency of 4 GHz and a diameter of 3 m. This resolution value can be interpreted as the minimum angle between two objects that the dish can distinguish.
 

FAQ: Calculating Dish Resolution at 4 GHz with 3m Diameter - Homework Problem

What is dish resolution and how does it affect my viewing experience?

Dish resolution refers to the level of detail and clarity in the picture displayed on your screen. It is measured in pixels and the higher the resolution, the sharper and more detailed the image will appear. A higher resolution can enhance your viewing experience, especially for larger screens or when watching high-definition content.

How do I know what resolution my dish is capable of?

Most modern dishes are capable of displaying content in 1080p resolution, which is considered high-definition. If you are unsure about your dish's capabilities, you can check the specifications on the manufacturer's website or consult your device's manual.

What is the difference between 1080p and 4K resolution?

1080p resolution, also known as Full HD, has a resolution of 1920 x 1080 pixels, while 4K resolution has a resolution of 3840 x 2160 pixels. This means that 4K provides four times more pixels than 1080p, resulting in a much sharper and clearer image. However, to fully appreciate the benefits of 4K resolution, you will need a compatible dish and content.

Why is it important to consider GHz when choosing a dish?

GHz, or gigahertz, is a unit of measurement for frequency. In the context of dishes, it refers to the speed at which the dish can receive and process data. A higher GHz can result in faster loading times and smoother streaming, especially for high-resolution content. Therefore, it is important to consider the GHz capabilities of a dish when choosing one for your viewing needs.

Can I upgrade my dish's resolution or GHz capabilities?

In most cases, the resolution and GHz capabilities of a dish are determined by its hardware and cannot be upgraded. However, you can always purchase a new dish with better resolution and GHz capabilities to enhance your viewing experience. Keep in mind that the resolution and GHz capabilities of your dish must also be supported by your TV and content to fully benefit from them.

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