Link Budget Antenna: use of effective aperture and the gain in a problem

In summary, the power at the output of the receiving antenna is: 1) calculated by dividing the power at the entry by the gain of the receiving antenna2) converted to power density3) based on the equation: $$ P_r = \frac{P_t G}{4 \pi R^2} $$
  • #1
Master1022
611
117
Homework Statement
If we have a system where we receive power ## x ## W at the receiver. Find the power at the input if the receiver and transmitting antennae are parabolic and the same size / transmission efficiency.
Relevant Equations
Power density = Power / Area
Hi,

I was just attempting this problem and was confused about the calculation process involved.

Context:
In earlier parts of the question, we calculate the gain ## G ## and effective aperture ## A ## for the parabolic antennae.

My Attempt:
We are given the power at the output ## x ## in Watts
1) The receiving antenna has a gain ## G ## and therefore we must divide by that to get the power at the entry to the receiving antenna ## \frac{x}{G} ##
2) Convert the power to power density $$ P_{receiver} = P_r = \frac{x}{G \cdot A} $$
3) We know that:
$$ P_r = \frac{P_t G}{4 \pi R^2} $$ and therefore, we can find
$$ P_t = \frac{4 P_r \pi R^2}{G} $$

However, the answer only includes the gain ## G ## once, that is it uses the formula:
$$ P_t = \frac{4 x \pi R^2}{G A} $$

I cannot understand why this is the case. I know that the effective aperture and gain related to one another, but I thought the effective aperture was about the effectiveness of the physical antenna and the gain was about the amplification of the signal.

Should I not be counting the gain twice?

Any help is greatly appreciated
 
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  • #2
I have answered this question and I should not include the gain twice. The antenna does not (according to my notes) act like an op-amp which physically amplifies the signal. The gain is a measure of directivity of the beam, which can also be represented by its physical characteristics (eg. its effective area). Therefore, there is no need to include the gain twice.
 
  • #3
It seems like you might want to apply the gain twice if you are accounting for both the TX and RX antennas? But I can't tell it that's what you are wanting to do.
 
  • #4
berkeman said:
It seems like you might want to apply the gain twice if you are accounting for both the TX and RX antennas? But I can't tell it that's what you are wanting to do.

Apologies, my post may have not been too clear. I also haven't seen the terms TX and RX, but I assume they stand for transmitting and receiving. So yes, we need to account for gain twice, but we shouldn't be including both gain and the effective aperture for the same antenna (as they are related to one another and describe the same phenomenon). So in my formula I should have included ## G_t ## and only one of ## G_r ## or ## A_{eff} ## (with the respective conversion formula).

Otherwise, I could have used the effective aperture for antennae as they have the same dimensions.
 

Related to Link Budget Antenna: use of effective aperture and the gain in a problem

1. What is a link budget antenna?

A link budget antenna is a calculation that determines the total gain and loss of a wireless communication system. It takes into account factors such as the transmitter power, antenna gain, cable loss, and receiver sensitivity to determine the overall performance of the system.

2. How is effective aperture used in a link budget antenna?

Effective aperture is used in a link budget antenna to calculate the received power at the receiving antenna. It takes into account the physical size of the antenna and its efficiency in capturing the incoming signal. The larger the effective aperture, the more power can be received by the antenna.

3. What is the relationship between effective aperture and antenna gain?

Effective aperture and antenna gain are directly related. The gain of an antenna is determined by its effective aperture, as well as its directivity and efficiency. A larger effective aperture results in a higher antenna gain, which means a stronger received signal.

4. How does the gain of an antenna affect the link budget?

The gain of an antenna is a crucial factor in the link budget calculation. A higher gain antenna will result in a stronger received signal, which can compensate for other losses in the system. This can improve the overall link budget and increase the range and reliability of the wireless communication system.

5. Can the gain of an antenna be increased to improve the link budget?

Yes, the gain of an antenna can be increased to improve the link budget. This can be achieved by using a larger antenna or by using a directional antenna with a higher gain. However, it is important to consider other factors such as cost, size, and practicality when selecting an antenna with a higher gain for a specific application.

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