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- 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.

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

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

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