- #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
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