Antenna gain and tv Resistance requirements

[Mastur]

Homework Statement

A satellite link has a transmitted power output of 0.5W. This power is increased in the direction of transmission by the transmitter antenna, which has a 20dB gain. The RF signal is attenuated by a path loss of 200 dB. The total noise level at the receiver input is estimated to be 2dBf. The desired SNR at the input receiver is 15dB. Determine the min. antenna gain G(dB) that will meet the specifications

The front end of a television receiver, having a bandwidth of 7 MHz and operating at a temperature of 27°C, consists of an amplifier having a gain of 15 followed by a mixer whose gain is 20.The amplifier has a 300-Ω input resistor and a shot noise equivalent resistance of 500 Ω. For the converter, these values are 2.2 kΩ and 13.5 kΩ respectively, the converter load resistanceis 470 kΩ. Calculate Req for this television receiver

Homework Equations

The Attempt at a Solution

I have no idea on how to do it. I was thinking of getting the antenna gain in the receiver then get the sum of receiver input and output to 0. Unfortunately, I do not know how to convert SNR to antenna gain.

In the second problem, I totally got no idea.

The answer was given to us, which is 50dB and 875ohms respectively.

Please guide me to achieve the answer.

 

[KataKoniK]

Hello!

For the first problem, you can use the following formula to calculate the minimum antenna gain G(dB) that will meet the specifications:

G(dB) = SNR(dB) - (noise level at receiver input - 10log(Pt) + PL)

Where SNR is the desired signal-to-noise ratio (15 dB in this case), noise level at receiver input is 2 dBf (convert to dB using the formula dB = 10log(F) where F is the noise level in watts), Pt is the transmitted power (0.5 W in this case), and PL is the path loss (200 dB in this case).

So, plugging in the values, we get:

G(dB) = 15 dB - (2 dBf - 10log(0.5 W) + 200 dB) = 15 dB - (2 dBf - (-3 dB)) = 15 dB - (-5 dBf) = 20 dBf

Therefore, the minimum antenna gain required is 20 dB.

For the second problem, you can use the following formula to calculate Req:

Req = (R1 + R2)/(1 + R2/R1)

Where R1 is the input resistance of the amplifier (300 Ω) and R2 is the shot noise equivalent resistance (500 Ω).

So, plugging in the values, we get:

Req = (300 Ω + 500 Ω)/(1 + 500 Ω/300 Ω) = 800 Ω

Now, for the mixer, we can use the following formula to calculate Req:

Req = (R1 + R2)/(1 + R2/R1)

Where R1 is the input resistance of the mixer (2.2 kΩ) and R2 is the load resistance (470 kΩ).

So, plugging in the values, we get:

Req = (2.2 kΩ + 470 kΩ)/(1 + 470 kΩ/2.2 kΩ) = 875 Ω

Therefore, the total Req for the television receiver is 875 Ω.

I hope this helps! Let me know if you have any further questions.