TV antenna amplifier noise calculation

[bizuputyi]

Homework Statement

Hello everyone. A 4-way TV antenna amplifier has the following specifications:

Bandwidth = 40-862Mhz
Gain = 20dB
Noise figure = 6 dB
Max output = 85dBuV
Input impedance = output impedance = 75 ohm

Question 1: Calculate the required voltage on the input of the amplifier to achieve 85dBuV max output.

Question 2: If the aerial signal level is 5dBmV and the input noise level is 20dBuV, determine SNR (signal-to-noise ratio) on the output of the amplifier.

Homework Equations

$SNR = 20 log (\frac{V_{signal}}{V_{noise}})$

The Attempt at a Solution

Question 1:

Max output = max input neglecting noise and distortion + amplifier gain
85dBuV = max input + 20dB
Max input = 65dbuV

Input voltage = $antilog (\frac{65}{20})$ = 1.778mV

Question 2:

5dBmV = $antilog (\frac{5}{20})$ = 1.778mV
20dBuV = $antilog (\frac{20}{20})$ = 0.01mV

$SNR_{in} = 20 log (\frac{1.778}{0.01})$ = 45dB

$SNR_{out} = SNR_{in} - noise figure$ = 45 - 6 = 39dB

Am I thinking correctly? Thank you for your comments.

 

[marcusl]

1 is correct, 2 is not--you messed up an antilog There's no need to convert to volyage for #2. it's simpler to just work in dB straight through.

 

[bizuputyi]

Right, okay. In that case:

5dBmV + 60 = 65dBuV

$SNR_{in dB} = 65 - 20 = 45dB$
$SNR_{out dB} = SNR_{in dB} - noise figure = 45 - 6 = 39dB$

I get the same results. Where am I mistaken?

 

[marcusl]

Sorry, I wasn't looking carefully at the units. I agree with your calculation.

 

[bizuputyi]

Thank you.