Carrier-to-Noise Ratio Question

[Kartik.Sulakh]

Homework Statement

A receiving system consists of an antenna with an effective noise temperature of
70 K. This antenna is connected to a microwave front end of noise figure 7 dB
via a feeder. The feeder’s specific attenuation function is 0.2 dB/10m. The actual
feeder length is 2 m. Calculate the carrier to noise power spectral density at the
output of the microwave front end if the received carrier power at the antenna
terminals is -100 dBm?

Homework Equations

I'm assuming it as C_min = -174 + NF + 10Log₁₀B + C/N

Where,
NF = Noise Figure,
B = Bandwidth, and C/N is a Carrier-to-Noise Ratio which is asked?

The Attempt at a Solution

C_min = -110 dBm
Noise Figure (NF) = 7 dB & Struck up in knowing Bandwidth (B)

length of feeder is 2 meters,
feeder’s specific attenuation function is 0.2 dB/10m, What Next?

 

[KataKoniK]

To calculate the carrier to noise power spectral density at the output of the microwave front end, we need to use the formula:

C/N = (Cmin - NF - 10Log10B)/(-1)

Where Cmin is the minimum carrier power at the output of the microwave front end, NF is the noise figure, and B is the bandwidth.

In this case, Cmin = -110 dBm, NF = 7 dB, and we need to determine the bandwidth.

To calculate the bandwidth, we need to first determine the frequency of the received carrier signal. This can be done using the formula:

f = c/λ

Where c is the speed of light (3 x 10^8 m/s) and λ is the wavelength, which can be calculated using the formula:

λ = c/f

In this case, the frequency of the received carrier signal is not given, so we will assume a commonly used frequency of 2.4 GHz.

Therefore, f = 2.4 GHz = 2.4 x 10^9 Hz

And λ = (3 x 10^8 m/s)/(2.4 x 10^9 Hz) = 0.125 m

Now, we can calculate the bandwidth using the formula:

B = 2 x λ = 2 x 0.125 m = 0.25 m

Plugging in the values, we get:

C/N = (-110 dBm - 7 dB - 10Log10(0.25 m))/(-1)
= (-110 dBm - 7 dB - (-6 dB))/(-1)
= (-110 dBm - 7 dB + 6 dB)/(-1)
= (-111 dBm)/(-1)
= 111 dBm

Therefore, the carrier to noise power spectral density at the output of the microwave front end is 111 dBm.