Question E4C04:
What is the noise figure of a receiver?  

Choices:  
A: The ratio of atmospheric noise to phase noise  
B: The ratio of the noise bandwidth in hertz to the theoretical bandwidth of a resistive network  
C: The ratio in dB of the noise generated in the receiver to atmospheric noise  
D: The ratio in dB of the noise generated by the receiver to the theoretical minimum noise    

Correct Answer is  D: The ratio in dB of the noise generated by the receiver to the theoretical minimum noise  

To understand “noise figure,” think: How much does the receiver worsen the signal-to-noise ratio compared to an ideal, noiseless receiver at room temperature?

Why D is correct:
- Noise figure (linear) is defined as:
  $$F = \frac{SNR_{in}}{SNR_{out}}$$
  It is the ratio of input SNR to output SNR. In dB:
  $$NF_{dB} = 10\log_{10}(F)$$
- This is equivalent to expressing the receiver’s added noise relative to the theoretical minimum thermal noise at standard temperature $T_0 = 290\ \text{K}$. The “theoretical minimum noise” is the thermal noise floor:
  $$N_{min} = k\,T_0\,B$$
  where $k$ is Boltzmann’s constant and $B$ is bandwidth.
- Thus, “the ratio in dB of the noise generated by the receiver to the theoretical minimum noise” matches the noise figure concept.

Why the other choices are incorrect:
- A: “Atmospheric noise to phase noise” — Noise figure does not compare external atmospheric noise with oscillator phase noise; it quantifies total SNR degradation caused by the receiver.
- B: “Noise bandwidth vs theoretical bandwidth” — That describes equivalent noise bandwidth of filters, not receiver noise figure.
- C: “Receiver noise to atmospheric noise (in dB)” — Noise figure is referenced to the thermal noise of a matched source at 290 K, not to variable atmospheric noise.

Useful formulas and rules of thumb:
- Thermal noise floor density at 290 K:
  $$N_0 = kT_0 = -174\ \text{dBm/Hz}$$
- Total input noise for bandwidth $B$:
  $$N_{in} = -174\ \text{dBm/Hz} + 10\log_{10}(B\ [\text{Hz}])$$
- Receiver output noise (referenced to input) with noise figure:
  $$N_{sys} = N_{in} + NF_{dB}$$
- Equivalent noise temperature of the receiver:
  $$T_e = T_0(F - 1)$$
- Friis cascade formula (keep first stage low NF and with gain):
  $$F_{total} = F_1 + \frac{F_2 - 1}{G_1} + \frac{F_3 - 1}{G_1G_2} + \cdots$$

Key takeaway: Lower NF means the receiver adds less noise above the thermal minimum, preserving SNR better.