Question E4C10:
What is an advantage of having a variety of receiver bandwidths from which to select?  

Choices:  
A: The noise figure of the RF amplifier can be adjusted to match the modulation type, thus increasing receiver sensitivity  
B: Receiver power consumption can be reduced when wider bandwidth is not required  
C: Receive bandwidth can be set to match the modulation bandwidth, maximizing signal-to-noise ratio and minimizing interference  
D: Multiple frequencies can be received simultaneously if desired    

Correct Answer is  C: Receive bandwidth can be set to match the modulation bandwidth, maximizing signal-to-noise ratio and minimizing interference  

Correct answer: C — Receive bandwidth can be set to match the modulation bandwidth, maximizing signal-to-noise ratio and minimizing interference.

1) Why C is correct
- Thermal noise power is proportional to bandwidth:
  $$N = k T B$$
  where $k$ is Boltzmann’s constant, $T$ is temperature in kelvin, and $B$ is noise bandwidth (Hz).
- For a given signal level, narrowing $B$ reduces noise and adjacent-channel energy, improving SNR:
  $$\text{SNR} = \frac{S}{N} \propto \frac{1}{B}$$
- The practical rule: use the narrowest bandwidth that still passes the signal’s information without distortion (i.e., matches the modulation’s occupied bandwidth).

2) Why the other choices are incorrect
- A: “Adjust the noise figure of the RF amplifier...”  
  Noise figure (NF) is a property of the receiver front end and does not change with IF/DSP bandwidth selection. Bandwidth affects noise power at the detector, but it does not “adjust” the RF amplifier’s NF.
- B: “Reduce receiver power consumption when wider bandwidth is not required”  
  Selectable bandwidth (analog filters or DSP) has negligible effect on receiver power consumption. The benefit of bandwidth selection is SNR/adjacent-interference control, not saving power.
- D: “Receive multiple frequencies simultaneously”  
  A wider bandwidth may let you hear multiple signals in the passband, but that’s not equivalent to intentionally receiving multiple discrete frequencies. True simultaneous multi-frequency reception requires multiple receivers/sub-receivers, not just selectable bandwidth.

3) Useful formulas and rules of thumb
- Thermal noise density at room temperature:
  $$N_0 \approx -174 \text{ dBm/Hz}$$
- Receiver noise floor:
  $$P_N \ (\text{dBm}) \approx -174 + 10\log_{10}(B) + \text{NF (dB)}$$
- Rule of thumb: choose bandwidth ≈ occupied bandwidth of the mode to maximize intelligibility and SNR while minimizing adjacent-channel interference.
  - CW: ~200–500 Hz
  - SSB voice: ~2.1–2.8 kHz
  - AM: ~5–6 kHz (per sideband pair)
  - NBFM: ~12–15 kHz (receiver IF filter)