Question E4C12:
How does a narrow-band roofing filter affect receiver performance?  

Choices:  
A: It improves sensitivity by reducing front-end noise  
B: It improves intelligibility by using low Q circuitry to reduce ringing  
C: It improves blocking dynamic range by attenuating strong signals near the receive frequency  
D: All these choices are correct    

Correct Answer is  C: It improves blocking dynamic range by attenuating strong signals near the receive frequency  

Correct answer: C — It improves blocking dynamic range by attenuating strong signals near the receive frequency.

1) Why C is correct
- A roofing filter is a relatively narrow filter placed early in the IF chain. It limits the spectrum delivered to subsequent mixers/IF amplifiers, so strong off-channel but near-in signals are attenuated before they can drive later stages into gain compression or overload.
- This raises the level of an interfering signal required to cause blocking, thereby improving the receiver’s blocking dynamic range (BDR).

Useful definition:
- Blocking dynamic range:
  $$\text{BDR} \approx S_{\text{block}} - \text{MDS}$$
  where:
  - $S_{\text{block}}$ = interfering-signal level that causes 1 dB gain reduction (blocking)
  - MDS = minimum discernible signal
- A roofing filter increases $S_{\text{block}}$ by attenuating nearby interferers before sensitive stages.

2) Why the other choices are incorrect
- A: “It improves sensitivity by reducing front-end noise” — Sensitivity (MDS) is set mainly by the front-end noise figure. A roofing filter is usually after the first mixer, not the RF input; its insertion loss can slightly worsen sensitivity. It does not reduce front-end noise.
- B: “It improves intelligibility by using low Q circuitry to reduce ringing” — Roofing filters are narrow, hence high $Q$, not low. High $Q$ means:
  $$Q = \frac{f_0}{\text{BW}}$$
  Narrow bandwidth (small BW) gives large $Q$ and can increase ringing. Intelligibility is more a function of IF/DSP/audio filtering, not the roofing filter’s “low Q.”
- D: “All these choices are correct” — Since A and B are incorrect, D is incorrect.

3) Helpful formulas and rules of thumb
- Quality factor:
  $$Q = \frac{f_0}{\text{BW}}$$
- Noise floor (per bandwidth) for sensitivity estimates:
  $$N_{\text{dBm}} \approx -174\ \text{dBm/Hz} + 10\log_{10}(\text{BW in Hz}) + \text{NF}$$
- Rule of thumb: Put selectivity as early as practical. A narrow roofing filter protects downstream stages from strong adjacent signals, improving close-in BDR and intermod performance.