Question E4C13:
What is reciprocal mixing?  

Choices:  
A: Two out-of-band signals mixing to generate an in-band spurious signal  
B: In-phase signals cancelling in a mixer resulting in loss of receiver sensitivity  
C: Two digital signals combining from alternate time slots  
D: Local oscillator phase noise mixing with adjacent strong signals to create interference to desired signals    

Correct Answer is  D: Local oscillator phase noise mixing with adjacent strong signals to create interference to desired signals  

To understand reciprocal mixing, think of a strong nearby signal and a local oscillator (LO) that isn’t perfectly “pure.” The LO’s phase noise creates sidebands that, when mixed with that strong adjacent signal, produce noise inside your receiver’s passband, masking weak signals.

Why D is correct:
- Reciprocal mixing is the process where LO phase noise at an offset frequency mixes with a strong adjacent signal, translating that noise into the IF passband. This raises the noise floor near the desired signal, reducing copy of weak signals even if the front end is otherwise linear.

Useful model and formula:
- LO with phase noise: $v_{LO} = A\cos(\omega_0 t + \phi(t))$, where $\phi(t)$ causes phase-noise sidebands.
- If a strong interferer of power $P_s$ is at offset $f_{off}$ from the desired signal, the reciprocal-mixing noise power in bandwidth $B$ is approximately:
  $$P_{RM} \approx P_s + L(f_{off}) + 10\log_{10}(B)$$
  where $L(f)$ is the LO phase noise density in dBc/Hz at offset $f$.
- Rule of thumb: Better LO phase noise (lower $L(f)$) and narrower roofing/IF filters (smaller $B$) reduce reciprocal mixing. The metric often quoted is RMDR (Reciprocal Mixing Dynamic Range), which improves as $L(f)$ decreases at close-in offsets.

Why the other choices are incorrect:
- A: “Two out-of-band signals mixing to generate an in-band spurious signal” describes intermodulation/spurious responses in nonlinear stages, not reciprocal mixing.
- B: “In-phase signals cancelling in a mixer” would imply a conversion null or gain issue, not the LO phase-noise mechanism that raises the noise floor.
- C: “Two digital signals combining from alternate time slots” is about TDMA multiplexing, unrelated to analog mixing or LO phase noise.

Practical tips:
- Use radios with low LO phase noise (good RMDR specs).
- Employ narrow roofing/IF filters to limit $B$.
- Reduce nearby strong signals (e.g., effective preselector/roofing filter). Attenuation may help only if it reduces the interfering signal enough relative to the LO phase-noise contribution; it often reduces desired signal too, so improvement can be limited.