Question E7F11:
What sets the minimum detectable signal level for a direct-sampling software defined receiver in the absence of atmospheric or thermal noise?  

Choices:  
A: Sample clock phase noise  
B: Reference voltage level and sample width in bits  
C: Data storage transfer rate  
D: Missing codes and jitter    

Correct Answer is  B: Reference voltage level and sample width in bits  

Correct answer: B — Reference voltage level and sample width in bits

Why B is correct:
- In a direct-sampling SDR, the analog-to-digital converter (ADC) sets the internal noise floor when external noises are absent. That floor is the ADC’s quantization noise.
- Quantization noise depends on the ADC full-scale (set by the reference voltage, Vref) and the number of bits, N, which determines the step size (LSB).
- Smaller LSBs (more bits) and appropriate Vref reduce quantization noise, letting you detect weaker signals.

Key relations:
- LSB size:
  $$\Delta = \frac{V_{\text{FS}}}{2^N} \quad \text{with } V_{\text{FS}} \propto V_{\text{ref}}$$
- Quantization noise power (ideal ADC):
  $$P_q = \frac{\Delta^2}{12}$$
- Full-scale SNR for an ideal N-bit ADC (rule of thumb):
  $$\text{SNR}_{\text{FS}} \approx 6.02\,N + 1.76\ \text{dB}$$
- Each extra bit improves SNR (and lowers the MDS) by about 6 dB.
- Oversampling spreads quantization noise over the Nyquist bandwidth; noise density drops by about 3 dB each time the sample rate doubles.

Why the other choices are incorrect:
- A: Sample clock phase noise
  - Phase noise (reciprocal mixing) mainly limits close-in dynamic range in the presence of strong signals; it does not set the fundamental noise floor in the no-external-noise case.
- C: Data storage transfer rate
  - Throughput affects how fast samples can be moved/recorded, not the sensitivity or noise floor of the receiver.
- D: Missing codes and jitter
  - These are non-idealities that create spurs and add frequency-dependent noise (jitter noise increases with input frequency), degrading SFDR and SNR. However, the fundamental minimum detectable level (with no atmospheric/thermal noise) is governed by ideal quantization noise, i.e., Vref and N.

Rules of thumb to remember:
- +1 bit ≈ +6 dB SNR improvement.
- Doubling the sampling rate (with the same analog bandwidth) ≈ 3 dB reduction in in-band quantization noise density.
- Properly scaling the front-end gain to use most of the ADC full-scale (set by Vref) maximizes SNR without clipping.