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

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

### AI Response: (may contain errors)  

In a direct-sampling software-defined receiver, the minimum detectable signal level is primarily determined by the analog-to-digital converter (ADC) characteristics. Let's break down why the correct answer is "Reference voltage level and sample width in bits" and why the other choices are incorrect.

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

1. **Reference Voltage Level**: This determines the range of input signal amplitudes that the ADC can handle. A higher reference voltage allows for a larger dynamic range, which can improve the ability to detect weaker signals.

2. **Sample Width in Bits**: The number of bits used in the ADC determines the resolution. More bits mean finer resolution, allowing the ADC to distinguish smaller differences in signal amplitude. This directly affects the minimum detectable signal level because it defines how small a signal can be and still be detected above the quantization noise.

### Why the Other Choices are Incorrect

- **A: Sample clock phase noise**: While phase noise can affect the quality of the signal processing, it does not directly set the minimum detectable signal level. Phase noise is more related to frequency stability and purity.

- **C: Data storage transfer rate**: This affects how quickly data can be moved and stored but does not influence the minimum detectable signal level. It is more about handling the data after it has been sampled.

- **D: Missing codes and jitter**: These are imperfections in the ADC process. While they can degrade performance, they are not the primary factors in setting the minimum detectable signal level. Missing codes refer to certain output levels being skipped, and jitter refers to timing errors, both of which can affect signal quality but not the fundamental detection threshold.

### Useful Formula

The minimum detectable signal level can be related to the ADC's effective number of bits (ENOB) and the reference voltage. The signal-to-noise ratio (SNR) for an ideal ADC is given by:

$$
\text{SNR} = 6.02 \times \text{ENOB} + 1.76 \, \text{dB}
$$

This formula shows how the number of bits (ENOB) affects the SNR, which in turn influences the minimum detectable signal level. More bits result in a higher SNR, allowing for the detection of weaker signals.