This problem deals with the quantization signal-to-noise ratio (SNR) for an Analog-to-Digital Converter (ADC). Let's break it down step by step.

(a) RMS value of the noise of the A/D [6 marks]

The expectation of the squared quantization noise, $E\{e^2\}$, is given by:

$E\{e^2\} = \frac{1}{A} \int_{-A/2}^{A/2} e^2 \, de$

where $A$ is the quantization step size, which is equal to the Least Significant Bit (LSB).

The RMS value of the quantization noise, $V_{\text{rms, noise}}$, is the square root of this expectation:

$V_{\text{rms, noise}} = \sqrt{E\{e^2\}}$

Given that for a uniform distribution of the quantization error:

$V_{\text{rms, noise}} = \frac{A}{\sqrt{12}}$

So the RMS value of the noise is $\frac{A}{\sqrt{12}}$. Since $A$ is the quantization step size (LSB), you would need the specific value of $A$ to calculate this.

(b) RMS of the input voltage [2 marks]

Given the peak-to-peak voltage $V_{\text{pp}}$ is equivalent to $2\sqrt{2} V_{\text{rms}}$:

$V_{\text{rms}} = \frac{V_{\text{pp}}}{2\sqrt{2}}$

So the RMS value of the input voltage $V_{\text{rms}}$ is given by:

$V_{\text{rms}} = \frac{V_{\text{pp}}}{2\sqrt{2}}$

(c) SNR of your A/D [2 marks]

The SNR can be calculated using the formula:

$\text{SNR} = 20 \log_{10} \left( \frac{V_{\text{rms}}}{V_{\text{rms, noise}}} \right)$

Substituting the values:

$\text{SNR} = 20 \log_{10} \left( \frac{V_{\text{rms}}}{\frac{A}{\sqrt{12}}} \right)$

(d) SNR using the formula $6.02N + 1.76 \text{ dB}$ [1 mark]

Given that the SNR is also given by:

$\text{SNR} = 6.02N + 1.76 \text{ dB}$

Where $N$ is the number of bits of the ADC. Plug in the value of $N$ to calculate the SNR.

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Next Steps:

1. Clarify or find the value of the quantization step size $A$ (LSB) to calculate the exact RMS noise value.
2. Identify the number of bits $N$ in the ADC to compute the SNR using the formula in part (d).
3. Verify the peak-to-peak voltage $V_{\text{pp}}$ to determine the RMS value of the input voltage.
4. Recalculate the SNR in part (c) with the correct $V_{\text{rms}}$ and $V_{\text{rms, noise}}$ values.
5. Consider how the uniform distribution of quantization noise affects the SNR.

Tip:

For accurate calculations, always ensure the units and conversions are correct, especially when dealing with logarithmic scales like decibels (dB).