Question

A 10-bit A/D converter is used to digitize an analog voltage signal in $0 - 5\text{V}$ range. The maximum peak to peak ripple voltage that can be allowed in DC voltage is}

• A. nearly $100\text{ mV}$
• B. nearly $50\text{ mV}$
• C. nearly $25\text{ mV}$
• D. nearly $5\text{ mV}$

Hint:

Always relate allowable input noise or ripple to the LSB step size of the converter.
Input noise voltage should be less than $1\text{ LSB}$ to prevent jitter in the digital output.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We need to find the maximum allowed peak-to-peak ripple voltage on the analog input of a 10-bit ADC such that the noise does not cause fluctuating readings in the digital output.

Step 2: Key Formula or Approach:
The resolution of an ADC (also called the step size or the value of 1 LSB) is the minimum input change required to change the digital output by 1 count:
\[ \text{Resolution} = \frac{V_{ref}}{2^N - 1} \]
To ensure that noise or ripple does not fluctuate the output by even 1 LSB, the peak-to-peak ripple voltage must be kept below the value of 1 LSB (i.e., less than the resolution).

Step 3: Detailed Explanation:

• Given parameters:
Number of bits, $N = 10$.
Full-scale analog voltage range, $V_{ref} = 5\text{ V}$.

• Calculate the resolution (1 LSB value):
\[ \text{Resolution} = \frac{5\text{ V}}{2^{10} - 1} = \frac{5\text{ V}}{1023} \]
\[ \text{Resolution} \approx 0.004887\text{ V} = 4.887\text{ mV} \]

• To avoid unwanted output fluctuations, the maximum peak-to-peak ripple voltage must be less than $4.887\text{ mV}$.

• This is approximately $5\text{ mV}$.

Step 4: Final Answer:
The maximum allowable peak-to-peak ripple is nearly $5\text{ mV}$, which corresponds to Option (D).