D/A Converter Error Calculation Explained

Understanding the accuracy of a Digital-to-Analog Converter (D/A converter or DAC) is crucial in electronics, especially when dealing with precise voltage outputs. The accuracy specification tells us how close the actual output voltage is to the ideal or expected output voltage. In this problem, we need to find the maximum possible error in the output voltage based on the given full-scale voltage and accuracy percentage.

Given Parameters for the D/A Converter

• Full-scale input voltage (V_FS): \( 5 \, \text{V} \)
• Accuracy: \( \pm 0.2\% \)

Concept of Accuracy in D/A Converters

The accuracy of a D/A converter is typically specified as a percentage of its full-scale output voltage. This means that the maximum deviation (error) from the ideal output can be calculated by taking that percentage of the full-scale voltage. A \( \pm 0.2\% \) accuracy implies that the output voltage can be off by up to 0.2% of the maximum possible output voltage, which is the full-scale voltage in this specific case.

Step-by-Step Error Calculation

To find the maximum error for any output voltage, we will use the following formula:

\( \text{Maximum Error} = \text{Accuracy Percentage} \times \text{Full-scale Input Voltage} \)

Let's substitute the given values into the formula:

\( \text{Maximum Error} = 0.2\% \times 5 \, \text{V} \)

First, convert the percentage into a decimal value:

\( 0.2\% = \frac{0.2}{100} = 0.002 \)

Now, perform the multiplication to find the error in volts:

\( \text{Maximum Error} = 0.002 \times 5 \, \text{V} \)

\( \text{Maximum Error} = 0.01 \, \text{V} \)

Converting Error to Millivolts (mV)

The options provided in the question are in millivolts (mV), so it's essential to convert our calculated error from volts (V) to millivolts (mV). We know that \( 1 \, \text{V} = 1000 \, \text{mV} \).

\( \text{Maximum Error} = 0.01 \, \text{V} \times 1000 \, \text{mV/V} \)

\( \text{Maximum Error} = 10 \, \text{mV} \)

Conclusion on D/A Converter Error

The maximum error for any output voltage of the D/A converter, given a 5V full-scale input voltage and an accuracy of \( \pm 0.2\% \), is \( 10 \, \text{mV} \). This means that the actual output voltage produced by this D/A converter could be up to 10 mV higher or 10 mV lower than its ideal or intended value at any point.