Question

What is the formula for Digital-to-Analog Converter?

Answer 1

A Digital-to-Analog Converter (DAC) converts a digital (binary) signal into an analog signal (usually voltage or current). The formula for the output voltage of an **N-bit DAC** is given by:

\[
V_{out} = \left(\frac{D}{2^N}\right) \times V_{ref}
\]

Where:
- **\( V_{out} \)** is the output analog voltage.
- **\( D \)** is the decimal equivalent of the digital input code (which can range from 0 to \( 2^N - 1 \)).
- **\( N \)** is the number of bits in the DAC.
- **\( V_{ref} \)** is the reference voltage (maximum output voltage).

### Example
For a 3-bit DAC with a reference voltage of 5V:
- The digital input **D** can range from 0 (000 in binary) to 7 (111 in binary).
- The number of levels will be \( 2^3 = 8 \) levels.

If the input is **D = 5** (which is 101 in binary):
\[
V_{out} = \left(\frac{5}{2^3}\right) \times 5V = \left(\frac{5}{8}\right) \times 5V = 3.125V
\]

This gives an output of 3.125V for the digital input "101".

The DAC resolution is also important, as it determines the smallest step in voltage that the DAC can produce. The resolution is given by:
\[
\text{Resolution} = \frac{V_{ref}}{2^N}
\]

Answer 2

The **Digital-to-Analog Converter (DAC)** converts a digital signal into its corresponding analog voltage or current. The formula for a DAC output depends on the resolution (number of bits) and reference voltage (maximum output voltage). Here's a general formula for the output of an **n-bit DAC**:

\[
V_{out} = V_{ref} \times \frac{D}{2^n}
\]

Where:
- \( V_{out} \) = Output analog voltage
- \( V_{ref} \) = Reference voltage (maximum output voltage)
- \( D \) = Digital input code (binary number)
- \( n \) = Number of bits of the DAC

### Explanation:
- The digital input \( D \) is a binary number that ranges from 0 to \( 2^n - 1 \), where \( n \) is the number of bits in the DAC.
- The formula calculates the proportion of the reference voltage that corresponds to the digital input.

### Example:
For a 3-bit DAC with a reference voltage \( V_{ref} = 5V \), the number of possible digital values is \( 2^3 = 8 \) (ranging from 0 to 7). If the digital input is \( D = 3 \), the output voltage would be:

\[
V_{out} = 5V \times \frac{3}{2^3} = 5V \times \frac{3}{8} = 1.875V
\]

Thus, the output analog voltage for the digital input "3" is 1.875V.