ADC/DAC Calculator
Calculate resolution and step size for Analog-to-Digital and Digital-to-Analog converters.
Understanding ADC & DAC
ADC (Analog to Digital): Converts a continuous voltage (like from a microphone or temperature sensor) into a binary number.
DAC (Digital to Analog): Converts a binary number back into a voltage (like playing an MP3 file to headphones).
Key Formulas
1. Resolution (Steps)
The "Bit Depth" (n) determines how many discrete levels exist.
Steps = 2n (e.g., 10-bit = 1024 steps)
2. LSB (Least Significant Bit)
This is the smallest voltage change the system can detect or produce.
LSB Voltage = Vref / 2n
3. Dynamic Range (SNR)
The theoretical best Signal-to-Noise Ratio due to quantization noise.
SNR (dB) ≈ (6.02 × n) + 1.76
Practical Applications
- Audio: CD quality is 16-bit (96dB range). Studio quality is 24-bit (144dB range).
- Microcontrollers: Ensure your sensor output matches the ADC range. E.g., reading a 0-1V sensor with a 0-5V ADC wastes 80% of your resolution!
- Instrumentation: High precision voltmeters use 24-bit Delta-Sigma ADCs.
FAQ
What is "Quantization Error"?
Because an ADC has finite steps, there is always a rounding error between the real voltage and the digital value. This error shows up as noise. It is approximately +/- 0.5 LSB.
What is the "Sampling Theorem" (Nyquist)?
To perfectly capture a signal, you must sample it at least twice as fast as its highest frequency component. E.g., Audio goes up to 20kHz, so CDs sample at 44.1kHz.
What is "Aliasing"?
If you violate the Nyquist limit (sample too slow), high frequencies disguised as low frequencies appear in your data. It looks like wagon wheels spinning backward in movies. You need a Low Pass (Anti-Aliasing) filter before the ADC to prevent this.