ADC and DAC Fundamentals

Modified: Mar. 14, 2026

Published: Mar. 8, 2026

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The physical world is analog: temperature varies continuously, light intensity has infinite gradations, and sound is a smooth pressure wave. But your microcontroller processes discrete digital numbers. ADCs (Analog-to-Digital Converters) translate the analog world into numbers your code can work with, and DACs (Digital-to-Analog Converters) translate numbers back into analog voltages. Understanding how these conversions work helps you choose the right resolution, sample rate, and filtering for your application. #ADC #DAC #SignalConversion

ADC Fundamentals

What an ADC Does

An ADC takes a continuous analog voltage and produces a discrete digital number that represents that voltage. The process involves two steps:

1. Sampling: capturing the analog voltage at a specific instant in time
2. Quantization: mapping the captured voltage to the nearest digital value

Resolution

Resolution is the number of bits in the ADC’s output. It determines how finely the analog range is divided.

Least Significant Bit (LSB) Voltage

The LSB voltage is the smallest voltage change the ADC can detect:

where is the reference voltage and is the resolution in bits.

Example: A 12-bit ADC with :

This ADC can distinguish voltage changes as small as 0.8 mV. Any change smaller than this is lost in quantization.

ADC Transfer Function

The ADC produces a digital code based on the input voltage:

Example: What digital code does a 12-bit ADC (3.3V reference) produce for an input of 1.65V?

To convert back from a digital code to voltage:

In C:

// STM32 12-bit ADC, 3.3V reference
uint16_t adc_value = HAL_ADC_GetValue(&hadc1);
float voltage = (float)adc_value * 3.3f / 4096.0f;

Quantization Error

Because the ADC maps a continuous voltage to discrete levels, there is always a rounding error called quantization error. The maximum quantization error is LSB.

For a 12-bit ADC with 3.3V reference:

This is an inherent limitation. No amount of software can recover the information lost in quantization. If you need finer resolution, you need a higher-resolution ADC.

Other ADC Error Sources

For most embedded applications, the dominant error is noise. Good PCB layout, proper decoupling capacitors, and software averaging significantly improve ADC accuracy.

Successive Approximation ADC (SAR)

How It Works

The SAR ADC is the most common type in microcontrollers. It uses a binary search algorithm to find the digital code closest to the input voltage.

Components:

• A DAC (internal)
• A comparator
• A SAR register (shift register with control logic)
• A sample-and-hold circuit

  SAR ADC block diagram

  Vin ──→[S/H]──→(+)─┐
                      │ Comparator
  Vref ──→[DAC]──→(-)─┘
              ▲           │
              │       ┌───┴────┐
              │       │  SAR   │
              └───────┤Control │
                      │Register│
                      └───┬────┘
                          │
                     Digital Output
                      (n-bit code)

  S/H = sample and hold
  SAR = successive approximation register

Process for a 4-bit SAR ADC (simplified):

1. Sample and hold: The input voltage is captured and held steady on a capacitor.

2. Bit 3 (MSB) test: Set the DAC to 1000 (half of full scale). Compare: is the input greater than the DAC output? If yes, keep bit 3 as 1. If no, set bit 3 to 0.

3. Bit 2 test: Set the DAC to the current result + 0100 (quarter scale). Compare and keep or clear bit 2.

4. Bit 1 test: Set the DAC to the current result + 0010. Compare and keep or clear bit 1.

5. Bit 0 (LSB) test: Set the DAC to the current result + 0001. Compare and keep or clear bit 0.

6. Result: The 4-bit code in the SAR register is the closest digital representation of the input voltage.

Example: Converting 2.1V with a 4-bit ADC, 3.3V reference

Result: 1010 (decimal 10). Voltage: . The error is , which is less than one LSB ().

Why SAR Is Popular in MCUs

A 12-bit SAR ADC needs exactly 12 comparison cycles to produce a result. At a typical 14 MHz ADC clock (STM32F103), each conversion takes about 1 microsecond. This is fast enough for most sensor applications while using relatively little silicon area and power.

Sampling and the Nyquist Theorem

The Sampling Theorem

The Nyquist-Shannon sampling theorem states:

To accurately reconstruct a signal, you must sample at a rate at least twice the highest frequency present in the signal.

The minimum sampling rate () is called the Nyquist rate.

Why This Matters

If you sample too slowly, high-frequency components in the signal fold back as lower frequencies, a phenomenon called aliasing. The aliased signal looks real but is an artifact of insufficient sampling.

Example: You are measuring a 50 Hz power line signal.

• Sampling at 200 Hz: well above Nyquist (2 x 50 = 100 Hz). Signal reconstructed accurately.
• Sampling at 80 Hz: below Nyquist. The 50 Hz signal aliases to appear as a 30 Hz signal (|80 - 50| = 30 Hz). Your measurement shows a wrong frequency.

Anti-Aliasing Filter

Before the ADC, an analog low-pass filter removes frequencies above . This prevents aliasing. A simple RC filter works for many embedded applications:

Example: For a 1 kHz ADC sample rate, the anti-aliasing filter should cut off below 500 Hz. With a 10K resistor: . A 33 nF capacitor would work.

Practical Sampling Rates

DAC: Digital-to-Analog Converter

What a DAC Does

A DAC takes a digital number and produces a proportional analog voltage:

R-2R Ladder DAC

The simplest DAC architecture uses only two resistor values: R and 2R. This makes it inexpensive and easy to build from discrete components.

4-bit R-2R ladder:

  R-2R ladder DAC (4-bit)

  D3       D2       D1       D0
  │        │        │        │
 [2R]     [2R]     [2R]     [2R]
  │        │        │        │
  ├──[R]───├──[R]───├──[R]───├──[2R]─→GND
  │
  └──→ Vout (to op-amp buffer)

  D3 contributes Vref/2
  D2 contributes Vref/4
  D1 contributes Vref/8
  D0 contributes Vref/16

Each digital input (D0-D3) connects to either VCC (for a 1) or GND (for a 0). The resistor network creates a weighted sum of the inputs. D3 (MSB) contributes twice as much voltage as D2, which contributes twice as much as D1, and so on.

How it works conceptually:

For a 4-bit DAC with and code = 1010 (decimal 10):

DACs in Microcontrollers

Not all MCUs have a built-in DAC. The STM32F103 does not have one, but the STM32F4 and STM32F7 families have 12-bit DACs. The ESP32 has two 8-bit DACs.

PWM as a Pseudo-DAC

Concept

If your MCU does not have a hardware DAC, you can approximate an analog output using PWM (Pulse Width Modulation) combined with a low-pass filter.

A PWM signal switches between 0V and VCC at a fixed frequency. The duty cycle determines the average voltage:

Filtering PWM to Analog

A raw PWM signal is a square wave. To get a smooth analog voltage, pass it through an RC low-pass filter:

MCU PWM Pin ──[R]──┬──→ Analog Output
                    │
                   [C]
                    │
                   GND

Choose the filter cutoff frequency well below the PWM frequency:

• PWM frequency: 20 kHz (typical for LED dimming or audio)
• Filter cutoff: 200 Hz ( of PWM frequency)
• Calculation: , (use 100 nF)

The lower the cutoff relative to the PWM frequency, the smoother the output, but the slower the response to changes in duty cycle.

PWM Resolution

The effective resolution of PWM-as-DAC depends on the timer resolution and frequency:

Example: STM32F103 at 72 MHz, PWM frequency 20 kHz:

That is about 11.8 bits of resolution (), which is comparable to a 12-bit DAC. Increasing the PWM frequency reduces the number of steps (and resolution). Decreasing it gives more steps but requires a slower filter.

Practical Exercises

Exercise 1: ADC Voltage Calculation

Your STM32 has a 12-bit ADC with a 3.3V reference. The ADC reads a value of 2730. What is the input voltage?

float voltage = 2730.0f * 3.3f / 4096.0f;  // 2.199V

Exercise 2: Resolution Comparison

You need to measure a 0 to 5V signal with a precision of at least 5 mV. What is the minimum ADC resolution required?

Exercise 3: Sampling Rate

You are measuring vibration on a motor. The vibration frequency range is 10 Hz to 2 kHz. What is the minimum sampling rate? What rate would you choose in practice?

Exercise 4: PWM DAC Design

You want to generate a 0 to 3.3V analog signal using PWM on an ATmega328P running at 16 MHz. Using an 8-bit timer (256 levels), what is the PWM frequency? How many voltage levels can you produce?

How This Connects to Embedded Programming

Summary

In the next and final lesson, you will see how all of these building blocks (logic gates, memory, buses, ADC) come together inside a microcontroller CPU.