ADC · DAC · LEARNING LAB

ANALOG ↔ DIGITAL CONVERSION · INTERACTIVE INSTRUMENT SIMULATOR · MORAINE VALLEY COMMUNITY COLLEGE

SYSTEM READY

ADC Resolution

Levels: 1024 | Max code: 1023

Analog Voltage Range

Full-scale: 24 V

Analog Input Voltage

INPUT: -12 V → +12 V

-12 V+12 V

VOLTS

── CH1 ANALOG INPUT ── CH2 QUANTIZED

Digital Value (Dec)

—

Integer code

Hex Value

—

Base 16

Octal Value

—

Base 8

Step Size (LSB)

—

V per count

Quant. Error

—

±½ LSB max

% Full Scale

—

Input position

BINARY WORD — 10-BIT OUTPUT ▲ MSB ▲ LSB

Conversion History

#	Analog (V)	Decimal	Hex	Binary	LSB (mV)

DAC Resolution

Levels: 1024 | Max code: 1023

Output Voltage Range

Digital Input Code (Decimal)

CODE: 0 → 1023

01023

DEC

HEX CODE INPUT

── CH1 ANALOG OUTPUT (STAIRCASE) - - IDEAL ENVELOPE

Analog Output (V)

—

Reconstructed voltage

Decimal Code

—

Input code

Hex Code

—

Base 16

Binary Word

—

Bit pattern

Step Size (LSB)

—

mV per code

% Full Scale

—

Code utilization

BINARY WORD — 10-BIT INPUT

DAC History

#	Dec Code	Hex	Analog Out (V)	% FS

🔌 What is an ADC?

An Analog-to-Digital Converter (ADC) samples a continuous analog voltage and converts it to a discrete binary number. Every ADC performs two core operations:

Sampling — capturing the signal at uniform time intervals (must satisfy Nyquist: f_s ≥ 2f_max)
Quantization — mapping the sample to the nearest of 2ᴺ discrete voltage levels

Higher bit depth = more levels = finer resolution = less quantization error. Each added bit improves dynamic range by ~6 dB and halves the step size.

Digital Code = floor[ (V_in − V_min) / (V_max − V_min) × (2ᴺ − 1) ]
Step Size (LSB) = (V_max − V_min) / (2ᴺ − 1)
Max Quant. Error = ±½ × LSB
Dynamic Range ≈ 6.02 × N + 1.76 dB

Live Formula — Current ADC Settings

Step Size = 24 V ÷ 1023 = 23.46 mV

Max Error = ±11.73 mV

Dyn. Range = 62.0 dB

🔊 What is a DAC?

A Digital-to-Analog Converter (DAC) reconstructs a continuous voltage from a binary code. DACs are essential in audio playback, motor control, RF signal generation, and industrial process control.

R-2R Ladder — uses a precision resistor network; low cost, widely used
Weighted Resistor — each bit drives a differently weighted resistor
Delta-Sigma (ΔΣ) — oversampling + noise shaping for 16–24 bit audio
PWM-based — pulse width modulated output + low-pass filter

V_out = V_min + Code × [(V_max − V_min) / (2ᴺ − 1)]
Resolution = (V_max − V_min) / (2ᴺ − 1)
% Full Scale = (Code / (2ᴺ − 1)) × 100

The characteristic staircase waveform of a DAC output is smoothed by a reconstruction (low-pass) filter to recover the original continuous signal.

📊 Resolution Comparison Table

Bits	Levels	LSB @ 5V	LSB @ 24V	Dyn Range
8	256	19.6 mV	94.1 mV	49.9 dB
10	1,024	4.89 mV	23.5 mV	61.9 dB
12	4,096	1.22 mV	5.86 mV	73.9 dB
16	65,536	76 µV	366 µV	97.8 dB

Each additional bit doubles resolution and adds ~6 dB of dynamic range. Choosing bit depth is a trade-off between precision, speed, power, and cost.

Bipolar ranges (e.g., ±12V) require offset encoding; unipolar ranges (e.g., 0–5V) use straight binary coding.

🎓 Learning Competencies

Upon completing this module, students will be able to:

Explain the difference between analog and digital signals and why conversion is necessary in modern systems
Calculate the number of quantization levels for any N-bit ADC/DAC (2ᴺ levels)
Apply the ADC conversion formula to map a voltage to its correct digital code
Calculate step size (LSB) and maximum quantization error for any given configuration
Explain the trade-off between bit resolution, conversion speed, power, and cost
Describe flash, successive approximation (SAR), and delta-sigma ADC architectures
Perform DAC reconstruction and calculate the expected analog output voltage from a code
Interpret binary, hexadecimal, octal, and decimal representations of converter codes
Analyze the effect of bipolar vs. unipolar voltage ranges on code mapping
Apply Nyquist's theorem to determine minimum sampling rates for given signals

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