DE Notes
Complete guide to ADC: successive approximation ADC, flash ADC, sigma-delta ADC, resolution, sampling rate, quantization error, and GATE-level conversion calculations.
What is an ADC?
An ADC (Analog-to-Digital Converter) converts a continuous analog signal (voltage) into a discrete digital code.
Key parameters:
- Resolution (n): Number of output bits. An n-bit ADC has 2ⁿ quantization levels.
- Step size (Q): Q = V_FS / (2ⁿ - 1) where V_FS = full-scale voltage
- Conversion time: Time to complete one A-to-D conversion
- Sampling rate: Number of conversions per second (samples/sec)
Successive Approximation ADC (SAR)
Most common ADC type — used in microcontrollers (Arduino, STM32).
Algorithm: Binary search — tests bits from MSB to LSB.
| Step 1: Try MSB=1 | DAC output = 8V → 7.2 < 8 → MSB=0 |
| Step 2: Try next=1 | DAC output = 4V → 7.2 > 4 → bit=1 |
| Step 3: Try next=1 | DAC output = 6V → 7.2 > 6 → bit=1 |
| Step 4: Try next=1 | DAC output = 7V → 7.2 > 7 → bit=1 |
| Result | 0111 = 7 (closest below 7.2) ✓ |
| Conversion time | n clock cycles for n-bit SAR |
Advantages: Good balance of speed and accuracy, low power Used in: Microcontroller ADCs (10-12 bit, 100ksps–1Msps)
Flash ADC (Parallel ADC)
Fastest ADC type — converts in single clock cycle.
Uses 2ⁿ - 1 comparators, all operating simultaneously.
Conversion time: Single clock cycle Hardware: 2ⁿ - 1 comparators (8-bit = 255 comparators, 10-bit = 1023!) Used in: Oscilloscopes, video ADCs, very high-speed applications
Nyquist Sampling Theorem
To accurately reconstruct an analog signal from digital samples:
Example: Audio signal goes up to 20 kHz. Minimum sampling rate = 40 kHz. CD audio uses 44.1 kHz.
ADC Types Comparison
| ADC Type | Speed | Resolution | Complexity | Application |
|---|---|---|---|---|
| Flash | Fastest | Low (4-8 bit) | Very high | Oscilloscopes |
| SAR | Medium | Medium (8-16 bit) | Medium | MCUs, data acquisition |
| Sigma-Delta | Slow | Highest (16-24 bit) | High | Audio, precision measurement |
| Dual-slope | Slow | High | Low | Multimeters |
Numericals
Q1: A 10-bit ADC has a full-scale range of 0–5V. Find: (a) number of levels, (b) step size, (c) output code for 3.3V input.
Q2: An SAR ADC has n=4 bits, Vref=16V. Input = 11V. Trace the conversion.
| Step 1: D=1000 | DAC=8V → 11>8 → D3=1 |
| Step 2: D=1100 | DAC=12V → 11<12 → D2=0 |
| Step 3: D=1010 | DAC=10V → 11>10 → D1=1 |
| Step 4: D=1011 | DAC=11V → 11≥11 → D0=1 |
| Result | 1011 = 11 ✓ |
Interview Questions
Q1: What is the difference between resolution and accuracy in an ADC? Resolution is the number of discrete output levels (determined by bit count). Accuracy is how close the output is to the true value. A high-resolution ADC can still be inaccurate due to offset errors, gain errors, or noise. Resolution is a design parameter; accuracy depends on implementation quality.
Q2: Why is flash ADC the fastest but not commonly used for high-resolution? Flash ADC uses 2ⁿ-1 comparators. For 8-bit: 255 comparators — manageable. For 12-bit: 4095 comparators — impractical in terms of chip area, power, and input capacitance loading. High-speed applications use 6-8 bit flash ADCs and combine multiple stages (pipeline ADC).
Q3: What is quantization noise? Quantization noise is the error introduced by representing a continuous signal with discrete levels. The maximum quantization error is ±1/2 LSB. It appears as added noise to the digitized signal. Higher bit-count ADCs have smaller step sizes and lower quantization noise.
Exam Focus
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