15.1 Why we need ADCs
Almost every quantity we want to measure — temperature, voltage, pressure, microphone audio — is analog. The world is continuous. But the CPU we want to feed those signals into is digital — it understands only finite-precision numbers. An A/D Converter (ADC) is the bridge: it takes a continuous voltage at its input and produces an integer at its output.
Two operations happen inside every ADC, often interleaved:
- Sampling — taking snapshots of the analog input at fixed time intervals.
- Quantization & encoding — mapping each snapshot's voltage to one of
2^Ndiscrete codes and outputting the binary code.
15.2 Quantization
Divide the input range [V_min, V_max] into 2^N equal steps, each of width
Q = (V_max − V_min) / 2^NQ is called the quantum or LSB voltage. Any sample that falls inside step k gets the code k.
Quantization error
ε_q ∈ [−Q/2, +Q/2]That is the best-case error of any ADC. You cannot do better than ±½ LSB without using more bits.
Resolution table
| N (bits) | Codes (2^N) | Resolution (5 V FSR) | Typical use |
|---|---|---|---|
| 8 | 256 | 19.5 mV | Cheap MCU peripherals |
| 10 | 1024 | 4.88 mV | Most micro ADCs |
| 12 | 4096 | 1.22 mV | High-end MCUs |
| 16 | 65 536 | 76 µV | Audio, instrumentation |
| 24 | 16 777 216 | 0.30 µV | Lab-grade DMM / weigh scales |
15.3 Encoding — the output representation
| Encoding | Use |
|---|---|
| Straight binary | Most general-purpose ADCs (0 → 0000…, FSR → 1111…) |
| Offset binary | Bipolar inputs (midpoint = 1000…0) |
| Two's complement | Bipolar inputs that feed directly into a CPU adder |
| Sign-magnitude | Some audio codecs |
| Gray code | Some ADC internals (avoids decoder glitches before retiming) |
15.4 The four ADC architectures in this unit
| ADC | Speed | Resolution | Cost | Where you see it |
|---|---|---|---|---|
| Flash (parallel comparator) | Highest (Gsps) | Low (≤ 8 b) | Highest | Oscilloscopes, radar, gigabit ethernet |
| Successive approximation (SAR) | Medium (Msps) | Medium (8–18 b) | Low | Microcontroller peripherals, data acquisition |
| Counting / dual-slope | Low (Hz–kHz) | High (12–24 b) | Very low | Multimeters, voltage panel meters |
| Voltage-to-frequency / time | Low | High | Very low | Isolation barriers, integrating front ends |
15.5 The flash (parallel comparator) ADC
For N output bits, the flash ADC needs:
- 2^N equal resistors forming a voltage divider.
- 2^N − 1 comparators, each comparing V_in against one tap.
- A priority encoder to turn the thermometer code into binary.
How it works in one clock cycle
- The ladder produces 2^N − 1 reference voltages
(k+0.5)·Qfor k = 0…2^N − 2. - Every comparator simultaneously says "V_in > ref_k ?" → outputs 1 or 0.
- The resulting pattern is a thermometer code — all 1s below some threshold, all 0s above.
- The priority encoder reports the highest k that is still 1 → binary output.
Because everything happens in parallel, one clock cycle is enough.
Thermometer-to-binary mapping (3-bit example)
| V_in zone | Thermometer (C6..C0) | Priority encoder output |
|---|---|---|
| 0 ≤ V_in < Q | 0000000 | 000 |
| Q ≤ V_in < 2Q | 0000001 | 001 |
| 2Q ≤ V_in < 3Q | 0000011 | 010 |
| 3Q ≤ V_in < 4Q | 0000111 | 011 |
| 4Q ≤ V_in < 5Q | 0001111 | 100 |
| 5Q ≤ V_in < 6Q | 0011111 | 101 |
| 6Q ≤ V_in < 7Q | 0111111 | 110 |
| 7Q ≤ V_in | 1111111 | 111 |
Strengths and weaknesses
| Pros | Cons |
|---|---|
| Single-cycle conversion — fastest possible | 2^N − 1 comparators → area/power explode |
| Pipeline-friendly | Comparator offset → DNL/INL errors |
| No internal clock for the conversion itself | Huge input capacitance (one comparator gate × 2^N) |
This is why flash ADCs are pretty much always ≤ 8 bits.
15.6 Worked example — design a 3-bit flash ADC for 0–5 V
- FSR = 5 V, N = 3 → 8 codes, Q = 5 V / 8 = 0.625 V.
- Reference tap voltages: 0.3125 V, 0.9375 V, 1.5625 V, 2.1875 V, 2.8125 V, 3.4375 V, 4.0625 V.
- Components: 8 equal resistors (e.g. 1 kΩ) between V_ref and GND, 7 comparators (LM339 dies), 8-to-3 priority encoder (74LS148).
The total propagation delay is just t_comparator + t_encoder — typically under 50 ns even with garden-variety comparators.