Lesson 20 Flashcards — Analog-to-Digital Conversion

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1. Name the three stages of analog-to-digital conversion.

Sample (discretize in time), quantize (discretize in value), and encode (express as a binary number).

2. What is a transducer?

A device converting a physical quantity into an electrical signal — a thermometer, accelerometer, or microphone, and the distance sensor you will calibrate in Lesson 22.

3. State the Nyquist criterion.

\(f_s \geq 2f_\text{high}\) — you must sample at least twice the highest frequency present; sampling exactly at the Nyquist rate counts. \(2f_\text{high}\) is the floor, not a target.

4. What is aliasing, and can it be fixed afterward?

A high frequency masquerading as a low one because sampling was too slow. It cannot be fixed — once the samples are taken the information is gone. The only cure is filtering before sampling.

5. Where have you seen aliasing outside a circuits class?

Wheels that appear to spin backward on film or video. A frame rate is a sampling rate, and it sits below twice the spoke frequency.

6. How many levels does a b-bit ADC have, and what is its resolution?

\(\text{levels} = 2^b\) and \(\Delta V = (V_\text{max}-V_\text{min})/\text{levels}\). Objective 2.7 uses the same relation for truth-table rows, writing the exponent \(n\).

7. What is quantization error, and how large can it get?

The error from truncating a continuous input down onto the level below it: \(QE = V_\text{in} - V_\text{quant}\) with \(V_\text{quant} = QL\,\Delta V + V_\text{min}\). At worst it is a full step, \(QE_\text{max} = \Delta V\). Unlike noise it is permanent — the price paid for digital robustness.

8. How do you compute the digital output for a given input voltage?

Expected level \(EL = (V_\text{in}-V_\text{min})/\Delta V\), then quantized level \(QL = \lfloor EL \rfloor\) — truncate, never round. Watch a negative \(V_\text{min}\) — forgetting it is the most common error.

9. A 12-bit ADC spans 0 to 3.3 V. What is its resolution?

\(2^{12} = 4096\) levels, so \(\Delta V = 3.3/4096 = 0.806\ \text{mV}\).

10. How do you compute the memory needed for a recording?

\(\text{bits} = b \times f_s \times t\), times the number of channels. Divide by 8 for bytes — and say which prefix you mean: \(1\ \text{kB} = 1000\ \text{B}\) (decimal), while the equation sheet's \(1\ \text{kiB} = 2^{10}\ \text{B}\) (binary).

11. An ADC spanning 0 to 5 V must hold quantization error under 10 mV. How many bits?

Since \(QE_\text{max} = \Delta V\), the spec is really on \(\Delta V\): \(2^b \geq (5-0)/0.010 = 500\), so \(b = \lceil \log_2 500 \rceil = 9\) bits — round up, because there is no partial bit and \(b = 8\) would give \(\Delta V = 19.5\ \text{mV}\), worse than the spec. With 9 bits, \(\Delta V = 5/512 = 9.77\ \text{mV}\).

12. What happens to an input outside the ADC's range?

It saturates at the extreme code — that is clipping, and it is Objective 2.6's problem.