Instrumentation and DAQ

Why it matters

Every physics result starts as a voltage in an instrument. Data acquisitionThe chain that turns a physical quantity into numbers in a file: sensor, conditioning, ADC, timing and storage. (DAQ) is the chain that turns a physical quantity (temperature, acceleration, light, charge) into numbers in a file. Physicists design, calibrateTo compare an instrument against a known reference so its offset and scale errors can be corrected. and debug these chains constantly, and many analysis problems are really acquisition problems: the wrong sample rate, a missing timestamp, an uncalibrated sensor.

The DAQ chain

1. Sensor or transducer: converts the quantity into an electrical signal. Examples: a thermistor (resistance changes with temperature), a photodiode (current from light), a MEMS accelerometer (capacitance changes with acceleration), a photomultiplier (charge pulses from single photons).
2. Signal conditioning: amplifiers, filters and dividers that bring the signal into the converter's range and remove noise. An anti-aliasing low-pass filterA filter before the ADC that removes frequencies too high for the sample rate to capture correctly. removes frequencies the converter can't sample correctly.
3. Analog-to-digital converterA device that samples a voltage at fixed times and rounds it to an integer count. (ADC): samples the voltage at fixed times and rounds it to an integer.
4. Timing and storage: a clock stamps every sample; software writes the data with its metadata.

Resolution

An n-bit ADC splits its input range into 2^n steps.

step size = V_range / 2^n
10-bit, 0-5 V:   5 / 1024  = 4.9 mV per count
12-bit, 0-3.3 V: 3.3 / 4096 = 0.81 mV per count
16-bit, +/-10 V: 20 / 65536 = 0.31 mV per count

A reading of 512 counts on a 10-bit, 5 V ADC is 512 * 5 / 1024 = 2.50 V. Resolution is not accuracy: an ADC with tiny steps can still be offset or noisy, which is why you calibrate against a known reference.

Sampling rate and aliasing

The Nyquist criterionThe rule that you must sample faster than twice the highest frequency in the signal to avoid aliasing. says you must sample faster than twice the highest frequency in the signal. A 60 Hz signal sampled at 100 samples per second does not just look rough, it masquerades as a 40 Hz signal (100 - 60). Once aliased, no software can undo it, so you filter before the ADC and choose a sample rate well above twice the frequencies you care about (five to ten times is common).

Noise and averaging

Random noise shrinks when you average: the standard error of N independent readings is sigma / sqrt(N). Averaging does nothing for systematic errors, such as a sensor that reads 0.2 °C high; only calibration fixes those.

Phones and microcontrollers as DAQ

• Smartphone sensors are real MEMS instruments. The free phyphox app, from RWTH Aachen University (https://phyphox.org), records the accelerometer, gyroscope, magnetometer, light sensor and microphone and exports CSV files.
• Microcontrollers such as Arduino boards read sensors through built-in ADCs (analogRead returns 0 to 1023 on a 10-bit, 5 V Uno) and send data over USB serial. The free Wokwi browser simulator (https://wokwi.com) runs Arduino code with virtual sensors and potentiometers, so you can practise without hardware.

A minimal Arduino logger looks like this:

void setup() { Serial.begin(115200); }
void loop() {
  int counts = analogRead(A0);             // 0..1023
  float volts = counts * 5.0 / 1023.0;
  Serial.print(millis()); Serial.print(",");
  Serial.println(volts, 3);
  delay(10);                               // about 100 samples per second
}

Good data habits

• Record timestamps with every sample, not just a sample count.
• Save metadata: sensor model, settings, sample rate, units, date, who and where.
• Keep raw data untouched; write processed data to new files.
• Use plain, documented formats (CSV for small data, HDF5 for large arrays).

Real labs

Lab DAQ hardware, high-voltage detector supplies, lasers and cryogenics need institutional training and supervision. At home, stick to phones, simulators and battery-powered kits.

Common mistakes

• Sampling too slowly and analysing an aliased signal.
• Trusting raw counts without converting units and calibrating.
• Losing timing by assuming a perfectly steady sample rate; phones in particular vary.
• Averaging away a real signal with too long a window.

Recap

• Sensor, conditioning, ADC, timing and storage make up the chain.
• Step size = range / 2^n; resolution is not accuracy.
• Sample faster than twice the highest frequency, and filter first.
• Save timestamps, metadata and raw data.

Try it

Open the Do tab to record accelerometer data with phyphox (or a simulated sensor in Wokwi) and analyse its noise and sample rate.