Part 2: Understanding Sensors

Transducers vs Sensors

The terms “sensor” and “transducer” are often used interchangeably, but they have distinct technical meanings. A transducer converts energy from one form to another. A sensor is a transducer that converts a physical phenomenon into an electrical signal for measurement.

Sensor Classification

Sensors can be classified along multiple axes depending on the application context:

graph TD
    S["🔍 Sensor Classifications"] --> M["By Measurand"]
    S --> O["By Output"]
    S --> P["By Power Source"]
    S --> C["By Contact"]
    S --> T["By Technology"]
    M --> M1["Temperature"]
    M --> M2["Pressure"]
    M --> M3["Light"]
    M --> M4["Motion"]
    M --> M5["Chemical"]
    O --> O1["Analog
Continuous"]
    O --> O2["Digital
Discrete"]
    P --> P1["Active
Self-generating"]
    P --> P2["Passive
Needs excitation"]
    C --> C1["Contact"]
    C --> C2["Non-contact"]
    T --> T1["Resistive"]
    T --> T2["Capacitive"]
    T --> T3["Inductive"]
    T --> T4["Piezoelectric"]
    T --> T5["Optical"]
    style S fill:#3B9797,stroke:#3B9797,color:#fff
    style M fill:#e8f4f4,stroke:#3B9797,color:#132440
    style O fill:#e8f4f4,stroke:#3B9797,color:#132440
    style P fill:#e8f4f4,stroke:#3B9797,color:#132440
    style C fill:#e8f4f4,stroke:#3B9797,color:#132440
    style T fill:#e8f4f4,stroke:#3B9797,color:#132440
                            

Active vs Passive Sensors

Analog vs Digital Signals

Analog Signal Characteristics

Analog signals are continuous in both time and amplitude. They represent physical quantities as proportional voltages or currents. A temperature sensor might output 0–3.3V corresponding to 0–100°C.

Digital Signal Characteristics

Digital sensors output data in discrete formats — serial protocols (I2C, SPI, UART), pulse trains, or simple on/off states. They internally handle ADC conversion and often include calibration data in on-chip memory.

ADC Conversion Basics

An Analog-to-Digital Converter (ADC) samples a continuous voltage and quantizes it into a discrete digital value. The key parameters are:

For an $n$-bit ADC with reference voltage $V_{ref}$:

$$\text{Resolution} = \frac{V_{ref}}{2^n - 1}$$

$$V_{measured} = \text{ADC\_value} \times \frac{V_{ref}}{2^n - 1}$$

A 12-bit ADC with 3.3V reference has a resolution of $\frac{3.3}{4095} \approx 0.806 \text{ mV}$ per step.

// Reading an analog sensor with STM32 ADC
#include "stm32f4xx.h"

void adc_init(void) {
    // Enable clocks
    RCC->AHB1ENR |= RCC_AHB1ENR_GPIOAEN;
    RCC->APB2ENR |= RCC_APB2ENR_ADC1EN;

    // PA0 as analog input
    GPIOA->MODER |= (3U << (0 * 2));   // Analog mode (11)

    // ADC1 configuration
    ADC1->CR1  = 0;                     // 12-bit resolution
    ADC1->CR2  = 0;
    ADC1->SQR3 = 0;                     // Channel 0 (PA0)
    ADC1->SMPR2 = (7U << 0);           // 480 cycles sample time

    ADC1->CR2 |= ADC_CR2_ADON;         // Enable ADC
}

uint16_t adc_read(void) {
    ADC1->CR2 |= ADC_CR2_SWSTART;      // Start conversion
    while (!(ADC1->SR & ADC_SR_EOC));   // Wait for completion
    return (uint16_t)ADC1->DR;          // Read result (0-4095)
}

float adc_to_voltage(uint16_t raw) {
    return raw * (3.3f / 4095.0f);      // Convert to voltage
}

float voltage_to_temp_lm35(float voltage) {
    return voltage * 100.0f;            // LM35: 10 mV/°C
}

Sensor Characteristics

Selecting the right sensor requires understanding its static and dynamic characteristics. These describe how accurately, precisely, and quickly a sensor responds to changes.

Static Characteristics

Dynamic Characteristics

For a first-order sensor with time constant $\tau$, the step response is:

$$y(t) = y_{final} \left(1 - e^{-t/\tau}\right)$$

Error Sources

Signal Types & Outputs

Voltage Output

The simplest sensor output is a proportional voltage. Common ranges include 0–5V, 0–3.3V, and ±10V for industrial sensors.

// Voltage divider sensor reading (thermistor)
#include <stdio.h>
#include <math.h>

// Steinhart-Hart equation for NTC thermistor
float thermistor_to_temp(uint16_t adc_raw) {
    float R_fixed = 10000.0f;         // 10k reference resistor
    float V_ref = 3.3f;
    float V_adc = adc_raw * (V_ref / 4095.0f);

    // Calculate thermistor resistance
    float R_therm = R_fixed * (V_ref / V_adc - 1.0f);

    // Steinhart-Hart coefficients (for 10k NTC)
    float A = 1.009249e-3f;
    float B = 2.378405e-4f;
    float C = 2.019202e-7f;
    float ln_R = logf(R_therm);

    float T_kelvin = 1.0f / (A + B * ln_R + C * ln_R * ln_R * ln_R);
    return T_kelvin - 273.15f;        // Convert to Celsius
}

Current Loop (4–20 mA)

Industrial sensors often use 4–20 mA current loops because current signals are immune to voltage drops over long cable runs. The 4 mA baseline also enables broken-wire detection — if the current drops to 0 mA, the wire is broken.

The conversion from current to measured value:

$$\text{Value} = \text{Range}_{min} + \frac{(I - 4\text{ mA})}{16\text{ mA}} \times (\text{Range}_{max} - \text{Range}_{min})$$

Frequency & Pulse Output

Some sensors output a frequency or pulse train proportional to the measured quantity. Examples include flow meters (pulses per liter) and optical encoders (pulses per revolution).

// Timer Input Capture: Measure sensor frequency
#include "stm32f4xx.h"

volatile uint32_t capture_value = 0;
volatile uint32_t frequency_hz = 0;

void TIM3_IRQHandler(void) {
    if (TIM3->SR & TIM_SR_CC1IF) {
        TIM3->SR &= ~TIM_SR_CC1IF;

        uint32_t current = TIM3->CCR1;
        if (current > 0) {
            // Timer clock = 1 MHz (after prescaler)
            frequency_hz = 1000000 / current;
        }
    }
}

void input_capture_init(void) {
    RCC->APB1ENR |= RCC_APB1ENR_TIM3EN;
    RCC->AHB1ENR |= RCC_AHB1ENR_GPIOAEN;

    // PA6 = TIM3_CH1 (AF2)
    GPIOA->MODER  |= (2U << 12);
    GPIOA->AFR[0] |= (2U << 24);

    TIM3->PSC   = 84 - 1;           // 1 MHz timer clock
    TIM3->ARR   = 0xFFFF;
    TIM3->CCMR1 = TIM_CCMR1_CC1S_0; // Input capture on TI1
    TIM3->CCER  = TIM_CCER_CC1E;     // Enable capture
    TIM3->DIER  = TIM_DIER_CC1IE;    // Interrupt on capture

    NVIC_EnableIRQ(TIM3_IRQn);
    TIM3->CR1 |= TIM_CR1_CEN;
}

Sensor Interfacing Basics

Reading Analog Sensors

Analog sensors connect to ADC input pins. The interface typically involves a voltage divider or signal conditioning circuit to match the sensor output range to the ADC input range.

#!/usr/bin/env python3
"""Read analog sensor via MCP3008 ADC on Raspberry Pi"""

import spidev
import time

# Initialize SPI for MCP3008
spi = spidev.SpiDev()
spi.open(0, 0)          # Bus 0, Device 0
spi.max_speed_hz = 1350000

def read_adc(channel):
    """Read a single ADC channel (0-7) from MCP3008"""
    if channel < 0 or channel > 7:
        return -1
    # MCP3008 SPI protocol: start bit, single/diff, channel
    cmd = [1, (8 + channel) << 4, 0]
    result = spi.xfer2(cmd)
    value = ((result[1] & 3) << 8) | result[2]
    return value  # 10-bit: 0-1023

# Read temperature from LM35 on channel 0
for i in range(10):
    raw = read_adc(0)
    voltage = raw * (3.3 / 1023.0)
    temp_c = voltage * 100.0
    print(f"Reading {i+1}: ADC={raw}, V={voltage:.3f}V, Temp={temp_c:.1f}°C")
    time.sleep(1)

spi.close()

Reading Digital Sensors

#!/usr/bin/env python3
"""Read BME280 digital sensor via I2C on Raspberry Pi"""

import smbus2
import time

BME280_ADDR = 0x76
bus = smbus2.SMBus(1)

# Read chip ID (should be 0x60 for BME280)
chip_id = bus.read_byte_data(BME280_ADDR, 0xD0)
print(f"BME280 Chip ID: 0x{chip_id:02X}")

# Configure: forced mode, 1x oversampling
bus.write_byte_data(BME280_ADDR, 0xF2, 0x01)  # Humidity OS x1
bus.write_byte_data(BME280_ADDR, 0xF4, 0x27)  # Temp/Press OS x1, Normal mode

time.sleep(0.1)

# Read raw temperature (20-bit)
data = bus.read_i2c_block_data(BME280_ADDR, 0xFA, 3)
raw_temp = (data[0] << 12) | (data[1] << 4) | (data[2] >> 4)
print(f"Raw temperature: {raw_temp}")

# Read raw pressure (20-bit)
data = bus.read_i2c_block_data(BME280_ADDR, 0xF7, 3)
raw_press = (data[0] << 12) | (data[1] << 4) | (data[2] >> 4)
print(f"Raw pressure: {raw_press}")

bus.close()

Conclusion & Next Steps

You now understand the fundamental concepts behind sensors — the difference between transducers, active and passive sensors, analog vs digital signals, and the key characteristics that determine sensor suitability for any application.

In Part 3, we explore Sensor Categories — a comprehensive survey of temperature, pressure, proximity, motion, light, environmental, position, and biomedical sensors with interfacing guides for each.