Tutorial 19: Understanding the NTC Voltage Divider Circuit

Why Does an NTC Need a Voltage Divider?

Microcontrollers like the ESP8266, ESP32, and Pico W can only measure voltage on their ADC (Analog-to-Digital Converter) pins. They cannot measure resistance directly.

An NTC thermistor changes its resistance with temperature. To convert this changing resistance into a measurable voltage, we need a voltage divider circuit.

Simple Explanation:

NTC Thermistor → Changes Resistance → Voltage Divider → Changes Voltage → ADC Reads Voltage → Firmware Calculates Temperature

Without a voltage divider, the ADC would just read 0V or 3.3V with no useful information!

The Voltage Divider Circuit Explained

Here's the correct circuit that OceanRemote uses for NTC thermistors:

                    COMPLETE NTC VOLTAGE DIVIDER CIRCUIT
                    
                         3.3V (Reference Voltage)
                          │
                          ▼
                        ┌───┐
                        │NTC│  ← NTC Thermistor (resistance varies with temperature)
                        └───┘
                          │
                          ├──────► ADC Pin (Voltage measured here)
                          │
                        ┌───┐
                        │R  │  ← Fixed Series Resistor (R_series, typically 10kΩ)
                        │SER│
                        └───┘
                          │
                         GND

            Vout = 3.3V × (R_series) / (R_NTC + R_series)

            Where:
            - Vout = Voltage at ADC pin (0 to 3.3V)
            - R_NTC = Resistance of NTC (changes with temperature)
            - R_series = Fixed resistor value (you choose this)

How It Works Step by Step:

1. Cold Temperature (High Resistance): R_NTC is large (e.g., 100kΩ at -10°C). The voltage divider outputs a low voltage because most voltage drops across the NTC.
2. Room Temperature (Medium Resistance): R_NTC ≈ 10kΩ at 25°C. The voltage divider outputs about 1.65V (half of 3.3V).
3. Hot Temperature (Low Resistance): R_NTC is small (e.g., 1kΩ at 100°C). The voltage divider outputs a high voltage close to 3.3V.

The Math: Calculating Resistance from Voltage

OceanRemote firmware uses this formula to calculate R_NTC from the measured voltage:

From the voltage divider formula:
Vout = 3.3V × (R_series) / (R_NTC + R_series)

Rearrange to solve for R_NTC:
R_NTC = R_series × (3.3V / Vout - 1)

Example calculation:
- 3.3V reference
- R_series = 10,000Ω
- Measured Vout = 1.65V

R_NTC = 10000 × (3.3 / 1.65 - 1)
R_NTC = 10000 × (2 - 1)
R_NTC = 10000 × 1
R_NTC = 10,000Ω  (which matches 25°C, as expected!)

ADC Reading to Voltage Conversion

The ADC doesn't read voltage directly - it reads a digital number (counts). Different boards have different resolutions:

Converting ADC reading to voltage:

For ESP8266 (10-bit):
Voltage = (ADC_reading × 3.3V) / 1023

For ESP32 and Pico W (12-bit):
Voltage = (ADC_reading × 3.3V) / 4095

Example (ESP32 reading 2048):
Voltage = (2048 × 3.3) / 4095 = 1.65V

Choosing the Right Series Resistor (R_series)

The choice of R_series is critical for measurement accuracy. It determines which temperature range gives the best resolution.

The Golden Rule:

For best accuracy, choose R_series equal to the NTC's resistance at the center of your target temperature range.

ADC Resolution: 10-bit vs 12-bit Explained

The number of bits determines how finely the ADC can measure voltage. More bits = better temperature resolution.

ESP8266 (10-bit ADC):

• 1024 possible values (0 to 1023)
• Each step represents about 0.003225V (3.225mV)
• Temperature resolution: approximately 0.25°C to 0.5°C per step
• Good enough for most hobby projects

ESP32 and Pico W (12-bit ADC):

• 4096 possible values (0 to 4095)
• Each step represents about 0.000805V (0.805mV)
• Temperature resolution: approximately 0.06°C to 0.1°C per step
• 4x better resolution than ESP8266

Temperature Resolution Comparison (at 25°C, 10kΩ NTC, 10kΩ R_series):

ESP8266 (10-bit):
- ADC step size: 3.225mV
- Temperature change per step: ~0.35°C
- You'll see temperature changes in ~0.3-0.5°C increments

ESP32 / Pico W (12-bit):
- ADC step size: 0.805mV  
- Temperature change per step: ~0.09°C
- You'll see temperature changes in ~0.1°C increments (much smoother!)

Optimizing Your Voltage Divider for Accuracy

1. Use 1% Precision Resistors

The series resistor's tolerance directly affects accuracy. A 5% carbon resistor can cause ±0.5°C error. Use 1% metal film resistors for better results.

Error Example:
R_series labeled as 10,000Ω but actually 10,500Ω (+5% tolerance)

Actual Vout at 25°C: 3.3V × 10500 / (10000 + 10500) = 1.69V
Expected Vout at 25°C: 1.65V

The 0.04V difference causes ~0.5°C temperature error!

2. Add a Capacitor for Noise Filtering

ADC readings can be noisy, especially with long wires. Add a 0.1μF ceramic capacitor between the ADC pin and GND.

Improved Circuit with Noise Filtering:

    3.3V
     │
     ▼
   ┌───┐
   │NTC│
   └───┘
     │
     ├──────► ADC Pin
     │
   ┌───┐     ┌───┐
   │R  │     │0.1│  ← Capacitor (filters high-frequency noise)
   │SER│     │μF │
   └───┘     └───┘
     │         │
    GND       GND

3. Use Averaging in Firmware

OceanRemote firmware automatically averages 5 ADC readings to reduce noise. This gives more stable temperature readings.

4. Keep Wires Short

Long wires act as antennas and pick up electrical noise. Keep NTC wires under 50cm (20 inches) for best results. For longer runs, use shielded cable.

Common Voltage Divider Mistakes

Calculating Optimal R_series for Your Application

Here's how to calculate the best R_series value for your specific temperature range:

Step 1: Find R_NTC at your minimum temperature (T_min) and maximum temperature (T_max)
         Using the Beta equation: R(T) = R25 × exp(β × (1/T - 1/298.15))

Step 2: Calculate Vout at both extremes:
         Vout_min = 3.3V × R_series / (R_NTC_max + R_series)
         Vout_max = 3.3V × R_series / (R_NTC_min + R_series)

Step 3: Choose R_series so that Vout_min is close to 0V and Vout_max is close to 3.3V
         The optimal R_series is the geometric mean: R_series = √(R_NTC_min × R_NTC_max)

Example for 0°C to 50°C range (NTC β=3950, R25=10kΩ):
- R_NTC at 0°C ≈ 32,000Ω
- R_NTC at 50°C ≈ 3,600Ω
- Optimal R_series = √(32000 × 3600) = √115,200,000 ≈ 10,700Ω

So 10kΩ is very close to optimal!

Testing Your Voltage Divider

Before connecting to your microcontroller, test the voltage divider with a multimeter:

1. Build the circuit on a breadboard (3.3V → NTC → ADC point → R_series → GND)
2. Power the circuit with 3.3V from your board or a bench supply
3. Measure voltage between the ADC point and GND
4. At room temperature (~25°C), you should read approximately 1.65V (half of 3.3V)
5. Warm the NTC with your finger - voltage should increase (toward 3.3V)
6. Cool the NTC with ice in a bag - voltage should decrease (toward 0V)

Board-Specific ADC Considerations

ESP8266 (D1 Mini / D1 Large)

• ADC Pin: A0 only (one analog input)
• Range: 0-1V default! (Yes, this is a common trap)
• Fix for 0-3.3V range: Use voltage divider or set ADC mode

ESP8266 ADC Voltage Range Note:
By default, the ESP8266 ADC measures 0-1V (not 0-3.3V like other boards).

To measure 0-3.3V, you need to:
- Use a voltage divider on the input (not recommended, reduces accuracy)
- Or use `analogRead(A0)` and multiply by a calibration factor

OceanRemote firmware handles this automatically for ESP8266 boards!

ESP32

• ADC Pins: GPIO32-39 (but GPIO34-39 are input-only!)
• Best Pins for NTC: GPIO36 (VP) or GPIO39 (VN) - better linearity
• ADC Attenuation: Set to 11dB for 0-3.3V range (OceanRemote does this)
• Non-linearity: ESP32 ADC is slightly non-linear near extremes

Raspberry Pi Pico W

• ADC Pins: GP26 (ADC0), GP27 (ADC1), GP28 (ADC2)
• Best Pin for NTC: GP26 (ADC0) - default in OceanRemote
• ADC Quality: Excellent linearity, best among the three boards
• Internal Reference: 3.3V, very stable

Complete Example: Calculating Temperature from Voltage Divider

Complete walkthrough from ADC reading to temperature:

Given:
- Board: ESP32 (12-bit ADC, 0-4095 range)
- NTC: 10kΩ @ 25°C, β = 3950
- R_series = 10,000Ω
- ADC reading = 2048

Step 1: Convert ADC to voltage
Voltage = (2048 × 3.3V) / 4095 = 1.65V

Step 2: Calculate NTC resistance
R_NTC = R_series × (3.3V / Vout - 1)
R_NTC = 10000 × (3.3 / 1.65 - 1)
R_NTC = 10000 × (2 - 1)
R_NTC = 10,000Ω

Step 3: Convert resistance to temperature (Steinhart-Hart)
logR = ln(10000) = 9.21034
kelvin = 1 / (0.001129241 + 0.0002341077 × 9.21034 + 0.0000000877541 × 9.21034³)
kelvin = 1 / (0.001129241 + 0.002156 + 0.0000686)
kelvin = 1 / 0.0033538
kelvin = 298.15K

celsius = 298.15 - 273.15 = 25.0°C ✓

Next Steps

Now that you understand the voltage divider circuit, continue with:

• Tutorial 20: Calibrating Temperature Sensors with Offset
• Tutorial 18: NTC 10kΩ Thermistor Complete Guide (if you haven't read it)
• Return to Tutorial 02: Generate firmware with NTC support using your chosen R_series value