The Balco 500 Ω exhibits a nearly linear variation of its resistance with temperature, modeled by:

R(T) = R₀ [1 + α(T − 25) + β(T − 25)²]

avec :

• R₀ = 500 Ω

• α = 3,93 × 10⁻³

• β = −5,0 × 10⁻⁶

• (valable de −40 °C à +150 °C)

This relationship is more accurate than the pure linear formula while remaining easy to calculate.

🔹 Example 1 : calculation of resistance at 100 °C

R(100) = 500 × [1 + 3,93 × 10⁻³ × (100 − 25) − 5,0 × 10⁻⁶ × (100 − 25)²]

R(100) = 500 × [1 + 0,29475 − 0,028125]

R(100) = 500 × 1,266625 = 633,31 Ω

✅ Result : at 100 °C, the resistance of the Balco 500 Ω is approximately 633 Ω.

🔹 Example 2: calculating the temperature from a measured resistance

We measure R=570Ω.

What is the corresponding temperature ?

We solve the inverse equation :

β(T − 25)² + α(T − 25) + (1 − R / R₀) = 0

−5 × 10⁻⁶ (T − 25)² + 3,93 × 10⁻³ (T − 25) + (1 − 570 / 500) = 0

−5 × 10⁻⁶ (T − 25)² + 3,93 × 10⁻³ (T − 25) − 0,14 = 0

T − 25 = [−3,93 × 10⁻³ + √((3,93 × 10⁻³)² − 4 × (−5 × 10⁻⁶) × (−0,14))] / [2 × (−5 × 10⁻⁶)]

T − 25 ≈ 40,3 ⇒ T ≈ 65 °C

✅ Result: the equivalent temperature is approximately 65 °C.

🔹 Practical Remarks

• The Balco alloy exhibits superior stability compared to nickel and has natural linearity.
• The quadratic equation remains simple to implement on a microcontroller.
• This type of sensor is ideal for cost-effective devices requiring acceptable accuracy (±0.2 °C).

The Balco sensor is perfectly suited for measurement circuits using a voltage divider or Wheatstone bridge, thanks to its high resistance and nearly perfect linearity.

It can be directly connected to an ADC converter or a moderate-gain instrumentation amplifier.

🔹 Typical components

🔹 Functional diagram (ASCII)

                +3.3 V
                   │
          Current source (0.2 mA)
                   │
               [ Balco 500 Ω ]
            (2 wires or 3 shielded wires)
              │              │
              │              │
     Measurement bridge or amplifier
                   │
                [ ADC ]
                   │
          [ Microcontroller ]
      (calculation of T = 25 + (R/R25 - 1)/α)

🔹 Principe de fonctionnement

1. A constant current (0.2 mA) flows through the Balco resistance.
2. → at 25 °C: V = 500Ω × 0.2mA = 100mV
3. → at 100 °C: V = 694Ω × 0.2mA = 139mV
4. The measured voltage is proportional to the temperature.
5. It can be directly converted via the ADC of a modern microcontroller.
6. The microcontroller calculates the temperature using the equation:
7. T = 25 + R/R25−1 / α
8. The processed signal can then be displayed, sent via bus (I²C, RS485, etc.),
9. or used to control a regulator (heating, air conditioning, etc.).

🔹 Best Practices

⚡ Use a shielded cable if the sensor is far from the measurement module.

💧 Mechanically protect the probe from moisture and corrosion.

🧩 Prefer a 3-wire configuration if the cables exceed 2 m to compensate for losses.

🔄 Calibrate at 0 °C and 100 °C to adjust the coefficient α according to the production batch.

🧯 Avoid currents > 0.3 mA, which cause slight self-heating (≈ 0.05 °C).