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Transfer function

How the driver turns a voltage into a temperature, which coefficients it uses, and how large the errors are.

The equation

The datasheet characterises the sensor with a first-order transfer function (Equation 4-1):

VOUT = TC × TA + V0°C

The driver solves it for the temperature:

T = (V − v_zero_c) / v_per_c

v_zero_c is V0°C, the output at 0 °C, and v_per_c is TC, the temperature coefficient, both in volts. The constants are in namespace hf::mcp9700. They default to the datasheet's typical values and can be replaced per sensor (Configuration).

Coefficient Default Constant
v_zero_c 0.5 V kDefaultVoltsAtZeroC
v_per_c 0.01 V/°C kDefaultVoltsPerCelsius

Output over temperature

Typical MCP9700 output voltage against temperature: a straight line from 0.10 V at −40 °C through 0.50 V at 0 °C to 1.75 V at +125 °C

Temperature (°C) VOUT, typical (V)
−40 0.10
0 0.50
+25 0.75
+85 1.35
+125 1.75

These values follow from the typical coefficients. They do not depend on the supply voltage: the output is not ratiometric, and the line regulation is 0.1 °C/V typical.

Where the error comes from

Source Size What to do
Sensor accuracy ±4 °C (MCP9700), ±2 °C (MCP9700A), 0 °C to +70 °C Choose the grade; calibrate (Hardware)
Nonlinearity ±0.5 °C typical, 0 °C to +70 °C Left after a one-point calibration; AN1001 compensates it
ADC offset and gain Depends on the MCU Calibrated ADC readings in the adapter
ADC resolution 0.08 °C to 1 °C per code Choose the reference and range (Hardware)
Noise Depends on the board Decoupling, averaging (API guide)

A one-point calibration at +25 °C reduces the first row to ±0.5 °C typical between 0 °C and +70 °C (datasheet Section 4.1). Measuring a change relative to +25 °C is accurate to ±1 °C typical over the same range without any calibration.

Limits of the model

  • The driver applies the equation only inside the specified range plus a margin (−48 °C to +133 °C, 20 mV to 1.83 V by default). An open or grounded input (0 V, which would be −50 °C) and a shorted-to-supply input fail with Error::kOutOfRange instead of returning a temperature (API guide).
  • The coefficients are fixed when you construct the object. To change them, construct a new one.
  • There is no curve correction for the nonlinearity; the datasheet's AN1001 describes a lookup-table method.

Next

Configuration shows how to calibrate the coefficients; Hardware shows how to set up the ADC.