# Determining the Thermopile Time Constant

There are several methods available to determine the time constant of thermopile detectors based on the specific waveform of the radiation utilized in the excitation of the detector. The response of a detector, when it is exposed to a step function of radiation, follows the function Vt = Vmax (1-e-t/τ), of which Vt is the output of the detector at any time t.

The time taken when Vt reaches 63.2% of the maximum static value Vmax is defined as the time constant (τ) of the thermopile detector.

The frequency response of a thermopile detector when it is exposed to sinusoidally modulated radiation follows the function:

Vd = Vs [1+(2πτ/T) 2]-1/2,

Where,

Vd = The dynamic amplitude of the output voltage of the detector at any wave period T

Vs = The static amplitude of the output voltage produced by un-modulated radiation

Vd decreases by 3dB (.707 Vs) from the static value during To, which is correlated to the time constant of the thermopile detector by the following expression:

τ = To/kπ

Here, the value of the coefficient k is 2 for sinusoidally modulated signals. The waveform of chopper-modulated radiation resembles a square wave and the corresponding value of k is 1.124.

## Determination of Thermopile Time Constant

For both methods, a red LED can be employed when the thermopile window/filter transmits in the visible spectrum. It is necessary to apply the appropriate coefficient based on the waveform used. At Dexter Research Center (DRC) , the following methods have been used to determine the time constant:

• A square wave modulated red LED is used when the thermopile window/filter transmits in the visible spectrum
• A chopped blackbody is used when the thermopile window/filter does not transmit in the visible spectrum

It is simple and quick to perform direct measurement of the approximate time constant using a modulated signal. The peak-to-peak trace of the DC output of the thermopile detector is adjusted to seven divisions on an oscilloscope utilizing a very slow modulation frequency.

The frequency is increased until the peak-to-peak trace covers five divisions (.707 x 7div. = 4.95div.). This is roughly –3dB of Vmax. It is then possible to determine the time constant from the wave period or from the frequency by applying the suitable coefficient for the waveform employed. This information has been sourced, reviewed and adapted from materials provided by Dexter Research.

For more information on this source, please visit Dexter Research.

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