Meteorological Instrument Performance Characteristics

Dynamic Response » Transfer Functions and the Transfer-Function Diagram » Example: Temperature Response

As an example, consider a liquid-in-glass thermometer immersed at time t0 = 0 into a bath of fluid having temperature TF (the final bath temperature). If the thermometer reads T0 before immersion, it will start to move toward TF after immersion and will display a temperature T(t) that moves toward TF over some period of time. The rate at which heat is transferred to the thermometer depends on the temperature difference T(t) - TF, often in a linear relationship, so the displayed temperature will move faster at first and gradually move more slowly toward TF as the temperature difference becomes small.

A linear relationship between the time rate of change in temperature and the temperature difference between the sensor and the bath can be represented by a first-order linear differential equation like dT(t) / dt = (TF - T(t)) / 𝜏, where 𝜏 is a constant that determines the rate at which the sensor responds to its environment and TF is the final temperature. This equation has an exponential solution, such that T(t) approaches TF but never reaches that value, as shown in the figure. This first-order response is characteristic behavior for many sensors and electronic components of sensors.

The response of a first-order sensor with time constant 1

The response of a first-order sensor with time constant 1. The temperature to which the sensor is exposed (x) is shown as the green line and the measured temperature (M) as the blue line. At t = 0, x abruptly changes from 0 to Tf = 1. Image from NCAR/EOL.


Select whether the statement refers to a static performance characteristic or a dynamic performance characteristic.

a) Includes zero error and span error:
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b) First-order transfer function is a low-pass filter:
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c) Includes sensor time lag and hysteresis:
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d) Output depends directly on the measurand:
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e) Output depends on the measurand and on its history:
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The correct answers are shown above.

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