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T90 Equation:
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The sensor response time T90 represents the time required for a sensor to reach 90% of its final response when exposed to a step change in the measured parameter. It is a critical parameter in sensor performance characterization and system dynamics analysis.
The calculator uses the T90 equation:
Where:
Explanation: The equation calculates the time required for a first-order system to reach 90% of its final value based on the system's response rate constant.
Details: T90 is crucial for understanding sensor dynamics, designing control systems, determining sampling rates, and ensuring proper system response times in various applications including environmental monitoring, industrial processes, and medical devices.
Tips: Enter the response rate constant (k) in units of 1/second. The value must be positive and non-zero. The calculator will compute the corresponding T90 time in seconds.
Q1: What is the relationship between T90 and time constant?
A: For a first-order system, T90 ≈ 2.3 × τ, where τ is the time constant (τ = 1/k).
Q2: How is T90 different from T63.2?
A: T63.2 is the time to reach 63.2% of final value (one time constant), while T90 is the time to reach 90% of final value.
Q3: What factors affect sensor response time?
A: Sensor design, membrane thickness, diffusion coefficients, temperature, and the measured analyte concentration can all affect response time.
Q4: When is T90 measurement important?
A: Critical in applications requiring fast response times such as safety monitoring, process control, and real-time environmental detection.
Q5: How can response time be improved?
A: Through sensor design optimization, reduced membrane thickness, increased surface area, and operating at optimal temperatures.