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When testing or applying NTC thermistors, two parameters often come up: thermal time constant (τ) and response time. Both describe the sensor’s dynamic temperature response, and while closely related, they are defined differently. Understanding their relationship requires looking at both the conceptual definitions and the mathematical model.

1.Key Definitions

1）Thermal Time Constant (τ)：The thermal time constant quantifies the sensor’s thermal inertia. It is defined as:The time required for the sensor to reach 63.2% of the total temperature difference between its initial state and a new stable environment when subjected to a sudden temperature change.

A smaller τ means the thermistor reacts faster to temperature changes.A larger τ means greater thermal inertia and slower response. Factors influencing τ: Sensor size (smaller sensors → smaller τ)Encapsulation material (better thermal conductivity → smaller τ)Surrounding medium (liquids generally yield smaller τ than air due to higher thermal conductivity)

2）Response Time：Response time is a practical application-oriented parameter.

It is defined as:The time required for the thermistor’s output to reach a certain percentage of the final temperature (e.g., 90%, 95%, 99%).

Different industries adopt different standards: Medical devices often use the 90% response time.Industrial applications may require 95%.High-precision applications sometimes use 99% or higher.Thus, response time is relative and depends on the chosen stability percentage.

2. Mathematical Relationship

The thermal response of an NTC sensor can be approximated by a first-order exponential model:

T(t)=T0 +(T∞−T0)·(1−e-t/τ)

Where:

T(t): sensor temperature at time t

T0: initial temperature

T∞: final stable temperature

τ: thermal time constant

Key time points:

Thus: 90% response ≈ 2.3τ；95% response ≈ 3τ；99% response ≈ 5τ.

Response time is essentially a multiple of τ, depending on the stability criterion.

3. Summary of the Relationship

1) Foundation vs Application: The thermal time constant (ττ) is the base parameter; response time is derived from it.

2) Proportionality: Any factor reducing τ (e.g., smaller size, better thermal conduction) also proportionally reduces response time.

3) Fixed vs Relative: τ is a fixed property of the thermistor and its environment; response time is relative and depends on the definition (90%, 95%, 99%, etc.).

4. Example – Shiheng Electronics MF51E 503F3950

Thermal time constant τ = 0.8 s

90% response time ≈ 2.3 × 0.8 = 1.84 s；95% response time = 3 × 0.8 = 2.4 s；99% response time = 5 × 0.8 = 4.0 s；99.91% response time = 7 × 0.8 = 5.6 s.

This ultra-fast NTC thermistor achieves accurate body temperature measurement within ~5.6 seconds, making it ideal for medical thermometers.

5. Why Choose Shiheng Electronics?

With over 20 years of experience, Shiheng Electronics provides:

✔ High-precision, fast-response NTC thermistors

✔ Excellent consistency and long-term reliability

✔ Compact size and stable structure for diverse applications

✔ Proven solutions for consumer electronics, medical devices, energy systems, and industrial controls

Our fast-response MF51E series meets the growing demand for sub-6-second temperature sensing in medical and consumer applications.

Learn more about our NTC thermistors and application solutions on the Shiheng Electronics official website, or contact our team directly for technical support.