# 熱敏電阻

## 基本特性

${\displaystyle \sigma =q(n\mu _{n}+p\mu _{p})\,}$

${\displaystyle \Delta R}$ = 電阻變化
${\displaystyle \Delta T}$ = 溫度變化
${\displaystyle k}$ = 一階的電阻溫度系數

• ${\displaystyle k}$為正值，電阻隨溫度上昇而增加，稱為正溫度系數PTCPositive Temperature Coefficient）熱敏電阻。
• ${\displaystyle k}$為負值，電阻隨溫度上昇而減少，稱為負溫度系數NTCNegative Temperature Coefficient）熱敏電阻。

${\displaystyle \alpha _{T}={\frac {1}{R(T)}}{\frac {dR}{dT}}.}$

## 斯坦哈特-哈特公式

${\displaystyle {1 \over T}=a+b\,\ln(R)+c\,(\ln(R))^{3}}$

${\displaystyle R=e^{{\left(x-{1 \over 2}y\right)}^{1 \over 3}-{\left(x+{1 \over 2}y\right)}^{1 \over 3}}}$

{\displaystyle {\begin{aligned}y&={1 \over c}\left(a-{1 \over T}\right)\\x&={\sqrt {\left({\frac {b}{3c}}\right)^{3}+\left({\frac {y}{2}}\right)^{2}}}\end{aligned}}}

{\displaystyle {\begin{aligned}a&=1.40\times 10^{-3}\\b&=2.37\times 10^{-4}\\c&=9.90\times 10^{-8}\end{aligned}}}

## NTC熱敏電阻的參數

NTC熱敏電阻的電阻值隨溫度的上昇而下降，也可以用B（或β）參數來描述其特性，其實就是參數為${\displaystyle a=(1/T_{0})-(1/B)\ln(R_{0})}$, ${\displaystyle b=1/B}$${\displaystyle c=0}$

${\displaystyle {\frac {1}{T}}={\frac {1}{T_{0}}}+{\frac {1}{B}}\ln \left({\frac {R}{R_{0}}}\right)}$

• T：溫度，單位為K
• R0：為溫度T0 (25 °C = 298.15 K)時的電阻

${\displaystyle R=R_{0}e^{-B\left({\frac {1}{T_{0}}}-{\frac {1}{T}}\right)}}$

${\displaystyle R=r_{\infty }e^{B/T}}$

${\displaystyle T={B \over {\ln {(R/r_{\infty })}}}}$

B參數的方程也可以表示為${\displaystyle \ln R=B/T+\ln r_{\infty }}$，可以得熱敏電阻溫度及電阻的方程式轉換為${\displaystyle \ln R}$${\displaystyle 1/T}$的線性方程式。由其平均斜率可以得到B參數的估計值。

• 溫度偵測
• 電路開關
• 湧流抑制
• 馬達延時啟動
• 過熱保護

## 參考文獻

1. ^ "NTC Thermistors". Micro-chip Technologies. 2010.
2. ^ 李宏. 神奇的新材料（海洋與科技探索之旅）. 青蘋果數據中心. 11 December 2013: 167–. GGKEY:JUBFQGAWFWC.
3. ^ Thermistor Terminology. U.S. Sensor
4. ^ "Practical Temperature Measurements" 互聯網檔案館存檔，存檔日期2009-08-24.. Agilent Application Note. Agilent Semiconductor.
5. ^ 1833 - First Semiconductor Effect is Recorded. Computer History Museum. [24 June 2014].
6. ^ McGee, Thomas. Chapter 9. Principles and Methods of Temperature Measurement. John Wiley & Sons. 1988: 203.
7. ^ Jones, Deric P. (編). Biomedical Sensors. Momentum Press. 2009: 12.