???????? ??????? ????? ???????
??? ????? ???????? ???????
?????	????? ???????
???? ?????	????? ???? ???????? ????? ????? ???????
???????	????? ???????
????? ??????????
????? ????? - ?????

???????? ???????? ^[1] ?? ???????? ??????? ????? ??????? ( ??????????? : Thermistor )? ??????? ??????????? ? ?? ???? ???????? ?? ???? ????? ???????? ? ?????? ????? ???? ??????? ?????? ????? ??????? ????????? ??????? ?????? ?? ???? ???????? ????? ??? ?????? ???????? ? ????? ????? ????? ??????? ?? ?????? ???????? ?????? ??????? . ^{[2] [3] [4]}

??????????? ?? ????? ??????? ????????:

• ?? ??????????? "" NTC "? ????? ????????" "" "?? ?????? ???? ??????? ????? ???? ????? ????????? ??????? ???? ????? ??????? ??????? ?? ???? ???????. ?????? NTC ???? ???? ??????? ????? ???????? ?? ?? ????? ?? ????? ????? ???? ????.
• ?? ??????????? "" PTC ≪? ????? ????????≫ "" "" "" ?? ?????? ???? ??????? ???? ???? ????? ?????????? ??????? ???????? ???? ??? ??????? ?? ??????? ???????. ???? ?? ??? ????? ??????????? PTC ?? ????? ?? ?????? ??????? ??????? ?? ???? ≪?????? ??????≫? ??? ???????? ??????? ?????? ?????.

??? ????? ??????????? ???? ??? ???????? ?????? ??????? ????????. ^[5] ?? ????? ????????? ???????? ???? ???? ??? ???? ??????? ????? ??????? ^{[ ???? ]} ? ???? ???????? NTC ???? ????? ????? ??? ?????? ???? ????? ????? ??? ± 0.1 & nbsp? °C ?? ± 0.2 & nbsp? °C ?? 0 & nbsp? °C ??? 70 & nbsp? °C ?? ??????? ????? ??? ????? ??????. ???? ????? ????????? NTC ?? ?????? ?? ??????? ^[6] ??? ????? ?????? ?????? ??????? (??????? DO-35 ? DO-34 ? DO-41)? ?????? ????? ???????? ????? ?????????? ???? ????? ????? ?? ????? ???? ???????? ????? ????? ??????. ???? ???? ????? ??????? ???????? ????????? ?? 55 & nbsp ? ???? ????? ??? + 150 ???? ?????? ??? ????? ?? ?? ??? ??????????? ??? ????? ??????? ??? ???? ????? ????? ???? ???? + 300 ???? ?????.

????? ??????????? ?? ?????? ???? ????? ???????? (RTDs) ?? ?? ?????? ????????? ?? ????????? ???? ?????? ?? ????????? ?? ????????? ????? ?????? RTD ????? ????. ????? ??????? ???? ??????? ?????? ???? RTDs ????? ??? ?????? ????? ??????? ??????? ????? ???? ??????????? ????? ??? ???? ??? ???? ???? ????? ??????? ????? -90 & nbsp ? °C ??? 130 & nbsp ? ° ^[7]

??????? ???????? [ ??? ]

???????? ?????? ?? ?????? ??????? ?? ??????? ??? ???????? ????? ??????? ?? ??? ? ???

${\displaystyle \Delta R=k\Delta T,}$

???

${\displaystyle \Delta R}$, ??????? ?? ?????????

${\displaystyle \Delta T}$, ???? ?? ???? ????????

${\displaystyle k}$, ?????? ?????? ????? ???? ??????? ???????? .

???? ????? ??????????? ??? ?????? ???????? ??? ????? ${\displaystyle k}$. ??? ??? ${\displaystyle k}$ ?? ???? ? ????? ???????? ?? ????? ???? ???????? ????? ?????? ????? ???? ????? ???? (' PTC ) ????????? ?? ?????????? . ??? ???? ???? ${\displaystyle k}$ ?????? ??? ???????? ?? ????? ???? ???????? ????? ??? ?????? ??? ????? ???? ??????? ??????? ( NTC ) ?????????. ?? ????? ????????? ???? ???? ?? ??????? ??????????? ???? ???? ??? ${\displaystyle k}$ ???? ?? ???? ????? ??? ???????? ???? ??? ???????? ????? ??????? ??? ???? ???? ?? ????? ???????. ????? ?? ????? ???? ??????? "k"? ?? ??? ??????? ??? ??????? ≪????? ???? ??????? ????????≫ ${\displaystyle \ alpha_{T}}$ ("alpha sub T"). ??? ?????? ??? ???. ^[8]

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

??? ??? ????? ??? ????? ${\displaystyle \alpha _{T}}$ ?? ????? ${\displaystyle a}$ ?????.

?????? ?????????-???? [ ??? ]

?? ??????? ???????? ???? ????? ??????? ????? (?????) ?????? ??? ?? ???? ???? ????? ??????. ??? ??? ?????? ???? ????? ????? ???? ???????? ?????? ??????? - ???? ??????? ????? ????? ??????? ???? ??? ??????. ?????? ?????????-???? ?? ????? ?? ?????? ??????? ??????? ??? ???? ????:

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

??? ????? ??? "a" ? "b" ? "c" ?????? Steinhart-Hart ???? ??????? ??? ????. "T" ?? ???? ??????? ??????? ? ? "R" ?? ????????. ?????? ???????? ????? ????? ???????? ???? ?? ???????? ????????? ????? ?? ${\displaystyle \ln R}$ ? ????? ??? ????? ????? ??????? ??????

${\displaystyle \ln R={\frac {b}{3c\,x^{1/3}}}-x^{1/3}}$

???

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

????? ?? ?????? Steinhart-Hart ???? ??? ??? ?? 0.02 ???? ????? ?? ???? ???? ??????? ??? ??? 200 ???? ?????. ^[9] ?????? ????? ????????? ????????? ??????? 3 & nbsp ? kΩ ?? ???? ????? ?????? (25 & nbsp ? °C = 298.15 & nbsp ? K) ??:

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

B ?? β ?????? ??????? [ ??? ]

???? ????? ????? ??????????? NTC ??????? ??????? "B" (?? "")? ????? ?? ?????? ?????? ?????????-???? ?? ${\displaystyle a=1/T_{0}-(1/B)\ lnR_{0}}$ ? ${\displaystyle b=1/B}$ ? ${\displaystyle c=0}$ ? : ${\displaystyle {\frac {1}{T}}={\frac {1}{T_{0}}}+{\frac {1}{B}}\ln {\frac {R}{R_{0}}},}$ ??? ???? ????? ??????? ?? ???? ? ? "R" ₀ ?? ???????? ??? ???? ??????? "T" ₀ (25 & (25 °C = 298.15 K). ?? ?? ??? "R" ??????

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

?? ???? ?? ????

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

??? ${\displaystyle r_{\infty }=R_{0}e^{-B/T_{0}}}$.

???? ?? ??? ??????? ????? ???????:

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

???? ????? ????? ?????? ??????? "B" ?? ${\displaystyle \ lnR=B/T+\ lnr_{\ }infty}$. ???? ??????? ??? ?????? ????? ???????? ????? ???? ????? ????????? ??? ???? ???? ?? ${\displaystyle \ lnR}$ ????? ${\displaystyle 1/T}$. ????? ????? ??? ??? ??????? ??? ??? ??????? ????? ??????? `` B .

????? ??????? [ ??? ]

NTC (????? ???? ??????? ??????) [ ??? ]

?????? ?? ??????????? NTC ?????? ?? ??? ?????? ????? ????? ??? ?? ?? ????? ?? ????? ???????? ??? ????? ???? ?????? ???? ???? ??? ??? ???? ????? ????? ???????? ???? ?? ??? ????? ?????? ?????? ???? ?????? ??? ≪ ???? ??????? ≫. ???? ??? ??? ?????? ????? ????????? ???? ?????? ???? ???? ?????? ?? ???? ???. ?? ???? ????? ??? ????? ???????? (Fe ₂ O ₃ ) ?? ?????????? (Ti) ??? ????? ????? ???????? ?? ????? "n" ????? ?????? ?????? ??????? ?. ?? ???? ??? ????? ?????? (NiO) ?? ???????? (Li)? ??? ????? ????? ???????? ?? ????? "p-type"? ??? ???? hole ?????? ??????. ^[10]

??? ????? ?? ??????

${\displaystyle I=n\cdot A\cdot v\cdot e,}$

???

${\displaystyle I}$ = ?????? ????????? (?????)?

${\displaystyle n}$ = ????? ?????? ????? (????? / ? ³ )?

${\displaystyle A}$ = ????? ?????? ?????? ?????? (? ² )?

${\displaystyle v}$ = ???? ?????? ??????????? (? / ?)?

${\displaystyle e}$ = ???? ??????? ( ${\displaystyle e=1.602\times 10^{-19}}$ ?????).

PTC (????? ???? ??????? ?????????) [ ??? ]

???? ??????????? PTC ?????? ?? ????? ??????????? ??????? (????? ??? ??????? ???????? (BaTiO ₃ ) ??????? ????) ????? ??? ????? ?? ???????? ????? ???? ??? ???? ????? ???? ?????. ??????? ???????? ferroelectric ?????? ???? ????? ?? ???? ???????. ??? ???? ????? ???? ???? ? ???? ?????? ???? ????? ????? ????? ?????? ??? ?????? ?????????? ??? ???? ??? ?????? ??????. ?? ??? ???????? ????? ?????? ??? ????? ???? ????? ???? ????. ??? ???? ????? ???? ????? ????? ???? ????? ???? ???? ?????? ?????? ????? ?????? ??? ???? ??????? ?????? ???????? ???? ??? ?? ???? ???????. ?? ????? ????? ????? ???? ?????? ??? ???? NTC. ??? ??? ?? ????????? ?? "" ??????? ???????? "(??????? ???????? ???? ???????). ?????? ??????????? ????????? ????? ????? ??? ?????. ??? ??? ??????????? ??????? PTC ? ????? ??????????? ?????? ?????? ???? ????? ???? ???????. ^[11] ????? ?????? ???? ????? ?? ????????? NTC. ???? ????? ?????? ????? ??????? ?? ???? ????? ??????? ??????? ??????? ??? ??????. ^[12] ???? ??????? ??????????? ???? ??????? ???????? ??????? ????? ??????? ???? ????? ??? ???? ????????? ??? ???? ????? ?????? ??? ?????? ????????? ?????? ??? ????? ??????? ?? ?????????.

?????????? ??????????? PTC ???? ??? ??????? ???? ?????? ????? ?? ?????????. ????? ??? ?????? ???? ??? ????? ???? ????? ???? ???? ?????? ?? ???????? ???????? ????????? ???? ?? ????? ????????? ??????? ??? ????? ?????? ??? ??? ?????? ??? ???? ???? (????? ????? ?????? ?????? ????????). ???? ?? ??? ????? ???? ?????? ??? ????????. ?? ????? ????? ??????? ?????? ?? ????? CRT ?????? ?????????? ??? ????? ????????? ??????? ???? ????? ?? ????? ?? ??? ????? ???????. ???? ?? ??? ?????? ??? ?????? ?????? ????? ????? ???????. ????? ??? ????? ????? ??????? ??? ??? ????? ????? ?????? ?????? ????????? (?????? ?????? ??????) ???? ????.

??? ??? ?? ????????? PTC ?? ???????? PTC ? ????? ???? ??? ????? ?????? ??? ≪ ????? ?????? ????? ?????? ????? ≫ "Semifuse" ? "Multifuse". ????? ??? ?? ????????? ?? ?????? ????? ????? ???. ????? ???? ????????? ??????? ???? ?????? ??????? ???? ??? ????? ?? ????? ?????? ????? ?????? ???? ??? ??????. ????? ???? ?????????? ?????? ??? ???? ??? ????? ?????? ???????? ??? ???? ??? ?????? ?????? ??????? ??? ???? ??? ??? ??? ????? ??????? ?????? ???????? ???????. ??? ????????? BaTiO ₃ ? ????? ??? ?????? ??????? ??? ???? ?????? / ??????? ????? ??????? ????? ?????? ??????? ?? ?????? ?? ???????? ???? ????? ???? ???????. ??? ???? ????? ??????? ????????? ???? ?? ??????? ???? ??? ???????? ????? ??????? ??? ??? ????? ?? ????? ????? ?? ???? ??????? . ≪?????≫ ??????????? PTC ?? ???? ?????? ????? / ?????: ????? ?? ???? ?????? ????? ??? ?? ???? ???????? ??????? ???? ??? ????. ???? ??????? ??????? ?????? ?????? ????? / ????? ????? ? ???? ????? ??????? ???????? ?????????? PTC ?? ?????? ?? ???? ????? ???? ????? ?????????? ????? ????. ^[13]

??????? ??????? ?????? [ ??? ]

????? ????? ?????? ??? ?????????? ???? ???? ?????? ??? ???? ???? ????? ????????? ??? ???? ????? ?????. ??? ?? ??????? ????????? ????? ???? ????? ??????? ??? ???? ??? ??????? ????????? ??? ???? ??? ???? ??? ?? ??? ????? ?????. ???? ?? ???? ???? ??????? ??? ??????? ????. ?????? ??? ???? ??????? ??? ???? ???? ????? ?????? ?????? ?? ????? ?????? ???? ???? ??????? ?? ????? ????? ? ?? ???? ?????? ???? ?? ???? ??? ??? ???? ?????? ?? ???? ?????? .

?????? ?????? ?????????? ????????? ?????

${\displaystyle P_{E}=IV,}$

??? "I" ?? ??????? ? "V" ?? ?????? ????? ??? ?????????. ??? ????? ??? ?????? ??? ?????? ???? ??? ??? ?????? ???????? ??? ?????? ???????. ???? ????? ????? ????? ?????? ????? ??????? ?????? :

${\displaystyle P_{T}=K(T(R)-T_{0}),}$

??? "T" ("R") ?? ???? ????? ????????? ????? ???????? "R"? ? ${\displaystyle T_{0}}$ ?? ???? ????? ?????? ???????? ? "K "" ?? "???? ???????"? ????? ?? ??? ??????? ??? ?????? ??? ??? ??? ???? ?????. ??? ???????? ??? ?? ???? ???????? ???????:

${\displaystyle P_{E}=P_{T}.}$

????? ?????? ?????? ??? ????????? ??? ????? ??????? ??????. ????? ????? ??? ??? ????? ??? ????????? ??????? ???? ????? ??? ????? ${\displaystyle I=V/R}$ ? ????? ?? ?????? ??????? ????? ??????? ??????? ??? ???? ???????? ??????? ?????????:

${\displaystyle T_{0}=T(R)-{\frac {V^{2}}{KR}}.}$

???? ??????? ?? ????? ??????? ??????? ????????? ??????. ??? ?????? ?????? ??????? ??????? ?? ?????? ?????? ??? ????? ??? ???????. ????? ????????? ????????? ?? ????? ??????? ?????? ?? 1.5 & nbsp? mW / °C ?? ?????? ?????? ? 6.0 & nbsp? mW / °C ?? ????? ???????. ??? ???? ???? ????? ?????? ?????? ??????? ????? ??????? ????????? ????? ???? ???? ???????. ??? ???? ??????? ???? ??????? ????????? ??????? ????? ??????? ??? ???? ???? ??????? ?? ???? ???? ?????? ??? ?????????. ????? ?? ??? ?????? ??? ?????? ??????? ?? ????????? ??? ????? ????? ???? ????? ??? ??? ??? ?? ???? ???? ??????? ???? ??????? ??????. ??? ???? ????? ??? ??????? ????????? ??? ≪??????? ??????≫ ?????? ???? ???? ????? ????? ????????? ???? ????? ?? ???? ??????? ???????? ???????? ????? ???????? ??? ????????? ??????? ?? ??????? ??????? ??????. ????? ??? ??? ????????? ????? ?? ????? ?????? ????? ???? ?????? ????? ???? ??????.

????? [ ??? ]

• ????? ??????????
• ????? ????????
• ????? ??? ??????

?? ????? ??? ?????? ??: ?????? ??????