# Semiconductor sensors of temperature

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1 Semconductor sensors of temperature he measurement objectve 1. Identfy the unknown bead type thermstor. Desgn the crcutry for lnearzaton of ts transfer curve.. Fnd the dependence of forward voltage drop on the dode on temperature for constant forward current. 3. For the converter temperature to duty cycle SM-16 fnd the dependence of output varable (DUY rato) on temperature. he measurement procedure 1. hermstor 1.1 Measure the dependence of thermstor resstance on temperature = f() wth measurng current 5 µa for the range of temperature from C to 35 C. hermstor s nserted n water bath heated by hotplate. Calculate the constant of thermstor now. (You need t for further procedures.) 1. emove the bead thermstor from bath and measure the volt-ampere characterstc of thermstor n ar for the range of currents from 5 µa to 5 ma. In seres wth thermstor s connected protectng resstor wth resstance of 1 Ω. For adjustng the ntensty of small currents use the decade resstor (rheostat box) (see Fg. 1.1). For the hghest current I = 5 ma measure also the voltage drop on thermstor nserted n water bath (change water n bath to cold one) wth strrng swtched on and off. ecord the ambent temperature,.e. the temperature of ar and the temperature of water. Determne the self-heatng of thermstor due to measurng current and calculate the loadng constant D for three cases,.e. thermstor placed n ar, n strred water and n stll water. When performng the numercal calculatons n the formulas always use the temperature n Kelvn! 1.3 In a narrow regon around the temperature t = 5 C consder the functon = f() as beng lnear and fulfllng the relaton = (1 α ). Derve relaton for thermal coeffcent α correspondng to the tangent lne of the functon = f() and calculate ts value at the temperature t = 5 C. Compare the value of α wth the values of temperature coeffcent for platnum (e.g. Pt1) D. 1. Calculate the value of seral lnearzaton resstor S (Fg. 1.) whch sets the pont of nflexon of the functon I = f() to temperature t = 5 C. y means of the decade resstor nsert the calculated value of S nto the crcut. Do not forget to subtract the value of protectng resstor P 1 Ω. 1.5 Determne by measurement the lnearty of crcut n Fg. (1.),.e. the lnearty of the functon I = f() up to temperature t = 55 C. he voltage of the source should be set to the value at whch current 15 µa would flow at the ntal temperature. Approxmate the measured characterstc by a straght lne of the type I = I I α. 1

2 Fg. 1.1 Fg. 1.. Sensor of temperature wth PN juncton (dode thermometer) Determne the dependence of voltage drop on the transstor KC 37 connected as a dode. Fnd the lnearty of the measured relaton. What s the value of current flowng through the dode? he temperature of alumnum block s also measured by means of semconductor temperature sensor AD 59 (511). hs sensor behaves (after connecton to power supply) as the source of current controlled by temperature. he converson constant of ths sensor s 1 µa/k. he sgnal condtonng crcut n Fg.1.3 shfts the orgn of range (zero suppresson). Smultaneously (at the same heatng) measure the transfer functon of temperature to duty cycle converter (SM 16-3). Calculate the values of senstvty and offset. Fg he temperature to current converter AD 59 and transstor KC37

3 he hnts for measurement When usng the relatons shown below, the temperature should be expressed n K o step 1.1: see dscusson of -constant below, n he dervaton of the load characterstc o step 1.: he loadng constant D: (1.1) expresses the relaton between power appled by measurng current and resultng error by selfheatng. It can be converted to where [K] s the ambent temperature [K] s the constant of thermstor, U 1 [V] the voltage drop at thermstor at mnmal measurng current I = 5 µa, U [V] the voltage drop at thermstor at maxmal measurng current I = 5 ma. Prove the valdty of the relaton (1.). (1.) o step 1.3: When dervng the relaton for α substtute the rato / for > by dfferentaton d/d of the relaton = A.e / expressng the temperature dependence of the thermstor. o step 1.: he resstance of thermstor at the temperature of 5 C (whch s necessary for calculaton of S ) fnd by calculaton (extrapolaton) usng the constant. he relaton for the calculaton of lnearzng resstor value S dependng on the selected temperature of nflexon can be derved from the condton d I/d =. he dervaton of the load characterstc For the resstance of NC thermometers the followng equaton s vald: ( ) = he value of the constant A s usually not quoted n thermstor data sheet, the thermstor s characterzed by ts senstvty and the resstance o at the temperature. Ae he thermstor characterstc s mostly expressed by the equaton ( ) 1 1 o = e 3

4 where [Ω] s the resstance of thermstor at the temperature [K], [Ω] s the resstance of the thermstor at the temperature [K]. he constant can be found n a datasheet or by measurement. For the calculaton of D the measurement of voltage U 1 on thermstor for very small current I 1 (e.g. 5 µa), s necessary. For the low current the self-heatng effect of thermstor can be neglected (thermstor s practcally at ambent temperature ). he voltage drop U s measured for large current I (e.g. 5 ma), whch causes the warmng of thermstor above the ambent temperature of.e. on the temperature =. Neglectng the warmng effect of the small measurng current we obtan P D = U I = emperature can be calculated as After substtuton we have and fnally Dervaton of equaton for lnearzaton of thermstor transfer characterstc he connecton of the seral resstance S belongs to the most frequently used method of lnearzaton of exponental dependence of thermstor on temperature. he seral combnaton of S s drven from source of constant voltage, the current I represents the output varable. he value of S s chosen n such a way that the nflexon pont of resultant functon I=f() les n the mddle of the range for the selected value of temperature and the overall lnearty error s optmally spread over the range.

5 5 For I=f() s vald he nflexon pont s determned by condton that the second dervaton of the current (the bottom equaton wrtten above) s zero. t s gven by relaton After substtuton to prevous equaton we obtan ( ) = 3 S = S S = (1.9) he example of the effect of the seral resstor s shown n Fg.1.5. he exponental dependence of the thermstor resstance on temperature (Fg a)) s the reason of the consderable error of lnearty n connecton wth constant voltage (Fg b)). he nserton of the seral resstor wll decrease the senstvty, but the lnearty error s suppressed substantally (Fg c)). Fg. 1. Lnearzed crcut

6 [ Ω] I [ma] I [ma] t [ C] t [ C] t [ C] a) b) c) 6

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