Sensor and Measurement Resistive Sensors Spring, 2018 Prof. Jungkeun Park
Outline Resistive Sensors Potentiometers; 2.1 Strain gauge; 2.2 Resistive temperature detector (RTDs); 2.3 Thermistor; 2.4 Light dependent resistor (LDRs); 2.6 Resistive hygrometer; 2.7 Resistive gas sensor; 2.8 Liquid conductivity sensor; 2.9 2
Resistive sensors Potentiometers Resistive device with linear or rotary sliding contact x ( l R= ρ = R ) M A ρ A α
Power Rating Power rating The highest power input allowed to flow through particular equipment Temperature change may arise not only from fluctuation in ambient temperature, but also from self-heating due to finite power that the potentiometer dissipates. Dissipated power needs to be lower than the rated power Power rating: Vr < PR r T
Dual Potentiometer Single motion to adjust output voltage
Potentiometer specification
5 considering points of potentiometer Uniformity is assumed within input range Inductance and capacitance should be insignificant Resistor drift due to temperature Friction and inertia of the wiper(moving contact part of potentiometer) Noise associated with the wiper contact à resolution
Thevenin equivalent circuit for potentiometer The output voltage depends on both the supply voltage and the wiper position Potentiometers can be often directly connected to analog-todigital converters without any interfacing amplifier 8
Tilt Sensors using Potentiometer Electrolytic or liquid potentiometer Arranged for the tilt sensing 경사각따른전해질혹은전도성액체의방향에따라변하는저항을활용 10-8 rad 정도의 resolution 가능하나반응속도가비교적느린편
Level sensor and Force sensitive resistor Level sensor Hydraulic pressure shortens non-immersed strip Force sensitive resistor Conductance is proportional to applied force 응용: -평면 압력 측정(환자 진단) -재활치료시 힘의 측정 -무는 힘의 측정 -촉각센서 -좌석 착석 여부 체크 -골프 글러브에서 힘의 분포 측정 -조이 스틱의 힘의 측정
Sensing Cable for water, liquids, solvents Swelled conductive polymer 가 potentiometer 역할수행 Fuel, water, conductive liquids Solvents 등 액체류 leakage 검출
2.2 Strain Gages Strain gage Based on variation of conductor resistance under mechanical stress l R = ρ A dr d ρ dl da = + R ρ l A Mechanical Stress F dl σ = = Eε = E A l ε : strain E : Young's modulus
Strain Gage: Resistance Change with Strain Resistance derivation via strain dt / t Poisson's ratio: ν = - dl / l For a circular shape wire, 2 π D A = 4 da 2dD 2dl = = 2ν A D l d ρ dv = C ρ V C: Bridgman s constant 2 πld V = 4 dv dl 2dD dl = + = (1 2 ν ) V l D l dr dl dl = [1+ 2 ν + C(1 2 ν)] = G = Gε R l l dr R = R + dr = R (1 + ) R (1 + Gε ) 0 0 0 R0
Ex 2.1 350ohm strain gage with G=2.1 is attached to alluminum strut (E = 73GPa). Outside diameter 50mm, inside diameter 47.5mm With 1000kg load, compute the change in resistance
Variable resistance type strain gage 특징 Applied stress must not exceed the elastic limit of the gage Measurement is correct only if all the stress is transmitted to the gage Assume all strains are in the same plane Temperature interference occurs
Foil strain gage paprameters
Foil strain gage installation
Strain Gage types
Variable resistance detection is usually implemented by Wheatstone bridge configuration Strain Gage Application
Strain Gauge Strain gauge A resistive element used to measure strain on an object Contains one or more thin conductive strips Strip shrink Length decrease Area increase à Resistor decrease Strip Stretch Length increase Area decrease à Resistor increase R = L σ A https://en.wikipedia.org/wiki/strain_gauge#/media/file:strain_gauge.svg 20
Strain Gauge Gauge factor (GF) Ratio between change in resistance and change in length GF = ΔR ΔL / / R L Strain (ε) ε = ΔL L Change in resistance due to strain Δ R = 0 R GFε 21
Wheatstone Bridge Small scale of the change in resistance of strain gauge e.g.) 1.2Ω for a 120 Ω gauge Strain gauge + Wheatstone bridge à increase sensitivity L R 1 R 4 F 0 h width: w R 2 R 3 22
Wheatstone Bridge Vs + - R 1 R 4 V a R 2 R 3 V b V ab ΔR = VS = VS ( GF) ε R 6LF0 = VS ( GF) 2 wh Y 23
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Resistance Temperature Detector (RTD) Usual material: PRTs: Platinum Resistance Thermometers R 1 = R [1 + α ( T 0 1 For platinum, α = 3.95 10 3 T 0 ) + α ( T 2 2 T / K, α = 5.83 10 0 ) 2 +... + α ( T 7 Eq. 2.19 사용시, self heating 은없도록해야함 (Heat dissipation 은 HD constant 혹은 factor 로표시됨 ) Conductor 의 melting point 근처에서는측정불가함 / K 2 n T 0 ) n ]
PRT 에서 Example 2.2 self heating error 고려한전류량계산 Heat dissipation constant / heat dissipation factor δ = $ % ' (mw/k) P ) : dissipating power T: temperature increment Example 2.2 PRT: 100Ω δ = 6mW/K Maximal current through the sensor to keep the self-heating error below 0.1
tables
기계적 strain 은유사한효과로전기적저항을변화시키므로 RTD 의온도측정범위를제한함 RTD 의금속프로브사용시, linear range 에서 R= R [1 + α( T T )] α is termed temperature coefficient of resistance (TCR) or sometimes relative sensitivity Ex. 2.3 0 0 Sensitivity: S = 34 3' = αr / α = R R / (T T / )R / = S R / PRT: 100Ω α=0.00389 (Ω/Ω)/K at 0 Calculate its sensitivity and α at 25 and 50 S = α / R / = α 12 R 12 = α 2/ R 2/
개스가촉매에닿으면온도가올라가서 (Active Pellistor) Gas 의농도측정가능 Passive Pellistor 는주변온도 / 습도등의영향 보상용
Thermistor: Thermally sensitive resistor based on semiconductors NTC: Negative Temperature Coefficient PTC: Positive Temperature Coefficient 참고 : RTD is based on conductors 2.4 Thermistors R T R e o B(1/ T 1/ T o ) T in Kelvins B( β ): characteristic temperature of the material Relative Sensitivity: α = dr / dt R T = = T B 2 T RTD(PT100) 보다 10 배이상 Sensitive
Example 2.4 Alternative thermistor model R ' = R / e 9(: ' <: ' = ) = R / e <9 ' = e 9 ' = Ae 9 ' Determine A for a unit having B = 4200K and 100 KΩ at 25 Calculate α at 0 and 50
Example 2.5 Calculate B for an NTC thermistor that has 5000Ω at 25 1244Ω at 60 ln( R / R ) 1/ T 1/ T 2 1 B = = 1 2 B T 1 / T 2
Three Parameter model Three parameter model reduces error up to 0.01 degree celsius Empirical equation of the TP model R T = or 1 = T e ( A+ B / T + C / T a + bln R T 3 ) + c(ln R T ) 3 Four parameter model 0.00015 degree celsius
Thermistor 응용중 저항 - 온도특성대신 themistor current 와 voltage drop 을이용할수도있음 Thermistor voltage-temperature 관계식 2.33 유도
2.6 Light-Dependent Resistors /Photo Resistors LDR: 소자에빛을비추면저항이감소하는성질이용 λ = c h E R= A E 0.7 < α < 0.9 E V α ν : Illumination (lux) Plank constant h = 6.62 10 <GH J J s Energy E Velocity of light c = 300Mm/s
LDR applications TV 밝기및 contrast 자동조정 카메라노출자동조정 자동헤드라이트조정장치 불꽃검출 가로등자동스위치 연기감지기 카드리더 도둑경보기 계수기 탱크수위측정.
2.7 Resistive Hygrometers 공기중에있는습도측정 Usually relative humidity is measured Pressure of water vapor present as a percentage of saturated gas 습기는물질의저항을감소시킴
2.8 Resistive Gas Sensors 섭씨 700 도이상에서반도체산화물에흡착되거나흡수된산소가전자를빼앗으며산소이온으로변함 (O 1 )è 저항증가 Conductivity 변화이용산소분압측정 : O < σ = A: 상수 E P A O 2 Ae ( P ) EA /( kt) 1/ N O 2 : Activation energy for conduction : 산소분압 N: 4< N < 6 p 개스의연소이용한농도측정 (300~500 ) 1) 연소가능한기체가산화철표면에흡수된산소와반응 2) 흡수된산소감소 3) 저항변화. n-type oxide: 저항감소. p-type oxide: 저항증가
Gas Sensor
2.9 Liquid conductivity sensor 물에녹아있는전해질의농도에따른전기저항변화이용
Total current via charge transport Sum of charge transport I ( nqv) + ( nqv) = l + Thus conductivity n: number of ions of one polarity q: its charge v: its velocity l: distance between anode and cathode I l ( nqv) + ( nqv) = = VA l l = VA = ( Nqv) + ( Nqv) σ + + A: effective cross-sectional area of the conductivity cell
Summary resistive sensors Potentiometer Strain gage RTDs Thermistor LDRs Resistive hygrometer Resistive gas sensor Liquid conductivity sensor