physical quantities ducer) control signal pro- lecture...

PhysicalQuantities

Sensors(Trans-ducer)

Signal Con-ditioning

Signal Pro-cessing

Display

ControlSystem

Figure 1 Electrical measurement system flowchart.

Lecture Notes: 2304154 Physics and ElectronicsLecture 9 (2nd Half), Year: 2007Physics Department, Faculty of Science, Chulalongkorn University20/11/2007

Contents

1 Generating Sensors 2

2 Resistive and Electromagnetic Sensors 42.1 Resistive Sensors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 Signal Conditioning for Resistive Sensors . . . . . . . . . . . . . . . . . . . . 62.3 Electromagnetic Sensors and Their Signal Conditioning . . . . . . . . . . . 8

3 Digital Signal Processing 11

4 Problems 14

Electrical Measurement Systems (in Figure 1)

Classes of Sensors

1. Generating sensors: Thermocouples

2. Resistive sensors: Thermistors, strain gages, potentiometers

3. Electromagnetic sensors: Distance sensors, accelerating sensors

2304154 Physics and Electronics (file: lec09 2.tex) 1 Tianprateep, M.

Figure 2 A voltage proportional to temperature is generated when a thermocouple is heated.

1 Generating Sensors

Thermocouple (in Figure 3 )Seebeck voltage: A small voltage is produced across the junction of the 2 metals

when heated.

Types of Thermocouples

• chromel–alumel (type K)

chromel = nickel–chromium alloy;

alumel = nickel–aluminum alloy

• iron–constantan (type J)

constantan = copper–nickel alloy

• chromel–constantan (type E)

• tungsten–rhenium alloy (type W)

• platinum–10% Rh/Pt (type S)

Characteristics of Thermocouples (in Figure 4 )

Relation between T (oC) and V (mV)For type–J

V ( mV) = a0 + a1T + a2T2 + a3T

3 + · · ·

For type–K

V ( mV) = a0 + a1T + a2T2 + a3T

3 + · · · + e0 exp[e1(T − e2)2]

Thermocouple-to-Electronics Interface (Fig. 4 )


Figure 3 Output of some common thermocouples with 00 C as the reference temperature.

Cold junction

Figure 4 A thermocouple–to–electronics interface.


Figure 5 Using a reference thermocouple in a temperature–measuring circuit.

Cold Junction Correction (Fig. 5 )

2 Resistive and Electromagnetic Sensors

2.1 Resistive Sensors

Resistance Temperature Detectors and ThermistorResistance temperature detectors (RTD) and thermistor: their resistance changes

directly with temperature.RTD: a material, ex: platinum, nickel, or nickel alloys.Thermistor: a semiconductive material, such as, nickel oxide or cobalt oxide.

Strain Gaugestrain: the deformation, either expansion or compression, of a material due to a

force acting on it.strain gauges: are based on the principle that the resistance (R) of a material

depends on its length (L) and cross-sectional area (A).

R =ρL

A

ρ = resistivity

Gauge Factor (GF) (in Figure 6)

GF =∆R/R∆L/L

Pressure Gauge (in Figure 7 and Figure 8)


Figure 6 Defining gauge factor.

Figure 7 Basic pressure gauge construction.

Figure 8 (a) With no net pressure on diaphragm, strain gauge resistance is at its nominal value.(b) Net pressure forces diaphragm to expand, causing elongation of the strain gaugeand thus an increase in resistance.


Figure 9 Voltage Divider

Figure 10 The resistive potentiometer.

2.2 Signal Conditioning for Resistive Sensors

Voltage Divider (in Figure 9)

Vo =R1

R1 +R2Vi

Resistive Potentiometer (in Figure 10)Resistive potentiometer: for measuring translational displacement.

Vo

Vs=AC

AB

Rotary Motion Potentiometers in Fig. 11

Wheatstone Bridge (in Figure 12)


Figure 11 Rotary motion potentiometer: (a) circular; (b) helical

Figure 12 Wheatstone Bridge


Assume voltage measuring instrument (for Vo) has a high-impedance:

Im = 0I1 = I3

I2 = I4

Considering ADC: By Ohm’s law

I1 =Vi

Ru +R3

For ABC:

I2 =Vi

Rv +R2

VAD = I1RuViRu

Ru +R3

VAB = I2RvViRv

Rv +R2

Vo = VBD = VD − VB

= (VA − VB) + (VD − VA)= VBA − VAD

Vo = Vi(Ru

Ru +R3− Rv

Rv +R2)

At the null point Vo = 0

Ru

Ru +R3=

Rv

Rv +R2

R3

Ru=R2

Rv

Constant-Current Circuit in Fig. 13

Vout = −RRTD

R1Vin

2.3 Electromagnetic Sensors and Their Signal Conditioning

Displacement Sensors in Fig. 14Using linear variable differential transformer, LVDT


Figure 13 Constant–current circuit.

Figure 14 Linear variable differential transformer.


Figure 15 Structure of an accelerometer.

Vs = Vp sin(ωt)Va = Ka sin(ωt− φ)Vb = Kb sin(ωt− φ)

Since the core in the central position: Ka = Kb = K

Va = Vb = K sin(ωt− φ)

Since the core moves apart from the central position by x

Vo = (Ka −Kb) sin(ωt− φ) (move up)Vo = (Kb −Ka) sin(ωt− φ)

= (Ka −Kb) sin[ωt− (π − φ)] (move down)

Relationship between x and magnitude of output voltage Vom

Vom = Cx

Accelerometer in Fig. 15Given Fa = force causing acceleration of the body M

Fa = Mx

Given Fs = spring force

Fs = Kx

Given Fd = damping force

Fd = Bx

Kx+Bx = Mx


Figure 16 Noise obscures the information contained in an analog signal because the original am-plitude cannot be determined exactly after noise is added.

3 Digital Signal Processing

Why Digital Signal? in Fig. 16

Analog to Digital Conversion (ADC) in Fig. 17

ResolutionThe resolution of ADC depends on the number of bits (binary digits). The more

bits, the more accurate is the conversion and the greater is the resolution.

• 4-bit: ADC can represent 16 different values of analog signal (24 = 16)



• etc.

Flash Method of ADC in Fig. 18This method increases the resolution of ADC. But we need more comparator circuits,

which is take time for digital conversion.

Conversion Time in Fig. 19The data may be lost because of the long conversion time.

Quantization Error in Fig. 20The converted value is different from the wanted value.


Figure 17 The basic idea of analog–to–digital conversion.

Figure 18 A 3–bit flash ADC.


Figure 19 An illustration of analog–to–digital conversion time.

Figure 20 An illustration of the source of quantization errors in A/D conversion.


Figure 21 Using a sample–and–hold circuit to avoid quantization error.

Figure 22 Illustration of twe different sampling rates.

Fixing Quantization Error in Fig. 21By using a sample–and–hold circuit, a quantization error can be fixed.

Sampling Rate in Fig. 22Nyquist rate or frequency: the theoretical minimum limit of the sampling rate (at

least twice per cycle).


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