Chapter 1 INTRODUCTION TO INSTRUMENTATION

Chapter 1 INTRODUCTION TO INSTRUMENTATION

OBJECTIVES At the end of this chapter, students should be able to: 1. Explain the static and dynamic characteristics of an instrument. 2. Calculate and analyze the measurement error, accuracy, precision and limiting error. 3. Describe the basic elements of electronic instrument.

INTRODUCTION Instrumentation is a technology of measurement which serves sciences, engineering, medicine and etc. Measurement is the process of determining the amount, degree or capacity by comparison with the accepted standards of the system units being used. Instrument is a device for determining the value or magnitude of a quantity or variable. Electronic instrument is based on electrical or electronic principles for its measurement functions.

FUNCTION AND ADVANTAGES The 3 basic functions of instrumentation :- Indicating visualize the process/operation Recording observe and save the measurement reading Controlling to control measurement and process Advantages of electronic measurement Results high sensitivity rating the use of amplifier Increase the input impedance thus lower loading effects Ability to monitor remote signal

PERFORMANCE CHARACTERISTICS Performance Characteristics - characteristics that show the performance of an instrument. Eg: accuracy, precision, resolution, sensitivity. Allows users to select the most suitable instrument for a specific measuring jobs. Two basic characteristics : Static measuring a constant process condition. Dynamic - measuring a varying process condition.

PERFORMANCE CHARACTERISTICS Accuracy the degree of exactness (closeness) of measurement compared to the expected (desired) value. Resolution the smallest change in a measurement variable to which an instrument will respond. Precision a measure of consistency or repeatability of measurement, i.e successive reading do not differ. Sensitivity ratio of change in the output (response) of instrument to a change of input or measured variable. Expected value the design value or the most probable value that expect to obtain. Error the deviation of the true value from the desired value.

ERROR IN MEASUREMENT Measurement always introduce error Error may be expressed either as absolute or percentage of error Y Absolute error, e = n X n where Y n expected value X n measured value Y n X Y n n % error = 100

ERROR IN MEASUREMENT Relative accuracy, A 1 Y n Y n X n % Accuracy, a = 100% - % error = A 100 Precision, P = 1 X n X n X n where X n X n - value of the n th measurement - average set of measurement

The precision of a measurement is a quantitative or numerical indication of the closeness with which a repeated set of measurement of the same variable agree with the average set of measurements.

Example 1.1 Given expected voltage value across a resistor is 80V. The measurement is 79V. Calculate, i. The absolute error ii. The % of error iii. The relative accuracy iv. The % of accuracy

Solution (Example 1.1) Given that, expected value = 80V measurement value = 79V i. Absolute error, e = Y X = 80V 79V = 1V n n ii. % error = Y n X = 80 79 = 1.25% 100 100 Y n n 80 iii. Relative accuracy, Y = 0.9875 n X n A 1 Y iv. % accuracy, a = A x 100% = 0.9875 x 100%=98.75% n

Example 1.2 From the value in table 1.1 calculate Table 1.1 the precision of 6 th measurement? Solution the average of measurement value 98 101... 99 1005 X n 100.5 10 10 the 6 th reading Precision = 100 100.5 0.5 1 1 0. 995 100.5 100.5 No X n 1 98 2 101 3 102 4 97 5 101 6 100 7 103 8 98 9 106 10 99

LIMITING ERROR The accuracy of measuring instrument is guaranteed within a certain percentage (%) of full scale reading E.g manufacturer may specify the instrument to be accurate at 2 % with full scale deflection For reading less than full scale, the limiting error increases

LIMITING ERROR (cont) Example 1.6 Given a 600 V voltmeter with accuracy 2% full scale. Calculate limiting error when the instrument is used to measure a voltage of 250V? Solution The magnitude of limiting error, 0.02 x 600 = 12V Therefore, the limiting error for 250V = 12/250 x 100 = 4.8%

LIMITING ERROR (cont) Example 1.7 Given for certain measurement, a limiting error for voltmeter at 70V is 2.143% and a limiting error for ammeter at 80mA is 2.813%. Determine the limiting error of the power. Solution The limiting error for the power = 2.143% + 2.813% = 4.956%

Exercise A voltmeter is accurate 98% of its full scale reading. i. If the voltmeter reads 200V on 500V range, what is the absolute error? ii. What is the percentage error of the reading in (i).

Significant Figures Significant figures convey actual information regarding the magnitude and precision of quantity More significant figure represent greater precision of measurement Example 1.3 Find the precision value of X 1 and X 2? 101 X n X X 1 2 98 ===>> 2 s.f 98.5 ===>> 3 s.f

Solution (Example 1.3) X n X X 1 2 101 98 98.5 ===>> 2 s.f ===>> 3 s.f 98 101 X1 Precision = 1 101 0. 97 98.5 101 X Precision = 1 2 101 0.975 ===>more precise

Significant Figures (cont) Rules regarding significant figures in calculation 1) For adding and subtraction, all figures in columns to the right of the last column in which all figures are significant should be dropped Example 1.4 V 1 = 6.31 V + V 2 = 8.736 V Therefore V T = 15.046 V 15.05 V

Significant Figures (cont) 2) For multiplication and division, retain only as many significant figures as the least precise quantity contains Example 1.5 From the value given below, calculate the value for R 1, R 2 and power for R 1? I = 0.0148 A ===> 3 s.f V 1 = 6.31 V ===> 3 s.f V 2 = 8.736 V ===> 4 s.f

Solution (Example 1.5) R 1 V I 1 6.31V 0.0148A 426.35 426 ===> 3 s.f R 2 V I 2 8.736V 0.0148A 590.27 590 ===> 3 s.f P V I 6.31V 0. 0148 1 1 A = 0.09339 = 0.0934 ===> 3 s.f

Significant Figures (cont) 3) When dropping non-significant figures 0.0148 ==> 0.015 (2 s.f) ==> 0.01 (1 s.f)

TYPES OF STATIC ERROR Types of static error 1) Gross error/human error 2) Systematic Error 3) Random Error

TYPES OF STATIC ERROR 1) Gross Error cause by human mistakes in reading/using instruments may also occur due to incorrect adjustment of the instrument and the computational mistakes cannot be treated mathematically cannot eliminate but can minimize Eg: Improper use of an instrument. This error can be minimized by taking proper care in reading and recording measurement parameter. In general, indicating instruments change ambient conditions to some extent when connected into a complete circuit. Therefore, several readings (at three readings) must be taken to minimize the effect of ambient condition changes.

TYPES OF STATIC ERROR (cont) 2) Systematic Error - due to shortcomings of the instrument (such as defective or worn parts, ageing or effects of the environment on the instrument) In general, systematic errors can be subdivided into static and dynamic errors. Static caused by limitations of the measuring device or the physical laws governing its behavior. Dynamic caused by the instrument not responding very fast enough to follow the changes in a measured variable.

TYPES OF STATIC ERROR (cont) - 3 types of systematic error :- (i) Instrumental error (ii) Environmental error (iii) Observational error

TYPES OF STATIC ERROR (cont) (i) Instrumental error - inherent while measuring instrument because of their mechanical structure (eg: in a D Arsonval meter, friction in the bearings of various moving component, irregular spring tension, stretching of spring, etc) - error can be avoid by: (a) selecting a suitable instrument for the particular measurement application (b) apply correction factor by determining instrumental error (c) calibrate the instrument against standard

TYPES OF STATIC ERROR (cont) (ii) Environmental error - due to external condition effecting the measurement including surrounding area condition such as change in temperature, humidity, barometer pressure, etc - to avoid the error :- (a) use air conditioner (b) sealing certain component in the instruments (c) use magnetic shields (iii) Observational error - introduce by the observer - most common : parallax error and estimation error (while reading the scale) - Eg: an observer who tend to hold his head too far to the left while reading the position of the needle on the scale.

TYPES OF STATIC ERROR (cont) 3) Random error - due to unknown causes, occur when all systematic error has accounted - accumulation of small effect, require at high degree of accuracy - can be avoid by (a) increasing number of reading (b) use statistical means to obtain best approximation of true value

Dynamic Characteristics Dynamic measuring a varying process condition. Instruments rarely respond instantaneously to changes in the measured variables due to such things as mass, thermal capacitance, fluid capacitance or electrical capacitance. Pure delay in time is often encountered where the instrument waits for some reaction to take place. Such industrial instruments are nearly always used for measuring quantities that fluctuate with time. Therefore, the dynamic and transient behavior of the instrument is important.

Dynamic Characteristics The dynamic behavior of an instrument is determined by subjecting its primary element (sensing element) to some unknown and predetermined variations in the measured quantity. The three most common variations in the measured quantity: Step change Linear change Sinusoidal change

Dynamic Characteristics Step change-in which the primary element is subjected to an instantaneous and finite change in measured variable. Linear change-in which the primary element is following the measured variable, changing linearly with time. Sinusoidal change-in which the primary element follows a measured variable, the magnitude of which changes in accordance with a sinusoidal function of constant amplitude.

Dynamic Characteristics The dynamic performance characteristics of an instrument are: Speed of response- The rapidity with which an instrument responds changes in measured quantity. Dynamic error-the difference between the true and measured value with no static error. Lag delay in the response of an instrument to changes in the measured variable. Fidelity the degree to which an instrument indicates the changes in the measured variable without dynamic error (faithful reproduction).

Standard A standard is a known accurate measure of physical quantity. Standards are used to determine the values of other physical quantities by the comparison method. All standards are preserved at the International Bureau of Weight and Measures (BIMP), Paris. Four categories of standard: International Standard Primary Standard Secondary Standard Working Standard

Standard International Std Defined by International Agreement Represent the closest possible accuracy attainable by the current science and technology Primary Std Maintained at the National Std Lab (different for every country) Function: the calibration and verification of secondary std Each lab has its own secondary std which are periodically checked and certified by the National Std Lab. For example, in Malaysia, this function is carried out by SIRIM.

Standard Secondary Standard Secondary standards are basic reference standards used by measurement and calibration laboratories in industries. Each industry has its own secondary standard. Each laboratory periodically sends its secondary standard to the National standards laboratory for calibration and comparison against the primary standard. After comparison and calibration, the National Standards Laboratory returns the secondary standards to particular industrial laboratory with a certification of measuring accuracy in terms of a primary standard. Working Std Used to check and calibrate lab instrument for accuracy and performance. For example, manufacturers of electronic components such as capacitors, resistors and many more use a standard called a working standard for checking the component values being manufactured.

ELECTRONIC INSTRUMENT Basic elements of an electronics instrument Transducer Signal Modifier Indicating Device 1) Transducer - convert a non electrical signal into an electrical signal - e.g: a pressure sensor detect pressure and convert it to electricity for display at a remote gauge. 2) Signal modifier - convert input signal into a suitable signal for the indicating device 3) Indicating device - indicates the value of quantity being measure

INSTRUMENT APPLICATION GUIDE Selection, care and use of the instrument :- Before using an instrument, students should be thoroughly familiar with its operation ** read the manual carefully Select an instrument to provide the degree of accuracy required (accuracy + resolution + cost) Before used any selected instrument, do the inspection for any physical problem Before connecting the instrument to the circuit, make sure the function switch and the range selector switch has been set-up at the proper function or range

INSTRUMENT APPLICATION GUIDE Analog Multimeter

INSTRUMENT APPLICATION GUIDE Digital Multimeter

CHAPTER REVIEW Define the terms accuracy, error, precision, resolution, expected value and sensitivity. State three major categories of error. A person using an ohmmeter reads the measured value as 470 ohm when the actual value is 47 ohm. What kind of error does this represent? State the classifications of standards. What are primary standards? Where are they used? What is the difference between secondary standards and working standards? State three basic elements of electronic instrument.

THE END

CHAPTER 2 DC AND AC METER 43

OBJECTIVES At the end of this chapter, students should be able to: 1. Explain the basic contruction and working principle of D Arsonval meter movement. 2. Perfom basic electronic circuit analisis for D Arsonval meter family. 3. Identify the difference electronic circuit design for measurement meters using D Arsonval meter principle. 44

CHAPTER OUTLINE 1. D Arsonval Meter Movement 2. DC Ammeter 3. DC Voltmeter 4. Multi-range Voltmeter 5. Voltmeter Loading Effects 6. Ammeter Insertion Effects 7. Ohmmeter 8. Multi-range Ohmmeter 9. Multimeter 10. AC Voltmeter using half-wave rectifier 11. AC Voltmeter Loading Effects 12. Wheatstone Bridge 13. Kelvin Bridge 14. Bridge-controlled Circuit 45

2.1: D ARSORVAL METER MOVEMENT Also called Permanent-Magnet Moving Coil (PMMC). Based on the moving-coil galvanometer constructed by Jacques d Arsonval in 1881. Can be used to indicate the value of DC and AC quantity. Basic construction of modern PMMC can be seen in Figure 2.1. 46

2.1.1:Operation of D Arsonval Meter When current flows through the coil, the core will rotate. Amount of rotation is proportional to the amount of current flows through the coil. The meter requires low current (~50uA) for a full scale deflection, thus consumes very low power (25-200 Uw). Its accuracy is about 2% -5% of full scale deflection 47

Pointe r Permanent magnet Core Coil Air Gap Figure 2.1: Modern D Arsonval Movement 48

2.2: DC AMMETER The PMMC galvanometer constitutes the basic movement of a dc ammeter. The coil winding of a basic movement is small and light, so it can carry only very small currents. A low value resistor (shunt resistor) is used in DC ammeter to measure large current. Basic DC ammeter: 49

+ _ I Ish Im + Rsh Rm _ D Arsonval Movement Figure 2.2: Basic DC Ammeter 50

Referring to Fig. 2.2: Rm = internal resistance of the movement Rsh = shunt resistance Ish =shunt current Im = full scale deflection current of the movement I = full scale current of the ammeter + shunt (i.e. total current) 51

I sh R sh I m R m I sh I I m R sh I I m R I m m 52

EXAMPLE 3.1 A 1mA meter movement with an internal resistance of 100Ω is to be converted into a 0-100 ma. Calculate the value of shunt resistance required. (ans: 1.01Ω) 53

2.2.1: MULTIRANGE AMMETER The range of the dc ammeter is extended by a number of shunts, selected by a range switch. The resistors is placed in parallel to give different current ranges. Switch S (multiposition switch) protects the meter movement from being damage during range changing. Increase cost of the meter. 54

+ _ R1 R2 R3 R4 S + _ Rm D Arsonval Movement Figure 2.3: Multirange Ammeter 55

2.2.2: aryton shunt or universal shunt Aryton shunt eliminates the possibility of having the meter in the circuit without a shunt. Reduce cost Position of the switch: a) 1 : Ra parallel with series combination of Rb, Rc and the meter movement. Current through the shunt is more than the current through the meter movement, thereby protecting the meter movement and reducing its sensitivity. b) 2 : Ra and Rb in parallel with the series combination of Rc and the meter movement. The current through the meter is more than the current through the shunt resistance. c) 3 : Ra, Rb and Rc in parallel with the meter. Maximum current flows through the meter movement and very little through the shunt. This will increase the sensitivity. 56

Rc + 3 1 2 Rb + Rm _ D Arsonval Meter Ra _ Figure 2.4: Aryton Shunt 57

EXAMPLE 2.2 Design an Aryton shunt to provide an ammeter with a current range of 0-1 ma, 10 ma, 50 ma and 100 ma. A D Arsonval movement with an internal resistance of 100Ω and full scale current of 50 ua is used. 1m A + R4 10m A 50mA 100m A _ R3 R2 R1 + _ D Arsonval Movement 58

REQUIREMENT OF A SHUNT 1) Minimum Thermo Dielectric Voltage Drop Soldering of joint should not cause a voltage drop. 2) Solderability - never connect an ammeter across a source of e.m.f - observe the correct polarity - when using the multirange meter, first use the highest current range. 59

2.3: BASIC METER AS A DC VOLTMETER To use the basic meter as a dc voltmeter, must know the amount of current (I fsd ) required to deflect the basic meter to full scale. The sensitivity is based on the fact that the full scale current should results whenever a certain amount of resistance is present in the meter circuit for each voltage applied. S 1 I fsd 60

EXAMPLE 2.3 Calculate the sensitivity of a 200 ua meter movement which is to be used as a dc voltmeter. S Solution: 1 I fsd 1 200 ua 5k / V 61

2.4: A DC VOLTMETER A basic D Arsonval movement can be converted into a DC voltmeter by adding a series resistor (multiplier) as shown in Figure 2.3. + V Rs Multiplier Im Rm _ Figure 2.5: Basic DC Voltmeter Im =full scale deflection current of the movement (Ifsd) Rm=internal resistance of the 62

From the circuit of Figure 2.5: V I ( R R ) R R s s m V V I m s I I m m R R m m m V I m R m Therefore, 63

EXAMPLE 2.4 A basic D Arsonval movement with a full-scale deflection of 50 ua and internal resistance of 500Ω is used as a DC voltmeter. Determine the value of the multiplier resistance needed to measure a voltage range of 0-10V. Solution: V 10V Rs Rm 500 199. 5k I 50uA m 64

Sensitivity and voltmeter range can be used to calculate the multiplier resistance, Rs of a DC voltmeter. Rs=(S x Range) - Rm From example 2.4: Im= 50uA, Rm=500Ω, Range=10V S Sensitivity, 1 I m 1 50uA 20k / V So, Rs = (20kΩ/V x 10V) 500 Ω 65

2.5: MULTI-RANGE VOLTMETER A DC voltmeter can be converted into a multirange voltmeter by connecting a number of resistors (multipliers) in series with the meter movement. A practical multi-range DC voltmeter R1 R2 R3 R4 is shown in Figure 2.6. V1 V2 V3 Rm Im + V4 _ Figure 2.6: Multirange voltmeter 66

EXAMPLE 2.5 Convert a basic D Arsonval movement with an internal resistance of 50Ω and a full scale deflection current of 2 ma into a multirange dc voltmeter with voltage ranges of 0-10V, 0-50V, 0-100V and 0-250V. 67

2.6: VOLTMETER LOADING EFFECTS When a voltmeter is used to measure the voltage across a circuit component, the voltmeter circuit itself is in parallel with the circuit component. Total resistance will decrease, so the voltage across component will also decrease. This is called voltmeter loading. The resulting error is called a loading error. 68

2.7 AMMETER INSERTION EFFECTS Inserting Ammeter in a circuit always increases the resistance of the circuit and, thus always E I e reduces the current in the circuit. The expected R 1 current: (2-4) E Placing Ithe m meter in series with R1 causes the current R1 Rto mreduce to a value equal to: 69 (2-5)

2.7 AMMETER INSERTION EFFECTS Dividing equation (2-5) by (2-4) yields: I I m e R 1 R 1 R (2-6) Im The Ammeter 1insertion X100 I error is given by e : m Insertion Error (2-7) 70

2.8 OHMMETER (Series Type) Current flowing through meter movements depends on the magnitude of the unknown resistance.(fig 4.28 in text book) The meter deflection is non-linearly related to the value of the unknown Resistance, R x. A major drawback as the internal voltage decreases, reduces the current and meter will not get zero Ohm. R 2 counteracts the voltage drop to achieve zero ohm. How do you get zero Ohm? R 1 and R 2 are determined by the value of R x = R h where R h = half of full scale deflection resistance. R h R 1 ( R2 // Rm ) The total current of the circuit, It=V/R h The shunt current through R2 is I 2 =I t -I fsd R 1 R R 2 2 Rm R m (2-8) 71

2.8 OHMMETER (Series Type) The voltage across the shunt, Vsh= Vm So, Since I 2 R 2 =I fsd R m I 2 =I t -I fsd Then, Since R 2 I I t fsd R I m fsd I t =V/R h So, R 2 I fsd R V I m fsd R h R h (2-9) 72

2.8 OHMMETER (Series Type) From equation (2-8) and (2-9): R 1 R h I fsd R V m R h (2-10) 73

Figure 2.7: Measuring circuit resistance with an ohmmeter 74

Example: 1) A 50µA full scale deflection current meter movement is to be used in an Ohmmeter. The meter movement has an internal resistance R m = 2kΩ and a 1.5V battery is used in the circuit. Determine R z at full scale deflection. 2) A 100Ω basic movement is to be used as an ohmmeter requiring a full scale deflection of 1mA and internal battery voltage of 3V. A half scale deflection marking of 2k is desired. Calculate: i. value of R1 and R2 ii. the maximum value of R2 to compensate for a 5% drop in battery voltage 75

2.9 MULTI-RANGE OHMMETER Another method of achieving flexibility of a measuring instrument is by designing it to be in multi-range. Let us analyse the following examples. (figure 4.29 of your textbook) 76

2.10 MULTIMETER Multimeter consists of an ammeter, voltmeter and ohmmeter in one unit. It has a function switch to connect the appropriate circuit to the D Arsonval movement. Fig.4.33 (in text book) shows DC miliammeter, DC voltmeter, AC voltmeter, microammeter and ohmmeter. 77

2.11 AC VOLTMETER USING HALF-WAVE RECTIFIER The D Arsonval meter movement can be used to measure alternating current by the use of a diode rectifier to produce unidirectional current flow. In case of a half wave rectifier, if given input voltage, Ein = 10 Vrms, then: Peak voltage, Average voltage, E p 10Vrms 1.414 14. 14V Eave Edc 0.636 Ep 8. 99V o Since the diode conducts only during the positive half cycle as shown in Fig 4.18(in text book), the average voltage is given by: E ave / 2=4.5V 78

2.11 AC VOLTMETER USING HALF-WAVE RECTIFIER Therefore, the pointer will deflect for a full scale if 10 Vdc is applied and only 4.5 V when a 10 Vrms sinusoidal signal is applied. The DC voltmeter sensitivity is given by: 1 1 S 1k V dc I 1mA / m For the circuit in Figure 4.18, the AC voltmeter sensitivity is given by: Sac 0.45S dc 0.45k / V This means that an AC voltmeter is not as sensitive as a DC voltmeter. 79

2.11 AC VOLTMETER USING HALF-WAVE RECTIFIER To get the multiplier resistor, Rs value: o E R dc s 0.45 E I dc dc R E m rms 0.45 I (2-11) The AC meter scale is usually calibrated to give the RMS value of an alternating sine wave input. A more general AC voltmeter circuit is shown in Fig. 4.17 (in text book) A shunt resistor, Rsh is used to draw more current from the diode D1 to move its operating point to a linear region. Diode D2 is used to conduct the current during the negative half cycle. The sensitivity of AC voltmeter can be doubled by using a full wave rectifier. dc E rms R m 80

EXAMPLE Calculate the value of the multiplier resistor for a 10 Vrms range on the voltmeter shown in Fig 4.19 (in text book) 81

2.11 AC VOLTMETER USING FULL-WAVE RECTIFIER Consider the circuit in Fig 4.20 (in text book) Example: R s S ac range Calculate the value of the multiplier resistor for a 10 Vrms ac range on the voltmeter in Fig. 4.21 R m 82

2.12 WHEATSTONE BRIDGE Accurate method for measuring resistance between 1Ω ~ 1MΩ. Figure 11.1 shows the schematic diagram of a Wheatstone Bridge. When the bridge is set to null condition, I voltages 1R at 1 I point 2R C & 2 D are equal. Thus I 3R3 I4R4 83 (2-12) (2-13)

2.12 WHEATSTONE BRIDGE Since I 1 = I 3 and I 2 = I 4, divide equation 2-12 by equation 2-13: R R 1 R R 2 3 4 2 3 So, R X R4 R1 (2-14) Usually, the resistor R 3 is a variable resistor to balance the bridge. R X is the unknown resistor to be measured. When bridge is balance, the value of the unknown resistor R X is equal to resistance value of R 3 R R 84

2.12 WHEATSTONE BRIDGE Example: 1. Given the Wheatstone bridge with R 1 = 15 kω, R 2 = 10 kω, and R 3 = 4.5 kω. Find R X. 2. Calculate the current through the Galvanometer in the circuit. Given R 1 = 1 kω, R 2 = 1.6 kω, R 3 = 3.5 kω, R 4 = 7.5 kω, R G = 200Ω and V = 6V. 85

2.13 KELVIN BRIDGE Kelvin Bridge is used to measure resistance below 1 Ω. In low resistance measurement, the leads connecting the unknown resistor to the bridge may effect the measurement. Kelvin s Double Bridge known as Kelvin Bridge is constructed to overcome this problem. 86

2.13 KELVIN BRIDGE The resistor R Y represents the lead and contact resistance present in the Wheatstone Bridge. The resistors R a and R b are used to compensate this low leadcontact resistance. From circuit analysis, the unknown Resistor R X in a balanced Kelvin Bridge is given by: R R X 2 R R 3 1 R R b a (2-15) See example 11.4 (textbook) 87

2.14 BRIDGE CONTROLLED CIRCUIT E s When a bridge is imbalance, a potential difference exists at its output terminal. If it is used as an error detector in a control circuit, the potential difference at the output of the bridge is called an error signal. The error signal is given by: E R 1 R 3 R 3 R 2 R V R V (2-16) The unknown resistor R V can be any passive circuit elements such as strain gauge, thermistor and photo resistor. Since R V varies by only a small amount, an amplifier often needed before being used for control purposes. Fig. 11.14 shows the Wheatstone Bridge error detector. 88

What is a multimeter? A multimeter is a devise used to measure voltage, resistance and current in electronics & electrical equipment It is also used to test continuity between to 2 points to verify if there is any breaks in circuit or line There are two types of multimeter Analog & Digital Analog has a needle style gauge Digital has a LCD display (Referenced during this PPT)

There are 2 styles of multimeters Switched Manually switch between ranges to get most accurate reading. Auto Range Switches between ranges automatically for best reading. Both of these styles work the same

Meter leads Red meter lead Is connected to Voltage/Resistance or amperage port Is considered the positive connection Probes Are the handles used to hold tip on the tested connection Tips Are at the end of the probe and provides a connection point Black meter lead Is always connected to the common port Is considered the negative connection

Display & Dial Settings Digital Display Shows measured value. Meter Dial Turn dial to change functions. Turn dial to OFF position after use. Panel Indicator Shows each function and setting range to turn dial to. Probe Connections Specific for each function.

Common DMM Symbols ~ AC Voltage Ground --- DC Voltage ( Capacitor Hz Hertz F MicroFarad + Positive Micro Negative m Milli Ohms M Mega * Diode K Kilo These ))) symbols Audible are Continuity often found on OL multimeter Overload and schematics. They are designed to symbolize components and reference values.

Measuring Voltage Voltage (V) is the unit of electrical pressure; one volt is the potential difference needed to cause one amp of current to pass through one ohm of resistance Voltage is broke up into 2 sections AC & DC Alternating Current (AC) is house voltage (110vac) Direct Current (DC) is battery voltage (12vdc) On switched meters use one value higher than your expected value Be very careful to not touch any other electronic components within the equipment and do not touch the tips to each other while connected to anything else To measure voltage connect the leads in parallel between the two points where the measurement is to be made. The multimeter provides a parallel pathway so it needs to be of a high resistance to allow as little current flow through it as possible

Measuring Voltage

Measuring Voltage 9.3vdc

Measuring Resistance and Continuity Resistance ( ) is the opposition to current Resistance is measured in Ohm's Disconnect power source before testing Remove component or part from system before testing Measure using lowest value, if OL move to next level Testing for continuity is used to test to verify if a circuit, wire or fuse is complete with no open Audible continuity allows an alarm if circuit is complete If there is no audible alarm resistance of 1ohm to.1ohm should be present

Measuring Resistance

Measuring or Testing Continuity

Measuring Resistance 100

Measuring Continuity.5 Fuse 5 amp

Measuring Current Current (amps) is the flow of electrical charge though a component or conductor Current is measured in amps or amperes Disconnect power source before testing Disconnect completed circuit at end of circuit Place multimeter in series with circuit Reconnect power source and turn ON Select highest current setting and work your way down.

Measuring Current

Measuring Current 1.1amps

Review A meter capable of checking for voltage, current, and resistance is called a multimeter, When measuring Voltage the multimeter must be connected to two points in a circuit in order to obtain a good reading. Be careful not to touch the bare probe tips together while measuring voltage, as this will create a short-circuit! Never read Resistance or test for Continuity with a multimeter on a circuit that is energized. When measuring Current the multimeter must be connected in a circuit so the electrons have to flow through the meter Multimeters have practically no resistance between their leads. This is intended to allow electrons to flow through the meter with the least possible difficulty. If this were not the case, the meter would add extra resistance in the circuit, thereby affecting the current

Measurement of Voltages and Currents Chapter 11 Introduction Sine waves Square waves Measuring Voltages and Currents Analogue Ammeters and Voltmeters Digital Multimeters Oscilloscopes

Introduction 11.1 Alternating currents and voltages vary with time and periodically change their direction

Sine Waves 11.2 Sine waves by far the most important form of alternating quantity important properties are shown below

Instantaneous value shape of the sine wave is defined by the sine function y = A sin in a voltage waveform v = V p sin

Angular frequency frequency f (in hertz) is a measure of the number of cycles per second each cycle consists of 2 radians therefore there will be 2 f radians per second this is the angular frequency are rad/s) (units = 2 f

Equation of a sine wave the angular frequency can be thought of as the rate at which the angle of the sine wave changes at any time therefore sin 2 ft = t v = V p sin t or v = V p

Example see Example 11.2 in the course text From diagram: Determine the equation of the following voltage signal. Period is 50 ms = 0.05 s Thus f = 1/T =1/0.05 = 20 Hz Peak voltage is 10 V Therefore v V p sin 2 10 sin 2 ft 20t 10 sin 126t

Phase angles the expressions given above assume the angle of the sine wave is zero at t = 0 if this is not the case the expression is modified by adding the angle at t = 0

Phase difference two waveforms of the same frequency may have a constant phase difference we say that one is phase-shifted with respect to the other

Average value of a sine wave average value over one (or more) cycles is clearly zero however, it is often useful to know the 1 average magnitude of the Vav waveform Vpsin d independent of its polarity we can think of this as the average value over half a cycle or as the average value of the rectified signal V p 2V 0 θ p cos 0 0.637 V p

Average value of a sine wave

r.m.s. value of a sine wave the instantaneous power (p) in a resistor is 2 given by v p R therefore [average(or the average mean) power of v ] vis given by P av R 2 2 R 2 v

v 2 While the mean-square voltage is useful, more often we use the square root of this quantity, namely the rootmean-square voltage V rms where V rms = we can also define I rms = V 1 rms V 0. 707 2 p it is relatively easy to show that (see text for analysis) V p 2 i I 1 rms I 0. 707 2 p I p

r.m.s. values are useful because their relationship to average power is similar to the corresponding DC values P av V rms I rms P P av av V I rms R rms 2 2 R

Form factor for any waveform the form factor is defined as r.m.s. value Form factor average value Form factor 0.707V p 0.637V p 1.11 for a sine wave this gives

Peak factor for any waveform the peak factor is defined as peak value Peak factor r.m.s. value Peak factor V p 0.707V p 1.414 for a sine wave this gives

Square Waves 11.3 Frequency, period, peak value and peak-to-peak value have the same meaning for all repetitive waveforms

Phase angle we can divide the period into 360 or 2 radians useful in defining phase relationship between signals in the waveforms shown here, B lags A by 90 we could alternatively give the time delay of one with respect to the other

Average and r.m.s. values the average value of a symmetrical waveform is its average value over the positive half-cycle thus the average V value V p of a symmetrical square wave is equal to its peak value similarly, since V the Vinstantaneous value of rms p a square wave is either its peak positive or peak negative value, the square of this is

Form factor and peak factor from the earlier definitions, for a square V wave Form factor r.m.s. value average value p V p 1.0 Peak factor peak value r.m.s. value V p V p 1.0

Measuring Voltages and Currents 11.4 Measuring voltage and current in a circuit when measuring voltage we connect across the component when measuring current we connect in series with the component

Measuring Voltages and Currents 11.4 Loading effects voltage measurement our measuring instrument will have an effective resistance (R M ) when measuring voltage we connect a resistance in parallel with the component concerned which changes the resistance in the circuit and therefore changes the voltage we are trying to measure

Measuring Voltages and Currents 11.4 Loading effects current measurement our measuring instrument will have an effective resistance (R M ) when measuring current we connect a resistance in series with the component concerned which again changes the resistance in the circuit and therefore changes the current we are trying to measure this is again a loading effect

Analogue Ammeters and Voltmeters 11.5 Most modern analogue ammeters are based on moving-coil meters see Chapter 4 of textbook Meters are characterised by their full-scale deflection (f.s.d.) and their effective resistance (R M ) typical meters produce a f.s.d. for a current of 50 A 1 ma typical meters have an R M between a few ohms and a few kilohms

Measuring direct currents using a moving coil meter use a shunt resistor to adjust sensitivity see Example 11.5 in set text for numerical calculations

Measuring direct voltages using a moving coil meter use a series resistor to adjust sensitivity see Example 11.6 in set text for numerical calculations

Measuring alternating quantities moving coil meters respond to both positive and negative voltages, each producing deflections in opposite directions a symmetrical alternating waveform will produce zero deflection (the mean value of the waveform) therefore we use a rectifier to produce a unidirectional signal meter then displays the average value of the waveform meters are often calibrated to directly display r.m.s. of sine waves all readings are multiplied by 1.11 the form factor for a sine wave as a result waveforms of other forms will give incorrect readings

Analogue multimeters general purpose instruments use a combination of switches and resistors to give a number of voltage and current ranges a rectifier allows the measurement of AC voltage and currents additional circuitry permits resistance measurement very versatile but relatively low input resistance on voltage ranges produces considerable loading in some situations A typical analogue multimeter

Digital Multimeters 11.6 Digital multimeters (DMMs) are often (inaccurately) referred to as digital voltmeters or DVMs at their heart is an analogue-to-digital converter (ADC) A simplified block diagram

Measurement of voltage, current and resistance is achieved using appropriate circuits to produce a voltage proportional to the quantity to be measured in simple DMMs alternating signals are rectified as in analogue multimeters to give its average value which is multiplied by 1.11 to directly display the r.m.s. value of sine waves more sophisticated devices use a true r.m.s. converter which accurately produced a voltage proportional to the r.m.s. value of an input waveform A typical digital multimeter

Oscilloscopes 11.7 An oscilloscope displays voltage waveforms A simplified block diagram

A typical analogue oscilloscope

Measurement of phase difference

Key Points The magnitude of an alternating waveform can be described by its peak, peak-to-peak, average or r.m.s. value The root-mean-square value of a waveform is the value that will produce the same power as an equivalent direct quantity Simple analogue ammeter and voltmeters are based on moving coil meters Digital multimeters are easy to use and offer high accuracy Oscilloscopes display the waveform of a signal and allow quantities such as phase to be measured.