Subject -EMI

Unit 1 : Block schematics of

measuring system

1.Performance Characteristics

STATIC CHARACTE RISTICSThe static characteristics of an instrument are, in general, considered for

instruments which are used tomeasure an unvarying process condition. All the static performance

characteristics are obtained by oneform or another of a process called calibration. There are a number of

related definitions (orcharacteristics), which are described below, such as accuracy% precision,

repeatability, resolution,errors, sensitivity, etc.l. Instrument: A device or mechanism used to determine the present value

of the quantity undermeasurement.

2. Measurement: The process of determining the amount, degree, or capacity by comparison (direct or

indirect) with the accepted standards of the system units being used.3. Accuracy: The degree of exactness (closeness) of a measurement

compared to the expected (desired)value.4. Resolution: The smallest change in a measured variable to which

an instrument will respond.5. Precision: A measure of the consistency or repeatability of

measurements, i.e. successive readingsdoes not differ. (Precision is the consistency of the instrument output

for a given value of input).6. Expected value: The design value, i.e. the most probable value

that calculations indicate one shouldexpect to measure.7 Error: The deviation of the true value from the desired value.

8. Sensitivity: The ratio of the change in output (response) of the instrument to a change of input ormeasured variable.DYNAMIC CHARACTERISTICSInstruments rarely respond instantaneously to changes in the measured variables. Instead, they exhibitslowness or sluggishness due to such things as mass, thermal capacitance, fluid capacitance or electriccapacitance. In addition to this, 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 behaviour of the instrument is as important

as the static behaviour.

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 are as follows:l. Step change in which the primary element is subjected to an

instantaneous and finite change in measured variable.2.Linear change, in which the primary element is following a

measured variable, changing linearly with time.3,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

The dynamic characteristics of an instrument are (i) speed of response

(ii) Fidelity (iii) Lag (iv) dynamic error.(i) Speed of Response: It is the rapidity with which an instrument

responds to changes in the measuredquantity.(ii) Fidelity: It is the degree to which an instrument indicates the

changes in the measured variablewithout dynamic error (faithful reproduction).(iii) Lag: It is the retardation or delay in the response of an

instrument to changes in the measuredvariable.

(iv) Dynamic Error: It is the difference between the true values of a quantity changing with time and

the value indicated by the instrument, if no static error is assumed.

When measurement problems are concerned with rapidly varying quantities, the dynamic relations

between the instruments input and output are generally Defined by the use of differential equations

2.Static characteristicsThe set of criteria defined for the instruments, which are used to

measure the quantities which are slowly varying with time or mostly constant, i.e., do not vary with time, is called static characteristics.

The various static characteristics are:

i) Accuracyii) Precisioniii) Sensitivityiv) Linearityv) Reproducibilityvi) Repeatability

vi) Repeatability vii) Resolutionviii) Threshold ix) Drift x) Stability xi) Tolerance xii) Range or span

3 AccuracyIt is the degree of closeness with which the reading approaches

the true value of the quantity to be measured. The accuracy can be expressed in following ways:

a) Point accuracy:

Such accuracy is specified at only one particular point of scale.It does not give any information about the accuracy at any other Point on the scale.

b) Accuracy as percentage of scale span:

When an instrument as uniform scale, its accuracy may be expressed in terms of scale range.

• c) Accuracy as percentage of true value:

The best way to conceive the idea of accuracy is to specify it interms of the true value of the quantity being measured. Precision: It is the measure of reproducibility i.e., given a fixed value of a quantity, precision is a measure of the degree of agreement within a group of measurements. The precision is composed of two characteristics:

a) Conformity:

Consider a resistor having true value as 2385692 , which is being measured by an ohmmeter. But the reader can read consistently, a value as 2.4 M due to the nonavailability of proper scale. The error created due to the limitation of the scale reading is a precision error.

b) Number of significant figures:

The precision of the measurement is obtained from the number of significant figures, in which the reading is expressed. The significant figures convey the actual information about the magnitude & the measurement precision of the quantity. The precision can be mathematically expressed as:

Where, P = precisionXn = Value of nth measurementXn = Average value the set of measurement values

4.precision precision are defined in terms of systematic and random errors.

The more common definition associates accuracy with systematic errors and precision with random errors. Another definition, advanced by ISO, associates trueness with systematic errors and precision with random errors, and defines accuracy as the combination of both trueness and precision.

5. ResolutionThe smallest change in a measured variable to which an

instrument will respond.

6.Types of ErrorsThe static error of a measuring instrument is the numerical

difference between the true value of aquantity and its value as obtained by measurement, i.e. repeated

measurement of the same quantity givedifferent indications. • Static errors are categorized as gross errors or human errors • systematic errors• Random errors1. Gross ErrorsThis error is mainly due to human mistakes in reading or in using

instruments or errors in recording observations.

Errors may also occur due to incorrect adjustments of instruments and computational mistakes . These errors cannot be treated mathematically. The completeelimination of gross errors is not possible, but one canminimize them .Some errors are easily detected while others may be elusive. One of the basic gross errors thatoccur frequently is the improper use of an Instrument theerror can be minimized by taking proper care in readingand recording the measurement parameter. In general,indicating instruments change ambient conditions tosome extent when connected into a complete circuit.2. Systematic ErrorsThese errors occur due to shortcomings of, the instrument, such

as defective or worn parts, or ageing or effects of the

environment on the instrument.These errors are sometimes referred to as bias, and they

influence allmeasurements of a quantity alike. A constant uniform deviation

of the operation of an instrument isknown as a systematic error. There are basically three types of

systematic errors(i) Instrumental(ii) Environmental(iii) Observational(i) Instrumental ErrorsInstrumental errors are inherent in measuring instruments, because of their mechanical structure. For example, in the D'Arsonval movement friction in the bearings of various moving components, irregular

spring tensions, stretching of the spring or reduction in tension due to improper handling or over loadingof the instrument. Instrumental errors can be avoided by(a) Selecting a suitable instrument for the particular

measurement applications.(b) Applying correction factors after determining the amount of

instrumental error.(c) Calibrating the instrument against a standard.(ii) Environmental ErrorsEnvironmental errors are due to conditions external to the measuring device, including conditions in the area surrounding the instrument, such as the effects of change in temperature, humidity, barometric pressure or of magnetic or electrostatic fields.

(iii) Observational ErrorsObservational errors are errors introduced by the observer. The most common error is the parallax error introduced in reading a meter scale, and the error of estimation when obtaining areading from a meter scale.These errors are caused by the habits of individual observers. For example, an observer may always introduce an error by consistently holding his head too far to the left while reading a needle and scale reading.In general, systematic errors can also be subdivided into static and dynamic Errors. Static errors are caused by limitations of the measuring device or the physical laws governing its behavior.Dynamic errors are caused by the instrument not responding fast enough to follow the changes in a measured variable.

7. Gaussian ErrorsAmong the models proposed for the spot rate of interest, Gaussian models are probably the most widely used; they have the great virtue that many of the prices of bonds and derivatives can be easily computed in closed form. One drawback is that the spot rate process r, being Gaussian, may occasionally take negative values, though it is often claimed that if the probability of negative values is small, then there is no need to worry. It turns out that in many cases this is true, but there are some derivatives whose prices are very sensitive to the possibility of negative rates. One example is a knockout bond, which is a bond which becomes worthless if ever the interest rate drops below zero. Since we do not really believe

that interest rates can go negative, we can expect that Gaussian models will give prices at odds with intuition. But there are other, more subtle, examples, such as bonds of long maturity. The discrepancies which arise for these are happening because the bond price is of the form E exp(−X) for some Gaussian variable X and, although it may be very unlikely that X should be negative, when it is, we are exponentiating −X, and the contribution to the expectation can be overwhelming. For such derivatives, the prices which the Gaussian models predict can be absurd, yet we have no idea what the true price should be. This is because we have not clearly decided what should be the true interest rate model (which for convenience we approximate by a Gaussian). Until we address this, Gaussian models can continue to spring nasty surprises on us. In this article, we explore the problem, and suggest possible remedies.

To investigate this, we shall take the simplest model, the model of Vasicek [8], in which the spot rate process (rt)t≥0 solves a stochastic differential equation driven by a Brownian motion (Wt)t≥0

drt = σdWt + β(µ − rt)dt,

(1) where µ, β and σ are positive constants. 1 Firstly, let’s look at the prices of zero-strike caps and floors; if the zero-strike floor has a significantly positive price, this is a sign of trouble. In Table 1, you find the prices for zero-strike caps/floors for two different scenarios: in Scenario A, σ = 0.01, µ = 0.05, β = 0.125 and r0 = 0.02, while in Scenario B, σ = 0.025, µ = 0.10, β = 0.125 and r0 = 0.05. The prices are calculated assuming a sum borrowed of $ 1000.

8. Root Sum Squares formula

The root sum squared (RSS) method is a statistical tolerance analysis method. In many cases the actual individual part dimensions occur near the center of the tolerance range with very few parts with actual dimensions near the tolerance limits. This of course assumes the parts are mostly centered and within the tolerance range.

RSS assumes the normal distribution describes the variation of dimensions. The bell shaped curve is symmetrical and full described with two parameters, the mean, μ, and the standard deviation, σ.

The variances, not the standard deviations, are additive and provide an estimate of the

combined part variation. The result of adding the means and taking the root sum square of the standard deviations provides an estimate of the normal distribution of the tolerance stack. The formula to combine standard deviations of the stack is

Where σi is the standard deviation of the i’th part,And, n is the number of parts in the stack,And, σsys is the standard deviation of the stack.The normal distribution has the property that approximately

68.2% of the values fall within one standard deviation of the mean. Likewise, 95.4% within 2 standard deviation and 99.7% within 3 standard deviation.

9.Measuring instruments dc voltmeters

VoltmetersA voltmeter is an instrument that measures the difference in

electrical potential between two points in an electric circuit. An analog voltmeter moves a pointer across a scale in proportion to the circuit's voltage; a digital voltmeter provides a numerical display. Any measurement that can be converted to voltage can be displayed on a meter that is properly calibrated; such measurements include pressure , temperature, and flow.

In order for a voltmeter to measure a device's voltage, it must be connected in parallel to that device . This is necessary because objects in parallel experience the same potential difference.

10.  D' Arsonval Movement

An action caused by electromagnetic deflection, using a coil of wire and a magnetized field. When current passes through the coil, a needle is deflected.

Whenever electrons flow through a conductor, a magnetic field proportional to the current is created. This effect is useful for measuring current and is employed in many practical meters.Since most of the meters in use have D’Arsonval movements, which operate because of the magnetic effect, only this type will be discussed in detail. The basic dc meter movement is known as the D’Arsonval meter movement because it was first employed by the French scientist, D’Arsonval, in making electrical measurement.

This type of meter movement is a current measuring device which is used in the ammeter, voltmeter, and ohmmeter. Basically, both the ammeter and the voltmeter are current measuring instruments, the principal difference being the

method in which they are connected in a circuit. While an ohmmeter is also basically a current measuring instrument, it differs from the ammeter and voltmeter in that it provides its own source of power and contains other auxiliary circuits.

D’Arsonval Galvanometer :This instrument is very commonly used in various methods of

resistance measurement and also in d.c. potentiometer work.Construction of D’Arsonval galvanometer:The construction of D’Arsonval galvanometer is shown in figure

below. Let us discuss different parts of D’Arsonval galvanometer.

1) Moving Coil:It is the current carrying element. It is either rectangular or circular in shape and consists of number of turns of fine wire. This coil is suspended so that it is free to turn about its vertical axis of symmetry. It is arranged in a uniform, radial, horizontal magnetic field in the air gap between pole pieces of a permanent magnet and iron core. The iron core is spherical in shape if the coil is circular but is cylindrical if the coil is rectangular. The iron core is used to provide a flux path of low reluctance and therefore to provide strong magnetic field for the coil to move in. this increases the deflecting torque and hence the sensitivity of the galvanometer. The length of air gap is about 1.5mm. In some galvanometers the iron core is omitted resulting in of decreased value of flux density and the coil is made

narrower to decrease the air gap. Such a galvanometer is less sensitive, but its moment of inertia is smaller on account of its reduced radius and consequently a short periodic time.2) Damping:There is a damping torque present owing to production of eddy

currents in the metal former on which the coil is mounted. Damping is also obtained by connecting a low resistance across the galvanometer terminals. Damping torque depends upon the resistance and we can obtain critical damping by adjusting the value of resistance.

3) Suspension:The coil is supported by a flat ribbon suspension which also

carries current to the coil. The other current connection in a sensitive galvanometer is a coiled wire. This is called the lower suspension and has a negligible torque effect. This type of

galvanometer must be leveled carefully so that the coil hangs straight and centrally without rubbing the poles or the soft iron cylinder. Some portable galvanometers which do not require exact leveling have ” taut suspensions” consisting of straight flat strips kept under tension for at the both top and at the bottom.The upper suspension consists of gold or copper wire of nearly 0.012-5 or 0.02-5 mm diameter rolled into the form of a ribbon. This is not very strong mechanically; so that the galvanometers must he handled carefully without jerks. Sensitive galvanometers are provided with coil clamps to the strain from suspension, while the galvanometer is being moved.4) Indication:The suspension carries a small mirror upon which a beam of light is cast. The beam of light is reflected on a scale upon which the deflection is measured. This scale is usually about 1 meter away

from the instrument, although ½ meter may be used for greater compactness.

5) Zero Setting:A torsion head is provided for adjusting the position of the coil

and also for zero setting.

11. AC Voltmeters and Current Meters

AC electromechanical meter movements come in two basic arrangements: those based on DC movement designs, and those engineered specifically for AC use. Permanent-magnet moving coil (PMMC) meter movements will not work correctly if directly connected to alternating current, because the direction of needle movement will change with each half-cycle of the AC. Permanent-magnet meter movements, like permanent-magnet motors, are devices whose motion depends on the polarity of the applied voltage (or, you can think of it in terms of the direction of the current).

AC voltmeter

12. OhmmetersThe purpose of an ohmmeter, of course, is to measure the

resistance placed between its leads. This resistance reading is indicated through a mechanical meter movement which operates on electric current. The ohmmeter must then have an internal source of voltage to create the necessary current to operate the movement, and also have appropriate ranging resistors to allow just the right amount of current through the movement at any given resistance.

Starting with a simple movement and battery circuit, let’s see how it would function as an ohmmeter

13. MultimetersA multimeter measures ELECTRICAL PROPERTIES such as AAC or DC

voltage, current, and resistance. Rather than have separate meters, this device combines a VOLTMETER, an AMMETER, and An ohmmeter. Electricians and the general public might use it on batteries, components, switches, power sources, and motors to diagnose electrical malfunctions and narrow down their cause.

The two main kinds of a multimeter are analog and digital. A digital device has an LCD screen that gives a straight forward decimal read out, while an analog display moves a bar through a scale of numbers and must be interpreted. Either type will work over a specific range for each measurement, and users should select one that's compatible with what he or she meters most, from low-voltage power sources to high-voltage car batteries. Multimeters are specified with a

sensitivity range, so consumers should make sure they get the appropriate one.

As a voltmeter, the tool can measure the amount of AC or DC voltage flowing through a circuit. Voltage is a difference in potential energy between the two points. A fan, for example, should be drawing 120 volts (in the U.S.) from the plug in the wall, but a computer scanner might only draw 12 volts from a converter. To test these components, the user should choose AC or DC, select an upper limit on the voltage, and plug the machine in question right into the multimeter, without breaking the circuit. The readout should reveal whether the device is functioning normally, when compared to the data specified in the user's manual.

As an ohmmeter, it finds the resistance in a circuit, which is given in ohms. A user can find the resistance at any point in a circuit by first unplugging the machine from a wall outlet or battery source then putting in an approximate range he or she expects to contain the number of ohms. The measuring tool actually passes a small amount of electricity from its own battery through the circuit to measure resistance by comparing the voltage sent out to what it receives.

14. True RMS Responding Voltmeters

True RMS responding voltmeter Complex waveforms are most accurately measured with a true RMS responding voltmeter. This instrument produces a meter indication by sensing waveform heating power, which is proportional to the square of the RMS value of the voltage. This heating power can be measured by feeding an amplified version of the input waveform to the heater element of a thermocouple whose output voltage is then proportional to E2 RMS. One difficulty with this technique is that the thermocouple is often non-linear in its behavior. This difficulty is overcome in some instruments by placing two thermocouples in the same thermal environment, as shown in the block diagram of the true RMS responding voltmeter of Figure

The effect of the nonlinear behavior of the couple in the input circuit (the measuring thermocouple) is cancelled by similar non-linear effects of the couple in the feedback circuit (the balancing thermocouple). The two couple elements form part of a bridge in the input circuit of a DC amplifier. The unknown AC input voltage is amplified and applied to the heating element of the measuring thermocouple. The application of heat produces an output voltage that upsets the balance of the bridge. The unbalance voltage is amplified by the DC amplifier and fed back to the heating element of the balancing thermocouple. Bridge balance will be re-established when the feedback current delivers sufficient heat to the balancing thermocouple, so that the voltage outputs of both couples are the same. At this point the DC current in the heating element of the feedback couple is equal to the AC current in the input couple. This DC current is therefore directly proportional to the effective, or RMS, value of the

input voltage and is indicated on the meter movement in the output circuit of the DC amplifier. The true RMS value is measured independently of the waveform of the AC signal, provided that the peak excursions of the waveform do not exceed the dynamic range of the AC amplifier.

A typical laboratory-type RMS responding voltmeter provides accurate RMS readings of complex waveform having a crest factor (ratio of peak value to RMS value) of 10/1. At 10 per cent of full-scale meter deflection, where there is less chance of amplifier saturation, waveforms with crest factors as high as 100/1 could be accommodated. Voltages throughout a range of 100 µV to 300 V within a frequency range of 10 Hz to 10 MHz may be measured with most good instruments.