Electrical Measurements ELC 213eng.modern-academy.edu.eg/e-learning/comm/Electrical Measurements/Ch2... · (PMMC) –Electro-dynamic ... current passing through the two stationary

Electrical MeasurementsELC 213

25-Feb-18 1

Chapter 2 Deflection Instrument Fundamentals

25-Feb-18 2

• The deflection instruments have a pointer, which deflects over its scale to indicate the quantity to be measured (current, voltage, …etc).

• Three forces (torques) are required for proper operation of these instruments:

–Deflecting Force (Torque)

–Control Force (Torque)

–Damping Force (Torque)

25-Feb-18 3

Deflecting Force (Torque)

• It deflects the pointer to a deflecting angle proportional to the input quantity to be measured

• Deflection instruments are classified, according to the source of generation of this force, into

two main types:

– Permanent Magnet Moving Coil instrument (PMMC)

– Electro-dynamic instrument

25-Feb-18 4

Permanent Magnet Moving Coil instrument (PMMC)

• The deflection force is generated due to the interaction between:the permanent magnet field, and the magnetic field generated due to the current passing through the movable coil.

• The deflection force (FD) equation is known as the motor equation:

FD = B I L where B is the permanent magnet field, I is the current passing through the movable coil, and Lis the length of the coil.

25-Feb-18 5

Electro-dynamic instrument

• The deflection force is generated due to the interaction between: the magnetic field generated due to the current passing through the movable coil, and the magnetic field generated due to the current passing through the two stationary coils.

25-Feb-18 6

Control Force (Torque)

• The control force stops the pointer at its exact final position.

• It also returns the pointer to its zero position when the input quantity is removed or equal to zero.

• The control force is equal in magnitude and opposite in direction to the deflection force (at final position).

• The source of the control force depends on the typeof the instrument suspension.

25-Feb-18 7

• Two types of movable coil suspensions are considered: jewel bearing suspension, and taut band suspension

• jewel bearing suspension

25-Feb-18 8

• In the jewel bearing suspension, there are twonon-magnetic spiral springs wound opposite to each other.

• When the pivot rotates, they apply a controlforce on the pivot (pointer) opposite to the deflection force.

• The degree of winding of one spring can be adjusted by a lever in order to mechanically adjust the zero deflection of the pointer.

• The control springs are also used to connect the input current to the moving coil because of their very low resistance.

25-Feb-18 9

• Taut band suspension

• In the taut band suspension, the pivot is held under the tension of two taut band metals.

• When the deflection angle of the pointer increases the taut bands are twisted and apply a control force on the pivot opposite to the deflection force, and proportionalto the angle of deflection.

• Taut band suspension is used for the very sensitive instruments because it represents zero friction to the moving system.

25-Feb-18 10

Damping Force (Torque)

• The damping force minimizes the oscillation of the pointeraround its final position.

• Its direction is opposite to the direction of the pointer motion.

• Its magnitude is proportional to the pointer acceleration.

• Therefore, it is generated only if the pointer moves and equals to zero if the pointer does not move.

25-Feb-18 11

• If the damping force is small (under damping), a fastresponse (movement) and high oscillation is obtained.

• But in case of over damping, a slow response (movement) of the pointer is obtained.

• Correct (critical damping) should be designed to have a zero oscillation, and fast pointer response (movement).

25-Feb-18 12

• The source of the damping force is either due to: the eddy current, or the air-vane damping.

Eddy current

• Is naturally generated by induction due to a coil and its former(non magnetic and conducting) movement in a magnetic field.

• The direction of the damping force (caused by eddy current) opposes the motion of the coil.

Air-vane damping

• is designed to produce the same effect of opposing the coilmovement, as shown below:

25-Feb-18 13

Measurement errors are usually expressed in two ways: absolute, and relative (percentage) errors.

Absolute Error (X)

• is defined as the difference between the measured value (Xm) and the true (nominal) value (X):

X = Xm- X [Dimension of X]

Relative Errors (X)

• is defined as the ratio between the absolute error (X) and the true (nominal) value (X):

X = ± X / X [Dimensionless]

Measurement Errors

25-Feb-18 14

• The relative error can be expressed as a percentage value by multiplying it by (100), and It is called:

Percentage Relative Error (X %).

X% = (± X) (10)2

• If the errors are still very small, the relative error can be by multiplying (10)6, and expressed as follows:

Part Per Million relative error (PPM)

PPM = (± X) (10)6

• The percentage relative errors are always used by engineers rather than the absolute errors, since they give sufficient information about the accuracy.

• The relative errors are often called Accuracy or Toleranceespecially, when the percentage errors are used.

25-Feb-18 15

Examples

1. The true (nominal) value of a resistor is 500 . It is measured using repeated experiments. The result value is value between 490 and 510 . Calculate the absolute error, the relative error, and the percentage relative error of measurements.

• The absolute error is:

R = Rm- R = 490 – 500 = -10

Or = 510 –500 = +10

Then R = 10

• The relative error is:

R = ± R / R = 10 / 500 = ± 0.02

• The percentage relative error is:

R% = (10 / 500) 100 = 2 %

25-Feb-18 16

2. If the Temperature Coefficient of Resistance (TCR) of a resistor is 100 PPM /C, and its value is 100 KΩ at 25C. Find the its valuewhen its temperature rises from 25 C to 40 C.

Since PPM = (± R) (10)6

Then R = PPM / (10)6 = (10)2 / (10)6 = (10)-4

Also R = ± R/R

Then R = R (R) = (10)5 (10)-4 = 10 Ω /C

Thus R40C = R25C + (40 - 25). R

= (10)5 + (15). 10

= (10)5 + (15). 10 = 100.15 KΩ

25-Feb-18 17

Accuracy, Precision, and Resolution

Accuracy

• It is the closeness of the individual results of repeated measurements to its true value.

Precision

• It is the closeness of the individual results of repeated measurements to some mean value.

Note:

• Accurate measurements mean precisemeasurements. But precise measurements do not mean accurate measurements

25-Feb-18 18

Example:

• For the shown analog instrument: if its precision is one fourth of its minimum scale division, then its precision is

± 0.4 V/ 4 = ± 0.1 V = ±100 mV

• For the shown digital instrument: if its precision is its least significant digit, then its precision is ±0.001V = ±1 mV

• If the accuracy of a measuring instrument is ± 1 %, this means that the measured value is 99% to 101% of the actual value.

Note:

• The accuracy of an instrument depends on the accuracy of its internal components. Whereas, its precision depends on its scale division or the number of its displayed digits.

25-Feb-18 19

Resolution • It is defined as the smallest change in the measured quantity

that can be observed, therefore the resolution is related to both precision and accuracy.

• Thus, from its definition, the resolution of the shown analog voltmeter = ±100 mV, and that of the digital voltmeter = ±1 mV.

Note:

• The resolution is also defined as how precisely a variable can be set (adjusted), for example:

– the resolution of a potentiometer whose total resistance = 100 Ω and its number of turns = 1000 turn is equal to the resistance of one turn which is = 0.1 Ω, because the resistance of one turn is its minimum adjustable resistance.

25-Feb-18 20

Classifications of Measurement Errors

Measurement errors are classified into three main categories:

Two non-determined errors : Gross and Random errorsOne determent error: systematic error.

Gross Errors:• Gross errors are happened due to human mistakes, that

why they are non-determinant errors, and can not be calculated or estimated.

• These errors can only minimized by being careful when doing the experiments, and stop working when feelingtired.

25-Feb-18 21

Random Errors:

• These errors are due to the unexpected environmental changes such as:

– Changing of power supply voltage or frequency, …etc.

– Changing of the ambient temperature, aging of the instruments, …etc.

• These errors are non-determinant.

• These errors can be minimized by repeating the experiment many times and taking the average value of its results as the final result.

25-Feb-18 22

Systematic Errors:

• Systematic errors are determinant (their values can be calculated).

• These errors are due to the used measurement system, they are be classified into: connection errors, and instrumental errors.

o Connection Errors

• This type of errors is sometimes called: error of method.

• It is happened due to ignoring some essential quantitiesduring measurements.

• Therefore, it depends on the chosen connection diagram.

25-Feb-18 23

Example:

• Both connections 1 and 2 are used to measure the value of the unknown resistor R.

• In both cases the measured value:

• Conn. 1 assumes Im = Iv+ IR = IR i.e. it assumes that: Iv<< IR

• Conn. 2 assumes Vm = Va+ VR = VR i.e. it assumes that: Va<< VR

25-Feb-18 24

)(Re

)(Re

IadingAmmeter

VadingVoltmetermR

• Also, in conn.1 Rm = R//Rv , and in conn.2 Rm = R+Ra

• Best connection must be used to minimize the error(exact value = measured value – error)

• Different methods of resistance measurement in reasonable accuracy will be discussed later in this course.

o Instrumental Errors• This type of errors is due to the limited accuracy of the

used instruments. • For example: if the accuracies of voltmeter and the

ammeter in the previous example are V % and I % respectively, then the total instrumental error in both connections is:

R % = (V % + I %)

25-Feb-18 25

# Specified Accuracy• Measurement devices are classified according to their

accuracy.

• The device (instrument) accuracy is called: class accuracy, granted accuracy, or specified accuracy (a) (aI for ammeter, aV for voltmeter, …).

• The specified accuracy (a) is defined as a percentageerror of the full-scale deflection FSD or the range:

a = (%)FSD

• The Maximum Granted Error (Δ) is the absolute error at any pointer deflection on the scale(constant allover therange) is obtained from the accuracy (a) as follows:

Δ = ± (1)

25-Feb-18 26

100rangea

• The percentage error (δ%), which is the measurement accuracyof any reading on the scale is obtained as follows:

δ% = (2)

• From (1) and (2), you get δ% directly as follows:

(3)

Note: by definition (δ% = a) when (reading = range)

Conclusion:

• The reading must be as high as possible to decrease its percentage error (±δ%).

• Therefore the range of the instrument must be selectedsuch that the pointer deflection is near as possible to FSD.

25-Feb-18 27

reading100

δ% = readingrangea

Measurement Error Combinations• When the measurement is done using more than one

instrument, each has its own inaccuracy.• Then the resultant error should be considered as the

combination of the inaccuracies of these instruments.

• For example if you use instrument (A) and the instrument (B) to obtain the result of the measurement (Y) as described by the formula:

Y =

The following subsections will help us to find directly the inaccuracy of the result in terms of the inaccuracy of the used instruments.

25-Feb-18 28

2

.BA

BA

BA

Sum of Quantities

• If V = V1 + V2

then : ±ΔV = ±(ΔV1 + ΔV2) ,and ± δV = ±

Difference of Quantities

• If V = V1 - V2

then : ±ΔV = ±(ΔV1 + ΔV2) ,and ± δV = ±

Conclusion:

To reduce the relative error, use the sum instead of the difference of quantities if possible.

25-Feb-18 29

21

21VV

VV

21

21VV

VV

Product of Quantities

• If P = VI

then: ±δP % = ±( δV % + δI %)

±ΔP = ±(δV % + δI %).(VI)

Quotient of Quantities

• If R = V/I

then: ±δR % = ±(δV % + δI %)

±ΔR= ±(δV% + δI%).(V/I)

Note

The relative error of the product or quotient of quantities =the sum of the relative error of each quantity

Conclusion:

• To reduce the absolute error, use the quotient instead of the product of quantities if possible.

25-Feb-18 30

Quantities Raised to a Constant Power

• If A = Bc

then : ±δA % = ± c ( δB% )

±ΔA = ± ( c δB% )(B)c

where c is a constant.

Note:

The relative error of a quantity raised to a constant power = its constant power multiplied by the relativeerror of the quantity.

Example

• If P = I2R

then: ±δP % = ± [2(δI %)+ δR %]

25-Feb-18 31

Assignment 1

Instruments (A) and (B) are used to obtain the result of a certain measurement (Y) described by the formula:

Y =

Find percentage relative error (±δY %), of the resulting measurement, in terms of the percentage relative errorsof the used instruments (±δA %), and (±δB %).

25-Feb-18 32

2

.BA

BA

BA