Electrical Measurements

Juliusz B. Gajewski

Professor of Electrical Engineering

Fundamentals of Electrical

Engineering

INSTITUTE OF HEAT ENGINEERING

AND FLUID MECHANICS

Electrostatics and Tribology Research Group

Wybrze ż e S. Wyspia ń skiego 27

50-370 Wroc ł aw, POLAND

Building A4 „Stara kot ł ownia”, Room 359

Tel.: +48 71 320 3201; Fax: +48 71 328 3218

E-mail: juliusz.b.gajewski@pwr.wroc.pl

Internet: www.itcmp.pwr.wroc.pl/elektra

Contents

1. Terms. Fundamental Definitions and Units.

2. Electrostatics. Electrostatic and Electric Fields.

3. Electrodynamics. DC Current.

4. Electromagnetism. Magnetic Field of DC Current.

5. Electric Circuit Elements.

6. Sinusoidal AC Voltage.

7. Complex Frequency Concept.

8. Electric Filters.

9. Electrical Measurements.

10. Three-Phase Circuits.

11. Electrical Signals.

12. Electric Switches.

33

Electrical Measurements


55


Philosophy of Measurements

„Regardless of its character, information is usually encoded as a magnitude of a physical quantity, and measurement is necessary in order to determine it. In the measurement process the magnitude of the respective parameter is expressed by a number which is compared with an appropriate scale for that same parameter. Only two techniques for comparison are known. The first is an analog technique using a classical measuring instrument with a pointer. The position of the pointer is compared with a scale. The actual comparison is made by an observer. The second technique is based on an analog/digital (A/D) converter. The electric voltage, current or signal frequency is compared to a reference voltage, current or frequency by means of electronic digital techniques. The result of the comparison is a numerical value which is presented in a digital code. The great variety of physical parameters requires a great number of alternative techniques of comparison. If one is to measure such quantities, their magnitudes must be converted into magnitudes of a reference voltage, current or frequency, or into a magnitude of the displacement of the pointer of an instrument. All these cases of conversion involve energy exchange. Therefore the magnitude of the respective physical quantity, the magnetic field, for instance, is converted into a certain kind of energy, a definite relationship existing between it and the basic parameter ” .

*)

*)

Citation from „Solid State Magnetic Sensors” by Roumenin, C.S., Elsevier 1994


Analog, Pointer Measuring Instruments

Measurements of electrical quantities: voltage, current, power and work of current, etc. are performed with instruments in which the phenomena that follow or are a result of a current flow are used: t h e r m a l, c h e m i c a l and m a g n e t i c. The most significant phenomena from the practical point of view are the magnetic ones and forces that act in the magnetic field of current.

In the steady-state conditions measurements are carried out with the use of p o i n t e r m e a s u r i n g i n s t r u m e n t s

(meters). In these meters a d r i v i n g t o r q u e acts on a moving organ (part) and causes a pointer to moves over the scale of a meter to show the value of the quantity measured. In the case of measurements of periodically varying currents and voltages the meter’s scale is calibrated in average or effective values.

77



The moving organ produces a restoring torque that balances the driving torque and to do so spiral springs are used. To set up a pointer in the zero position an eccentric cam is used. A counterbalance balances the moving organ in order that its centre of gravity be on the axis of rotation.

Under the driving torque the pointer deflects by an angle

α

, at which the balance of the driving torque by the restoring torque. As a result of the moving part’s inertia the state of equilibrium can be achieved after some number of sways (oscillations) and not at once. To shorten the time of sways one uses a damper that produces a damping torque within the movement of the moving organ. The air and eddy-current dampers are most frequently used.



In the air damper the movement is attenuated with the drag of air in a chamber in which a wing of the damper moves. The eddycurrent dampers work is based on eddy currents induced in a plate moving in the field of a magnet.

The fundamental part of each meter is its measuring structure, that is that part of a meter in which any electrical quantity is measured and is converted into the deflection of a pointer. With regard to the construction and principle of operation, the magnetic field-based instruments are as follows: z m a g n e t o e l e c t r i c, z z z e l e c t r o m a g n e t i c, e l e c t r o d y n a m i c, i n d u c t i o n.



Pointer, counterbalance and restoring spring

Air damper and eddy-current damper



Magnetoelectric Meters

Types: z permanent-magnet moving-coil instrument — moving coil and stationary permanent magnet z moving-magnet instrument

1. Permanent magnet.

2. Coil at the aluminum frame.

3. Soft-iron armature core — core of the soft magnetic material.

4. Two spiral restoring springs.

5. Pole pieces.




M o v i n g-c o i l i n s t r u m e n t — A measuring instrument in which current or voltage is determined by the couple on a small coil pivoted between the poles of a magnet with curved poles, giving a radial magnetic field. When a current flows through the coil it turns against a return spring. If the angle through which it turns is

α

, the current I is given by I

= k

α

/ BAN , where B is the magnetic flux density, A is the area of the coil, and N is its number of turns; k is a constant depending on the strength of the return spring. The instrument is suitable for measuring DC but can be converted for AC by means of a rectifier network. It is usually made as a galvanometer and converted to an ammeter or voltmeter by means of a shunt or a multiplier.




M n

=

M d

=

2

Driving torque rFN

=

2 rBIlN

=

BANI

= k

1

I

Restoring torque

M z

=

M r

= k

2

α

Pointer’s deflection angle

α

= k k

2

1

I

= kI




The direction of the torque generated in a moving-coil instrument is dependent on the instantaneous direction of the current through the coil, that is the direction of the deflection depends on the polarity, so that unmodified indicators are usable only on DC and unidirectional pulsating currents, and may have a centre zero if required. Thus an alternating current produces no steady-state deflection and the pointer indicates zero. Moving-coil instruments are provided with an AC response by the use of a full-wave bridge rectifier. The bridge rectifier converts the AC signal into a unidirectional signal through the moving-coil instrument which then responds to the average DC current through it. Such instruments measure the mean absolute value of the waveform and are calibrated to indicate the RMS value of the wave on the assumption that it is a sinusoid.




Magnetoelectric moving-coil instruments can be used as: z g a l v a n o m e t e r s, z z v o l t m e t e r s, a m m e t e r s.

Coils are made of thin wires and in general are to be used for the low currents (up to several dozen miliampers), and because of its low resistance the range of the volatges measured is also narrow. To extend the measuring range of the instruments special resistors are connected in parallel with ammeters — s h u n t s — or in series with voltmeters — m u l t i p l i e r s.




Shunt

A

R a

I a

I

−

I a

I

R s

R a

I a

=

(

I

−

I a

)

R s

R s

=

R a

I

I a

−

I a

= n

R a

−

1




Multiplier

U v U

−

U v

I

V

R v

R m

U

U v

=

R v

I and U

−

U v

=

R m

I R m

=

R v

U

−

U v

U

=

( n

−

1

)

R v




18



Electromagnetic Meters

Types: z one-core (solenoid- or attraction-type) meter z two-core (repulsion-type) meter

1. Core (vane, disc) of the soft magnetic material.

2. Fixed foil.

3. Movable vane.

4. Unmovable fixed coil.

5. Fixed (unmovable) vane.




W

=

1

2

LI

2

M n

=

M d

= d W d

α

=

I

2

2 d L d

α

α = kI 2 d L d

α d L d

α

= const




In the one-core, attraction-type instruments current passes through a coil of wire (solenoid) wound on a hollow tube of some non-magnetic material. Therefore the coil becomes a magnet and its lines of force tend to pull the soft-iron plunger into the coil. The stronger the current, the greater is the magnetic field and the greater is the pull on the plunger which pulls the pointer attached to it over the face of the scale. The amount of deflection of the pointer over the scale is an indication of the strength of the current flowing through the coil and being measured.




In the more often used two-core, repulsion-type instruments in the interior of the cylinder-shaped coil are two soft-iron vanes (pieces): one of them is fixed and the other is free to move. A current passes through the coil and the vanes become magnetized in the magnetic field so produced. Since they are magnetized in the same way, the two vanes repel each other both for DC and AC currents. As a result, the movable vane is deflected around the centre shaft, turning the shaft and carrying the pointer with it. The greater the current flowing through the coil, the greater is the deflection of the pointer. The scale is not even, uniform; it is of the square-law type and cramped at the lower end. The pointer’s deflection is proportional to the RMS value of the current measured and thus the instrument provides a steady-state deflection from an AC current. The scale is calibrated in terms of RMS values. If the scale is also valid for DC currents, the adequate information (a sign) is given usually below the scale.




The electromagnetic meters are used to measure DC and AC current as: z v o l t m e t e r s, z a m m e t e r s.

The voltmeter has the coil made of thin wire with many turns to increase its resistance which results in a weak current flowing through it. The ammeter’s coil in turn is made of thick wire with the small number of turns to have low resistance.




Such instruments can measure the voltages from single volts even up to

600 V, while the currents measured can range from 50 mA to ca. 300 A.

To measure high voltages or very strong currents special measuring transformers are used which are called the c u r r e n t transformers and the v o l t a g e transformers.




I

1

Current transformer

K L z

1

K L k l

A k z

2

I

2

A l


U

1



Voltage transformer

M z

1 N

I

1

I

2

≅ z

2 z

1

∧

U

1

U

2

≅ z

1 z

2 m z

2

U

2

V n






Electrodynamic Meters

1. Unmovable fixed coil.

2. Movable coil.

3. Spring.

α = kI

1

I

2 cos ϕ

α = kI

2

I

= v

U

R v




The electrodynamic meters are used to measure DC and AC current as: z a m m e t e r s, z v o l t m e t e r s, z w a t t m e t e r s.

Both unmovable and movable coils are connected in series (an ammeter) or in parallel (a voltmeter) and put into a measuring circuit. Te deflection of the pointer is proportional to the square of current that flows through the measuring structure. Electrodynamic ammeters and voltmeters have more complex structure and are more expensive than magnetoelectric and electromagnetic meters and therefore are not too often used; they are mainly the standard laboratory instruments of high accuracy.




The electrodynamic instruments are mainly used to measure the electric power of AC current as e l e c t r o d y n a m i c w a t t m e t e r s. The wattmeter consists of a pair of fixed coils, known as current coils, and a movable coil known as the potential coil. The fixed coils are made up of a few turns of a comparatively large conductor. The potential coil consists of many turns of thin wire. It is mounted on a shaft, carried in jeweled bearings, so that it may turn inside the stationary coils. The movable coil carries the pointer which moves over a suitably marked scale. Spiral coil springs hold the needle to a zero position.




The fixed unmovable current coil is connected in series with the circuit

(load), and the movable potential coil is connected across the line. When line current flows through the current coil, the magnetic field is set up around the coil. The strength of this field is proportional to the line current and in phase with it. The potential coil generally has a highresistance resistor connected in series with it. This is for the purpose of making the potential-coil circuit of the meter as purely resistive as possible. As a result, current in the potential-coil circuit is practically in phase with line voltage. Therefore, when voltage is applied to the circuit, current I v is proportional to and in phase with the line voltage U :

U

I v

=

R v




α = kII v cos ϕ = kI

U

R v cos ϕ = c w

UI cos ϕ = c w

P c w

=

U n

I

α n cos max ϕ n

Wattmeter constant






Induction Watt-Hour Meters




In induction watt-hour meters an effect of a magnetic filed flux on the eddy currents induced in a metal (aluminium) disc by the current flowing in the coil of an electromagnet. To increase a driving torque two-flux meters.

The induction meter operates by counting the revolutions of the aluminium disc which is made to rotate at a speed proportional to the power. The number of revolutions is thus proportional to the energy usage. It consumes a small amount of power, typically around 2 watts.




The metallic disc is acted upon by two coils. One coil is connected in such a way that it produces a magnetic flux in proportion to the voltage and the other produces a magnetic flux in proportion to the current. The field of the voltage coil is delayed by 90 degrees using a lag coil. This produces eddy currents in the disc and therefore a force is exerted on the disc in proportion to the product of the instantaneous current and voltage. A permanent magnet exerts an opposing force proportional to the speed of rotation of the disc. The equilibrium between these two opposing forces results in the disc rotating at a speed proportional to the power being used. The disc drives a register mechanism which integrates the speed of the disc over time by counting revolutions in order to render a measurement of the total energy used over a period of time.




M

= d cI

1

I

2 f cos

ψ

M d

= k

α = c

1

UI cos ϕ = c

1

P

M r

= c

2 n

N

= t

∫

0 n d t n

= c

= c

2 c

1 c

2

1 P t

∫

0

P d t

= cA

Angular velocity

Revolutions







Technical Method of Resistance Measurement

Accurate DC Measurement of Voltage

U

I

A

R x

I v

I

−

I v

V

R v

R v

→ ∞

I v

=

R x

U

=

R v

I

U

−

I v

=

U

I

−

U

R v

R * x

=

U

I

δ =

R * x

−

R x

R x

= −

R * x

R v

R x

< <

R v

R x

<

1.0

Ω


Technical Method of Resistance Measurement

Accurate DC Measurement of Current

U V

I

A

R a

R x

R x

=

U

I

−

R a

R a

→

0

R * x

=

U

I

δ =

R * x

−

R x

R x

=

R * x

R a

−

R a

R x

> >

R a

R x

>

1.0

Ω

41

A

E

R x

R

1

D

Resistance Measurement

Wheatstone Bridge

C

V

W

1

R

2

R n

U

AC

=

U

AD i U

CB

I

1

R x

=

I

1

R n

=

I

2

R

I

2

R

2

1

=

U

DB

B

W

2

R x

=

R n

R

1

R

2

R x

< 0.1 (1.0) Ω — Thomson ( Kelvin ) bridge

0.1 (1.0) Ω <

R x

< 10 6 Ω

42


Measurement of Active and Apparent Powers and Power Factor

Active Power and Resistance

I

W

U R

P

=

UI

43



Active Power and Impedance

I

W

U Z

P

=

UI cos ϕ

, since

α = c w

UI cos ϕ = c w

P

44



Apparent Power, Power Factor and Impedance

I

W A

U V

Z

P

=

UI cos ϕ

, S

=

UI

∧ cos ϕ =

P

S

45

46


Oscilloscope

47


Oscilloscope cathode-ray tube

Y input amplifier internal synchronization system time-base generator

230 V

~ power supply amplifier X input

48


Oscilloscope

49


Oscilloscope

Frequency Measurement

Lissajous figures

1:1 2:1 1:5

50

Electrical Measurements y y

0

=

0 y max

Oscilloscope

Phase Measurement y y

0

=

0.5

y max

=

1.0

x x ϕ =

0° sin ϕ = y

0 y max ϕ =

30°

51

Electrical Measurements y y

0

=

0.707

y max

=

1.0

Oscilloscope

Phase Measurement x y y

= y max x ϕ =

45° sin ϕ = y

0 y max ϕ =

90°

52


53


Measurement of Non-Electric Quantities with

Electrical Methods

To measure a non-electric quantity a special device must be used which is a first input unit of a given measuring instrument and which converts the quantity X measured into a proportional electric signal Y : Y

= f ( X ).

Such an element is called a t r a n s d u c e r or often a s e n s o r.

The transducer is any device or element which converts an input signal into an output signal of a different form. For example: the microphone, phonograph pickup, loudspeaker, barometer, photoelectric cell, automobile horn, doorbell, and underwater sound transducer. The sensor in turn is a device that senses either the absolute value or a change in a physical quantity such as temperature, pressure, flow rate, or pH, or the intensity of light, sound, or radio waves and converts that change into a useful input signal for an information-gathering system; a television camera is therefore a sensor, and a transducer is a special type of sensor.

54




X

transducer or sensor or probe

Y

=

f

(

X

) processing electronics display or meter electric energy source

55




Sometimes the sensor can be an input unit of the transducer. Where this element is not brought into contact with the object measured or does not disturb (or disturbs to a small extent) a given process occurring in this object, such a transducer is called a p r o b e. Once it was permitted that the probe could be in contact with the object or process measured.

The electric transducer converts the non-electric quantity measured into voltage, current or charge and then it does not require any auxiliary source of electric energy. It is called the a c t i v e t r a n s d u c e r. The transducer that changes one or more parameters of a measuring circuit under the effect of the quantity measured, e.g. R , L , C , etc., is called the p a s s i v e t r a n s d u c e r since it must be powered from an external source of energy.

56




Active transducers: z i n d u c t i o n (electrodynamic, electrostatic, electromagnetic, etc.), z p i e z o e l e c t r i c, z t h e r m o e l e c t r i c, z h a l l o t r o n (Hall effect), z p h o t o e l e c t r i c, z other

Passive transducers: z r e s i s t a n c e (potentiometer, tensometric, etc.), z i n d u c t a n c e (differential transformer, eddy-current, etc.), z c a p a c i t a n c e, z c o n d u c t a n c e, z t h e r m i s t o r, z e l e c t r o l y t i c, z other.

57




58




59




60




61




62




63

Thank you for your attention!

© 2010 Juliusz B. Gajewski

64

Electrical Measurements

Juliusz B. Gajewski

Professor of Electrical Engineering

Fundamentals of Electrical

Engineering