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CONTENTS

19-Jan-23

MEASURING INSTRUMENTS

MOTIVATION
MOVING COIL INSTRUMENT

2.1 PERMANENT MAGNET MOVING COIL (PMMC) TYPE

2.1.1 Operating Principle

2.1.2 Constructional Features

2.1.3 Torque Equation

2.1.4 Shape of the Scale

2.1.5 Use as D.C. Ammeter or as D.C. Voltmeter (Extension of Range):

2.2 ELECTRODYNAMIC (ELCTRODYNAMOMETER) TYPE

2.2.1 Construction (more to follow)

3. MOVING IRON INSTRUMENT (IRON-VANE INSTRUMENT)

3.1 CLASSIFICATION OF MOVING IRON (M.I.) INSTRUMENTS

3.2 ATTRACTION TYPE (OR SINGLE IRON TYPE)

3.3 REPULSION TYPE (DOUBLE IRON TYPE)

3.4 COMBINED ATTRACTION-REPULSION TYPE

3.4.1 Basic Principle and Construction

3.5 GENERAL TORQUE EQUATION

3.6 SHAPE OF SCALE

3.7 ADVANTAGES OF M.I. INSTRUMENTS

3.8 DISADVANTAGES OF M.I. INSTRUMENTS

Prepared by – M. R. Mohanta

MSE, BARIPADA

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MEASURING INSTRUMENTS

1. MOTIVATION

Diff. instruments are better suited for diff. applications.
Instruments augment / enhance the faculties / capabilities of human beings.
For all applications, guiding principle: measuring device, by defn. is meant only to measure & not to load /change /modify the measurand (qty. to be measured).
So, impedance (Z) or resistance (R) of instrument & its connection to circuit (in which measurements are to be made) should be such (in fact, high) that existing circuit conditions aren’t changed.
For the same season, power consumed by a measuring instrument should be small, else instrument will cause loading on the measurand.

19-Jan-23

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

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2. MOVING COIL INSTRUMENT

19-Jan-23

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

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19-Jan-23

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

Fig. 1(a) Suspension Type (Laboratory Type) PMMC (D’Arsonval) Movement;

(b) Light-beam and mirror arrangement

Fig. 2 Pivot & Bearing Type (Portable Type) PMMC (D’Arsonval) Movement.

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D’Arsonval & PMMC movements are same types of movements, yet Fig.1 is more popularly called D’Arsonval movement & Fig.2 is known as PMMC movement.
As galvanometer normally designed to have higher sensitivities than other instruments (like ammeters, voltmeters, etc.), so D’Arsonval movement quite often used for sensitive galvanometers & PMMC movement is commonly used for less sensitive ammeters & voltmeters.

2.1.2 Constructional Features:

We deal with only the moving coil and the core, the other constructional features touched upon in other sections (3.5 and 2.6 sections of chapters-3 & 2).
MOVING COIL & THE CORE:
Moving coil is made of many turns of enamelled or silk-covered copper wire; aluminum wire can be used to reduce weight & inertia.
Coil: wound on an insulated former/ frame/ bobbin of a light non-magnetic material.
Normally, voltmeter coils: wound on metallic formers to provide electromagnetic damping. Ammeter coils: wound on non-metallic formers as coil turns are effectively shorted by ammeter shunt &, so, coil itself provides electromagnetic damping.

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Ph.: 9416351300, Email: jssain@rediffmail.com

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Apart from damping, the ‘former’/ bobbin provides support to the fragile coil.
Normally, rectangular coils used; accordingly bobbin is also of rectangular shape.
But, sometimes long sides (A & B of Fig. 3b) of the former (frame) are curved to a radius so as to make the coil concentric with core & hence to make air gap (b/n magnet & core) minimum & uniform. The air gap is typically 1 mm radially.

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

Fig. 3 Coil and Former / Bobbin Shapes

Fixed soft iron core (armature) is placed concentrically with pole faces. Core: spherical if shape of coil is circular but core is cylindrical if coil is rectangular. Fn. of core: provide a low reluctance to flux path & ensure greater strength of magnetic field for the coil.

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Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

2.1.3. Torque Equation:

Dimensions of a PMMC instrument are as in Fig. 4:

Fig. 4 Dimensions of a PMMC instrument.

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α = angle between the direction of magnetic field and the active coil side. This angle is 90° since the field is radial and active coil side is vertical and it moves within the radial field region (i.e., it moves within the pole-arcs).

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

= NiAB Newton metre (1)

Since N, A, B are constants for a given instrument,

where G = NBA is ‘instrument constant’.

If spring control (usually used in PMMCs) is used, then controlling torque is:

where K_i = K/G = a constant

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2.1.4 Shape of the Scale:

From =n 4, in a spring controlled PMMC instrument, deflection is proportional to current passing through meter & so such an instrument has a uniform scale (provided, of course, current being measured is directly passed through meter).
Uniform scale holds good only if deflecting torque is independent of deflection, θ (as indicated by =n 1) which is ensured by having a uniform air gap & a radial field.
But if flux distribution is uneven in air gap (due to, say, eccentric core or specially shaped pole faces), scale will be non-uniform.
If qty. being measured is not proportional to current passed thro’ meter, scale is again non-uniform (provided, of course, that air gap is uniform & field is radial).
E.g., if quantity being measured is heat, which is proportional to I², then heat ∝ θ² (as θ ∝ I), thus scale will be cramped at lower end.

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

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2.1.5 Use as D.C. Ammeter or as D.C. Voltmeter (Extension of Range):

PMMC instrument: the most accurate for D.C. measurements.
Can’t measure A.C. as torque depends upon dir. of current. At very low freq. A.C. (< 1 Hz), pointer oscillates with freq. of current, but, at higher frequencies (say, 50 Hz or more), inertia of moving system prevents the pointer from moving at all in either dir.
Coil of basic PMMC meter instrument has ltd. current carrying capacity, say, it can safely carry current upto ≈ 20 mA. To measure currents usually, > 20 mA, shunt is connected across moving coil (Fig. 5) to bypass a major portion of total current.
A shunt is a low resistance (tube / strip / wire) connected across the meter circuit.
Galvanometer (note: galvanometer scale, is marked, but not calibrated) can read very small currents by calibrating its scale, so converting it into a micro- or milli-ammeter. But, range can be extended by use of shunts, thus making an ammeter.

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

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19-Jan-23

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

Fig. 5 Basic PMMC meter in conjunction with a shunt to form an ammeter.

Fig. 6 Basic PMMC meter in conjunction with a multiplier to form a voltmeter.

Similarly, basic PMMC meter can read micro or milli volts by calibrating its scale in micro or millivolts. But, to convert it into a volt-meter (capable of reading >100 mV, say), suitable high resistance (called multiplier) to be connected in series with meter (Fig. 6).

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2.2 ELECTRODYNAMOMETER (OR DYNAMOMETER OR ELECTRODYNAMIC) MOVING COIL TYPE:

Motivation for studying this instrument comes from following 4 facts:
It has two independent ckts. (thus 2 independent i/ps to movement) that permit its use in diff. applications such as I-, V-, W-, VAR-meters, p.f. meters and freq. meters.
To calibrate all indicating type instruments, standards of V and R reqd. As available standard of voltage, i.e., Weston Standard Cell, is a D.C. cell, so, impossible to calibrate an A.C. instrument directly against fundamental standards.
Need arises of instrument (called ‘transfer instrument’) equally accurate on both A.C. & D.C. The Electrodynamic instrument, is an ideal ‘transfer instrument (separte sec.)
PMMC can’t measure A.C., but electrodynamic instrument can measure both A.C. (since product of two –ve currents yields +ve qty.) & D.C.

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

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2.2.1 Construction:

Its construction similar to that of PMMC instrument, except: in PMMC, air gap flux produced by permanent magnet, in the electrodynamic instrument, it is produced by an air-cored electromagnet.
Electromagnet is made of an air-cored fixed coil (called field coil) which carries current from (or a current proportional to) the qty. being measured.
Fixed coil in 2 sections (2 coils) to give uniform field near centre of these 2 coils & to allow a moving coil (again air-cored) to be housed at centre; fixed coils spaced far apart to allow passage of shaft of movable coil as in Fig. 7. Schematic: Fig. 8.

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech., Ph.: 9416351300, Email: jssain@rediffmail.com

Fig. 7 Electrodynamic Instrument

Fig. 8 Schematic diagram of electrodynamic movement.

… More to follow

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3. MOVING IRON INSTRUMENT (IRON-VANE INSTRUMENT)

PMMC can’t be used for A.C. The Electrodynamic type can be used both on A.C. & D.C., but expensive. M.I. instruments work on A.C. or D.C., are inexpensive, rugged & can be constructed to give accuracy required for most engg. applications.
Their use at power frequencies is particularly attractive. These instruments, thus, find common use in labs. & switch-boards at power frequencies.

3.1 CLASSIFICATION OF MOVING IRON (M.I.) INSTRUMENTS

M.I. instruments classified into 2 groups: (a) Attraction Type & (b) Repulsion Type. Features of attraction & repulsion type combined: Attraction-Repulsion Type.
In actual measurements, only repulsion type or combined attraction-repulsion type are used (for reasons: comparatively economic production & wider scale). But, attraction type lends ease of understanding.

3.2 ATTRACTION TYPE (OR SINGLE IRON TYPE) :

BASIC PRINCIPLE & CONSTRUCTION:
If a piece of un-magnetized soft iron (of high permeability) is brought near either of two ends of a current-carrying coil (electromagnet), it would be attracted into the coil in same manner as it would be attracted by pole of a permanent magnet.

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Ph.: 9416351300, Email: jssain@rediffmail.com

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The electromagnet carries either current to be measured (or part thereof) or a current proportional to voltage to be measured.
Very basic set-up of Fig. 9 demonstrates the above principle.
As current, I, to be measured, is passed thro’ the coil, the soft iron core is pulled into the stronger magnetic field inside the coil so as to increase the flux of electromagnet.
This is because soft iron piece tries to occupy a position of minimum reluctance (or maximum inductance for the coil). Pointer deflection is controlled by a spring.

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

Fig. 9 Basic set-up to demonstrate principle of operation of Attraction Type Moving Iron Instrument.

Let, I, be reversed in dir.; core still attracted inside electromagnet, as a soft magnetic material, was not permanently magnetized due to previous flow of current in coil.
Thus an ‘unpolarized’ instrument, i.e., independent of direction of current passing through it. Hence, such instruments can be used for D.C. as well as for A.C.

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In actual practice, basic set-up (Fig.9) rarely used as its primitive construction ⟹ it prone to outer vibrations and accelerations which restrict its sensitivity. However, it is used for voltage testers, just to distinguish line voltage from phase voltage, such as 220 V from 400 V etc.
Consider a more practical construction as in Fig. 10.

19-Jan-23

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

Fig.10 Construction of Attraction Type Moving Iron Instrument.

Coil of insulted Cu wire wound on a non-metallic hollow bobbin to give flat-shaped solenoid.
Soft iron moving element (a thin oval-shaped disc) eccentrically mounted on a spindle just outside solenoid such that greatest bulk of disc moves, on deflection, into center of solenoid.
Spindle pivoted, at the ends, b/n bearings (not shown in sectional view of Fig.10).
Al pointer attached to spindle. Non-metallic control-wts. (for gravity control) & balance-wts. attached to 2 arms fixed to spindle. Gravity control (as in Fig.10) but spring control is almost universally used (except for panel instruments mounted vertically).

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Since neither permanent magnet nor moving non-magnetic metallic disc forms a part of operating sys, so, eddy current damping ≠ right choice for such instruments. Air friction damping used which uses a light Al piston moving in a sector-shaped chamber.
All inner system components consist of non-magnetic materials except for soft-iron vanes. This ensures a very symmetrical coil field.
Construction of Fig.10 has following improvements over primitive construction of Fig.9:
Eccentric mounting of moving element allows its rotational motion (instead of linear motion), thus achieving immunity against linear accelerations, which are usually encountered ones such as for meters installed on vehicles etc.
Solenoid is flat-shaped, it gives a concentrated field with minimum energy expenditure.
Moving element is a thin disc, it allows a significant bulk (area) of iron to be attracted into solenoid (so developing a substantial torque) & at same time keeps moving sys. light in wt.
We digress to discuss basic principle & construction of other 2 types of M.I. instruments:

3.3 REPULSION TYPE (DOUBLE IRON TYPE):

BASIC PRINCIPLE AND CONSTRUCTION:
Construction is similar to that of attraction type except that solenoid is cylindrical (instead of flat-shaped) & moving elements which are 2 in no. (contrasted to one in attraction type).
Further 2 different designs/variants of moving elements, so repulsion-type classed as:

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

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19-Jan-23

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

Fig. 11 Basic set-up to demonstrate the principle of operation of Repulsion Type Instruments

+ –

A C

B D

Soft iron rods

Coil

Radial Vane Type
Co-axial (Concentric) Vane Type.
Basic principle of repulsion type instruments illustrated with basic set-up of Fig.11.
As current flows through coil, 2 soft iron rods (placed in parallel) are magnetized with similar polarity at all sections. Adjacent ends, i.e., A & C turn S-poles; ends B & D become N-poles (for coil-current direction as shown). So, two bars will repel each other.
Diagonally opposite ends, i.e., A & D and also ends B & C (being of opposite polarities) tend to attract each other, but being far off, don’t contribute significantly to net repulsion process.
If coil current is reversed, polarity of both magnetized rods is reversed, so again repel.
Now, if one bar fixed & other is free to move, repulsion force can be made to indicate amt. of current flow in coil by causing movable bar to move a pointer across a calibrated scale.
Better use thin (but larger x-section) soft-iron vanes (strips) instead of solid rods, making the moving system considerably light & adding something to the damping (due to larger area).

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19-Jan-23

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

Two sub-types (designs) of repulsion type instruments are now discussed.

RADIAL VANE TYPE: Vanes placed radially within coil (Fig.12). Fixed vane attached to coil/ bobbin & movable one to spindle. Repelled, movable vane moves along circular arrow (12b).
CO-AXIAL (CONCENTRIC) VANE TYPE: Fig. 13: fixed & movable vanes: sections of co-axial cylinders; when developed, assume shapes as in Fig.14.
Moving vane moves co-axially inside static tapered (tongue-shaped) vane, keeping same radial distance, d, (Fig. 4.22b) but torque results as wider portion (end B: Fig.14) of fixed vane produces a stronger repulsive force compared to that by thinner portion (end A). So, movable vane moves in direction of taper.

Fig. 12 Radial Vane Type (a) Front Section View Fig.13 Co-axial Vane Type (a) Front Section View

(b) Plan View (b) Plan View

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Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

Fig.14 Developed view of Fixed & Movable Co-axial vanes.

3.4 Combined Attraction-Repulsion Type:

BASIC PRINCIPLE AND CONSTRUCTION: Prac. designs of attraction type & repulsion type limited: give deflections not more than ≈100°. Range extended to 240° by combining, in a single meter, the features of both repulsion type & attraction type instruments.
Such meter also called ‘Long-scale’ / ‘Circular scale’ instrument (Fig.15). Diff. vanes (3 fixed & 1 movable), when developed, assume shapes as in Fig.16.
Attraction feature not exploited in sense of Fig. 10, i.e., no vane mounted outside solenoid gets attracted into it. Rather, 2 concentric (co-axial) tapered vanes used (attraction vanes), whose taper ↑es as taper of middle vane (repulsion vane) ↓es. So, middle vane: just same as co-axial (concentric) vane of repulsion type.
In lower portion of scale, movable vane mainly confronted by fixed middle vane (wider in this region). So, in lower part of scale, movable vane experiences mainly repelling force. As deflection ↑es, outer stationary (attraction) vanes exert attractive force on movable vane & add to torque. Scale distribution made useful for about 240° by suitably shaping vanes.

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Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

3.5 GENERAL TORQUE EQUATION

Let initial current (instantaneous) in instrument be ‘i’ Amp., instrument inductance L Henry & deflection θ radians.
Let applied voltage be increased by ‘e’ volts above zero which results in increment di in current, dθ in deflection & dL in inductance.

Fig.16 Developed view of one movable and three fixed vanes.

Fig.15 Combined attraction-repulsion type (front section view).

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Now, electrical energy supplied = (voltage)x(current)x(time increment)

…

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

So, Incremental energy supplied = (incremental voltage)x(current)x(time increment)

= eidt which, by using =n 5, becomes:

= i²dL + iLdi (6)

Now, assuming: stray capacitance neglected (this assumption not justified at high frequencies), ⟹ energy stored in electric field neglected, so energy stored only in magnetic field as (½)Li². For the case at hand, the energy stored changes from (½)Li² to (½)(L + dL)(i + di)².

So, Change in stored energy = (½)(L + dL)(i² + 2idi + di²) – (½)Li² (neglect di²)

= (½)Li²+ Li di + (½)(dL)i² + I di dL – (½)Li² (neglect I di dL )

= Li di + (½)i²dL (7)

For circular motion, mechanical work done = Torque x angular displacement

(just as for linear motion, Work done = Force x covered distance)

So, Mechanical work done = (τ_d)_idθ (8)

Where (τ_d)_i = instantaneous deflecting torque in N-m.

From the principle of conservation of energy,

Incremental energy supplied = Increase in stored energy + Mechanical work done

So, using Eqns. 6 to 8, we have:

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i²dL + iLdi = Li di + (½)i²dL + (τ_d)_idθ

19-Jan-23

Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

So, (τ_d)_idθ = (½)i²dL

Or, (τ_d)_i = (½)i²(dL/dθ) (9)

Instantaneous torque is a function of square of instantaneous current & will, therefore, have a non-zero +ve average value. It is a mathematical proof that M.I. instruments can be used on D.C. as well as on A.C.

Case-I Use on D.C.:

In this case, i = I_dc = steady D.C. current = I (say)

So, Average torque = (τ_d)_av = (½)I²(dL/dθ) (10)

Case-II Use on Sinusoidal A.C.:

The Average torque = (τ_d)_av = (1/T) dt

where T = Time period of one cycle.

So, (τ_d)_av = (1/2)(dL/dθ)

As term in square bracket ⟹, by defn., the square of RMS value of A.C. current,

So, (τ_d)_av = (½)I²(dL/dθ) (11)

Where I = RMS value of A.C. current.

As pointed earlier, spring control is normally used, we have controlling torque,

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Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

τ_c = Kθ

where K = spring constant; N-m/rad & θ = deflection in rad.

At equilibrium (final steady) position, τ_c = τ_d

So, Kθ = (½)I²(dL/dθ)

Or, Deflection, θ = (½)(I²/K)(dL/dθ) (12)

So, steady deflection is a fn. of sq. of rms value (D.C. value in case D.C.) of current.

3.6 SHAPE OF SCALE

General torque =n.9 or general scale =n.12 applicable to any type of M.I. instrument. In general ⟹ deflecting torque or, deflection (for spring controlled M.I instrument) is proportional to square of instrument current & rate of change of inductance with deflection.
[Note: In attraction type, ↑ in inductance with ↑ in deflection is due to change in extent to which the iron is within the coil; & in repulsion type, it is due to ↑ of flux by a ↓ in demagnetizing effect of one iron on the other as two irons move apart.]
If no saturation, L is a const. times θ [Note: Due to assumptions in derivation, not reflected in torque eqn., L not only depends upon θ, but also upon I due to presence of ferromagnetic material (moving iron).] i.e., rate of change of L with θ is constant, then a ‘square-law’ scale results, i.e., graduations in lower portion of scale are crowded & at higher side spread out.
So scale still non-linear whereas a linear scale is required. Next paragraph: what to do?

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Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

LINEARISATION OF SCALE:
Clue to linearization of scale lies in the scale Eqn. itself (i.e., Eqn. 12).
A linear scale possible if (dL/dθ) is made an inverse function of I or else(dL/dθ) is made an inverse function of θ

3.7 ADVANTAGES OF M.I. INSTRUMENTS

a) Robust due to their simple construction & no current-carrying moving parts.

b) Can be used both for A.C. & D.C., although not with the same accuracy.

c) Less prone to frictional errors due to their high torque to wt. ratio & as their moving system can be made light (because not to carry any current).

d) No current-carrying moving parts, so identical moving sys’s may be used for an entire range of instruments, thus M.I. instruments can be produced at less cost. Possible because for a given displacement of moving sys. (i.e., to produce a given m.m.f.), either a coil of a few turns of thick cross section, or a coil with large number of turns of thin cross section may be used.

e) Attraction type M.I. instruments usually have lower L & hence more accurate over a wider range of frequency, as compared to repulsion type M.I. instruments.

f) For repulsion type M.I. instruments, a comparatively (compared to attraction type) wider & nearly uniform scale is more easily obtainable.

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Dr. J.S. Saini, Prof., EED; Dean, Faculty of Engg. & Tech.,

Ph.: 9416351300, Email: jssain@rediffmail.com

3.8 DISADVANTAGES OF M.I. INSTRUMENTS

a) Serious errors due to hysteresis, eddy currents, freq. changes & waveform changes, thus can’t be calibrated with D.C. & used on A.C. and vice-versa. They need to be calibrated separately for D.C. & separately for each frequency of A.C. at which they are used.

b) Their scale is cramped at the lower end, giving less accurate readings at this range.

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