## Harmonic distortion analyzers:

### Harmonic distortion:

When we give a sinusoidal signal input to any electronic instrument there should be output in sinusoidal form, but generally the output is not exactly the replica of input, because of various types of distortion that my occur.

Distortion is occur due to inherent non-linear characteristics of different components used in electronic circuit. Nonlinear behavior of electronic component introduces harmonics in the output waveform and the resultant distortion is often referred as harmonic distortion.

### 1)    Frequency distortion:

This type of distortion occurs in amplifiers because of amplification factor of amplifier is different for different frequencies.

### 2)    Amplitude distortion:

It occurs because amplifier introduces harmonic of fundamental of input frequency. Harmonics always generates distortion in amplitude. E.g. when amplifiers are overdriven it clips the waveform.

### 3)    Phase distortion:

This distortion occurs due to energy storage elements in the system which causes the output signal to be displaced in phase with the input signal. Signals with different frequencies will be shifted by different phase angles.

### 4)    Intermodulation distortion:

This type of distortion occurs as a consequence of interaction or heterodyning of two frequencies, giving an output which is sum or difference of the two original frequencies.

### 5)    Cross-over distortion:

This type of distortion occurs in push-pull amplifiers on account of incorrect boas levels as shown in figure. cross over distortion

### Total harmonic distortion (THD): In a measurement system noise is read in addition to harmonics and the total waveform consisting of harmonics, noise and fundamental is measured instead of fundamental alone ## Phase sequence indicator:

These instruments are used to measure the phase sequence of three phase supplies. They are of two types 1) Rotating type and 2) Static type.

### 1)    Rotating type: Rotating type phase sequence indicator

The principle of rotating type meters is similar as three phase induction motor.

• They consist of three coils connected 120 degree apart in space.
• The three ends of the coils are brought out and connected to three terminals marked RYB as shown in figure.
• The coils are star connected and are excited by the supply whose phase sequence is to be determined.
• An aluminium disc is mounted on the top of the coils.
• The coils produces rotating magnetic field and Eddy emfs are induced in the disc.
• These emfs cause Eddy currents to flow in the aluminium disc .
• A torque is produced with the interaction of the Eddy currents with the field.
• The disc revolves because of the torque and the direction of rotation depends upon the phase sequence of the supply.
• An arrow indicates the direction of the rotation of the disc.
• If the direction of the rotation is same as that of indicated by arrow head, the phase sequence of the supply is the same as marked on the terminals of the instrument.
• However, if the disc revolves opposite to the direction indicated by the arrowhead, the sequence of the supply is opposite to that marked on the terminals.

### 2)    Static type: Static type phase sequence indicator

It consists of two lamps and one inductor connected as shown in figure. If the sequence is RYB then lamp L1 will dim and lamp L2 will glow brightly. If phase sequence is RBY then lamp L1 will glow brightly and lamp L2 will be dim.

Vry=V(1+j0)

Vyb=V(-0.5-j0.866)

Vbr=V(-0.5+j0.866)

Thus the voltage drop across lamp 1 is only 27% of that across lamp 2.

Thus if the phase sequence is RYB lamp 1 glows dimly while lamp 2 glows brightly.

It can be shown that, if the inductor is replaced by capacitor of such value that Xc=XL, the ratio (Ir/Iy) is 3.7, which means in this case lamp 1 glows brightly and lamp 2 glows dimly if the phase sequence is RYB.

## Hay’s bridge for measurement of inductance :

The Hay’s bridge is modification of the Maxwell’s bridge. The connection diagram of the Hay’s bridge is shown in figure below. This Hay’s bridge uses a resistor in series with a standard capacitor (unlike the Maxwell’s bridge which uses a resistance in parallel with the capacitor). Hay’s bridge for measurement of inductance

Let

L1=unknown resistance having a resistance R1,

R2, R3, R4=known non-inductive resistance,

C4=standard capacitor.

At balance, Separating real and imaginary term, we obtain: Solving the above two equations we have, The Q factor of the coil is : ### Advantages of the Hay’s bridge:

1)      This bridge gives very simple expression for unknown inductance for high Q coils, and is suitable for coils having Q > 10.

2)      This bridge also gives the simple expression for Q factor.

3)      From expression of Q factor it is clear that for high Q factor the value of resistance R4 should be small.

1)      The Hay’s bridge is suited for measurement of high Q inductors, specially those inductors having Q > 10. For inductors having Q values smaller than 10, the term (1/Q)^2 in the expression for inductance L1 becomes rather important and thus cannot be neglected. Hence this bridge is not suited for measurement of coils having Q less than 10 and for thse applications a Maxwell’s bridge is more suited.

## Maxwell’s inductance capacitance bridge: In Maxwell’s inductance capacitance bridge the value of inductance is measured by the comparison with standard variable capacitance. The connection for Maxwell’s inductance capacitance bridge is shown in figure below.

Let

L1=unknown inductance,

R1=effective resistance of inductor L1,

R2, R3, R4=known noninductive resistances,

C4=variable standard capacitor.

And writing the equation for balance Separating the real and imaginary terms, we have Thus we have two variables R4 and C4 which appear in one of the two balance equations and hence the two equations are independent.

The expression for Q factor ### Advantages of Maxwell’s inductance capacitance bridge:

1)      The two balance equations are independent if we choose R4 and C4 as variable elements.

2)      The frequency does not appear in any of the two equations.

3)      This bridge yields simple expressions for L1 and R1 in terms of known bridge elements.

### Disadvantages of Maxwell’s inductance capacitance bridge:

• This bridge requires a variable standard capacitor which may be very expensive if calibrated to the high degree of accuracy. Therefore sometimes a fixed standard capacitor is used, either because a variable capacitor is not available or because fixed capacitors have a higher degree of accuracy and are less expensive than the various ones. The balance adjustments are then done by:

a)      Either varying R2 and R4 and since R2 appears in both the balance equations, the balance adjustments become difficult; or

b)      Putting an additional resistance in series with the inductance under measurement and then varying this resistance and R4.

• The bridge is limited to the measurement of low Q coils (1<Q<10). it is clear from the Q factor equation that the measurement of high Q coils demands a large value of resistance R4, perhaps 10^5 or 10^6 O. The resistance boxes of such high values are very expensive. thus for values of  Q>10, the Maxwell’s bridge is unsuitable.

## Maxwell’s inductance bridge: Maxwell’s inductance bridge measures the value of given inductance by comparison with a variable standard self inductance. The circuit diagram of Maxwell’s inductance bridge is shown in figure below. Maxwells inductance bridge for measurement of inductance

Let

L1 = unknown inductance of resistance R1,

L2 = variable inductance of fixed resistance r2,

R2 = variable resistance connected in series with inductor L2,

R3, R4 = known non-inductive resistances.

At balance, Resistance R3 and R4 are normally a selection of values from 10, 100, 1000 and 10,000O. r2 is decade resistance box. In some cases, an additional known resistance may have to be inserted in series with unknown coil in order to obtain balance.

Let us solve one simple problem for clear understanding of Maxwell’s inductance bridge.

### Problem:

A Maxwell’s inductance comparison bridge is shown in the figure above. Arm ab consists of a coil with inductance L1 and resistance r1 in series with a non-inductive resistance R. arm bc and ad are each a non-inductive resistance of 100O. Arm ad consists of standard variable inductor L of resistance 32.7O. Balance is obtained when L2 = 47.8mH and R = 1.36O. Find the resistance and inductance of the coil in arm ab.

### Solution:

At balance [(R1+r1)+jwL1]*100 = (r2+jwL2)*100

Equating the real and imaginary terms

R1+r1 = r2 and L2=L1

Therefore, resistance of coil:

r1 = r2 – R1 = 32.7 – 1.36 = 31.34O.

Inductance of coil:

L1 = L2 = 47.8mH.

tags: maxwell’s inductance bridge ppt pdf maxwell’s bridge theory anderson bridge for the measurement of inductance. maxwell bridge experiment applications uses and disadvantages and advantages of maxwell inductance bridge.

## Potentiometer:

### Introduction:

A potentiometer is an instrument used to measure an unknown e.m.f. which is compared with known e.m.f. thus it is a device used for measurement of unknown e.m.f. is compared with a known e.m.f. The known voltage may be supplied by a standard cell or any other known voltage. Measurements using comparison methods are capable of a high degree of accuracy because the result obtained does not depend on the actual deflection of a pointer, as is the case in deflection methods, but only upon the accuracy with which the voltage of the reference source is known.

Another advantage of the potentiometer is that since potentiometer makes use of balance or null condition, no current is flow and no power is consumed in the circuit containing the unknown e.m.f.  when the instrument is balanced. Thus the determination of voltage by potentiometer is quite independent of the source resistance.

Since the potentiometers measure the voltage, it can also be used to determine the current simply by measuring the voltage drop produced by the unknown current passing through a standard known resistance.

The potentiometer is extensively used for a calibration of voltmeters and ammeters and has in fact become the standard for the calibration of these instruments. For the above mentioned advantages the potentiometer has become very important in the field of electrical measurements and calibrations.

The principle of operation of all potentiometers is based on the circuit of figure, which shows the schematic diagram of the basic slide wire potentiometer.

With switch S in the operate position and the galvanometer key K open, the battery supplies the working current through the slide wire and the rheostat. We can vary the current by adjusting rheostat. The method of measuring the unknown voltage E depends upon finding the position of slide wire such that galvanometer shows zero deflection. It means unknown voltage E equals to the voltage drop E1 across the portion ac of the slide wire.

The slide wire has the uniform cross-section and hence it has uniform resistance along its length. Slide wire consists of cm scale along its length. Since the resistance of the slide wire is known accurately, the voltage drop along the slide wire can be controlled by adjusting the value of working current. So knowing the value of unknown voltage E and working current I, we can calculate resistance using the formula R=V/I.

## Kelvin double bridge circuit for measurement of low resistance

In this post we will see the Kelvin double bridge. It is used for the measurement of low resistances. The Kelvin double bridge is the modification of the Wheatstone bridge and provides greatly increased accuracy in measurement of low value resistance.

An understanding of the Kelvin bridge arrangement may be obtained by the study of the difficulties that arise in a Wheatstone bridge on account of the resistance of the leads and the contact resistances while measuring low valued resistance.

The Kelvin double bridge incorporates the idea of a second set of ratio arms-hence the name double bridge-and the use of four terminal resistors for the low resistance arms.

Figure shows the schematic diagram of the Kelvin bridge. The first of ratio arms is P and Q. the second set of ratio arms, p and q is used to connect the galvanometer to a point d at the appropriate potential between points m and n to eliminate effect of connecting lead of resistance r between the unknown resistance, R, and the standard resistance, S.

The ratio p/q is made equal to P/Q. under balance conditions there is no current through the galvanometer, which means that the voltage drop between a and b, Eab is equal to the voltage drop Eamd.

Now the voltage drop between a and b is given by,

Above equation is the usual working equation for the Kelvin Double Bridge. It indicates that the resistance of connecting lead, r, has no effect on the measurement, provided that the two sets of ratio arms have equal ratio. The former equation is useful, however, as it shows the error that is introduced in case the ratios are not exactly equal. It indicates that it is desirable to keep r as small as possible in order to minimize the errors in case there is a difference between ratios P/Q and p/q.

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## Direct deflection method:

The figure shows the measurement of high resistance using direct deflection method. For measurement of high resistance such as insulation resistance of cables, a sensitive galvanometer of d’Arsonval type is used in place of the microammeter. In fact many sensitive type of galvanometers can detect currents from 0.1-1nA.therefore, with an applied voltage of 1kV, resistance as high as 10^12 to 10*10^12O can be measured.

The first figure shows the direct deflection method for measurement of high resistance having metallic sheath. The galvanometer G shows the current between the conductor and the metallic sheath. The leakage current  is carried by the guard wire wound on the insulation and therefore does not flow through the galvanometer as shown in figure.

Cables without metal sheaths can be tested in a similar way if the cable, except the ends or ends on which connections are made, is immersed in water in a tank. the water and a tank then forms the return path for the current .the cable is immersed in slightly saline water for about 24 hours and the temperature is kept constant at about 20 degree Celsius and then the measurement is taken as shown in second figure

The insulation resistance of the cable is given by,

In some cases, the deflection of the galvanometer is observed and its scale is afterwards calibrated by replacing the insulation by a standard high resistance (usually 1MO), the galvanometer shunt being varied, as required to give a deflection on the same order as before.

In tests on cable the galvanometer should be short-circuited before applying the voltage. The short-circuiting connection is removed only after sufficient time is elapsed so that charging and absorption currents cases to flow. The galvanometer should be well shunted during the early stages of measurement, and it is normally desirable to influence a protective series resistance (of several megaohm) in the galvanometer circuit. The value of this resistance should be subtracted from the observed resistance value in order to determine the true resistance. A high voltage battery of 500V emf is required and its emf should remain constant throughout the test.

## Construction and working principle of Megger for measurement of High resistances

We know that the ratiometer ohmmeters may be designed to cover a wide range of resistances. The principle of ratiometer ohmmeters is particularly adapted to application in portable instruments measuring insulation resistance. This principle forms the basis of insulation testing instrument known as Meggar. Megger for measurement of high resistance

## Construction and working of Megger:

The main parts of the Megger are shown in the figure.

The current coil is same as that of permanent magnet moving coil instrument. V1 and V2 these are the two potential or voltage coils. The voltage coil V1 embraces the annular magnetic core. As shown in figure voltage coil V1 is in weak magnetic field when the pointer is at infinity and hence this coil exerts very little torque.

The torque exerted by this voltage coil increases as it moves into a stronger field and this torque will be maximum when it is under the pole face and under this condition the pointer will be at its zero end of the resistance scale.

In order to modify further the torque in the voltage circuit, another voltage coil V2 is used. This coil is also located in such a way it cam move from infinity to zero position of the resistance scale. The coil finally embraces the extension H of the pole piece.

The combined action of the two voltage coils V1 and V2 may be considered as though the coils constituted  a spring of variable stiffness ,being very stiff near the zero end of the scale where the current in the current coil is very small (on account of unknown resistance Rx is very large).

Thus this effect compresses the low resistance portion of the scale and opens up the high resistance of the scale. This is a great advantage since this instrument is meant to be used as “insulation tester” as the insulation resistances are quite high.

The voltage range of the Meggar can be controlled by voltage selector switch. This can be done by varying the resistance R connected in series with the current coil.

The test voltages usually 500,1000 or 2500 V can be generated using hand driven generator G. A centrifugal clutch is incorporated in the generator drive mechanism which slips at a predetermined speed so that a constant voltage is applied to the insulation under test. This voltage provides a test of strength of low voltage insulation as well as a measure of its insulation resistance  since it is sufficient to cause breakdown at faults. Such breakdowns are indicated by sudden motion of the pointer off scale at zero end. As the same magnet system supplies magnetic fields for both instrument and generator, and as current and voltage coils moves in a common magnetic field, the instrument indications are independent of the strength of the magnet.

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## Ammeter Voltmeter method:

This is very popular method for measurement of medium resistances since instruments required for this method are usually available in laboratory. The two types of connections employed for ammeter voltmeter method are shown in figure. In both the methods if readings of ammeter and voltmeter are taken then we can measure value of resistance by using formula: The measured value of resistance Rm, would be equal to the true value R, if the ammeter resistance is zero and the voltmeter resistance is infinite, so that the conditions in the circuit are not disturbed. But in actual practice this is not possible and hence both methods give inaccurate results.

Consider circuit of figure (a): voltmeter ammeter method

In this method ammeter measures the true value of current flowing through resistance but voltmeter does not measures the true value of the voltage across the resistance. the voltmeter indicates the sum of the voltage across resistance and ammeter.

Let Ra be the resistance of the ammeter. It is clear from the above equation that the error will be small if the value of the measuring resistance is large as compare to the internal resistance of the ammeter .therefore circuit should be used when measuring resistances are high.

Consider circuit of figure (b): voltmeter ammeter method

In this circuit the voltmeter measures the true value of the voltage across the measuring resistance but the ammeter does not measures the true value of the current flowing through the resistance .the current through the ammeter is the sum of the current through the voltmeter and resistance.

Let Rv be the resistance of the voltmeter. From the above equation it is clear the true value of the resistance will be equal to the measured value only when the voltmeter resistance is equal to the infinite. However, if the resistance of the voltmeter is very large as compared to the resistance under measurement:  It is clear from the above equation that the relative error will be small if the resistance under measurement is very small as compared to the resistance of the voltmeter .hence the circuit should be used when the measuring values of resistances are low.