Frequency Meter

Types

• Mechanical Resonance (Vibrating Reed)• Electrical Resonance (Ferro-dynamic)• Electrodynamometer• Weston Type• Ratio-meter Type• Saturable Core

Vibrating Reed

• Consist of thin steel strips call reeds• All reeds are not similar to each other• The natural frequency of the reed depends upon their

weight and dimensions• Reeds are arranged in the ascending order of

frequency, the difference in frequency is 0.5 Hz.• Reeds are free at the bottom ends and are free at top

ends• Reeds have a portion bent over at the free end to

serve as a flag.

Construction

Working• When supply is connected the coil of electromagnet

carries a current I which alternates at the supply frequency.

• Force of attraction between reeds and electromagnet is proportional to i2 and therefore this force varies twice the supply frequency.

• Thus force applied on the reeds varies every half cycle and reeds will tend to vibrate. But the reed whose frequency is twice of supply frequency will be in resonance and will vibrate most.

Contd…

Electrical Resonance( Ferro-Dynamic)It Consist of a magnetizing coil connected across The supply. It is mounted on a laminated iron core.Cross-section of iron core varies over the length, Being maximum at the end, where the magnetizing coil is mounted and the minimum at the other end.The terminal of moving coil are connected to the capacitor C.No provision of controlling torque.

Working

Magnetizing coil carries current I which produces a flux Φ which is in phase with I. Φ induces an EMF in the moving coil which lags by 900 This emf circulates a current in moving coil. The phase of this current Im depends upon the Inductance L of the moving coil and the capacitance CIf moving coil is Inductive then If Moving Coil is Capacitive thenIf Moving coil is purely resistive then Td = 0

Contd…

• At mean position value of inductive reactance is equal to capacitive reactance.

• If frequency increases above normal value inductive reactance becomes larger than capacitive reactance. Thus the circuit becomes more inductive and therefore a torque is produced.

• This torque tries to pull the moving coil to an equilibrium position i.e. position where inductive reactance will be equal to capacitive reactance.

• Since XL > XC , this can be obtained if moving coil moves away from magnetizing coil. The coil will come to rest when XL = XC .

• Its reverse will happen if frequency will decrease.

Dynamometer Type frequency Meter

• Assignment

Weston Frequency MeterIt consists of two sets of A and B each in pair and of equal size, which are fixed to each other so that the magnetic axis is 900 to each other. At the center of the coil group, a soft iron needle is placed.The coil is in the series with an induced LA, is connected across a resistance RA so that the current flowing in A, is depended upon the voltage drop in RA. Similarly coil B is connected in series with a resistance RB so that the voltage available to the coil B is the impedance drop across the inductance LB. The inductance L is in series and damp out harmonic in the supply wave.

Working• The meter is connected across the supply and the two coils carry currents.• These two currents setup two magnetic fields which are at right angles to

each other and depends on the current flowing through the coil.• Both these fields act upon the relative magnitudes of the two fields and

hence current.• The meter is so designed that the value of various resistances and

inductances are such that for normal frequency needle takes a position which is at 450 to both the coils and the pointer is at the center of the scale.

ElectrodynamometerIn this type of frequency meter, the field coil forms two separate parts of resonant circuits. Field coil 1 is in series with inductor and capacitor C1 and formed a resonant circuit, which is tuned to a frequency slightly below the low end of the instrument scale. Field coil 2 is in series with inductor L2 and capacitor C2 and forms a resonant circuit, which is tuned to a frequency slightly higher than the end of the instrument scale.

Working• In case of power frequencies, the circuit would

be tuned to frequencies of 40 Hz to 60 Hz respectively with 50 Hz in the middle of the scale. The return path of power line is provided through the moving coil. The torque on the movable coil is proportional to the current through the moving coil. This current is the sum of two-field currents i1 and i2.

• For an applied frequency, the circuit of the field coil 2 operates above the resonant frequency with current i1 lagging the applied voltage. The circuit of the field coil 1 operates below its resonant frequency and is therefore capacitive with current i2 leading the applied voltage. The deflecting torque is developed due to the reaction of field of moving coil with the resultant field from coil 1 and coil 2. The range of this instrument is limited to the power line frequency.

Ratiometer Type

Construction and Working• It consists of a ratiometer, which gives linear relationship

between the current ratio and the deflection. The two coils of ratiometer are fed with rectified current of two separate bridge rectifiers. The input side of two bridge rectifiers are connected to AC supply whose frequency is to be measured.

• Let V = Supply voltage• f = Frequency of supply• Output current of bridge rectifier 1 is I1α IC α 2πfVC

• Output of bridge rectifier 2 is I2α IR α V/R

• Deflection =KI1/I2 = K 2πfVC /(V/R) =K2πfCR

• Or θ = K2 f

• Here K, C and R = constant• Here supply voltage does not appear in the expression for

deflection. Thus the instrument may be used for a fairly wide range of voltages. This meter may be used up to a frequency of 5000 Hz.

Measurement of Speed

• Linear Speed• Angular SpeedLinear speed measurement is of two typesMoving Magnet typeMoving Coil Type

Moving Magnet TypeWe know that an emf is induced in the coil when the flux linking with the coil changes and the magnitude of emf is proportional to the component of velocity in the direction perpendicular to magnetic field e=Blv Sin θ VoltWheree = Induce emfB = Flux density of magnetic field (Wb/m2)l = Length of moving coil in MeterV = Relative velocity of coil and magnet (m/Sec)q= Angle of coil movement with the direction of magnetic fieldIn figure The sensing element is a rod that is rigidly coupled to the device whose velocity is being measured. This rod is made up of permanent magnet. It can move inside the coil which induces an emf in the coil proportional to the velocity of the magnet. Polarity of the induce emf in the coil gives the direction of movement of the magnet.

Contd…

• Advantages:-• Negligible maintenance is required• The output voltage is nearly

proportional to the velocity• Robust and inexpensive instrument• Disadvantages:-• Stray magnetic field effects the

performance of this device• Limited frequency response

Moving Coil Type

• As shown in figure it operates through the action of a coil moving in a magnetic field. A voltage is generated in the coil, which is proportional to the velocity of the coil.• Advantages:The whole device isenclosed in an antimagnetic case in order to reduce the effect of stray magnetic

fields.• Disadvantages:- Maintenance problem is

main drawback of this instrument.

Measurement of Angular Velocity

• DC Tacho-generator

Contd…• DC generator tachometer consists of a small

armature, which is coupled to the machine whose speed is to be measured. The armature revolves in the field of permanent magnet. The emf generated is proportional to the product of flux and speed. The polarity of output voltage indicates the direction of rotation. This emf is measured with the help of a moving coil voltmeter having a uniform scale and calibrated directly in terms of speed.

• Advantages:- The direction of rotation is directly indicated by the polarity of output voltage.

• Disadvantages:- Maintenance problem occurs due to the brushes and commutator.

Contd…

• AC Tacho-generator

Contd…• It is an ordinary rotating field type alternator. The magnetic

field is produced either by permanent magnet or electromagnets mounted on rotor, which is coupled to the shaft of the test machine. The coil is wound on the stator.

• The rotation of magnet induces an AC voltage in the coil, the amplitude and frequency of which are proportional to the rotational speed. The output voltage is first rectified and then passed through the filter to smoothen the ripples. The output voltage is measured by a permanent magnet moving coil voltmeter, which can be calibrated directly in terms of rotational speed.

• Advantages:- No maintenance problem of commutator and brushes.

• Disadvantages:- At very low rotational speed the frequency of output voltage became very low so the ripples are not smoothen out by the filter circuit which can affects the measurement of voltage.