These are the set of certain notes that were used to make my presentation on measurement of frequency. Hope you find this useful as well.

1. Measurement of frequency
 Frequency measurement is very important in many application of AC, especially in AC
power systems designed to run efficiently at one and only one particular frequency.
 Frequency measurement is done by frequency meter.
 Frequency meter is an instrument that displays the frequency of a periodic electrical
signal.
 The two types of electrical resonance frequency meter are described below:
I. Ferrodynamic Type Frequency Meter
Construction:
 A fixed coil called the magnetizing coil is connected across supply whose frequency is to
be measured. This magnetizing coil is mounted on a laminated iron core.
 This iron core has a variable cross-section area which varies gradually over length, being
maximum over the end where magnetizing coil is mounted & minimum over the other
end.
 A moving coil is pivoted over this iron core. A pointer is attached to this moving coil.
 The terminals of moving coil are connected to the capacitor of suitable value.

2. Operation:
 The magnetizing coil carries a current “I” and this current produces a flux “ø”. If we
neglect the resistance &iron losses in the core, flux will be in phase with the current”I”.
 Flux”ø” being alternate in nature induces an e.m.f”E” in the moving coil. EMF lags
behind flux by 90°.
 The EMF induced causes current “𝐼 𝑚 ” in the moving coil. The phase of this current” 𝐼 𝑚”
depends upon inductance”L” of the moving coil &capacitance “C”.
 The operation of instrument can be understood by three phasor diagram:
In Fig.(a)
Crkt. Of the moving coil is assumed to be inductive. So,” 𝐼 𝑚” lags behind “E” by an angle “𝛼”.
So, torque acting on moving coil,
𝑇𝑑 𝛼 𝐼 𝑚 cos(90 + 𝛼).

3. In fig.(b)
Crkt of moving coil is assumed to be largely capacitive “𝐼 𝑚" leads e.m.f “E” by angle𝛽. So,
deflecting Torque
𝑇𝑑 𝛼𝐼 𝑚 cos(90 − 𝛽).
In Fig.(c)
Inductive reactance = capacitive reactance &circuit is under resonance condition. So, moving
coil is purely resistive & so, “𝐼 𝑚 ” is in phase with “E”.
𝑇𝑑 𝛼 𝐼 𝑚 cos(90°) = 0
So, deflecting torque of moving coil is zero when inductive reactance= capacitive reactance.
 In actual operation of instrument for a fixed frequency, the capacitive reactance is
constant but inductive reactance of moving coil isn’t constant. This is because
inductance of moving coil depends on the position it occupies on iron core. This
inductance and inductive reactance is maximum when moving coil is close to
magnetizing coil &minimum when it’s on other end.
 The value of capacitance is chosen such that moving coil occupies a convenient mean
position on iron core, when frequency is at its normal value. At this position, inductive
reactance=capacitive reactance.

4.  When frequency increases above normal value, inductive reactance (𝑋𝑙) becomes larger
than capacitive reactance (𝑋 𝑐) as 𝑋𝑙 𝛼 𝑓 &𝑋 𝑐 𝛼
1
𝑓
. So, a torque is produced, this torque
tries to pull the coil to an equation position where𝑋𝑙 = 𝑋 𝑐.
 Therefore, 𝑋𝑙 > 𝑋 𝑐. So, we have to reduce𝑋𝑙. So, moving coil is moved away from
magnetizing coil to reduce𝑋𝑙.
 The coil will come to rest at 𝑋𝑙 = 𝑋 𝑐; f=
1
2𝜋√𝐿𝐶
Advantages:
Instrument has great sensitivity.
II. Electrodynamometer Type Frequency Meter

5.  There are two parts of fixed coil part1 & part2.
 The 2 parts form separate resonance circuit.
 Fixed Coil 1 is in series with 𝐿1& 𝐶1form a resonance frequency f1, slightly above
the lower end of instrument scale.
 Fixed coil 2 is in series with 𝐿2 & 𝐶2 forms a resonance frequency f2, slightly
higher than upper end of instrument scale.
 2 parts of fixed coil having their return circuit through movable coil.
 Torque on movable element 𝛼 current in moving coil & this current is sumof
current in 2 parts of fixed coil.
 For an applied frequency in frequency range of instrument circuit of fixed coil 1
operates above resonant frequency (𝑋𝑙1 > 𝑋 𝑐1) current𝐼1, through it, lags
applied voltage.
 Fixed coil 2 operates below resonant frequency, (𝑋 𝑐2 > 𝑋𝑙2) with current 𝐼2
leads applied voltage.
 One current coil is inductive while other current coil is capacitive in nature.
Torque produced by 2 currents I1 &I2 will be in opposition on moving coil. The
resultant torque will be a function of applied frequency of applied voltage & so,
meter scale can be calibrated in terms of frequency.
 This meter is used for Power Frequency Measurement.
III. Weston Frequency Meter

6.  Consists of 2 coil A & B mounted perpendicular to each other.
 Branch circuit of coil A has a resistance 𝑅 𝐴 connected in series with it & coil B has a
reactance 𝐿 𝐵 in series with it.
 Coil A is parallel reactance coil𝐿 𝐴.
 Coil b is parallel𝑅 𝐵.
 Moving element is soft iron needle. This needle is pivoted on a spindle which also
carries a pointer.
 The meter is connected across the supply & 2 coils carry current.
 These current set up 2 magnetic fields which are at right angles to each other. The
magnitude of field depends upon value of current in coil.
 Both these fields act on needle & needle takes up a position which depends upon
relative magnitude of 2 fields.
 Metre is so designed that at a normal f,𝐿 𝐴&𝑅 𝐵 sends equal current in coil A&B. so,
needle takes up position which is 45° to both coils and points at center of scale.
 Now, if frequency increase above normal value (𝐿 𝐴 & 𝐿 𝐵) increase & (𝑅 𝐴 & 𝑅 𝐵) remain
same.
 Coil A is parallel𝐿 𝐴.
 Coil B is parallel𝑅 𝐵.
 As, f increases, 𝐿 𝐴increases,V in coil A increases, I in coil A increases. While I in coil B
decreases. So, magnetic field of coil A is stronger than that of B.
 Tendency of needle to deflect towards stronger field. So, it tends to set itself in line with
coil axis A. so, pointer deflects to left.
 When f decreases then opposite action takes place &pointer deflects to right.

7. IV. Ratiometer Type Frequency Meter
 Ratiometer type frequency meter consist of a ratiometer which gives linear relationship
between current ration & deflection.
 The 2 coils of this ratiometer are fed with rectified output currents of 2 separate bridge
rectifier.
 The input sides of 2 bridge rectifier are connected to alternating current supply whose
frequency is to be measured.
 The input side of one of bridge rectifier has a series capacitance “C” &other has series
resistance”R”.
 Let, V be the supply voltage &” f” be supply frequency
Output of bridge rectifier 1 is:
𝐼1 𝛼 𝐼𝐶 𝛼 𝑓𝑉𝐶
Output of bridge rectifier 2 is:
𝐼2 𝛼 𝐼 𝑅 𝛼
𝑉
𝑅
Ratiometer,

8. Deflection (𝜃)
=𝐾
𝐼1
𝐼 2
=K
2𝜋𝑓𝑉𝐶
𝑉
𝑅
= 2𝜋𝐾1 𝐶𝑅𝐹
𝐾1, 𝐶, 𝑅 𝑎𝑟𝑒 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝜃 = 𝐾2F
 Instrument has a linear scale of frequency ratiometer is so designed that deflection (𝜃)
𝛼 ratio of two current.
Advantage:
 Supply voltage (V) dosen’t appears in expression of deflection (𝜃). Hence, this
instrument can be used fairly for wide range of voltage.
Saturable Core Frequency Meter
 This meter has a saturable core transformer as its primary detector.
 The deflection of meter is 𝛼 frequency to be measured.
 These frequency meter have the advantage that it can measure frequencies over a wide
range & is well suited especially for use I tachometer systems.