Measurement of Frequency - GATE EE Electrical and Electronic Measurements

Frequency meter:

• Frequency meter is used to measure the frequency of periodic signals, by balancing two opposite forces.
• Change in the frequency which is to be measured causes a change in the balance and measured by the deflection of pointer.
• There are two modes of measurement that can be possible. Periodic mode and Frequency mode

Let f_x = unknown frequency, f_c = crystal frequency, f_o = crossover frequency

Then, If f_x < f_o periodic mode

And f_x > f_o frequency mode

Calculation:

The given configuration corresponds to wien bridge

Under the condition of tridge balance,

Put the relevant Values in equation

Put the relevant Values in equation

= 398 HZ

Therefore, correct Answer is option (b).

In an Anderson bridge, the unknown inductance is measured in terms of known capacitance and resistance.

The circuit diagram of Anderson Bridge is shown in the figure.

L₁ = self-inductance to be measured

R₁ = resistance of the self-inductor

r₁ = resistance connected in series with self-inductor

r, R₂, R₃, R₄ = known non-inductive resistances

C = fixed standard capacitor

Under the Balance condition,

Vibrating reed type frequency meter:

• A vibrating-reed frequency meter is a measuring instrument that is used to measure the frequency of various electric circuits. 
• Vibrating Reed Frequency meters indicate the supply frequency by means of individual reeds when rated voltage ± 20% is applied across the terminals of the meter.
• It consists of 7 vibrating reeds and each vibrating reed has a specific value. 
• These reeds vibrate when this frequency meter is connected to the supply for the measurement of frequency.
• The reed which will vibrate the most is the one whose natural frequency is equal to twice the frequency of the supply.

​Features of vibrating reed meter:

• No aging effect
• Faster response
• Lighter in weight
• Low power consumption
• Rugged construction
• High reliability

Weston Type Frequency Meter:

• Weston type frequency meter is based on the principle of the deflection, where the unknown value of the frequency of an input signal can be determined using this meter.
• It consists of 2 coils inductive coil and resistive coil, which are the right angle to one another.
• The 2 pairs, resistor R_A, and coil A and inductor L_A and coil B pair are placed in series, other pairs, L_A and coil A, and R_B, and coil B are placed parallelly.
• The meter consists of a soft pointer made up of iron and a magnetic needle which is placed at the center.
• The inductor “L” connected is in series with “L_A and R_B ” minimizes the errors.

• When the supply is given to the Weston frequency meter, the current starts flowing into the coil A and B.
• The perpendicular magnetic field set up in the coils because of the current. The magnitude of the field depends on the current passes through the coils.
• The magnetic field of both the coil A and coil B acts on the soft iron and the magnetic needle.
• The position of the needle depends on the relative magnitude of the magnetic field acts on it.
• The meter designs such a way that when the normal frequency passes through the coil then the voltage drops across the L_A, L_B, R_A, and R_B remains same.
• Thus, same magnitude current passes through the coils. In this situation, the magnetic needle makes an angle of 45° concerning the coils and the soft iron needle places at the centre of the scale.
• When the high frequency passes through the meter, the reactance L_A and L_B of the coil increases and the R_A and R_B remains same.
• ​The inductance increase the impedance of the coil A. The impedance means the opposition offered by the circuit in the flow of current.
• As the magnitude of current in the coil A decreases, the field develops because of the coil, A current also decreases.
• The more current flows through the coil B because of the parallel connections with coil A.
• ​The magnetic field develops in the coil B becomes stronger than the coil A.
• The magnetic needles align themselves parallel to the axis of the strong magnetic field, and the pointer deflects towards the coil B or strong magnetic field.

• Finally, the frequency which is to be determined reduces from its normal value, and the pointer indicates the value of unknown frequency towards the left side.

Electrical Resonance Type Frequency Meter:

• The electrical resonance type frequency meter is an indicating type instrument.
• Its action depends upon the electrical resonance.
• Construction of Electrical Resonance Type Frequency Meter
• It mainly consists of a fixed coil and a moving coil. There is a laminated iron core of varying cross-sections.
• This varying laminated core holds the fixed coil at its one end. Then we connect this fixed coil across the supply mains.

f_L is the lower frequency
f_H is the higher frequency
f_N is normal frequency

Working Principle of Electrical Resonance Type Frequency Meter:

• Due to the current in the moving coil, the moving coil produces a flux in phase with the current.
• This flux flows along with the extended core of the fixed coil. Therefore the flux links the moving coil.
• Hence, the flux induces an emf across the moving coil and this induced emf lags the flux by 90°.
• Since the moving coil will have some inductive reactance. Again, as it is connected across a capacitor, it will have some capacitive reactance also.
   

Torque Equation:

Let us consider I₁ is the supply current of the fixed coil and I₂ is the induced current of the moving coil.

We have the phase angle between the supply current I₁ (current in the fixed coil) and the emf induced in the moving coil is 90°.

Again there is a phase difference between the induced emf and the induced current I₂ (current in the moving coil).

Let us consider the angle of this phase difference is α.

So, the actual phase difference between I₁ and I₂ will be (90° - α).

Therefore, we can write the expression of the torque (T) as,

T = I₁I₂ cos (90° - α)

From the above expression of the torque, we can see that the torque will be zero when α is zero.

That means there must not be any phase difference between the induced current and the induced emf in the moving coil.

Wein bridge oscillator:

The circuit diagram of the Wein bridge oscillator is shown below:

The frequency of oscillation is given by:

Schering bridge is used to measure relative permittivity, dielectric loss and power factor of a capacitor. 

Important Points 

Schering Bridge:

Schering bridge is used to measure the dissipation factor (dielectric loss) and capacitance.

The circuit of the Schering bridge as shown below:

When the bridge is in the balanced condition, zero current passes through the detector, which shows that the potential across the detector is zero.

At balance condition

Z₁ Z_x = Z₂ Z₃

Important Notes:

Owen’s bridge:

• Owen’s bridge circuit is defined as, the AC bridge that is used to measure a wide range of unknown inductance of low Q coils in terms of resistance and capacitance.
• It usually works on the principle of comparison.
• It means the measured unknown inductance value is compared with the standard or known capacitor.
• This type of bridge circuit uses a standard capacitor and a variable resistor connected with AC sources for excitation.

• The ab, bc, cd, and da are the four arms of Owen’s bridge.
• The arms ab are purely inductive and the arm bc is purely resistive in nature.
• The arm cd has a fixed capacitor and the arm ad consists of the variable resistor and capacitor connected in series with the circuit.
• The unknown inductor L1 of arm ab is compared with the known capacitor C4 connected to the arm cd.
• The bridge is kept in a balanced condition by independently varying the resistor R2 and the variable capacitor C2.
• At the balanced condition, no current flows through the detector.
• The endpoints (b and c) of the detector are at the same potential.

Schering Bridge:

• Schering bridge is used to measure the dissipation factor (dielectric loss) and capacitance.
• The circuit of the Schering bridge as shown below:

When the bridge is in the balanced condition, zero current passes through the detector, which shows that the potential across the detector is zero.

At balance condition:

• Anderson bridge is used for the measurement of inductance
• Wien parallel bridge is used for the measurement of frequency
• Schering bridge is used for the measurement of capacitance and loss angle
• Kelvin double bridge is used to measure low resistance.

Important Points: