Electrical & Electronic Measurements - AC & DC Bridges Complete Study Notes

In this article, you will find the study notes on Bridges  which will cover the topics such as Maxwell’s inductance bridge, Maxwell’s inductance-capacitance bridge, Hay’s bridge, Anderson’s bridge, Owne’s bridge, De-Sauty Bridge, Wein’s Bridge, D.C Potentiometer & A.C Potentiometer etc.

AC Bridges: AC bridges are used to measure self-inductance, mutual inductance, capacitance and frequency.

Types of Sources

1. At low frequency, the power line is used as a source.
2. At high frequency, the electronic oscillator is used as a source

Types of Detectors

1. Vibration galvanometer at low power frequency and audio frequency (up to 1000 Hz)
2. Headphones at an audio frequency (250 Hz to 4 kHz)
3. Tunable amplifier for frequency range (10 Hz to 100 kHz)

General Bridge Circuit

At balanced bridge 

Magnitude condition 

Angle condition 

For balanced bridge both the magnitude

Measurement of Self Inductance

• Maxwell’s inductance bridge
• Maxwell’s inductance-capacitance bridge
• Hay’s bridge
• Anderson’s bridge
• Owne’s bridge

Maxwell’s Inductance Bridge

Where, L₁ = Unknown inductance of resistance R₁

L₂ = Variable induactance

R₂ = Standard variable resistance

R₃, R₄ = Fixed non-inductance resistance

Maxwell’s Inductance - Capacitance Bridge

Q-factor, 

Q-factor range 1 < Q < 10, for medium Q-coils

Where, R₄ = Variable non-inductive resistance

C₄ = Standard variable capacitance

Note: If C₄ is fixed, then balanced bridge obtained as

• Either by varying R₂ and R₄.
• Put a resistance in series with L₁ and varying R₄.

Hay’s Bridge

Where, C₄ = Standard capacitance

Q-factor 

for Q > 10 i.e., high Q-coils

L₁ = R₂R₃C₄

Anderson’s Bridge

Where, L₁ = Unknown self-inductance with an internal resistance R₁

R₂, R₃, R₄ = Fixed standard non-inductive resistance

r = A variable resistance

C = A fixed capacitance

• Anderson’s bridge is suitable for small Q-factor i.e., Q < 1.
• It can also be used for the measurement of capacitance in terms of inductance.

Key Points

• Maxwell’s bridge is used to measure the inductance of a low Q-inductor.
• Hay bridge is used to measure the inductance of a high Q-inductor.
• Inductance is measured in terms of capacitance, resistance by Anderson’s bridge.

Owen’s Bridge

Where, L₁ = Unknown self-inductance with internal resistance R₁

R₂ = Variable non-inductive resistance

R₃ = Fixed standard non-inductive resistance

C₂ = Standard variable capacitor

C₄ = Fixed standard capacitor

Measurement of Capacitance

The capacitance can be measured with the help of the following bridges

De-Sauty Bridge

Where C₁ = Unknown capacitor

C₂ = Standard capacitor

R₃, R₄ = Fixed non-inductive resistance

The de-Sauty bridge can be used for the measurement of either air-cored or gas-filled capacitance only (lossless capacitor).

Schering Bridge

Dissipation factor D₁ = tan δ = ωC₁r₁ = ωC₄ R₄

Where C₁ = Unknown capacitor with loss component r₁

C₂ = Fixed standard capacitor

R₃ = Fixed standard non-inductive resistance

C₄ = Variable capacitor

R₄ = Variable non-inductive resistance

Key Points

• High voltage Schering bridge is used for the determination of capacitance of insulators, capacitor bushings and insulating oil and other insulating materials.
• Schering bridge is also used to measurement of relative permittivity of dielectric materials.
• The Schering bridge is one of the most widely used AC bridges.
• In order to measure the low value of capacitance Schering bridge is used.

Measurement of Frequency

Frequency by Wein’s bridge.

Wein’s Bridge

Frequency, 

For R₁ = R₂ = R

and C₁ = C₂ = C

and C₁ = C₂ = C

• Wein’s bridge used as a notch Filter in harmonic distortion analyzer.
• A frequency isolator in high-frequency oscillator and amplifier circuit.
• A notch filter in a harmonics distortion analyzer where it is used to isolate and eliminate the fundamental frequency component from the output of the amplifier under test.

Comparison between Different Types of Bridges

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