Owen’s Bridge: Construction, Theory, Balance Equations, Advantages & Disadvantages

Introduction

Several AC bridges are used for measuring inductance and quality factor (Q). Hay’s bridge is suitable for measuring high-Q inductors (Q > 10), Maxwell’s bridge for medium-Q inductors (Q = 1 to 10), and Anderson’s bridge is effective for measuring inductance ranging from a few microhenry to several henry. However, all these bridges have a limited measurement range. To overcome this limitation, Owen’s Bridge is used because it can measure a wider range of inductors accurately.

What is Owen’s Bridge?

Owen’s Bridge is an AC bridge used to measure an unknown inductance in terms of a known standard capacitance. Like other AC bridges, it uses a combination of standard capacitors, inductors, and variable resistors excited by an AC source.

The bridge has four arms: ab, bc, cd, and da:

• Arm ab: Contains the unknown inductor L₁ with resistance.
• Arm bc: Contains a pure resistor.
• Arm cd: Contains a fixed capacitor C₄.
• Arm ad: Contains a variable resistor R₂ and variable capacitor C₂ in series.

The unknown inductance L₁ is compared with the known capacitance C₄. Balance is achieved by adjusting R₂ and C₂ independently. At balance, no current flows through the detector, and points b and c are at the same potential.

Theory of Owen’s Bridge

An AC supply is connected between points a and c. Arm ab contains the unknown inductor having resistance r₁ and inductance l₁. Arm bc contains a pure resistance r₃. Arm cd contains a capacitor C₄, and arm ad contains variable components R₂ and C₂.

At balance, AC bridge theory states:

Z₁ × Z₄ = Z₂ × Z₃

Substituting impedances and separating real and imaginary parts gives the balance equations for the unknown inductance L₁ and resistance r₁.

Incremental Inductance Measurement

In a modified Owen’s Bridge, a valve voltmeter is connected across resistor r₃. The bridge is fed from both AC and DC sources in parallel:

• The inductor isolates the DC source from AC.
• The capacitor prevents DC from entering the AC source.
• An ammeter measures the DC component.
• The voltmeter measures the AC component.

At balance, the incremental inductance is:

l₁ = R₂ × R₃ × C₄

Incremental Permeability

Incremental permeability is given by:

μ = (l₁ × l) / (N² × A)

where:

• N = Number of turns
• A = Cross-sectional area of flux path
• l = Length of flux path
• l₁ = Incremental inductance

Phasor Diagram Explanation

Let the voltage drops across arms ab, bc, cd, and ad be e₁, e₃, e₄, and e₂.
At balance, e₁ = e₂.

Current i₁, flowing through the inductive arm, lags the most and is taken as the reference for drawing the phasor diagram.

The inductive drop is perpendicular to i₁, while the capacitive drop is perpendicular to i₂. The sum of all voltage drops forms the complete phasor shown in the bridge analysis.

Advantages of Owen’s Bridge

• Two independent balance conditions make adjustment easy because both R₂ and C₂ are in the same arm.
• Balance equations are simple and independent of frequency.
• Capable of measuring a wide range of inductances accurately.

Disadvantages of Owen’s Bridge

• Uses a variable standard capacitor, which is expensive and typically accurate only up to 1%.
• For high-Q measurements, the required capacitor value becomes large, increasing cost and size.