Maxwell’s Bridge: Types, Construction, Working Principle, Advantages & Applications

Introduction

Maxwell’s Bridge is a modification of the Wheatstone Bridge used for accurate measurement of unknown inductance (typically of low or medium Q). The measurement is performed by comparing the unknown inductance with known standard resistance and inductance or resistance and capacitance. When a calibrated resistor–capacitor pair is used, the circuit is known as the Maxwell–Wien bridge. The bridge was first described by James C. Maxwell in 1873.

The principle of operation is based on compensating the positive phase angle of an inductive impedance with the negative phase angle of a capacitive impedance. At the balance point, the detector shows zero voltage, meaning no current flows through it. Under these conditions, the unknown inductance can be determined precisely.

Types of Maxwell’s Bridge

• Maxwell’s Inductance Bridge
• Maxwell’s Inductance–Capacitance Bridge

1. Maxwell’s Inductance Bridge

In this bridge, the unknown inductance is measured by comparing it with a known variable inductance and standard resistances. Arms BC and CD are purely resistive, while arms AB and AD are responsible for phase balance.

Definitions

• L₁: Unknown inductance
• r₁: DC resistance of the unknown inductor
• L₂: Variable standard inductance
• R₂: Variable standard resistance

Balance Condition

According to AC bridge balance conditions:

Z₁ × Z₄ = Z₂ × Z₃

Using resistance boxes, R₃ and R₄ can be varied from 10 Ω to 10,000 Ω to achieve balance.

Phasor Diagram

The phasor diagram represents the voltage and current relationships when the bridge is balanced. By adjusting L₂ and R₂, the bridge reaches a state where no current passes through the detector. Phase relationships help ensure both magnitude and phase components satisfy the balance equation.

2. Maxwell’s Inductance–Capacitance Bridge

In this version, the unknown inductance is measured by comparison with a standard capacitor instead of a known inductance. This method is especially useful for low-Q inductors.

Components

• L₁: Unknown inductance
• R₁: Resistance of the unknown inductor
• R₂, R₃: Non-inductive standard resistances
• R₄: Variable standard resistance
• C₄: Standard variable capacitor

Balance Equations

Under null conditions:

Z₁ × Z₄ = Z₂ × Z₃

Separating real and imaginary parts yields expressions for L₁ and R₁.

Determination of Q-Factor

The Q-factor (or storage factor) of the inductor is:

Q = ωL₁ / R₁

From Maxwell’s inductance–capacitance bridge:

Q ∝ R₄ C₄

Since C₄ is usually in the microfarad or picofarad range, a very high resistance (megaohms or more) is required for high Q measurement, making this method unsuitable for coils with Q > 10. For higher Q-factor coils, Hay’s Bridge is preferred.

Special Note

If R₂ and R₃ are both set to 10⁶ Ω, then:

L₁ = C₄

Thus, the dial reading of the variable capacitor directly gives the value of inductance.

Advantages of Maxwell’s Bridge

• Bridge balance equations are frequency-independent.
• Useful for a wide range of inductance measurements at audio and power frequencies.
• Inductance can be directly read from calibrated resistance scales.
• Suitable for comparing large inductance values to a standard.

Disadvantages of Maxwell’s Bridge

• Fixed capacitor may cause interaction between resistive and reactive balances.
• Not suitable for very high Q-factor coils (Q > 10).
• Requires an expensive variable standard capacitor.
• Not suitable for very low Q-factor coils.

Applications

• Used in communication systems for inductance measurement.
• Used in electronic and instrumentation circuits.
• Useful in power and audio frequency applications.
• Comparing unknown inductances with standard values.
• Determining the quality of medium-Q coils.
• Used in filter circuits and both linear and non-linear circuits.
• Power conversion circuits.