Campbell’s Bridge

05/04/2025

Campbell Bridge: Definition and Function
Definition
The Campbell bridge is a specialized electrical bridge designed to measure unknown mutual inductance. Mutual inductance refers to the physical phenomenon where a change in the current flowing through one coil induces an electromotive force (emf) and, consequently, a current in a neighboring coil. This bridge is not only useful for determining mutual inductance values but can also be employed to measure frequency. It does so by adjusting the mutual inductance until a null point is achieved in the bridge circuit.
In electrical engineering, accurately measuring mutual inductance is crucial for understanding the interaction between different coils in circuits, such as in transformers, inductive coupling systems, and various electrical machinery. The Campbell bridge provides a precise and reliable method for these measurements. When used for frequency measurement, the null - point detection principle allows engineers to establish a relationship between the mutual inductance setting and the frequency of the electrical signal under test.
The following figure illustrates the concept of mutual inductance, which forms the foundation for the operation of the Campbell bridge.

Let:

$M1$ represent the unknown mutual inductance
$L1$ denote the self - inductance of the secondary of mutual inductance $M1$
$M2$ signify the variable standard mutual inductance
$L2$ be the self - inductance of the secondary of mutual inductance $M2$
$R1$ , $R2$ , $R3$ , $R4$ stand for non - inductive resistances

Achieving the balanced position of the Campbell bridge necessitates a two - step procedure:

Step 1: Initial Setup and First Balance Condition

The detector is initially connected between points ‘b’ and ‘d’. In this configuration, the circuit functions analogously to a simple self - inductance comme

First Balancing Step To bring the bridge to a balanced condition in the first stage, resistors $R3$ or $R4$ , along with $R1$ and $R2$ , are adjusted. This adjustment process fine - tunes the electrical parameters of the circuit, ensuring that the electrical potential differences across the relevant parts of the bridge are equalized, much like adjusting the weights on a balance scale to achieve equilibrium.
Second Balancing Step In the next phase, the detector is reconnected between points $b'$ and $d'$ . Building on the adjustments made in the first step, the variable standard mutual inductance $M2$ is then systematically varied. Through this process of varying $M2$ while maintaining the previously set resistor adjustments, the overall electrical configuration of the bridge is further optimized. Eventually, a balance point is reached, indicating that the bridge has achieved a state of equilibrium where the electrical signals in the circuit are in harmony, and accurate measurements of the unknown mutual inductance $M1$ can be made.