Chapter 27: What is an A.C Bridge?

A.C bridges are used for measuring the values of inductors and capacitors, and for converting the signals measured from inductive or capacitive components into a suitable form such as voltage. Inductors and capacitors can also be measured using voltage division, though this is an approximate method. They work the same way as Wheatstone bridges, which measure resistive quantities only. A.C bridges provide precise ways of measuring inductance, capacitance, and resistance.

27.1 Types of Detector

The types of zero current detector used with an A.C bridge depend on the type of bridge and the frequency at which it operates.

• An oscilloscope is the most versatile and is used for a varying range of frequencies.
• Earphones are used up to 10kHz but often at 1kHz.
• Various electronic detectors use tuned circuits to detect current at the correct frequency.
• Vibration galvanometers are used for mains operated frequencies from 10 Hz to 300 Hz.

27.2 Balance Conditions in an AC Bridge

There are two conditions to be simultaneously satisfied for balance in an a.c bridge. At balance, the current flowing through the detector branch is zero, meaning the current flowing through Z₁ is the same as Z₂, and the current through Z₃ is the same as Z₄. By equating the voltage drops across the arms, the general balance equation is derived as:

In polar form, this requires that the magnitude |Z₁||Z₃| = |Z₂||Z₄| and the phase angles α₁ + α₃ = α₂ + α₄.

Procedure for Determining Balance Equations

1. Determine the impedance in each arm in complex form and write down the balance equation.
2. Isolate the unknown terms on the left-hand side of the equation in the form a + jb.
3. Manipulate the terms on the right-hand side of the equation into the form c + jd.
4. Equate the real parts of the equation, and then equate the imaginary parts.
5. Substitute ωL for X_L and 1/(ωC) for X_C where appropriate and express the final equations in their simplest form.

27.3 Types of a.c Bridge Circuits

The different types of a.c bridge measure different aspects of the impedance. A ratio-arm bridge is one where two of the balancing impedances are of the same nature, either consisting of both capacitors or both resistors. A product-arm bridge is one where a pair of opposite arms are pure components. A ratio-arm bridge can only be used to measure reactive quantities of the same type, whereas in a product-arm bridge, the reactive component of the balancing impedance must be of opposite sign to the unknown reactive component.

a) The Simple Maxwell Bridge

This bridge measures the resistance and inductance of a coil having a high Q-factor. At balance, expressions for R_x and L_x may be derived in terms of known components R₂, R₃, R₄, and L₄.

c) The Owen Bridge

This is used to measure the resistance and inductance of coils having a large value of inductance. By equating real and imaginary parts at balance, the expressions are given by:

d) The Maxwell-Wien Bridge

This bridge is used to measure the resistance and inductance of a low Q-factor coil. At balance, the unknown resistance and inductance values are:

e) The De Sauty Bridge

This bridge provides a very simple method of measuring capacitance by comparison with another known capacitance. The general balance equation yields C_x = (R₃C₄) / R₂. However, this simple bridge is usually inadequate in most practical cases because the power factor of the capacitor under test is significant due to internal dielectric losses.

f) The Schering Bridge

This bridge is used to measure the capacitance and equivalent series resistance of a capacitor. From the measured values, the power factor of insulation may be determined. At balance, the values are given by:

g) The Wien Bridge

The Wien bridge circuit can be used for three purposes: to measure frequency in terms of known components, to measure capacitance if the frequency is known, or as a frequency stabilizing network. Equating the real and imaginary parts at balance yields the standard formula for frequency: