AC bridges (alternating current bridges) are derived from the DC Wheatstone bridge. It is mostly used for the measurement of unknown electrical quantities (inductance, capacitance, etc.).

Table of Contents

## What are ac bridges?

**The alternating current bridges (AC bridges) are the electrical circuits that are treated for the measurement of various unknown electrical quantities such as inductance, capacitance, loss factor, and more.**

AC bridges come with very fine accuracy and they can operate only with the AC supply.

The AC bridges operate on the principle that the balance ratio of the impedance gives the balance condition to the circuit which is indicated by the detector.

The circuit diagram of ac bridges is shown below:

This bridge circuit consists of 4 arms each having some impedance, power supply, and detector. The detector and the power supply are connected in opposite nodes, because if both are connected in the same node then the detector will not indicate the balance condition of the circuit.

The source in the circuit changes according to the need. For low-frequency measurement power line is used as the source, whereas for high-frequency measurement an electric oscillator can be used as the source.

Similarly, the detector in the circuit is keep changing according to the requirement of the circuit. Tuned detectors are applied in the circuit for detection purposes.

Different tuned detectors are applied according to the frequency at which the AC bridge circuit is operating.

The vibration galvanometer is applied when the frequency of operation ranges from 5 Hz to 1000 Hz.

Headphones are applied when the frequency ranges from 250 Hz to above 3-4 kHz

The tunable amplifier with the facility of frequency tuning can be effectively used as a balanced detector. And it operates over a frequency range of 10 Hz to 100 kHz

## What is the balance condition?

Balance condition in a circuit refers to a condition, that is achieved when no current flows through the detector i.e., at balance condition, there is no potential difference across the detector.

## Equation of ac bridge

The 4 arms in the bridge circuit have impedance Z_{1}, Z_{2}, Z_{3}, Z_{4}

To achieve the balance in the circuit one arm is to be adjusted so that the detector indicated 0 response or null deflection.

this is possible only If the voltage drop across A-B is equal to the voltage drop across A-C.

**V _{1} = V_{2}**

Or **I _{1}Z_{1} = I_{2}Z_{2} …eq. 1**

At balance position,

**I _{1} = I_{3} = V/(Z_{1}+Z_{3}) …eq. 2**

And

**I _{2} = I_{4} = V/(Z_{2}+Z_{4}) …eq.3**

Combining eq.3 and eq.2 in eq.1

**VZ _{1}/(Z_{1}+Z_{3}) = VZ_{2}/(Z_{2}+Z_{4})**

**Z _{1}/(Z_{1}+Z_{3}) = Z_{2}/(Z_{2}+Z_{4})**

**Z _{1}(Z_{2}+Z_{4}) = Z_{2}(Z_{1}+Z_{3})**

**Z _{1}Z_{2 }+ Z_{1}Z_{4} = Z_{2}Z_{1 }+ Z_{2}Z3**

**Z _{1}Z_{4} = Z_{2}Z_{3} …eq.4**

**Z _{1}/Z_{3} = Z_{2}/Z_{4}**

Eq.4 represents the general balance equation of the ac bridges. It indicates that underbalanced condition of the circuit, the product impedances of one pair of opposite arms must be equal to the product of impedances of the other pair of opposite arms.

In polar form eq.4 expressed like this

**(Z _{1}∠Ѳ_{1})*(Z_{4}∠Ѳ_{4}) = (Z_{2}∠Ѳ_{2})*(Z_{3}∠Ѳ_{3})**

**Z _{1}Z_{4}∠(Ѳ_{1}+Ѳ_{4}) = Z_{2}Z_{3}∠(Ѳ_{2}+Ѳ_{3}) …eq.5**

In eq.5

Z_{1}Z_{4} = Z_{2}Z_{3} represents the magnitude of the impedances

∠(Ѳ_{1}+Ѳ_{4}) = ∠(Ѳ_{2}+Ѳ_{3}) represents the phase angle of the impedances.

## Applications of ac bridges

- Providing feedback path and phase-shifting path to the oscillator.
- AC bridges are used for the measurement purpose of capacitance, frequency, and inductance.