AC Bridges

AC bridge principle

An AC bridge balances complex impedances. Label the left series branch Z1 above Z2 and the right Z3 above Z4. Connect an AC source between top and bottom nodes and a null detector between the two midpoints. At balance, Z2/(Z1 + Z2) = Z4/(Z3 + Z4), giving Z1Z4 = Z2Z3. Both real and imaginary conditions must be satisfied. A magnitude-only equality is not enough. Different bridge arrangements use known resistive and reactive elements to compare unknown inductance, capacitance or frequency. Maxwell, Hay, Schering and Wien bridge formulas depend on their exact topology; first draw and label the arms rather than memorizing an unlabeled ratio.

Worked example: impedance comparison

At a specified frequency, Z1 = 100 Ω, Z2 = 200 Ω and Z3 = 50 + j100 Ω. Balance requires Z4 = Z2Z3/Z1 = 100 + j200 Ω. At f = 1 kHz, if Z4 is represented as a series resistor and inductor, R4 = 100 Ω and L4 = 200/(2π × 1000) = 31.83 mH. Its quality factor is 200/100 = 2 at that frequency. Check both parts: Z1Z4 = 10000 + j20000 Ω² and Z2Z3 gives the same value.

Measurement considerations

Balance sensitivity depends on excitation, detector and component values. Stray capacitance, inductive coupling, leakage and frequency dependence can shift the null. Shielding and guarding have different functions and must match the bridge arrangement. A detector null does not mean every parasitic effect is absent.

Quick check

1. How many scalar balance equations are normally obtained? Two: real and imaginary.
2. Can equal impedance magnitudes alone establish balance? No.
3. Why state test frequency? Reactive impedances and real-component losses depend on it.