Q4Electronic Measurement & Instrumentation

Hay's bridge is an AC bridge used primarily for the precision measurement of self-inductance of coils having a high Quality Factor ($Q>10$). It is a modification of Maxwell's bridge.

Circuit Setup: - Arm 1 ($AB$): Unknown inductor $L_1$ and its resistance $R_1$. - Arms 2 & 3 ($BC$ & $AD$): Pure resistors $R_2$ and $R_3$. - Arm 4 ($CD$): Standard capacitor $C_4$ in series with variable resistor $R_4$.

By putting $C_4$ and $R_4$ in series (instead of parallel like Maxwell's), it avoids the need for impractically large resistance values when balancing high-Q coils.

Balance Equations: The balance equations are dependent on frequency ($\omega$): $L_1=\frac{R_2{R}_3{C}_4}{1+(\omega C_4{R}_4{)}^2}$ For high-Q coils, the term $(\omega C_4{R}_4{)}^2$ is very small, so $L_1\approx R_2{R}_3{C}_4$.