Maxwell Bridge vs. Hay Bridge: AC Bridge Comparison for Inductance and Capacitance Measurement

Maxwell and Hay bridges are both AC bridge circuits used for precision measurement of inductive and capacitive components. While sharing a four-arm diamond topology, their variable elements and optimal applications differ significantly.

Maxwell Bridge: Inductance Specialist

Circuit Configuration

• Arm 1: Unknown inductor (Lx, Rx) – series RL model
• Arm 2: Standard capacitor (Cs) – high-quality, stable
• Arms 3 & 4: Known resistors (R3, R4) – ratio arms

Balance Equations

At balance (detector null):

Lx = R3 × R4 × Cs
Rx = (R3 / R4) × (1 / (ω² × Cs² × R3² + 1)) ≈ R3 × R4 × Cs × ω²  (for high Q)

Where ω = 2πf (angular frequency). Independent balance for Lx and Rx achieved by adjusting R3/R4 ratio and Cs.

Strengths

• Wide inductance range – 1 mH to 100 H (with appropriate Cs)
• Direct L and R reading – No frequency knowledge needed for Lx
• High Q coils – Excellent for Q > 10
• Standard capacitor stability – Cs is fixed, precise component

Limitations

• Low Q coils – Balance equations interact; difficult for Q < 1
• Variable capacitor not used – Less convenient for capacitance measurement
• Frequency dependence for Rx – Requires known frequency for resistance balance

Hay Bridge: Capacitance and High-Frequency Specialist

Circuit Configuration

• Arm 1: Unknown capacitor (Cx) – series RC model
• Arm 2: Variable capacitor (Cv) – adjustable for balance
• Arms 3 & 4: Known resistors (R3, R4); Arm 3 often includes standard inductor

Balance Equations

At balance:

Cx = Cv × (R4 / R3)
Rx = (R3 × R4) / (ω² × Cv² × R3² + 1)  (series resistance of capacitor)

Strengths

• Precise capacitance measurement – Variable capacitor allows fine null adjustment
• High-frequency capability – Suitable for RF coils/inductors (up to MHz range)
• Low-loss capacitors – Excellent for measuring small dielectric losses
• Simple balance – Single variable (Cv) for capacitance null

Limitations

• Inductance measurement indirect – Requires known standard inductor in arm 3
• Variable capacitor stability – Cv less stable than fixed standard capacitor
• Frequency sensitivity – Balance depends on ω; must be known precisely

Comparison Summary

Practical Selection

• Choose Maxwell for power-frequency inductors (transformers, chokes, motors)
• Choose Hay for capacitor characterization, RF components, dielectric testing
• Modern alternative – LCR meters (impedance analyzers) automate both; bridges now primarily calibration/education