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Derive an expression for inductance measurement using Hay bridge
1 Answer
written 3.9 years ago by |
Hay Bridge is used to measure high value inductances.
The circuit diagram is shown below.
When bridge is balance,
Z1 Zx=Z2 Z3Z2=R2Z3=R3Zx=Rx +jωLx
From equation 1,
(R1−jωC1)(Rx+jωLx)=R2R3
R1Rx+jωLxR1−jRxωC1+LxC1=R3 R2
(R1Rx+LxC1)+j(ωLxR1−RxωC1)=R2R3
Equating real and imaginary terms,
R1Rx+LxC1=R2R3
ωLxR1− RxωC1=0
∴Lx=Rxω2R1C1
R1 Rx+Rxω2R1C2=R2 R3Rx ⌊R1+ 1ω2R1C12⌋=R2 R3Rx ×ω2 R12C12+1ω2R1C12=R2 R3∴ Rx=ω2C12R1R2R31+ω2R12C12∴Lx=ω2C22R1R2R3(1+ω2R12C12) (ω2R1C1)∴Lx=C1R2R3(1+ω2R12C12)
A w appears in the expression for Lx, this bridge is frequency sensitive.
Quality Factor (Q) for capacitance is
Q=1ωR1C1Or ωR1C1=1/Q∴Lx=C1R2R31+1/Q2