Hay's bridge - Phasor diagram - Disadvantages

Ram Swaroop March 10, 2017
The hay's bridge is particularly useful for measuring inductance of coils of high quality factor (Q >10).
The Hay's bridge is a modification of Maxwell’s bridge. The modification is done in the capacitance arm.  This bridge uses a comparatively smaller resistance R4 in series with the standard capacitor C4 unlike the Maxwell bridge which uses very large value resistance in parallel with capacitor.

Hays bridge for inductance measurement
Hay's bridge circuit

where,
L1= unknown inductance having resistance R1
R2 ,R3 ,R4 = known non-inductive resistances
C4 = standard capacitor     

The bridge is balanced when current through galvanometer becomes zero, then
e1 = e2   and   e3 = e4
or   
Z1 Z4 = Z2 Z3
(R1+jwL1)[R4-(j/wC4)] = R2 R3

Multiplying and equating real and imaginary parts  
R1 R4 + (L1/C4) = R2 R3           ...(1)
and  jwL1R4 - ( jR1/ wC4) = 0         ...(2)

Solving (1) and (2)
L1 = R2R3C4/(1+w2C42R42)
R1 = w2C42R2R3C4 / (1+w2C42R42)

Now, Q factor of the coil is given by
Q=wL1/R1
     =1/wC4R4


Hay’s bridge Phasor diagram is shown below


Hay's bridge phasor diagram
Hays bridge phasor diagram



Disadvantages of Hay’s bridge :-
  1. The balance equation is dependent of frequency and therefore any changes in frequency will affect the measurements.
  2. Hay's bridge is less efficient for measurement of low quality factor (Q<10) and Maxwell’s bridge must be used.


Closely related topics :-
(1) Maxwell’s Inductance bridge 
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