Hay’s Bridge Osama Mustafa Abdullah Quran

Agenda: Introduction to hay’s bridge. Using of hay’s bridge. Definition of Q-factor. Advantages and disadvantages. Numerical example. Application.

What is Hay’s Bridge ? It is a four-arm alternating-current bridge used to measure inductance in terms of capacitance, resistance, and frequency. Hay’s bridge is a modification of Maxwell bridge. The “galvanometer” is used to find the balance point.

= Unknown inductance having resistance = known resistances. = standard capacitor. Note: are variable resistors used to tune the bridge and Bring it to the balance point.

At the balance point: Let:

From this equation : we get : By simplifying :

Complex form: Polar form: magnitude phase NOTE: (resistive elements)

So we have: recall:, hence, =

Thus, can be rewritten as : NOTE: For high Q coil (> 10), the term can be neglected. Then

But what is Q factor ? The inductor's series resistance converts electric current through the coils into heat, thus causing a loss. As resistance increases, heat “power loss” increases and Q-factor decreases.

Continue... The quality factor (or Q) of an inductor is the ratio of its inductive reactance to its resistance at a given frequency, and is a measure of its efficiency.

Advantages of hay’s bridge. 1) This bridge gives very simple expression for unknown inductance for high Q coils (Q > 10). 2) This bridge also gives the simple expression for Q factor. 3) From expression of Q factor it is clear that for high Q factor the value of resistance should be small.

Disadvantages of hay’s bridge. 1) For low Q coils (<10) hay’s bridge becomes less efficient so, it’s preferable to use Maxwell bridge. 2) The balance equation is dependent of frequency and therefore any changes in frequency will affect the measurements.

Example 1 An ac bridge is in balance with the following parameters:,, The oscillator frequency is 1 kHz. Find &.

Solution:- &

Example 2 Given the Hay’s bridge Find, (i) The equivalent series resistance, R x. (ii) The inductance, L x.

Solution 1 Solution 2

Application: After inductors being produced they subjected to a test to measure the inductance, resistance and Q factor. All inductors must have the same value of those parameters. This test can be made using Hay’s Bridge.

Thank you for your attention. Hope you learned something.