1. Hay’s Bridge Osama Mustafa 0128341 Abdullah Quran 0127270

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

3. 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.

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

5. At the balance point: Let:

6. From this equation : we get : By simplifying :..........1..........2

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

8. So we have: recall:, hence, =

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

10. 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.

11. 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.

12. 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.

13. 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.

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

15. Solution:- &

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

17. Solution 1 Solution 2

18. 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.

19. Thank you for your attention. Hope you learned something.