1. Guided by - Prof. J B Patel Prepared by - 130230109018 : Hemaxi Halpati 130230109019 : Priyank Hirani 130230109020 : Manish Jatiya 130230109022 : Rakesh Joshi 130230109023 : Piyush Kanani

2. Chart of preparation of presentation July August

3. Synopsis Maxwell’s inductance bridge Maxwell’s capacitance bridge Hay’s bridge Anderson bridge Owen bridges De Sauty’s bridge Schering bridge

4. Maxwell’s inductance bridge The bridge circuit is used for medium inductances and can be arranged to yield results of considerable precision. As shown in Fig., in the two arms, there are two pure resistances so that for balance relations, the phase balance depends on the remaining two arms.

5. Conti. L 1 = unknown inductance of resistance R 1 L 4 = variable inductance of fixed resistance r 4 R 4 = variable resistance connected in series with inductor L 4. R 2,R 3 = known pure resistances At balance, (R 1 + jωL 1 )R 3 = (R 4 + jωL 4 )R 2 Finally, L 1 = L 4 (R 2 /R 3 ) R 1 = (R 4 + r 4 )(R 2 /R 3 )

6. Maxwell’s inductance capacitance bridge In this bridge, an inductance is measured by comparison with a standard variable capacitance. The connection is shown in figure. One of the ratio arms has a resistance and capacitance in parallel.

7. Conti. L 3 = unknown inductance C = variable standard capacitor R 1, R 2, R 4 = known pure resistances. R 3 =effective resistance of inductor L 3 At balance, R 1 (R 3 + jωL 3 ) = R 2 R 4 (1 + jωCR 1 ) Finally, L 3 = CR 2 R 4 R 3 = R 4 R 2 /R 1 Q = ωCR 3

8. Advantages The balance equation is independent of frequency. It is useful for measurement of wide range of inductance at power and audio frequency. Disadvantages It cannot be used for measurement of high Q values (Q≥10). It cannot be used for measurement of very low Q values, because of balance converge problem.

9. Hay’s bridge The Hay’s bridge is a modification over the Maxwell’s inductance-capacitance bridge. Figure shows the connection diagram. It uses a resistance in series with capacitor. For large phase angles R 1 should have a very low value. This circuit is used for measuring high Q.

10. Conti. L 3 = unknown inductance having a resistance R 3. C 1 = standard capacitor R 1, R 2, R 4 = known pure resistances. At balance, (R 1 + j/ωC 1 )(R 3 + jωL 3 ) = R 2 R 4 Finally, L 3 = C 1 R 2 R 4 (1 + ω 2 C 1 2 R 1 2 ) R 3 = ω 2 C 1 2 R 1 R 2 R 4 & Q = 1/ωC 1 R 1 (1 + ω 2 C 1 2 R 1 2 )

11. Advantages It is used for the measurement of high Q inductors especially those having a Q greater than 10. Disadvantages For inductances having Q values less than 10 then (1/Q 2 ) becomes important and cannot be neglected.

12. Anderson’s bridge This bridge, in fact, is a modification of the Maxwell’s inductance- capacitance bridge. In this method, the self-inductance is measured in terms of a standard capacitor. Figure shows the connections and the phasor diagram of the bridge for balanced conditions.

13. Conti. L 1 = self inductance to be measured. C = fixed standard capacitor R 2, R 3, R 4, R 5 = known pure resistances. R 1 = resistance connected in series with L 1. At balance, (R 1 + jωL 1 ) (R 3 /jωC) = R 2 R 4 + R 3 R 5 (R 3 + R 5 + 1/jωC) (R 3 + R 5 + 1/jωC) Finally, R 1 = R 2 R 4 /R 3 L 1 = CR 2 + R 4 + R 5 + (R 5 R 4 /R 3 )

14. Advantages Anderson’s bridge balance is easily obtained for low Q coils. The bridge can be used for accurate determination of capacitance in terms of inductance. Disadvantages It is complex. The bridge balance equations are not simple. They are rather more tadious.

15. Owen’s bridge This bridge may be used for measurement of an inductance in terms of resistance and capacitance. The arrangement of the connections is shown in figure.

16. Conti. L 3 = unknown inductance of resistance R 3. C 4 = variable standard capacitor. C 1 = fixed standard capacitor. R 2 = fixed pure resistances. R 4 = variable pure resistances. At balance, -j (R 3 + jωL 3 ) = R 2 (R 4 + j/ωC 4 ) ωC 1 Finally, R 3 = R 2 C 1 /C 4. L 3 = C 1 R 2 R 4

17. Advantages The balance equations are quite simple and don’t contain any frequency content. The bridge can be used over a wide range of measurement of inductances. Disadvantages The bridge requires a variable capacitor which is an expensive item and also its accuracy is about 1%. The value of capacitance C 4 become rther large when measuring high Q coils.

18. De Sauty’s bridge This bridge is the simplest method of comparing two capacitances. The connection diagram of this bridge is shown in figure.

19. Conti. C 2 = capacitor whose capacitance is to be measured C 3 = a standard capacitor. R 3, R 4 = pure resistances. At balance, R 1 -j = R 4 -j ωC 3 ωC 2 Finaaly, C 2 = C 3 R 4 R 1

20. Advantages The bridge is simple. It is economical. Disadvantages If both the capacitors are not free from dielectric loss, then it is not possible to achieve bridge balance. This method is only suitable for the measurement of lossless capacitors.

21. Schering bridge It is used extensively fo the measurement of capacitors. It is also useful for measuring insulating properties i.e. phase angles very nearly 90 o. One of the ratios are consists of a resistance in parallel with a capacitor and standard arm consists only a capacitor. The standard capacitor is a high quality mica capacitor or an air capacitor for insulation measurement.

22. Conti. C 2 = capacitor of unknown capacitance. r = a series resistance representing the loss in the capacitor C 1. C 1 = a standard capacitor. R 3 = a pure resistance. C 4 = a variable capacitor. R 4 = a variable pure resistance. At balance, r + 1 R 4 = 1 R 3 jωC 2 (1 + jωC 4 R 4 ) jωC 1 Finally, r = R 3 C 4 & C 2 = C 1 R 4 & D = ωC 4 R 4 C 1 R 3

23. Advantages The bridge is widely used for testing small capacitors at low voltages with high precision. Since C 4 is a variable decade capacitance box, its setting in μF directly gives the value of the dissipation factor. Disadvantages The calibration of C 4 is only for particular frequency, as ω term present in the equation. Commercial Schering bridge measures capacitors from 100 pF - 1μF with ±2% accuracy.