![Anderson Bridge
Balance Equation
R1 = R2R3
R4
− r1
L1 = C R3
R4
[r(R4 + R2) + R2R4]
Pros
1 Fixed capacitor is used
2 Accurate determination of
inductance (millimetre range).
3 Accurate result for
determination of capacitance
in terms of inductance.
4 Easy to balance (convergence
point of view -low Q values)
Cons
1 Complicated in terms of the
number of components,
balance equation used.
2 The bridge cannot be easily
shielded.
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Chapter2
- 1. Electrical and Electronic Measurement Measurement of Resistance, Inductance and Capacitance Parveen Malik Assistant Professor School of Electronics Engineering KIIT University [email protected] February 6, 2019 Parveen Malik () E and EM February 6, 2019 1 / 48
- 2. Outline 1 Measurement of Resistance Range of Resistances Classification of Methods - Low, Medium and High Medium Resistance measurement Ammeter & Voltmeter Method Substitution Method Wheatstone Bridge Low Resistance measurement Kelvin’s double bridge High Resistance Measurement Mega-ohm Bridge Megaohmmeter - Megger 2 A.C. Bridges Measurement of Inductance Measurement of Capacitance 3 Errors in Bridge Measurement 4 Wagner’s earthing device Parveen Malik () E and EM February 6, 2019 2 / 48
- 3. Resistance Measurement Range of Resistances
- 4. Range of Resistances1 Low Resistances - Order of 1 Ω or under Copper , Gold, silver and aluminium. Resistance series field winding generator, resistance of armature winding, Earth winding Resistance Medium Resistances - 1 Ω to 100, 000 Ω Resistance of field winding of D.C. shunt generator, Resistance of long transmission line High Resistances - 100, 000 Ω to upwards Resistance of cable insulation, resistance of insulator disk of transmission line 1 This classification is not rigid Parveen Malik () E and EM February 6, 2019 4 / 48
- 5. Resistance Measurement Methods of Measurement Classification
- 6. Resistance Measurement Low, Medium and High Resistances Low resistance 1 Ammeter and Voltmeter Method 2 Kelvin Double Bridge 3 Potentiometer Method 4 Ducter Medium resistance 1 Ammeter and Voltmeter Method 2 Substitution Method 3 Wheatstone Bridge 4 Ohmmeter method High resistance 1 Megaohm Bridge 2 Meggar 3 Loss of Charge Method 4 Deflection Method Parveen Malik () E and EM February 6, 2019 6 / 48
- 7. Measurement of Resistance Medium Resistance Ammeter & Voltmeter Method
- 8. R Measurement (M) - Ammeter & Voltmeter Method (a) (b) Low Resistance values Fig.(a) - Accurate and most suitable when R ≪ RV Rm = R 1+ R RV High Resistance values Fig(b) - Accurate and most suitable when R ≫ RA Rm = R 1 + RA R Application Suitable for laboratory purpose. Cons Rough Method Accuracy depends upon the accuracy of voltmeter and ammeter. Parveen Malik () E and EM February 6, 2019 8 / 48
- 9. Measurement of Resistance Medium Resistance-Substitution Method
- 10. R Measurement (Medium) - Substitution Method Substitution Method Pros More accurate than ammeter voltmeter. Cons Accuracy depends upon constancy of the battery emf. sensitivity of instrument. accuracy of standard resistance. Applications Used in High frequency a.c. measurements. Parveen Malik () E and EM February 6, 2019 10 / 48
- 11. Measurement of Resistance Medium Resistance Wheatstone Bridge
- 12. Resistance Measurement - Wheatstone Bridge Wheatstone Bridge Balanced Condition P Q = R S Pros Highly Reliable easy to use Highly Accurate as reading is independent of characteristics of Null indicating instrument. Cons Insufficient sensitivity of null detector. Changes in resistance due to heating effect. Thermal emf Error due to resistance of leads and contacts. Parveen Malik () E and EM February 6, 2019 12 / 48
- 13. Sensitivity of Wheatstone Bridge
- 14. Resistance Measurement Sensitivity of Wheatstone Bridge Sensitivity is used for Selecting a galvanometer with which unbalance may be observed. Determining the minimum unbalance with a given galvanometer Determining the deflection to be expected for a given unbalance. Parveen Malik () E and EM February 6, 2019 14 / 48
- 15. Low Resistance Measurement Problems in Measurement of Low Resistances
- 16. Kelvin’s bridge Problems in Measurement of Mow Resistances When resistance under measurement is comparable to connecting leads resistance. At Point m, R = P(S + r) Q At Point n, R = PS Q − r At Point d, R = PS Q P Q = r1 r2 Parveen Malik () E and EM February 6, 2019 16 / 48
- 18. Kelvin’s double bridge Balance Equation (2nd ratio arm) R = PS Q + qr p + q + r P Q − p q Accuracies 1000 µΩ to 1 µΩ - 0.05% 100 µΩ to 1000 µΩ - 0.2% to 0.05% 10 µΩ to 100 µΩ - 0.5% to 0.2% Cons Accuracy is constrained by thermoelectric emf. Parveen Malik () E and EM February 6, 2019 18 / 48
- 19. High Resistance Measurement Parveen Malik () E and EM February 6, 2019 19 / 48
- 20. Mega-ohm Bridge
- 21. High Resistance Measurement - Wheatstone Bridge Resistance in the range - MΩ Let us Consider RBG = RBG = RAB = 100MΩ, the equivalent resistance becomes 200/3 = 66.67Ω. Therefore, Output error is 33.33% ( RAB = 100MΩ) We need to modify Wheatstone bridge in order to get exact RAB value which is 100MΩ Parveen Malik () E and EM February 6, 2019 21 / 48
- 22. Megaohm Bridge Modification to Wheatstone Bridge Connect b to G point. When bridge is balanced,the potential difference across RBG is zero and there is not current flowing through it. We can ignore this branch. Now RAG comes in parallel to P. Thus, balance equation becomes (RAG | | P) · S = R · Q and R = (RAG | | P)·S Q Parveen Malik () E and EM February 6, 2019 22 / 48
- 24. Megaohmmeter - Megger2 2 Electronic Instrumentation and Measurements- David A. Bell, P 182, Sec 7-7 Parveen Malik () E and EM February 6, 2019 24 / 48
- 25. Megaohmmeter - Megger3 Controlling Force τC ∝ FC ∝ I1 ∝ V R1 Deflecting Force τd ∝ Fd ∝ I2 ∝ V Rx + R2 Case 1 - When Rx is open , no current will flow through the current coil (Deflecting Coil) and only current that would flow is through the controlling coil which brings the pointer to infinity scale. Case 2 - When Rx is closed, no current will flow through the voltage Coil ( control coil), only current that would flow is through the current coil ( Deflecting Coil) which brings the pointer to 0 scale. Case 3 - When Rx is put, current start flowing through the both coils. The pointer stops when both controlling and deflecting forces are equal. At this point, Rx = R1 − R2 Parveen Malik () E and EM February 6, 2019 25 / 48
- 26. A.C. Bridges
- 27. A.C. Bridges Balance Equation Z1 · Z4 = Z2 · Z3 Magnitude Condition |Z1| · |Z4| = |Z2| · |Z3| Angle Condition ∠θ1 + ∠θ4 = ∠θ2 + ∠θ3 Parveen Malik () E and EM February 6, 2019 27 / 48
- 29. Maxwell’s bridge
- 30. Maxwell Inductance Bridge Balance Equation L1 = L2R3 R4 , R1 = R2R3 R4 Q = ωL2R2 Parveen Malik () E and EM February 6, 2019 30 / 48
- 31. Maxwell Inductance - Capacitance Bridge
- 32. Maxwell Inductance - Capacitance Bridge Balance Equation L1 = R2R3C4, R1 = R2R3 R4 Pros 1 Balance equation independent of frequency. 2 Scale of resistance can be calibrate to read inductance directly. 3 Scale of R4 can be calibrate to read Q value directly. Cons 1 Variable Capacitor is very expensive. 2 Limited to measurement of low Q coils (1 Q 10). Parveen Malik () E and EM February 6, 2019 32 / 48
- 33. Hay’s bridge
- 34. Hay’s Bridge Balance Equation L1 = C4R2R3 1+ω2C2 4 R2 4 R1 = ω2R2R3R4C2 4 1+ω2C2 4 R2 4 Pros 1 Suitable for High Q coils. 2 Q = 1 ωC4R4 expression is simple and require low value of R4 and C4. Cons Hays bridge is not suitable for measurement of quality factor (Q 10). Parveen Malik () E and EM February 6, 2019 34 / 48
- 35. Anderson Bridge
- 36. Anderson Bridge Balance Equation R1 = R2R3 R4 − r1 L1 = C R3 R4 [r(R4 + R2) + R2R4] Pros 1 Fixed capacitor is used 2 Accurate determination of inductance (millimetre range). 3 Accurate result for determination of capacitance in terms of inductance. 4 Easy to balance (convergence point of view -low Q values) Cons 1 Complicated in terms of the number of components, balance equation used. 2 The bridge cannot be easily shielded. Parveen Malik () E and EM February 6, 2019 36 / 48
- 37. Owen’s Bridge
- 38. Owen’s Bridge Balance Equation L1 = C4R2R3, R1 = C4 R3 C2 Q = ωC2R2 Pros 1 Balance equation independent of frequency. 2 Balance equation independent if R2 and C2 are made variable. Cons 1 Variable Capacitor is very expensive. 2 C2 tends to be high while measuring high Q coils. Applications Used in measurement of wide range of inductances, incremental inductance and permeability with a slight modification. Parveen Malik () E and EM February 6, 2019 38 / 48
- 41. Schering’s Bridge Balance Equation R1 = R3C4 C2 , C1 = R4C2 R3 D = ωR4C4 Pros 1 Balance eq. is independent of frequency. Cons Calibration for dissipation holds only for one particular frequency. Applications Widely used for capacitance, relative permittivity and D factor measurement. It is used for measuring the insulating properties of electrical cables and equipment’s. It can measure small capacitors at low voltages precisely Parveen Malik () E and EM February 6, 2019 41 / 48
- 42. Wein’s Bridge Measurement of Frequency
- 43. Wein’s Bridge Frequency Range- 100 Hz to 100 kHz Accuracy- 0.1 % to 0.5 % Balance Equation R4 R3 = R2 R1 + C1 C2 f = 1 2π √ R1R2C1C2 Pros Can be calibrated by a single control if R1 = R2 and C1 = C2. Cons Difficult to balance if input is not sinusoidal and contain harmonics. Applications Measuring the frequency in audio range. Audio and HF oscillators as the frequency determining device. Harmonic distortion analyser, as a notch filter. Parveen Malik () E and EM February 6, 2019 43 / 48
- 44. Causes of Error in Bridge Measurement Errors in Bridge Measurement Stray Conduction effects due to imperfect insulation. Mutual-Inductance effects, due to magnetic coupling between various components of the bridge. Stray-capacitance effects, due to electrostatic fields between conductor at different potentials. ’Residual’ in components e.g. the existence of small amount of series inductance or shunt capacitance in nominally non-reactive resistors. Parveen Malik () E and EM February 6, 2019 44 / 48
- 46. Wagner’s earthing device To remove earth capacitance from bridge network. Cab,Cbc,Ccd and Cad - Stray Capacitances Parveen Malik () E and EM February 6, 2019 46 / 48
- 47. Wagner’s earthing device Some of disadvantages of Wagner Earthing devices can be overcome by using double ratio A.C. bridge (additional inductively coupled arms). First adjust the bridge to get minimum detection current by connecting detector at d point. Connect the detector at ground potential and Start balancing by adjusting Z5 or Z6. Bring Vb to ground position (0 V). Then connect the arms at d point again and start balancing to bring detector at zero current. Repeat the process again. Parveen Malik () E and EM February 6, 2019 47 / 48
- 48. Any Questions ?