INSTRUMENTATION AND MEASUREMENT

1. INSTRUMENTATION &
MEASUREMENTS
(EE-302)
WEEK 3
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2. Measurement of High Resistance
 Such resistances may include:
 insulation resistance of machines and cables.
 Leakage resistance of capacitors
 Resistance of high voltage circuit elements like vacuum
tubes etc.
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3.  Very small current due to high resistance, hence its
measurement difficult.
 Leakage currents comparable with the measurement
current, hence errors possible.
 Stray charges due to electrostatic effects.
 Insulation resistance measurement at times involves a
certain time delay between application of the test
voltage and subsequent measurement of resistance. For
accurate measurements, this time delay has to be
mentioned accurately.
 Requirement of high applied test voltage since
resistances are high.
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Measurement of High Resistance:
Difficulties

4. Use of Guard Circuits
 Used to eliminate errors due to leakage currents.
 Provide a bypass mechanism for the leakage current so
that it could not get mixed with the actual measurement
current.
 A typical guard arrangement is shown below:
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5. Guard Circuit
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6.  A Guard terminal is added to the resistance terminal
block.
 Terminal surrounds the resistance entirely, connecting it
to the battery side of the ammeter.
 The leakage current IL has now a separate path to
circulate and bypass the micro ammeter.
 Actual guard arrangement is shown below:
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Guard Circuit

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Guard Circuit: practical
implementation

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Guard Circuit: used with the
bridge

9. AC Bridges
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10. Sources & Detectors
 At very low frequencies, the power line itself can act as
source of supply.
 For high frequencies, electronic oscillators are used as
supply.
 A typical oscillator has a range of 50 Hz to 125kHz with
a power output of around 7 W.
 Common detectors for AC bridges are Headphones,
Vibration galvanometers and Tunable amplifier
detectors.
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11.  Headphones: from 250 Hz upto 4kHz.
 Vibration Galvanometers: low audio frequencies 5 Hz to
1000 Hz.
 Tunable amplifier detectors: 10 Hz to 100 kHz.
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12. Bridge balance equations
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13. UIT SPRING 201613

14. The summary….
 THE PRODUCTS OF THE MAGNITUDES OF THE OPPOSITE
ARMS MUST BE EQUAL WHILE SUM OF THE PHASE
ANGLES OF THE OPPOSITE ARMS MUST BE EQUAL.
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15. UIT SPRING 201615

16. Example
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17. Example (contd.)
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18. Capacitance Comparison bridge
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19. Capacitance comparison bridge
 For this bridge the ratio arms are resistive in nature.
 Z3 consists of known standard capacitance.
 R3 is the variable resistance used to balance the bridge.
 Z4 contains Cx the unknown capacitance and its small
leakage resistance Rx.
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20. UIT SPRING 201620
Capacitance comparison bridge
For this bridge, under the balanced condition:

21. Example
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22. Inductance Comparison bridge
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23.  By this bridge unknown inductance and its internal
resistance can be calculated.
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Inductance Comparison bridge

24. UIT SPRING 201624
Inductance Comparison bridge

25. Example
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26. Maxwell’s Bridge
 Maxwell’s bridge can be used to measure inductance by
comparison either with a variable standard self
inductance or with a standard variable capacitance.
 Thus divided into:
 Maxwell’s Inductance Bridge
 Maxell’s Inductance Capacitance Bridge
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27. Maxwell’s Inductance bridge
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28.  Inductance can be measured by comparing it with a
standard variable self inductance.
 Note that two branches 1 and 2 have non inductive
resistances R1 and R2.
 Standard inductance L3 is accompanied by its resistance
‘r’ serially connected with it.
 One arm contains the unknown inductance Lx.
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Maxwell’s Inductance bridge

29. UIT SPRING 201629
Maxwell’s Inductance bridge

30. Maxwell’s Inductance bridge
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31. Maxwell’s Inductance bridge
under balance: Phasor Diagram
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32. Maxwell’s Inductance
Capacitance bridge
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33. UIT SPRING 201633
Maxwell’s Inductance
Capacitance bridge: Phaser
diagram

34.  Since the bridge contains one arm in which the
resistance and inductance is in parallel, hence it would
be better to write the equations in the admittance form.
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Maxwell’s Inductance
Capacitance bridge

35. UIT SPRING 201635
Maxwell’s Inductance
Capacitance bridge

36. UIT SPRING 201636
Maxwell’s Inductance
Capacitance bridge

37. Advantages of using standard
known capacitor for
measurement
 Less expensive as compared to inductors.
 Almost lossless.
 External fields have lesser effect on the capacitor as
compared to inductor.
 Comparatively quicker measurement.
 Smaller in size.
 Greater reliability
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38. Advantages of Maxwell’s bridge
 Balance equation is independent of the losses associated
with the inductor.
 Balance equation is independent of frequency.
 Scale of resistance could be calibrated to read the
inductance directly.
 Scale of R1 could be calibrated to read the Q value
directly.
 When the bridge is under balance the only component in
series with the coil is R2. If R2 is chosen so that it could
carry high current, then heavy current carrying coils can
also be tested.
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39. Limitations of the Maxwell’s
bridge
 Useful only for the low Q values measurement ( i.e Q
varies from 1 to 10). Its proof is thru the phase balance
condition. We kn𝑜𝑤 that 𝜃1 + 𝜃4 = 𝜃2 + 𝜃3, but 𝜃2 𝑎𝑛𝑑 𝜃3 are
zero because of the pure resistances. For high Q values,
𝜃4 is almost 900. Hence 𝜃1 should be -900, for which the
value of R1 should be very high as 𝜃1 is governed by the
parallel combination of R1 and C1. Practically such high
resistances are not possible.
 Interaction between the balance of resistance and
reactance, thus balancing a bit tricky and difficult.
 Not suitable for coils having Q<1 because of the balance
convergence problem.
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40.  Though the bridge balance equations are independent of
frequency, but practically the properties of coils under
test may vary with frequency, which can cause errors.
 Commercial Maxwell bridge measures the inductance
from 1-1000H with an error of about ± 1%.
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Limitations of the Maxwell’s
bridge

41. Example
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42. Example
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43. Anderson bridge
 Its in fact a modification of the basic Maxwell’s bridge
used to find the self inductance value using the
comparison technique.
 Used for precise measurement over a large range of
values.
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44. Anderson bridge
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45. Anderson bridge Phasor diagram
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