The document discusses various types of bridges used for instrumentation and measurement, including the Anderson bridge, Hay's bridge, Schering bridge, and Wien bridge. It also covers digital to analog conversion techniques such as binary weighted and R-2R ladder DACs. Key aspects like resolution, accuracy, monotonicity, conversion time, and stability are discussed as performance parameters for DACs.

1. INSTRUMENTATION &
MEASUREMENTS
(EE-302)
WEEK 4
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2. 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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3. Anderson bridge
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4. Anderson bridge Phasor diagram
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5. Anderson bridge under balance:
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Under the balance condition the Anderson bridge’s
unknown parameters are:

6. Advantages:
 Accurate measurement of capacitance in terms of
inductance is possible.
 Requires a fixed capacitor instead of a variable capacitor.
 Bridge comparatively easier to balance with respect to
the Maxwell’s bridge.
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7. Disadvantages:
 Anderson’s bridge is more complicated than other
bridges.
 Uses more components.
 Balance equations are more complicated to drive.
 Bridge cannot be easily shielded due to additional
junction points, to avoid effect of stray capacitances.
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8. Example
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9. Example
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10. Example
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11. Hay’s Bridge
 Maxwell’s bridge is not suitable for high Q values.
 Hay’s bridge is suitable for coils having high Q values.
 In Hay’s bridge, capacitor is connected in series with the
variable resistance, a change from the Maxwell’s bridge.
 For larger phase angles, R1 is needed to be very low
which is duly practical.
 The bridge is shown below:
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12. Hay’s bridge
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13. Hay’s bridge
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For the balanced condition of the bridge:

14. Example
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15. Example
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16. Advantages and Disadvantages of
Hay’s Bridge
 Best suitable for inductances having Q factor higher than
10.
 Quite simple expression for Q factor in terms of the
bridge elements.
 Disadvantage is that it is suitable only for the
measurement of inductances with high Q factor.
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17. Schering bridge
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 One of the most widely used AC bridge for the
measurement of unknown capacitance, dielectric losses
and power factor.
 The Schering bridge is widely used for testing small
capacitors at low voltages with very high precision.

18. UIT SPRING 201618
Schering bridge and its balance
equations

19. Power Factor, loss angle and
dissipation factor
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The dissipation factor is the reciprocal of Q factor and is
given by:

20. High Voltage Schering bridge
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 A stepped up transformer is used to rectify the errors
caused by the Schering bridge low voltage
measurements. This bridge is shown here:

21. Wien Bridge
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 Primarily it is used to measure the frequency but it can
also be used to measure an unknown capacitance with
accuracy.

22. Wien bridge
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Hence 𝑓 = 1/2𝜋𝑅𝐶

23. Digital to Analog Conversion
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24.  For the DAC the binary input is of the form:
 And its subsequent Vout is given by the formula:
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25. The basic DAC symbol
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26. The DAC transfer characteristics
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27. DAC conversion techniques
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28. DAC: binary weighted
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29. UIT SPRING 201629
DAC: binary weighted

30.  Wide range of resistors are required. For an 8 bit DAC,
the largest resistor is 128 times the smallest, hence
greater chances of damaging the smallest resistor due to
heavy current flow through it.
 Integrated Circuit fabrication limitations when it comes
to so many varying resistors.
 Finite resistances of the switches disturb the resistors
values and hence cause errors.
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Binary Weighed DAC Limitations

31. Inverted R-2R ladder DAC: an
improved version
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32. Why this DAC is better?
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33. 4 Bit R-2R Binary DAC
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34. UIT SPRING 201634

35. Resolution of the R-2R DAC
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36. Example
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37. Advantages of R-2R DAC
 Only Two resistors used, hence far more practical as
compared to binary weighed ladder.
 Any number of bits are possible by just adding more R-
2R sections.
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38. Performance Parameters of DACs
 Resolution: Could be defined in terms of the total
number of the output values that could be provided by
the DAC i.e 2n where n is the number of bits.
 It could also be defined as the change in the output
voltage of the DAC as a result of change in the LSB at
the input only. This could be defined as:
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39.  If we are using an 8 bit DAC the resolution of the DAC in
terms of the possible output states would be 28 = 256.
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Performance Parameters of DACs

40.  Accuracy: It could be defined as the difference between
the actual output voltage of the DAC and the expected
output. It is expressed in percentage. It must be ±
1
2
of
its LSB. For the full scale output of 10.2, and for an 8 bit
DAC, it could be given as:
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Performance Parameters of DACs

41.  Monotonicty: Good monotonicity means the converter is
not missing any steps while stepping through its entire
range.
 Conversion Time: Also called the setting time. It is the
time required for the conversion from application of the
digital input to the generation of final analog output
voltage.
 Settling Time: Time required by the DAC to get settled to
±
1
2
𝐋𝐒𝐁 of its final value for a given digital input voltage i.e
zero to full scale.
 Stability: The performance of the converter changes with
temperature, age and power supply variations. Hence the
relevant parameters such as offset, gain, linearity, error and
monotonicity must be within a certain limit during the entire
operating range of temperature and supply fluctuations.
This constitute to stability.
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Performance Parameters of DACs