INSTRUMENTATION AND MEASUREMENT

1. INSTRUMENTATION &
MEASUREMENTS
(EE-302)
WEEK 4
UIT SPRING 20161

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.
UIT SPRING 20162

3. Anderson bridge
UIT SPRING 20163

4. Anderson bridge Phasor diagram
UIT SPRING 20164

5. Anderson bridge under balance:
UIT SPRING 20165
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.
UIT SPRING 20166

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.
UIT SPRING 20167

8. Example
UIT SPRING 20168

9. Example
UIT SPRING 20169

10. Example
UIT SPRING 201610

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:
UIT SPRING 201611

12. Hay’s bridge
UIT SPRING 201612

13. Hay’s bridge
UIT SPRING 201613
For the balanced condition of the bridge:

14. Example
UIT SPRING 201614

15. Example
UIT SPRING 201615

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.
UIT SPRING 201616

17. Schering bridge
UIT SPRING 201617
 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
UIT SPRING 201619
The dissipation factor is the reciprocal of Q factor and is
given by:

20. High Voltage Schering bridge
UIT SPRING 201620
 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
UIT SPRING 201621
 Primarily it is used to measure the frequency but it can
also be used to measure an unknown capacitance with
accuracy.

22. Wien bridge
UIT SPRING 201622
Hence 𝑓 = 1/2𝜋𝑅𝐶

23. Digital to Analog Conversion
UIT SPRING 201623

24.  For the DAC the binary input is of the form:
 And its subsequent Vout is given by the formula:
UIT SPRING 201624

25. The basic DAC symbol
UIT SPRING 201625

26. The DAC transfer characteristics
UIT SPRING 201626

27. DAC conversion techniques
UIT SPRING 201627

28. DAC: binary weighted
UIT SPRING 201628

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.
UIT SPRING 201630
Binary Weighed DAC Limitations

31. Inverted R-2R ladder DAC: an
improved version
UIT SPRING 201631

32. Why this DAC is better?
UIT SPRING 201632

33. 4 Bit R-2R Binary DAC
UIT SPRING 201633

34. UIT SPRING 201634

35. Resolution of the R-2R DAC
UIT SPRING 201635

36. Example
UIT SPRING 201636

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.
UIT SPRING 201637

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:
UIT SPRING 201638

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.
UIT SPRING 201639
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:
UIT SPRING 201640
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.
UIT SPRING 201641
Performance Parameters of DACs