This document discusses various types of signal conditioning circuits used in electrical measurement systems. It introduces bridge circuits, amplifiers, and filters. For bridge circuits, it covers Wheatstone bridges, current balance bridges, and their applications in potential measurements. For amplifiers, it discusses op-amp characteristics and various circuit configurations like summing amplifiers, non-inverting amplifiers, and differential amplifiers. It also introduces integrators, differentiators, and linearization circuits. Finally, it covers low-pass, high-pass, band-pass, band-reject, and twin-T notch filters, discussing their transfer functions and applications. Several examples and exercises are provided to illustrate the design and analysis of these signal conditioning circuits.

1. Chapter 4 :
Signal conditioning
4.1 Introduction to signal conditioning
4.2 Bridge circuits
4.3 Amplifiers
4.4 Protection
4.5 Filters

2. Introduction

3. ELECTRICAL MEASUREMENT SYSTEM
WHY?
1. Easy to transmit signal from measurement site
the data collection site
2. Easy to amplify, filter and modify
3. Easy to record the signal

4. Signal conditioning
• Used in factory or machine automation : to convert
sensor or transducer measurement signal levels to
industry standard control signals
• Provide computer and control system manufacturers a
common communication method to effectively receive
and transmit measurement and control data
• Examples of measurement data : temperature or AC/DC
voltage/current signals from various transducers
• Examples of control data : on/off signals for a heating
element or proportional signals for a valve actuator.

5. Signal conditioning

6. Bridge circuits

7. Bridge circuits
• Used to convert impedance variations into
voltage variations
• Can be design so the voltage produced varies
around zero
• Amplification can be used to increase voltage
level for increased sensitivity to variation of
impedance

8. Wheatstone bridge
• D : voltage detector
  
4
1
2
3
4
2
3
1
4
1
2
3
4
2
4
3
1
3
R
R
R
R
V
R
R
R
R
R
R
R
R
V
V
R
R
R
V
V
R
R
R
V
V
V
V
b
a
b
a














9. Exercise 1
Determine;
1. R4 if a Wheatstone bridge nulls with
R1 = 1000 Ω, R2 = 842 Ω, and R3 =
500 Ω.
2. The voltage offset if the supply
voltage is 10.0 V. The resistors in a
bridge are given by R1 = R2 =
R3 = 120 Ω and R4 = 121 Ω.

10. Galvanometer detector
  
G
Th
Th
G
Th
Th
R
R
V
I
R
R
R
R
R
R
R
R
R
V
R
R
R
R
R
R
R
R
V










4
2
4
2
3
1
3
1
4
2
3
1
4
1
2
3

11. Exercise 2
A bridge circuit has a resistance of
R1 = R2 = R3 = 2.00 kΩ and
R4 = 2.05 kΩ and a 5.00 V supply. If
a galvanometer with a 50.0 Ω
internal resistance is used for a
detector, calculate the offset current.

12. Bridge resolution
• Resolution function of detector : to
determine the bridge offset
• Resistance resolution : resistance change in
1 arm bridge that causes an offset voltage
equal to detector resolution
• Detector can measure change of 100 µV

13. Resolution
• The smallest discernible change in input; the
smallest change in input that manifests itself
as perceptible change in output that can be
measured (example : 0.000 1 mm)
• Primary factor in deciding precision
• Good resolution does not imply in good
precision

14. Current balance bridge

15. Current balance bridge
• Used current to null bridge
 
5
5
4
2
5
4
3
1
3
5
5
4
2
5
4
5
4
2
5
4
IR
V
R
R
R
R
R
V
R
R
R
V
IR
V
R
R
R
R
R
V
R
R
R
R
R
b

















16. Exercise 3
A current balance bridge has a 10 V
supply voltage and resistors
R1 = R2 = 10 kΩ, R3 = 1 kΩ,
R4 = 950 Ω, R5 = 50 Ω and a high
impedance null detector. Determine the
current required to null the bridge if R3
increased by 1 Ω.

17. Potential measurements
using bridges

18. Potential measurements
using bridges
0
0
0
5
5
5
4
2
5
4
3
1
3
4
2
4
3
1
3




















IR
V
IR
V
R
R
R
R
R
V
R
R
R
V
V
R
R
R
V
R
R
R
V
V
V
V
V
V
V
x
x
x
b
c
a
x
c

19. Exercise 4
A bridge for potential measurement
nulls when R1 = R2 = 1 kΩ, R3 =
605 Ω, and R4 = 500 Ω with a 10.0 v
supply. Determine the unknown
potential.

20. Exercise 5
A current balance bridge is used for
potential measurement. The fixed
resistors are R1 = R2 = 5 kΩ, R3 = 1 kΩ,
R4 = 990 Ω, and R5 = 10 Ω with a 10 V
supply. Calculate the current necessary to
null the bridge if the potential is 12 mV.

21. Amplifiers

22. Op amp
characteristic

23. Summing amplifier








 2
3
2
1
1
2
V
R
R
V
R
R
Vout

24. Noninverting amplifier
in
out
out
in
in
V
R
R
V
R
V
V
R
V
I
I













1
2
2
1
2
1
1
0
0

25. Exercise 7
Design a high impedance
amplifier with a voltage
gain of 42 if R1 = 1 kΩ is
chosen.

26. Differential amplifier
 
CMRR
CMR
A
A
CMRR
V
V
V
cm
b
a
cm
10
log
20
2




 
b
a
out V
V
A
V 

• The transfer function;
• Common mode rejection;
 
1
2
1
2
V
V
R
R
Vout 


27. Voltage-to-Current converter
 
 
5
4
3
3
5
4
4
2
5
3
1
3
1
2
R
R
R
R
I
V
R
R
R
R
R
R
R
R
V
R
R
R
I
m
sat
ml
in
















28. Current-to-Voltage converter
IR
Vout 


29. Exercise 8
For a voltage-to-current converter using an op-amp, show
that the relationship between current and voltage is given by
.
in
3
1
2
V
R
R
R
I 

R1 R2
R3
R4
R5
RL
I
-
+
Vin

30. Integrator
t
RC
K
V
dt
V
RC
V
dt
dV
C
R
V
out
in
out
out
in







1
0

31. Exercise 9
Use an integrator to
produce a linear ramp
voltage rising at 10 V per
ms. Determine the R and C.

32. Differentiator
dt
dV
RC
V
R
V
dt
dV
C
in
out
out
in



 0

33. Linearization
 









R
V
G
V
V
I
R
V
in
out
out
in
0

34. Linearization
   
   
R
I
V
V
V
I
V
I
e
in
c
out
out
out
0
0
log
1
log
1
exp







35. Filters

36. Filters
• Filter : a circuit that is designed to pass signals with
desired frequencies and reject or attenuate others
• 4 types of filters:
1. Low-pass filter: passes low frequencies and stops
high frequencies
2. High-pass filter: passes high frequencies and rejects
low frequencies
3. Band-pass filter: passes frequencies within a
frequency band and blocks or attenuates
frequencies outside the band
4. Band-reject filter: passes frequencies outside a
frequency band and blocks or attenuates
frequencies within the band

37. Low-pass RC filter

38. Low-pass RC filter
• Critical frequency:
• Output-to-input voltage ratio:
RC
fc

2
1

 2
/
1
1
c
in
out
f
f
V
V



39. Exercise 10
A measurement signal has a frequency less than
1 kHz, but there is unwanted noise at about 1
MHz. Design a lowpass filter that attenuates the
noise to 1% if a capacitor 0.01 µF has been
used. What is the effect on the measurement
signal at its maximum of 1 kHz?

40. High-pass RC filter

41. High-pass RC filter
• Critical frequency:
• Output-to-input voltage ratio:
RC
fc

2
1

 
 2
/
1
/
c
c
in
out
f
f
f
f
V
V



42. Exercise 11
Pulses for a stepping motor are
being transmitted at 2000 Hz.
Design a highpass filter to reduce
60 Hz noise and reduce the pulses
by no more than 3 dB.

43. Design Methods
1. Determine critical frequency, fc
2. Select standard capacitor (µF – pF)
3. Calculate required resistance (1 kΩ - 1 MΩ)
4. Use nearest resistance standard value to
calculated value
5. Consider tolerance in resistors and capacitors

44. Practical considerations
1. Very small resistance -> lead to large currents and
loading effects -> avoid large capacitance
(R= kΩ -MΩ, C= µF – pF)
2. The exact fc is not important, choose R and C of
approximately to the fc
3. Isolation filter input/output with voltage follower
4. Cascade RC filters to improved fc sharpness ->
consider loading

45. Band-pass
RC filter

46. Band-pass RC filter
• Critical frequency:
• Output-to-input voltage ratio:
H
H
L
C
R
f

2
1

   
 
L
H
H
L
L
H
H
in
out
R
R
r
f
f
r
f
f
f
f
f
f
V
V






2
2
2
2
1
L
L
H
C
R
f

2
1


47. Exercise 12
A signal conditioning system uses a frequency
variation from 6 kHz to 60 kHz to carry
measurement information. There is considerable
noise at 120 Hz and at 1 MHz. Design a
bandpass filter to reduce the noise by 90%.
What is the effect on the desired passband
frequencies if r = 0.01? Determine all the
resistors and capacitors.

48. Band-pass RC filter

49. Band-reject RC filter

50. Twin-T notch
filter

51. Twin-T notch filter
• Critical frequency:
• Grounding resistor and capacitor:
c
n f
f 785
.
0
 RC
fC

2
1

c
H f
f 57
.
4

c
L f
f 187
.
0

10
1
R
R



C
C
10
1 

52. Exercise 13
A frequency of 400 Hz prevails aboard an aircraft.
Design a twin-T notch filter to reduce the 400 Hz
signal if 0.01 µF has been used and calculate the
grounding resistor and capacitor. What effect
would this have on voice signals at 10 to 300 Hz?
Determine the higher frequency when the output
is down by 3 dB.