Chapter 4 : Signal conditioning

4.1 Introduction to signal conditioning 4.2 Bridge circuits 4.3 Amplifiers 4.4 Protection 4.5 Filters NH BMCC 3743Signal Conditioning 1

Introduction

NH BMCC 4743 Signal Conditioning 2

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

NH BMCC 4743 Signal Conditioning 3

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.

NH BMCC 4743 Signal Conditioning 4

Signal conditioning

NH BMCC 4743 Signal Conditioning 5

Bridge circuits

NH BMCC 4743 Signal Conditioning 6

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 NH BMCC 4743 Signal Conditioning 7

NH

Wheatstone bridge

• D : voltage detector 

V



V a



V b V a



R

1

R

3 

R

3

V V b



R

2

R

4 

R

4

V



V R

3

R

2   

R

1

R

3 

R

2

R

3

R

1

R

4  

R

1

R

2

R

4 

R

4 

V

BMCC 4743 Signal Conditioning 8

Exercise 1

Determine; 1. R 4 if a Wheatstone bridge nulls with R 1 = 1000 Ω, R 2 500 Ω.

= 842 Ω, and R 3 = 2. The voltage offset if the supply voltage is 10.0 V. The resistors in a bridge are given by R 1 = R 2 = R 3 = 120 Ω and R 4 = 121 Ω.

NH BMCC 4743 Signal Conditioning 9

NH

Galvanometer detector

V Th

 

R

1

R

3 

R

2

R

3  

R

1

R

4

R

2 

R

4 

V R Th



R

1

R

1 

R

3

R

3 

R R

2 2 

R

4

R

4

I G



R Th V Th



R G

10 BMCC 4743 Signal Conditioning

Exercise 2

A bridge circuit has a resistance of R 1 = R 2 = R 3 = 2.00 kΩ and R 4 = 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.

11 NH BMCC 4743 Signal Conditioning

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 NH BMCC 4743 Signal Conditioning 12

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 NH BMCC 4743 Signal Conditioning 13

Current balance bridge

NH BMCC 4743 Signal Conditioning 14

Current balance bridge

• Used current to null bridge 

R

4

R

2

V b

  

R

5

R

4  

R

5

R

2

R

4  

R

4

R

5 

R

5

V



V



R

1

R

3 

R

3

V

 

IR

5

R

2

R

4  

R

4

R

5 

R

5

V



IR

5 NH BMCC 4743 Signal Conditioning 15

Exercise 3

A current balance bridge has a 10 V supply voltage and resistors R 1 = R 2 = 10 kΩ, R 3 = 1 kΩ, R 4 = 950 Ω, R 5 = 50 Ω and a high impedance null detector. Determine the current required to null the bridge if R 3 increased by 1 Ω.

NH BMCC 4743 Signal Conditioning 16

Potential measurements using bridges

NH BMCC 4743 Signal Conditioning 17

Potential measurements using bridges

V c



V



V x



V c



V a



V b V x



R

1

R

3 

R

3

V V x V x

 

R

1

R

3 

R

3

IR

5  0

V

 

R

2

R

4 

R

4

V



R

2

R

4  

R

4

R

5 

R

5 0

V



IR

5  0 NH BMCC 4743 Signal Conditioning 18

Exercise 4

A bridge for potential measurement nulls when R 1 = R 2 = 1 kΩ, R 3 = 605 Ω, and R 4 = 500 Ω with a 10.0 v supply. Determine the unknown potential.

NH BMCC 4743 Signal Conditioning 19

Exercise 5

A current balance bridge is used for potential measurement. The fixed resistors are R 1 = R 2 = 5 kΩ, R 3 = 1 kΩ, R 4 = 990 Ω, and R 5 = 10 Ω with a 10 V supply. Calculate the current necessary to null the bridge if the potential is 12 mV.

20 NH BMCC 4743 Signal Conditioning

Amplifiers

NH BMCC 4743 Signal Conditioning 21

Op amp characteristic

NH BMCC 4743 Signal Conditioning 22

Summing amplifier

NH

V out

   

R

2

R

1

V

1 

R

2

R

3

V

2   BMCC 4743 Signal Conditioning 23

Noninverting amplifier

I

1

V in R

1 

I

2  0 

V in



R

2

V out V out

   1  

R

2

R

1  

V in

0 NH BMCC 4743 Signal Conditioning 24

Exercise 7

Design a high impedance amplifier with a voltage gain of 42 if R 1 = 1 kΩ is chosen. NH BMCC 4743 Signal Conditioning 25

NH

Differential amplifier

• • The transfer function;

V out



A



V a



V b



V out



R

2 

V

2 

V

1 

R

1 Common mode rejection;

V cm



V a



V b

2

CMRR CMR

 

A

20

A cm

log 10 

CMRR

 BMCC 4743 Signal Conditioning 26

Voltage-to-Current converter

I

 

R

1 

R

3

R

2

V in R

1

R

3 

R

5  

R

2

R

4

R ml

 

R

4 

R

3

R

5    

V sat I m R

4  

R

5

R

3   NH BMCC 4743 Signal Conditioning 27

Current-to-Voltage converter

V out

 

IR

NH BMCC 4743 Signal Conditioning 28

Exercise 8

For a voltage-to-current converter using an op-amp, show that the relationship between current and voltage is given by I   R 2 R 1 R 3 V in .

V in R 1 R 2 + R 3 I R 5 R 4 R L 29 NH BMCC 4743 Signal Conditioning

Integrator

V in R



C dV out dt V out

 

K RC t

 0

V out

  1

RC



V in dt

NH BMCC 4743 Signal Conditioning 30

Exercise 9

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

NH BMCC 4743 Signal Conditioning 31

Differentiator

C dV in dt



V out R



V out

 

RC dV in dt

0 NH BMCC 4743 Signal Conditioning 32

Linearization

V in



I

 

out

 0

R V out



G V in R

NH BMCC 4743 Signal Conditioning 33

Linearization

NH

I

 

out



I

0 exp  

V out



V out

 1  log

c

 

in

 1  log

e

  0 BMCC 4743 Signal Conditioning 34

Filters

NH BMCC 4743 Signal Conditioning 35

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 NH BMCC 4743 Signal Conditioning 36

Low-pass RC filter

NH BMCC 4743 Signal Conditioning 37

Low-pass RC filter

• Critical frequency:

f c

 2  1

RC

• Output-to-input voltage ratio:

V out V in

 1  

f

1 /

f c

 2 NH BMCC 4743 Signal Conditioning 38

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?

NH BMCC 4743 Signal Conditioning 39

High-pass RC filter

NH BMCC 4743 Signal Conditioning 40

High-pass RC filter

• Critical frequency:

f c

 2  1

RC

• Output-to-input voltage ratio:

V out V in

 

f

1  

f

/ /

f c



f c

 2 NH BMCC 4743 Signal Conditioning 41

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.

NH BMCC 4743 Signal Conditioning 42

Design Methods

1. Determine critical frequency, f c 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 NH BMCC 4743 Signal Conditioning 43

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 NH BMCC 4743 Signal Conditioning 44

Band-pass RC filter

NH BMCC 4743 Signal Conditioning 45

Band-pass RC filter

• Critical frequency:

f L

 2  1

R H C H f H

 2  1

R L C L

• Output-to-input voltage ratio:

V out V in



r



R H R L



f

2 

f H f L

 2 

f



H f L f

  1 

r



f H

 2

f

2 NH BMCC 4743 Signal Conditioning 46

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.

NH BMCC 4743 Signal Conditioning 47

Band-pass RC filter

NH BMCC 4743 Signal Conditioning 48

Band-reject RC filter

NH BMCC 4743 Signal Conditioning 49

Twin-T notch filter

NH BMCC 4743 Signal Conditioning 50

Twin-T notch filter

• Critical frequency:

f n

 0 .

785

f c f L

 0 .

187

f c f f C

 2  1

RC H

 4 .

57

f c

• Grounding resistor and capacitor:

R

1   10

R C

1  10

C

 NH BMCC 4743 Signal Conditioning 51

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.

NH BMCC 4743 Signal Conditioning 52