365 signal conditioning

8/12/2019 365 Signal Conditioning

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Slide 1

Signal Conditioning I) Filters

Passive Filters (L, R, C circuits)

Active Filters (Op Amp circuits) Loading Effect

Energy Flow Between Two Subsystems

Operational Amplifiers Golden Rules

Op Amp Circuits


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Anti-Aliasing Filteran analog filter that removes signal frequenciesabovefs /2, wherefs is the sample frequency

Amplifier Low-pass

Filter ADC

Input

Signal

Computer

Slide 2


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Slide 3

Filters

Characterized in thefrequency domain through frequencyresponse function.

Can be implemented usingpassive elements (R,L,C), activeelements (Op Amps, transistors) or digital components.

Filter G(jw)Input Output

x(t) y(t)Electrical Quantities:

Voltage, Current,Impedance ...

Electrical Quantities:Voltage, Current,

Impedance ...

Adjust Gain (Scaling);

Clean up Noise;

Isolate Interested Signal;

Change frequency range;

Integrate; Differentiate;

...


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Slide 4

Low Pass Filters (LP)Frequency Response

K : Static Sensitivity (Gain)t : Time Constant

Cut-off Frequency (wC )

At wC,

Passive Filters

G j K

j

w

t w

1

wt

C rad/sec1

G K

KwC of 2

70%10

-110

010

1

-30

-60

-90

0

Frequency (rad/sec)

Phasedeg

10-1

100

101

-30

-20

-10

0

Gain

dB

Bode Plot for a 1st Order Low Pass Filter

PASS BAND

-45o

wC


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Slide 6

High Pass Filters (HP)Frequency Response

K : Sensitivity (Gain)t : Time Constant

Cut-off Frequency (wC )

At wC,

Passive Filters

G j K j

j

wt

t w

1

wt

C rad/sec1

G K

KwC of 2

70%

10-1

100

101

-30

-20

-10

0

GaindB

Bode Plot for 1st Order High Pass Filter

10-1

100

101

0

30

60

90

Frequency (rad/sec)

Phasede

g

PASS BAND

-45o

wC


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Slide 7

High Pass Filters (LP)Passive Implementation (RC Network)

Impedance (Z) Analysis:

Resistance ( ZR ):

Capacitance ( ZC):

Passive Filters

G j Vo

Vin

R j

R jHP w

w

w

C

C 1

HP RC

RC

K

Time Constant

Cut - off Frequency

Gain as

C

1

1

VoR

C

Vin

Z V

I RR R

R

Z V

I C jC

C

C

1

w


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Slide 8

Band Pass FiltersFrequency Response

Passive Implementation

Passive Filters

G j K

j

LP

j

j

HP

BPLP

HP

HP

HP LP

HP LP

w

t w

t w

t w

t t

w w

1

1 1

10-2

10-1

100

101

102

103

-90

0

90

Frequency (rad/sec)

Phasedeg

10-2

10-1

100

101

102

103

-30

-20

-10

0

Gain

dB

Bode Plot for a Band Pass Filter

PASS BAND

wLPwHP

Vin Vo

RLP

CLP RHP

CHP

Low Pass High Pass

Notice theLOADING EFFECT


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Vin Vout

R1

C1 R2

C2

Low Pass High Pass


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Slide 9

Notch (Band Stop) FiltersFrequency Response

Implementation

Passive Filters

G j

j

LP

j

j

HP

BPLP

HP

HP

HP LP

HP LP

w

t w

t w

t w

t t

w w

1

1 1

10-2

10-1

100

101

-15

-10

-5

0

Gain

dB

Bode Plot for a Notch (Band Stop) Filter

10-2

10-1

100

101

-30

0

30

Frequency (rad/sec)

Phasede

g

wLP wHP

STOP BAND

Low Pass

Filter

High PassFilter

+

+

VoVin


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Slide 10

Loading Effect Electrical System

Ex: Band Pass Filter

Mechanical SystemsEx: Two DOF Oscillator

Vin Vo

RLP

CLP

RHP

CHP

Low Pass High Pass

V1

G jV

V R CLP

in LP LP

1 1

1j

G jV

V

R C

R CHP

o HP HP

HP HP

1 1

j

j

G jV

V

R C

R

RR C

G j G j

BP o

in

HP HP

LP HPLP

HPHP HP

Load ing

HP LP

j

j j j1 1

M2

K2

D2

M1

K1

D1

F

X1

X2

Interactions between the two mass-spring-damper subsystems (loading)were considered while balancing theinternal forces.


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Loading Effect Thevenin equivalent circuit:

Eth is the voltage Vout when Zin is infinite (no loading):

Zout is the impedance seen at the output when voltagesource is short-circuited

Zout

Zin

Eth

Vout

Slide 11


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Loading Effect

Slide 12

Vout=


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Slide 14

EX:

(A) Derive the frequency response function (from Vin to Vout) for the passive filter shown

below:

(B) You are asked to design a band pass filter using the above circuit with a pass band from

10 Hz to 250 Hz. Present your design by choosing an appropriate set of R1, C1, R2, and

C2 as well as the Bode plots of the filter's ideal and actual frequency responses.

Loading EffectC

2

R2

R1

C1V

in

Vout

V1


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Slide 15

EX:

(C) One of your purchasing people wants you to use the same value of capacitance for both

C1 and C2. Will this still work? Why or why not?

Loading Effect


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Slide 16

EX:

Shown above is a block diagram of a measurement system, please find:

(A) The individual frequency response functions: G1(jw), G2(jw), G3(jw).

(B) The frequency response function of the entire system: Vout/ A

Loading EffectAccelerometer

G1(j)

K1 = 100 V/(m/s 2)

z = 0.01

n = 5000 rad/s

High Pass FilterG2(j)

K2 = 1

= 0.2 s

AmplifierG3 = K3K3 = 10

Acceleration

AVoltage

Vout

G1 G2 G3

Input Impedance ------- 1000 1000 Output Im pedance 40 10 ---------


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Slide 18

Op Amps Op Amp Characteristics

Ideal Reality

Infinite High Open Loop Gain 104 to 106

Infinite High Input Impedance 300 K to 1000 G0 Low Output Impedance 10 to 5 K

(150 - 200 typical)

Implications:

Used seldom in open-loop mode:

Almost exclusively used in feedback mode.


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Slide 19

Op Amps Feedback Operation

Assumption I

High Input Impedance

- Assumption II

High Gain (GO >> 1), forw< 105 Hz

E E

ZI I

E E

Zi d

II F

d o

F

I II F

EoE +

E -

ZF

ZI Ed

Ei

E G EO O d

E E

ZI I

E E

Z

E

E

i d

II F

d o

F

O

iZZ G G

I

F O O

1

1 1 1

1

0

1

1 1 1

G

E

E

Z

Z

O

O

iZ

Z G G

F

IIF O O


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Slide 20

Op AmpsGolden Rules of Op Amps: Voltages at the input terminals (inverting and non-inverting)

are the same.

The output of the Op Amp will do whatever is necessary to makethe voltage difference between the inputs zero:

It looks at the input terminals and changes its output voltagesuch that the external feedback network will bring the inputdifference to zero.

No current flows into the Op Amp.

Op Amp draws very little input current (0.5 mA for a 741C); we canround it to zero for practical calculation.


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Slide 21

Op Amps Examples) Inverting Amplifier Non-inverting Amplifier

Q: What if RF= 0 and Ri ?

Eo

E

E

Z

Z

R

R

E RR

E

O

i

F

i

F

i

OF

ii

E R

R RE E

R R

RE

E RR

E

ii

i FO O

i F

ii

OF

ii

1

E +

E -

Ed

IF

EiRi Ii

RFEo

E -

E +Ei

RFRi


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Slide 22

Differential AmplifierOp Amps Examples) Voltage Follower (Buffer)

E EO i

E R

R RE

E E

R

E E

R

E E

E R RR

RR R

E RR R

E

R R R R

E R

RE E

O

O

O

4

2 42

1

1 3

1 3

1

4

2 42

3

1 31

1 2 3 4

3

12 1

,

If and

Eo

E-

E +Ei Eo

E

+

E -E1R1

R3

E2 R2 R4


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Slide 23

Op Amps Examples) Multi-Stage Filters

+

--

m F

mF


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Slide 24

Op Amps Examples) Summing Junction

I E

RI

E

R

I I I ER

FO

F

11

12

2

2

1 2

,

If ,

E R

R E R

R E

R R R

E R

RE E

O F F

OF

11

22

1 2

1 2

E R

RE

R

RE

R

REO

F F F

NN

11

22

EoE +

E -

Ed

E1

RF

R2

R1

E2

IF

I1

I2

RNEN


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Slide 25

Op Amps Examples) Integrator Differentiator

Eo

E +

E -

Ed

CF IF

EiRi Ii

E

E

Z

Z

R C R j

O

i

F

i

C j

i F i

F

11w

w

IF

Eo

E +

E -

Ed

CiEi

RF

Ii

E

E

Z

Z

RC R j

O

i

F

i

F

C j

i F

i

1

w

w


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Slide 26

Op Amps Examples) Low Pass Filter

Eo

E +

E-Ed

CF

EiRi Ii

RF

ZF

E

E

R

R R C

O

i

F

i F F

LP

1

1

t

w

j

High Pass Filter

Eo

E +

E-Ed

Ei

Ri IiCi

RFZi

E

E

R

R

j

j

O

i

F

i

HP

HP

R C

R C

i i

i i

t

w

t

w

1


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