04/19/2304/19/23 Lecture 5Lecture 5 11

بسم الله بسم الله الرحمن الرحیمالرحمن الرحیمIn the name In the name

of godof god

04/19/2304/19/23 Lecture 5Lecture 5 22

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omomدر این وبالگ سعی گردیده در این وبالگ سعی گردیده مطالبی ارایه گردد که برای مطالبی ارایه گردد که برای دانشجویان دوره کاردانی دانشجویان دوره کاردانی مثمر ثمر بوده و یاور آنان مثمر ثمر بوده و یاور آنان

..باشدباشد..مطالب جدید نیز در راه استمطالب جدید نیز در راه است

این فایل به صورت زبان این فایل به صورت زبان اصلی به دانشجو ارایه میگردد اصلی به دانشجو ارایه میگردد

امید است که بهروری الزم امید است که بهروری الزم ببردببرد..را را

04/19/2304/19/23 Lecture 5Lecture 5 33

Contents of this Lecture: Outlines of signal conditioning circuits

design: amplification and filtering

Learn from Examples

WhyWhy Need Signal Amplification?Need Signal Amplification?

04/19/2304/19/23 Lecture 5Lecture 5 44

Outlines of Signal AmplifiersOutlines of Signal Amplifiers

Designed to amplify input signals to a right level to be noticeable for further uses.

Typical input signals are: thermocouple, RTD, pressure, strain, flow, pH, etc.

Typical outputs include: high level dc voltages (0 to 5 or 0 to 10 volts), process current (0 to 20 mA or 4 to 20 mA)

There are commercial signal conditioners with computer interface ready.

04/19/2304/19/23 Lecture 5Lecture 5 55

Operational Amplifier (Op Amp)Operational Amplifier (Op Amp)

An operational amplifier (Op Amp) is an integrated circuit of a complete amplifier circuit.

Op amps have an extremely high gain (A=10A=1055 typically typically).

Op amps also have a high input impedance (R=4 MR=4 M , ,

typicallytypically) and a low output impedance (in order of 100 in order of 100

, typically, typically) .

04/19/2304/19/23 Lecture 5Lecture 5 66

-

+

Vi1 VoutA

B

Vi2

AVVV iiout 21

Characters of Operational Characters of Operational Amplifiers Amplifiers

high open loop gain

high input impedance

low output impedance

low input offset voltage

low temperature coefficient of input offset voltage

low input bias current

wide bandwidth

large common mode rejection ratio (CMRR)

04/19/2304/19/23 Lecture 5Lecture 5 77

11 22 33 44

88 77 66 55

Offset nullOffset null

Offset nullOffset nullNot usedNot used

Voltage Output from an AmplifierVoltage Output from an Amplifier

The linear range of an amplifier is finite, and limited by the supply voltage and the characteristics of the amplifier.

If an amplifier is driven beyond the linear range (overdrivenoverdriven), serious errors can result if the gain is treated as a constant.

04/19/2304/19/23 Lecture 5Lecture 5 88

AA

LinearLinearregionregion

Non-linearNon-linearregionregion

VVoutout

VVinin

Analysis of Op-Amp CircuitsAnalysis of Op-Amp Circuits

The following rules can be applied to almost all op-amp circuits with external feedback:

o The current to the input is very small, and may assume that the inputs current is negligible.

o It is a reasonable approximation to assume that both inputs are at the same voltage.

04/19/2304/19/23 Lecture 5Lecture 5 99

-

+

Vi1 VoutA

B

Vi2

VVAV OGout

CM

OG

A

ACMRR

Ideal Amplifiers with or without Ideal Amplifiers with or without feedbackfeedback

04/19/2304/19/23 Lecture 5Lecture 5 1010

1

2

VV

G

1

2

VV

G VVSS

VV11 VV22

1

2

VV

G VVSS

VV11 VV22

R1

R2

VVFF

An ideal op-amp has very high open gain at 0 Hz.

Actual amplifier commonly hasexternal feedback.

FS VVV 1

21

1

2 RRR

VV

H F

HGHG

VV

AS

11

2

2112 HVVGGVV

Inverting AmplifierInverting Amplifier

Point B is grounded, so does point A (very small).

Voltage across R1 is Vin, and

across RF is Vout.

The output node voltage determined by Kirchhoff's Current Law (KCL).

Circuit voltage gain determined by the ratio of

R1 and RF.

04/19/2304/19/23 Lecture 5Lecture 5 1111

1R

R

V

VG F

in

out

-

+

Vin

Vout

R1

RF

A

B

F

F

RRRR

R

1

13

Analysis of Inverting AmplifierAnalysis of Inverting Amplifier

Ideal transfer characteristics:Ideal transfer characteristics:

04/19/2304/19/23 Lecture 5Lecture 5 1212

-

+

Vin

Vout

R1

RF

A

BR

ii++

VV++

iiFF

ii11

ii--

VV--

0 ii

VV

OG

OGout

A

VVAV

FF iiii 1

F

outF

IN

R

VViand

R

VVi

11

000 VVi

F

outIN

R

V

R

V

1oror

1R

R

V

V F

in

out

Noninverting AmplifierNoninverting Amplifier

Op-amp circuit is a voltage divider.

04/19/2304/19/23 Lecture 5Lecture 5 1313

-

+Vin

Vout

R1

RF

A

BF

outA RR

RVV

1

1

1

1R

R

V

VG F

in

out

Circuit voltage gain determined by the ratio of R1 and RF.

Point VA equals to Vin .

Differential AmplifierDifferential Amplifier

Point B is grounded, so does point A (very small).

Voltage across R1 is V1, and

across R2 is V2.

Normally: R1 = R2, and RF

= R3.

Commonly used as a single op-amp instrumentation amplifier.

04/19/2304/19/23 Lecture 5Lecture 5 1414

)( 121

VVR

RV Fout

RF

-

+

V1

Vout

R1

A

BR3

V2

R2

Design an Instrumentation Design an Instrumentation AmplifierAmplifier

Design a single op-amp instrumentation amplifier.

R1 = R2, RF = R3

Determine the instrumentation gain.

04/19/2304/19/23 Lecture 5Lecture 5 1515

-

+

V1

Vout

R1

RF

A

B

R3

V2

R2A

F

OUTAA iR

VV

R

VV

1

1

32

2

R

Vi

R

VV BB

B

0 BA ii

2

2

31

1

R

VV

R

V

R

VV

R

VV BB

F

OUTAA

1

12

R

VVVV

R

VVV BA

F

BAOUT

)( 121

VVR

RV Fout

BA VV

Instrumentation amplifierInstrumentation amplifier

04/19/2304/19/23 Lecture 5Lecture 5 1616

15

621R

R

R

RA Fd

Difference Gain:Difference Gain:

R6

R5R6

-

+

+

-

V2

V1

Vcm

-

+ Vout

R1

RF

R3

R2

VB

VA

Outlines of Filter DesignOutlines of Filter Design

04/19/2304/19/23 Lecture 5Lecture 5 1717

Filterinput output

Filtering: Certain desirable features are retained Other undesirable features are suppressed

Classification of FiltersClassification of Filters

04/19/2304/19/23 Lecture 5Lecture 5 1818

Signal Filter

Analog Filter Digital Filter

Element Type Frequency Band

Active Passive Low-Pass

High-Pass

Band-Pass

Band-Reject

All-Pass

Terminology in Filter DesignTerminology in Filter Design

Signal-To-Noise Ratio (S/N)

04/19/2304/19/23 Lecture 5Lecture 5 1919

dBW

WNS

N

S

log10

Bandwidththe range of frequencies of |G(j)|>0.707

Cutoff Frequency

the end of pass-band frequency Break-point of a filter

the point with a gain of -3dB

Passive Low-Pass FilterPassive Low-Pass Filter

The pass-band is from 0 to some frequency wp.

Its stop-band extends form some frequency ws, to infinity.

In practical circuit design, engineers often choose amplitude gain of 0.95 for passive RC filters:

04/19/2304/19/23 Lecture 5Lecture 5 2020

p s

)( jH

Vout

Vin

C

R

VVoutoutVVinin RL

Passive High-Pass FilterPassive High-Pass Filter

Its stop-band is form 0 to some frequency s

The pass-band is from some frequency p to infinity.

In practical circuit design, engineers choose amplitude gain of 0.95 for passive CR filters:

04/19/2304/19/23 Lecture 5Lecture 5 2121

s p

)( jH

Vout

Vin

R

C

VVoutoutVVinin

Design of Passive FiltersDesign of Passive Filters

04/19/2304/19/23 Lecture 5Lecture 5 2222

1

1

jRCjH

1

1

RCs

sH

Transfer Function

21

1

RCV

V

in

out

The amplitude response:

2

1

2

13

RCf dB

The 3dB break-point is at:

LF

L

ZZ

ZG

The amplitude gain:

C

R

VVoutoutVVinin RL

Guideline of Pass Filter DesignGuideline of Pass Filter Design

04/19/2304/19/23 Lecture 5Lecture 5 2323

R

1

1

s

sH

Transfer Function

C VVoutoutVVinin RL

RC

Time Constant

Select resistor based on amplitude gain:

95.0

LF

L

ZZ

ZG

LLF RZRZ 053.095.0

05.0

Select capacitor based on cut-off freq:

dBRfRC

32

1

Higher Higher Order FiltersOrder Filters

04/19/2304/19/23 Lecture 5Lecture 5 2424

C

R

VVoutoutVVinin

First Order RC Low Pass Second Order RC Low Pass

C2 VVoutoutVVininC1

R1 R2

The higher the order of the filter, the closer it approaches ideal characteristics.

Active FiltersActive Filters

Active filters employ Op-Amps to attenuate select frequencies and amplify signal during filtering process.

Q factor of a filter is defined as the ratio of the center frequency fc to the bandwidth fH - fL :

04/19/2304/19/23 Lecture 5Lecture 5 2525

LH

Cff

fQ

Design of Low Pass Active FiltersDesign of Low Pass Active Filters

Example:Design a low pass filter with cut-off frequency of 5kHz, and DC gain of 10:

Two equations, three unknowns

04/19/2304/19/23 Lecture 5Lecture 5 2626

-

+

Vin

Vout

R1

RF

A

B

C2

Transfer Function: Transfer Function:

0

0..

s

KFT LP

221

CRfF

H

The -3 dB cut-off frequency:

1RRK F

LP

The DC gain:

Design of High Pass Active FiltersDesign of High Pass Active Filters

The -3 dB cut-off frequency:

The DC gain:

Two equations, three unknowns

Select one component based on other conditions, and determine the values of the other two components.

04/19/2304/19/23 Lecture 5Lecture 5 2727

Vout

-

+

Vin

R1

RF

A

B

C1

1121

CRfH

1RRK F

HP

Transfer Function: Transfer Function:

0

..

s

sKFT HP

Filter ClassFilter Class

o A filter of a given order can be made to approximate to ideal characteristics in a number of ways, depending on the values of the filter components (or say: depending on the filter class.

o Two useful classes are Butterworth (maximally flat) and Chebyshev (equal-ripple) filters (n is the filter order)

04/19/2304/19/23 Lecture 5Lecture 5 2828

n

C

in

out

ffV

V2

1

1

Butterworth Filter

Chebyshev Filter

Cn

in

out

ffCEV

V

221

1

Higher Order Active FiltersHigher Order Active Filters

04/19/2304/19/23 Lecture 5Lecture 5 2929

Vout

-

+Vin

R2

Rb

C1

R1

Ra

C2

Gain=K

Filter Class R1 R2 C1 C2 K

Buterworth3.01 dB at H

1.00 1.001.001.00 1.59

Chebyshev1 dB ripple

1.00 1.000.94 0.97 2.00

The above list gives the gain and component valves for one of themany choices for H=1. You may find more combinations from filter design handbook(s).

Learn from Example: Learn from Example: Filter Filter DesignDesign

04/19/2304/19/23 Lecture 5Lecture 5 3030

Problem:Problem: Assume a torque sensing device outputs very noisy voltage signal at millivolt range, and the shift being measured is turning at 3,000 rpm. Try to design a signal conditioner for this sensing device. (Assume the input impedance of the signal display device is very large).

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