w05 operational amplifiers - deukisi.deu.edu.tr/aytac.goren/elk2018/h5.pdf · 2012. 3. 26. ·...

Yrd. Doç. Dr. Aytaç Gören

W05 Operational Amplifiers(19.03.2012)

ELK 2018 - Contents

W01 Basic Concepts in Electronics

W02 AC to DC Conversion

W03 Analysis of DC Circuits (self and condenser)

W04 Transistors and Applications (H-Bridge)

W05 Op Amps and Applications

W06 Sensors and Measurement (1/2)

W07 Sensors and Measurement (2/2)

W08 Midterm

W09 Basic Concepts in Digital Electronics (Boolean Algebra, Decimal to binary, gates)

W10 Digital Logic Circuits (Gates and Flip Flops)

W11 PLC’s

W12 Microprocessors

W13 Data Acquisition, D/A and A/D Converters.

2Yrd. Doç. Dr. Aytaç Gören

ELK 2018 – W01 Contents

1. Electrical Model of OpAmp

2. Structure of an OpAmp

3. Voltage Source of OpAmp

4. Inputs of OpAmp

5. Output of an OpAmp

6. Operation Modes of OpAmps

7. Op-Amp Properties

8. Ideal Op-Amp Analysis

9. Applications of Opamps

10. Opamps at a glance

3• Yrd. Doç. Dr. Aytaç Gören


IntroductionAn amplifier is a device that accepts a varying input signaland produces a similar output signal with a largeramplitude.An Operational Amplifier (Op-Amp) is an integratedcircuit that uses external voltage to amplify the inputthrough a very high gain.

The name “operational amplifier” comes from the factthat they were originally used to perform mathematicaloperations such as integration and differentiation.


Electrical Model of OpAmp• Voltage difference at input terminals are multiplied with a gain

value. The resultant voltage defines the OpAmp output.

+

+

V0AV1

+

V1

Ri

Circuit Model in linear region

Ro


Structure of an OpAmp• A complete op amp is realized by combining analog circuit building

blocks.

• Lots of transistors

• few resistors

• one capacitor

• Two power supplies

• Two inputs

• One output


Structure of an OpAmp• There are actually more

connections to the device that are not shown.

• The device connects to a power supply, which is needed for proper operation, as well as ground.

• There are 8 pins in a common Op-Amp, like the 741 which is used in many applications.


Voltage Source of OpAmp

• Opamp is connected to bipolar volatge source to operate properly.


Voltage Source of OpAmp• The supply voltage values determine the upper and lower limits of

output voltage.


Inputs of OpAmp (Single ended connections)• The operational amplifier or op-amp, has two input terminal:

• V+ is called the non-inverting input terminal.

• V- is called the inverting input terminal.

+

Vo

~ Vi

+

Vo

~ Vi

• + terminal : Source• – terminal : Ground• 0o phase change

• + terminal : Ground• – terminal : Source• 180o phase change

Inputs of OpAmp (Differential input)• The operational amplifier or op-amp, has two input terminal:

• V+ is called the non-inverting input terminal.

• V- is called the inverting input terminal.

~ V1

+

Vo

~ V2

V1

V2

Output of an OpAmp• As mentioned earlier, the maximum output value is the supply

voltage, positive and negative.

• Supply voltage will limit the output voltage VO if VO attempts to exceed the boundaries.

Vd

+

Vo

+Vcc=+5V

Vcc=5V

0

+5V

5V

Output of an OpAmp - Gain• The gain of the opamp is the amount of amplification produced by

an Op-Amp. Gain is independent from the supply voltage but supply voltage limits the output.

• The gain (A) is the slope between saturation points.

Vout

Vin

Vs-

Vs+

Output of an OpAmp - Bandwidth• The bandwidth is the range of frequency at which an Op-Amp will

function.(Ideal = ∞)

• An ideal operational amplifier can amplify any frequency signal from DC to the highest AC frequencies so it is therefore assumed to have an infinite bandwidth.

• With real op-amps, the bandwidth is limited by the Gain-Bandwidth product (GB).

20 log (0.707) = 3dBBW = 10 Hz (A = 70.7)

Output of an OpAmp – Common Mode• Same voltage source is applied at both terminals

• Ideally, two input are equally amplified

• Output voltage is ideally zero due to differential voltage is zero

•

• Practically, a small output signal can still be measured

+

Vo

Vi ~

Operation Modes of OpAmps• Open-Loop Mode:

• There is no connection between and the input voltages and theoutput voltage. The command (input) is amplified with the gain of opamp which is generally a large number. Therefore, the Op-Amp operates as a comparator and not as a linear amplifier.

• A comparator compares the V– and V+ inputs to see which is greater and returns a result.

VOUT

VIN

Ideal response VOUT = A0VIN

Practical response (clipped)

Operation Modes of OpAmps• Open-Loop Mode:

If A0 is large, practical response can be approximated as :VIN > 10 V+ > V- VOUT = +VSAT

VIN < 10 V+ < V- VOUT = -VSAT

Digital

circuit or

system

+V

-V

Variable

voltage

source

Vref

+10V

Comparator

Comparator

input

Comparator

output

High

Low

VH

VL

+10V

Operation Modes of OpAmps• Close-Loop Mode:

• There is a connection between and the input voltages and the output voltage. The command (input) is amplified with the controlled gain of circuit (not the opamp) which is defined by passive components.

• Closed loop uses negative feedback of output voltage to control gain

+Vin

Vo

RaRf

Op-Amp Properties

(1) Infinite Open Loop gain - The gain without feedback- Equal to differential gain- Zero common-mode gain- Pratically, Gd = 20,000 to 200,000

(the opamp gain is assumed to be infinite, hence it drives the output voltage to any value required to satisfy the input conditions.)

(2) Infinite Input impedance- Input current ii ~0A (the current flow into

the input leads of the op amp is zero.)

- T- in high-grade op-amp - m-A input current in low-grade

op-amp

+

V1

V2

Vo

+

Vo

i1~0

i2~0

Op-Amp Properties

(3) Zero Output Impedance- act as perfect internal voltage source- No internal resistance- Output impedance in series with load- Reducing output voltage to the load- Practically, Rout ~ 20-100

+

Rout

Vo'Rload

Ideal vs Practical Op-Amp

Ideal Practical

Open Loop gain A 105

Bandwidth BW 10-100Hz

Input Impedance Zin >1M

Output Impedance Zout 0 10-100

+

~

AVin

Vin Vout

Zout=0

Ideal op-amp

+

AVin

Vin Vout

Zout

~

Zin

Practical op-amp

Ideal Opamp Applications

•Non-inverting Amplifier

•Inverting Amplifier

•Multiple Inputs

•Integrator

•Differentiator

•Differential Amplifier

•Unity-Gain Buffer

•Current-to-Voltage Converter

•Voltage to Current Converter

Ideal Op-Amp Analysis• There is no such thing as an ideal op amp, but present day op amps

come so close to ideal that Ideal Op Amp analysis becomes close to actual analysis.

• When working at low frequencies, several kHz, the ideal OpAmp analysis produces accurate answers.

• Analysis Method is based on two ideal Op-Amp Properties:

• The voltage between V+ and V is zero V+ = V

• The current into both V+ and V terminals is zero

Ideal Op-Amp Analysis• Op-Amp circuits usually take some input voltage and perform

some “operation” on it, yielding an output voltage.

Step 1: KVL around input loop (involves Vin and op-amp inputs)Use Rule 1: V+-V- = 0

Step 2: Find the current in the feedback pathUse Rule 2: No current into/out of op-amp inputs

Step 3: KVL around output loop (involves Vo and feedback path)Remember current can flow in/out op-amp output

V0+

R1 R2

VIN

Input Loop

Feedback Path

Output Loop

Noninverting AmplifierKirchhoff node equation at V+ yields,

Kirchhoff node equation at V yields,

Setting V+ = V– yields

iVVV

00

f

o

a R

VV

R

V

0

f

oi

a

i

R

VV

R

V

a

f

i

o

R

R

V

VA 1

+Vin

Vo

RaRf

Inverting Amplifier• Kirchhoff node equation at V+ yields,

• Kirchhoff node equation at V yields,

• Setting V+ = V– yields

• Notice: The closed-loop gain Vo/Vin is dependent upon the ratio of two resistors, and is independent of the open-loop gain. This is caused by the use of feedback output voltage to subtract from the input voltage.

0V

0_

f

o

a

in

R

VV

R

VV

a

f

in

o

R

R

V

V

+

~

Rf

Ra

Vin

Vo

a

f

i

o

R

R

V

VA

Multiple Inputs or Summing Amplifier• Kirchhoff node equation at V+ yields,

• Kirchhoff node equation at V yields,

• Setting V+ = V– yields

0V

0_

c

c

b

b

a

a

f

o

R

VV

R

VV

R

VV

R

VV

c

aj j

j

f

c

c

b

b

a

afo

R

VR

R

V

R

V

R

VRV

+

Rf

Va

Vo

Rb

Ra

RcVb

Vc

Summing Amplifier• The Summing Amplifier is a very flexible circuit based upon the

standard Inverting Operational Amplifier configuration that can be used for combining multiple inputs

• A simple 4 bit D/A converter circuit

Inverting Integrator

Now replace resistors Ra and Rf by complex components Za and Zf, respectively, therefore

Supposing(i) The feedback component is a capacitor C,

i.e.,

(ii) The input component is a resistor R, Za = RTherefore, the closed-loop gain (Vo/Vin) become:

where

What happens if Za = 1/jC whereas, Zf = R? Inverting differentiator

in

a

f

o VZ

ZV

CjZ f

1

dttvRC

tv io )(1

)(

tj

ii eVtv )(

+

~

Zf

Za

Vin

Vo

+

~

R

Vin

Vo

C

Op-Amp Differentiator

RCdt

dVv i

o

+

R

C

VoVi

0to t1 t2

0

to t1 t2

Op-Amp IntegratorExample:

(a) Determine the rate of changeof the output voltage.

(b) Draw the output waveform.

Solution:

+

R

VoVi

0

+5V

10 k

0.01FC

Vo(max)=10 V

100s

(a) Rate of change of the output voltage

smV/

F k

V

50

)01.0)(10(

5

RC

V

t

V io

(b) In 100 s, the voltage decrease

VμssmV/ 5)100)(50( oV

0

+5V

0

-5V

-10V

Vi

Vo

Differential Amplifier

v v

11

1

v vi

R

01

2

v vi

R

+

-1R

2R

1vov

v

v1i

1i

2v

1R

2R

22

1 2

Rv v

R R

01

1 2

v vv v

R R

2 21 2 2 0

1 2 1 2

1 2

R Rv v v v

R R R R

R R

Differential Amplifier

+

-1R

2R

1vov

v

v1i

1i

2v

1R

2R

2 21 2 2 0

1 2 1 2

1 2

R Rv v v v

R R R R

R R

2

2 2 20 1 2 2

1 1 2 1 1 2

R R Rv v v v

R R R R R R

2 2 20 1 2

1 1 2 1

1R R R

v v vR R R R

20 2 1

1

Rv v v

R

Unity-Gain Buffer or Voltage Follower• s the input signal is connected directly to the non-inverting input

of the amplifier the output signal is not inverted resulting in the output voltage being equal to the input voltage, Vout = Vin.

• This then makes the voltage follower circuit ideal as a Unity Gain Buffer circuit because of its isolation properties as impedance or circuit isolation is more important than amplification while maintaining the signal voltage.

+

-ov

v

viv o

F

i

vA

v

1oF

i

vA

v

i ov v v v

Current-to-Voltage Converter

i fi i

0v v

00 f Fv i R

0 i Fv i R

+

-ov

v

v

ii

FR fi

f

i

o Ri

V

It is sometimes necessary to convert small current inputs to scalled voltage outputs.

Current-to-Voltage Converter - Photodiode Circuit

25 A per milliwatt of incident radiationii

650 25 10 1.25mAii

Assume 3.2kFR

3 3

0 1.25 10 3.2 10 4Vi Fv i R

+

-ov

v

v

ii

FR fi

h

At 50 mW

Voltage-to-current converter

• This circuit takes an input voltage and converts it to an output current.

• The input impedance of the voltage-to-current converter is the input impedance of the op amps input.For an ideal op amp the input impedance is infinite.

out

in

fino

Z

Z

RviA /1/

Applications of Opamps• Piezoelectric sensors:

• Piezoelectric crystal generates an electric charge in response to deformation. Therefore iti is used to measure force, pressure, acceleration.

• An integrator opamp converts acceleration signal to a velocity scalled voltage output

Applications of Opamps• Instrumentation Amplifier:

• Instrumentation Amplifiers (in-amps) are very high gain differential amplifiers which have a high input impedance and a single ended output.

• Instrumentation amplifiers are mainly used to amplify very small differential signals from strain gauges, thermocouples or current sensing devices in motor control systems.

Applications of Opamps

• Instrumentation Amplifier (EKG) :

Opamps at a glance

Opamps at a glance

•The amplifier output voltage does not depend on the “load” (what is attached to the output).•The “form” of the output voltage (the signs of the scaling factors on the input voltages, for example) depends on the amplifier circuit layout.•To change the values (magnitudes) of scaling factors, adjust resistor values.•Input voltages which are attached to the + (non-inverting)amplifier terminal get positive scaling factors. •Inputs attached to the – (inverting) terminal get negative scaling factors.•You can use these principles to design amplifiers which perform a particular function on the input voltages.

43• Yrd. Doç. Dr. Aytaç Gören

w05 operational amplifiers - deukisi.deu.edu.tr/aytac.goren/elk2018/h5.pdf · 2012. 3. 26. ·...

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