Module 2 handouts part 1

Dr. Bonnie H. FerriProfessor and Associate ChairSchool of Electrical and Computer Engineering

School of Electrical and Computer Engineering

Module 2: Op AmpsIntroduction and Ideal Behavior

Introduce Op Amps and examine ideal behavior

Introduce Operational Amplifiers Describe Ideal Op Amp Behavior Introduce Comparator and Buffer Circuits

Lesson Objectives

2

Operational Amplifiers (Op Amps)

Uses: Amplifiers Active Filters Analog Computers

Specialized circuit made up of transistors, resistors, and capacitors fabricated on an integrated chip

+Vs

-Vs

vo

v+ +

-v-

3

Vs = 10V, 15V

Op Amps in Circuits

Active Element: has its own power supply Symbol ignores the +/- Vs in the symbol since it

does not affect circuit behavior

Symbol:+Vs

-Vs

vo

v+ +

-v-

+

-

+Vs

-Vs

vov+

v-

4

Open Loop Behavior

+Vs

-Vs

vo

v+ +

-v-

vo= A(v+ - v-)

v+ - v-

voVs

-Vs

5

V

Comparator Circuit+Vs

-Vs

vo

v+ +

-v-

vin

voVs

-Vs

<−>

−=00

ins

inso vifV

vifVV

vin

6

Csin(ωt)

Example

+Vs

-Vs

vo

v++

-v- v+ - v-

voVs

-Vs

7

i+ = i- = 0v+ - v- = 0

Ideal Op Amp Behaviorv+

v-

vo+

-

i+

i-

+Vs

-Vs

vo

v+

v- Ri

RovinAvin

8

Buffer Circuit

vin = vo

vo+-

vin vo+-

vin

9

Summary

Op amps are active devices that can be used to filter or amplify signals linearly

Ideal op amps:

Circuits: comparator and buffer

i+ = i- = 0v+ - v- = 0

v+

v-

vo+

-

i+

i-

10

Buffer Circuit Basic Amplifier Configurations Differentiators and Integrators Active Filters

Remainder of Module 2: Op Amps

11



Buffer Circuits

Demonstrate buffer circuit behavior

Introduce physical op amps in circuits Examine Buffer Circuit behavior

Lesson Objectives

13

Use to boost power without changing voltage waveform

Buffer Circuit

vin = vo

vo+-

vin

vin

voVS

-VS

14

Example: Without Buffer

vin R+vo+

15

Vs = 15V

Physical Op Amps

Signal PIN

v- 2

v+ 3

-Vs 4

vo 6

+Vs 7

+Vs

-Vs

vo

v+ +

-v-

16

Example: With Buffer

+-vin

+vo+

R

vin R+vo+

17

Example: With Buffer

+-vin

+vo+

R

18

Summary

Buffers boost the power without changing the voltage waveform

Demonstrated physical op amp circuits

19



Basic Op Amp AmplifierConfigurations

Introduce Inverting and Non-Inverting Amplifiers, Difference and Summing Amplifiers

Introduce Inverting and Non-Inverting Configurations Difference and Summing Configurations

Introduce the Gain of a circuit

Lesson Objectives

21

Non-Inverting Amplifiers

in3

32o V

RRR

V+

=

R

RRG :Gain

3

32 +=ino GVV =

+-vin

vo

R2

R3

R1

22

If R2 = R3 = 200Ω,

Since,G > 1, the input is amplified

If G < 1, the input is attenuated

Non-Inverting Amplifier Example+-vin

vo

R2

R3

R1

23

Inverting Amplifier

ino GVV =

in1

fo V

RRV −=

+

-

vin

vo

Rf

R1

24

R1 = 1000Ω, Rf = 2000Ω

If,G > 1, the input is amplified If G < 1, the input is attenuated

Inverting Amplifier Example

+

-

vin

vo

Rf

R1

25

Difference Circuit

+

-

v1

vo

Rf

R1

v2

R1

R2

)( 121

Fo VVRRV −=

26

Difference Circuit

+

-

v1

vo

Rf

R1

v2

R1

R2

)( 121

Fo VVRRV −=

27

Summing Amplifier

+

-v1

vo

Rf

R2

v2

R1

2

F2

1

F1

2211o

RRG

RRG

VGVGV

−=−=

+=

28

Summary

Gain: Amplifier Circuit Configurations

Non-Inverting Amplifier Inverting Amplifier Difference Amplifier Summing Amplifier

ino GVV =

29



Introduce Integrating and Differentiating Op Amp Circuits

Differentiators and Integrators

Introduce Differentiators and Integrators Demonstrate the performance of both circuits on an

oscilloscope

Lesson Objectives

31

Differentiator Circuit

dtdVRCV in

o −=

+

-

vin

vo

R

Cv-

v+

cc V

dtdV

Ci=

32

Differentiator Circuit

Derivation:1. KVL: Vin = Vc + Ri + Vo

2. Vin = Vc

3. Vo = -Ri = -RC(dVin / dt)

dtdVRCV in

o −=

+

-

vin

vo

R

Cv-

v+

33

Differentiator Example

+

-

vin

vo

1000Ω

1µFv-

v+

vin v+

vo+VS= 15v

-VS = -15v

-VS

v-

+VS

34

Results

dtdVRCV in

o −=

35

Integrator Circuit

dtVRC

Vt

ino ∫−

=0

1

cc V

dtdV

Ci= ∫=t

c idtC

V0

1

+

-

vin

voR

v-

v+

C

36

Integrator Circuit

Derivation:For t<0: Vin = iR and Vo = 0For t>0: Vin = iR i = Vin/RVin = iR + Vc + Vo

Vo = -Vc = -1/C ∫t Vin/R dt0

dtVRC

Vt

ino ∫−

=0

1

cc V

dtdV

Ci= ∫=t

c idtC

V0

1

+

-

vin

voR

v-

v+

C

37

Integrator Examplevin v+

vo

+VS= 15v

-VS = -15v

-VSv-

+VS

+

-

vin

vo1000Ω

v-

v+

1µF

38

Results

dtVRC

Vt

ino ∫−

=0

1

39

Summary

Differentiator and Integrator Op Amp circuits examined

40



Active Filters

Introduce active filters and show different types of filters

Introduce active filter circuits

Lesson Objectives

42

Analog Filters

Analog FilterVin Vout

0 0.05 0.1 0.15 0.2 0.25-2

-1

0

1

2

Time (sec)

v(t)

0 0.05 0.1 0.15 0.2 0.25-1.5

-1

-0.5

0

0.5

1

1.5

Time (sec)

v(t)

0 200 400 600 800 10000

0.2

0.4

0.6

0.8

1

ω

Mag

nitu

de

H(ω)

|H(ω)|

ω (rad/sec)43

Quiz

Vin = 1 + cos(10(2πt)) + cos(100(2πt)) Vout = 0.45cos(10(2πt)+θ1) + 0.97cos(100(2πt) +θ2)

44

Summary of RC and RLC (Passive) Filters

vinR +

-voC

vin

R +

-vo

CL

vin R+

-vo

C

ω

Mag

nitu

de (d

B)

Bode Plots

ω

Mag

nitu

de (d

B)

ω

Mag

nitu

de (d

B)

45

Depletes power

No isolation

Limitations of RLC Passive Filters

Analog FilterVin Vo

vinR +

-voC

46

– has its own power supply Most common active filters are made from op amps Provide isolation

Active Filters

Op Amp CircuitVin Vout

47

An is a circuit that has a specific shaped frequency response

A is made of op amps and has its own power supply. Advantages over RLC passive filters: Provides isolation (cascade filters) Boosts the power Can provide sharper roll-off

Summary

48

Derivation: Vin = iZ1

Vo = -iZf = -(Zf/Z1)Vin

Impedance Gain

inin

Fo V

ZZV −

=

49



First-OrderLowpass Filters

Introduce lowpass filters

Introduce active lowpass filters

Lesson Objectives

51

Lowpass Filters

ω

Linear Plot

Mag

nitu

de

KDC

ωB

0.707KDC ω

Bode Plot

Mag

nitu

de (d

B)

20log10(KDC)3dB

Lowpass filters pass low frequency components and attenuate high frequency components

Transfer Function H(ω)

52

First-Order Filter

Bandwidth, ωB = 1/τDC Gain = H(0) = KDC

ω

Linear Plot

Mag

nitu

de

KDC

ωB

0.707KDC

0

1j1KH DC +ωτ

=ω)(

53

From Passive to Active Lowpass Filters

CircuitVin VoVin Vo

RC

Vo

RC

+-vin

Vin

RC

+-

vo

54

First-Order Inverting Lowpass Filter

+

- voR1

C

Rf

vin

inf1

fo V

1CjR1

RRV

+ω−=

55

Frequency Characteristics of LP Filter

ω

|H(ω)|Rf/R1

.707 Rf/R1

ωb

180°90°

H(ω)

ω1

f

RRGainDC −=

)()(

1CjR1

RRH

f1

f

+ω−=ω

1)ωCR(

1RR)|ω(H|

2ff

f

1 +=

)ωCRarctan(180)ω(H ff−=∠

fb CR

1ω,Bandwidthf

=

56

Derivation: Lowpass Filter

+

- voZ1vin

Zf

+

- voR1

C

Rf

vin

57

Design an inverting lowpass filter to have a DC gain of -2 and a bandwidth of 500 rad/s:

Example

+

- voR1

C

Rf

vin

1CjR1

RRH

f1

f

+ω−=ω)(

58

A passes low frequency signals and attenuates high frequency signals

Three first-order lowpass configurations: Noninverting, isolation at the input

Noninverting, isolation at the output

Inverting, isolation at input and output

Summary

Vo

RC

+-vin

Vin

RC

+-

vo

+

- voR1

C

Rf

vin

59



First-OrderHighpass Filters

Introduce highpass filters

Introduce active highpass filters

Lesson Objectives

61

Passes high frequency components and attenuates low frequency components

Highpass Filter

Linear Plot

ω

Mag

nitu

de

62

First-Order Filter

Corner Frequency, ωc = 1/τPassband Gain= KPB = K/τ

Linear Plot

1jKjH+ωτω

=ω)(

ω

Mag

nitu

de

KPB

ωc

0.707KPB

0

63

Inverting Highpass Filter Configuration

in1

fo V

1CjRCjRV

)( +ωω−

=

+

- vo

R1C

Rf

vin

+

- voZ1vin

Zf

64

Frequency Characteristics of HP Filter

CR1FreqCorner1

c =ω.,1

f

RRGainPassband −=∞→ω )(

)arctan()( ω−°−=ω∠ CR90H 1

)()(

1CjRCjRH

1

f

+ωω−

=ω

1CR

CRH2

1

f

+ω

ω=ω

)(|)(|

|H(ω)|Rf/R1

ωc = 1/R1C ω

0.707KPB

0

-90°

H(ω)ω0°

65

Design a highpass filter to have a passbandgain of 2 and a corner frequency of 1k rad/s:

Example

+

- vo

R1C

Rf

vin

66

A passes high frequency components in signals and attenuates low frequency components

First-order highpass filter

Design based on Corner frequency of the passband, ωc Passband gain, KPB

Summary

+

- vo

R1C

Rf

vin

)()(

1CjRCjRH

1

f

+ωω−

=ω

67