Lecture 20

Operational Amplifiers (cont’d)

Op-Amp 1-1

Outline

Quick Review on Op-Amp

Op-Amp Applications

Controlled Sources

Active Filters

Practical Op-Amp Circuits

Op-Amp 1-2

Quick Review

Op-Amp 1-3

For Ideal Op-Amp: • Input current I equal zero (infinite input

impedance) • Zero output impedance • V- ≈ V+ (Infinite gain) • Constant gain w.r.t. frequency change What is the value of Vo if V1 = 0 ?

V-

V+

I

Difference Amplifier

Op-Amp 1-4

2

43

121

1

2

||1

||1V

RR

RRV

R

RVo

Applications

Controlled Sources

Voltage-controlled voltage source

Voltage-controlled current source

Current-controlled voltage source

Current-controlled current source

Op-Amp 1-5

Voltage-Controlled Voltage Source

The output voltage is the gain times the input voltage.

Op-Amp 1-6

Non-inverting Amplifier Version

Voltage-Controlled Current Source

Op-Amp 1-7

The output current is: 1

1

1o Vconstant

R

VI

Current-Controlled Voltage Source

Op-Amp 1-8

This is simply another way of applying the Op-Amp operation. Whether the input is a current determined by Vin/R1 or as I1: or

in1

fout V

R

RV

L1out RIV

Current-Controlled Current Source

Op-Amp 1-9

in

in

f

out

21

in

f

out

inin

fout

R

V

R

V

R||R

V

R

V

VR

RV

kIR

R1II

R

RR

R

VI

RR

RRVI

R||R

VI

2

1o

2

21

1

ino

21

21ino

21

ino

-

+

vo

Rf

R1

R2

vi

Ii

Io

I

Active Filters

Adding capacitors to op-amp circuits provides external control of the cutoff frequencies. The op-amp active filter provides controllable cutoff frequencies and controllable gain Low-pass filter

High-pass filter

Bandpass filter

Op-Amp 1-10

 

Vout ( jw )

VS ( jw )= -ZF

Z S

 

Vout ( jw )

VS ( jw )= 1+

ZF

Z S

Active Low-Pass Filter

Op-Amp 1-11

 

ALP ( jw )= -ZF

Z S= -ZF

RS

 

ZF = RF ||1

jwCF= -

RF

1+ jwCFRF

FF

SF

FF

SF

S

FLP

RfCj

RR

RCj

RR

Z

ZfA

21

/

1

/)(

2)2(1log20log20|)(| FF

S

FdBLP RfC

R

RfA

Amplification

FF

OHCR2

1f

π

The upper cutoff frequency (-3dB

of gain) and voltage gain are given by:

Active High-Pass Filter

Op-Amp 1-12

S

F

S

FHP

Z

R

Z

ZjA )( ZS = RS +

1

jwCS=jwCSRS +1

jwCS

SF

SS

SSSF

SS

SS

S

S

SS

FS

S

FHP RR

RCj

RCjRR

RCj

RCj

R

R

RCj

RCj

Z

ZfA /

21

2/

11)(

2)2(1log202log20log20|)(| SSSS

S

FdBHP RfCRfC

R

RfA

Amplification

SS

OLCR2

1f

π

The lower cutoff frequency (-3dB

of gain) and voltage gain are given by:

Active Band-Pass Filter

Op-Amp 1-13

 

ABP ( jw )= -ZF

Z S

 

Z S = RS +1

jwC S=jwC SRS +1

jwC S

 

ZF = RF ||1

jwCF= -

RF /RS

1+ jwCFRF

)21)(21(

2

)1)(1()(

SSFF

FS

SSFF

FS

S

FBP

RfCjRfCj

RfCj

RCjRCj

RCj

Z

ZfA

Low pass frequency High pass frequency

22 )2(1log20)2(1log202log20|)(| SSFFFSdBBP RfCRfCRfCfA

FSRfC2

FFRfC2SSRfC2

Lecture-related Question

Op-Amp 1-14

I

Op-Amp 1-15

Lecture Summary

Covered material

Quick Op-Amp Review Op-Amp Applications

Controlled Sources Active Filters Practical Op-Amp Circuits Examples

Material to be covered next lecture

Limitations of Op-Amp Power Amplifiers