Active Filter

S

F

S

out

Z

Z

V

V

S

F

S

out

Z

Z

V

V1

It is phasor time again

Active Low Pass Filter

FF

SF

FF

F

FFF

S

F

S

out

CRj

RRjA

CRj

R

CjRZ

Z

Z

V

VjA

1

/)(

1

1||

)( • Amplification: RF/RS

• low pass factor 1/(1+jRFCF)• Cut off frequency: RFCF=1

RF/RS=10, 1/RFCF=1

Figure 8.24,

Active high-pass filter

SS

S

F

SS

F

SSS

S

F

S

out

CRjR

R

CjR

RjA

CjRZ

Z

Z

V

VjA

11

1

1)(

1

)(

RF/RS=10, 1/RFCF=1

Figure 8.26, 8.27

8-11

Active bandpass filterFigure 8.26

Normalized amplitude response of active bandpass filterFigure 8.27

SSFF

SF

CRjCRj

CRjjA

11)(

Let’s build an integrator

Let’s start with the following insight:

We need to somehow convert voltage vI to current

First try…use resistor

R

vi IBut, v0 must be very

small compare to vR, or else

When is v0 small compare to vR?

For good integratorRC >> 1

There’s a better way…

Op Amp Integrator

t

SFS

out

S

SoutF

SF

dttvCR

tv

R

v

dt

vdC

ii

')'(1

)(

)0(

Examples: 8.6, 8.7

Drafting problem

Op Amp differentiator

dt

tdvCRtv

dt

dvC

R

v

ii

SSFout

SS

F

out

SF

)()(

Triangle wave to square wave