passive low pass and high pass filter

7/25/2019 Passive Low Pass and High Pass Filter

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Lab 08: Passive First Order LowPass & High Pass Filter

Experiment 08

To design R low pass & high pass !lter "ir"#it with "#to$%re#en"' o% ()H*+ also draw a %re#en"' response: ,a-

magnit#de response ,b- phase response.

To design RL low pass & high pass !lter "ir"#it with "#to$

%re#en"' o% ()H*+ also draw a %re#en"' response: ,a-

magnit#de response ,b- phase response.

/ntrod#"tion:

This laboratory studies the use of passive components to create lters to separateportions of time-dependent waveforms. Filters are an essential tool in our complexworld of mixed signals both electronic and otherwise. Passive components(resistors capacitors and inductors! have long served as lter components foreverything from selecting radio stations to ltering out electrical noise.

E12T/O32L O45ET/6E7"(#! $earn the general lter types" %igh-pass $ow-pass.

(&! $earn to alter lter type by changing contacts for output voltage.

('! $earn phase angle at cuto for simple )* and )$ lters.

(+! ,esign simple lter.

(! Freuency response (amplitude and phase!.

EPER/9E3T2L O45ET/6E7"

(#! *alculate and measure cuto freuency for series )* and )$ lters.

(&! ,esign simple )* low-pass / high pass lter.

('! ,esign simple )$ low-pass / high pass lter.

(+! 0ode plots for series lters.

PREL24"

Reading"

(#! 1tudy the 0ac2ground section of this $aboratory.(&! 1tudy textboo2 *hapter #+ (#+.# -#+.+!.

;ritten"

3ote: 4e%ore the starts o% sim#lation ma


2/30


(#!1imulate the circuit shown in Fig (! Fig (3! Fig (4! and Fig (5! in $Tspice and)ecord the simulation result in Table # Table & Table ' and Table +.

(&!12etch the 0ode Plots of the simulation results recorded in Table # Table &Table ' and Table +.


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E=1/P9E3T 23 92TER/2L7

,igital Function 6enerator ,igital 7scilloscope with Probes. 0read 0oard *apacitors 8nductors )esistors

4a"


4/30


P(c)=Pmax

2

Filter; lter is a circuit that is designed to pass signals with desired freuencies andre


5/30


Phase Bode Plot for First-Order Low Pass Filter

High Pass Filter

; high pass lter passes high freuencies and re


6/30


Phase Bode Plot for First-Order High Pass Filter


7/30


esign o% R Low Pass Filter

The cuto freuency for )* circuit is given below

c= 1

RC, fc=

1

2RC(1)

The derivation of equation (1) is given in Appendix A Fig ,(- R

Low Pass Filter ir"#it

Let C=10nF ,C=9.08nF(By Capacitance Meter )Put C=9.08n F fc=5KHzEquatin(1)

510

2(3)(9.08109)

R=1

R=3.5K!

Ma"e #ure t$at t$e CapacitrRe#i#trf t$i# %a&u#i# a%ai&a'&eLa'( t$er)i#e * t$e

ca&acu&atin# accr*in+ t$e a%ai&a'&e %a&ue#

The transfer function of circuit shown in g ('! is

H()= 1

1+-RC >>Derivation is given in Appendix A

Equatin(1 ) c= 1

RC

H()= 1

1+-

c

|H()|= 1

(1 )2+( c)

2(2)


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=tan1(c)(3)

.t can 'e #eenequatin# (2 )(3 ) t$at at =0,|H( )|=1=0

.t can 'e #eenequatin# (2 )(3 ) t$at at =/ ,|H( )|=0=900


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esign o% R High Pass Filter

The values of ) and * are same as found in)* low pass lter circuit.

The transfer function of circuit shown in g (3! is

H()= 1

1+ 1

-RC

(4)

>>,erivation is given in ;ppendix 0 Fig ,>- R HighPass Filter ir"#it

Equatin(1 ) c= 1

RC

Put RC= 1

ct$e Equatin(4)

H()= 1

1+ 1

-RC

= 1

1-c

|H()|= 1

(1 )2+(c)

2(5)

=tan1(c)=tan1(c

)(6)

.t can 'e #eenequatin# (5 )(6 ) t$at at=0,|H()|=0=900

.t can 'e #eenequatin# (5 )(6 ) t$at at=/ ,|H( )|=1=00

C=10nF

R=3.5K !


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esign o% RL Low Pass ir"#it

The cuto freuency for )* circuit is given below

c=R

L, fc=

R

2L(7)

The derivation of equation (7) is given in Appendix C

Let L=10mH Fig ,?- RL Low Pass Filter

ir"#it

Ma"e #ure t$at t$e in*uctr f t$i# %a&u# i# a%ai&a'&eLa'

Put L=1mH fc=5KHzt$e Equatin(7)

R=2 fcL

R=2 510310103

R=314.1!

Ma"e #ure t$at t$e in*uctrre#i#trf t$i#%a&u# i# a%ai&a'&eLa' ( t$er)i#e * t$e

ca&acu&atin# accr*in+ t$e a%ai&a'&e in*uctr %a&ue

The transfer function of circuit shown in g ('! is

H()= 1

1+-L

R

(8) >>Derivation is given in Appendix C

Equatin(7 ) c=R

L

Put L

R=

1

c t$e Equatin(8)


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H()= 1

1+-

c

|H()|= 1

(1 )2+( c)

2(9)

=tan1(c)(10)

.t can 'e #eenequatin# (9 )(10 ) t$at at =0,|H()|=1=0

.t can 'e #eenequatin# (9 )(10 ) t$at at =/ ,|H( )|=0=900

esign o% RL High Pass ir"#it:

The values of ) and $ is same as foundin )$ low pass lter circuit.

The transfer function of circuit shown in g (5! is

Fig ,8- RL High Pass

Filter ir"#it

H()= 1

1+ R

-L

(11)

Equatin(7 ) c=RL

PutR

L=ct$e Equatin(11)


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H()= 1

1+R

-L

= 1

1-c

|H()|= 1

(1 )2+(c)

2(12)

=tan1(c)=tan1(c

)(13)

.t can'e #eenequatin# (12)(13 )t$at at =0,|H( )|=0=900

.t can'e #eenequatin# (12)(13 )t$at at =/,|H( )|=1=00


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Tas< @ R Low Pass Filter:

#! 1et up the circuit shown in Fig ,(-. ?se the function generator F6=@ for thesupply voltage vin#: AP-P.

&! *onnect channels # and & of the oscilloscope to measure As and Aoutsimultaneously.

'! Aary the freuency from :: %B to #: 2%B in steps indicated in Table # andrecord the indicated value. Cith each freuency change ma2e sure that Ain isstill #:App.

a! ?sing the data of Table # s2etch a 0ode plots of the of the lterDs output

voltage.

Tas< A R High Pass Filter:

)epeat the Tas2 # for the circuit shown in Fig (3! and record your result in Table

&

Tas< B RL Low Pass Filter:


'

Tas< C RL High Pass Filter:


+

Post Lab:

#! Chy are capacitors preferred over inductors in lter designE&! *reate 0ode plots of the magnitude transfer functions of your low-pass and

high-pass lters. The theoretical plots (using measured values of resistorsand capacitors! should be drawn as lines. 8nclude your data (ta2en at #>#:

# & and #: times the cuto freuency! as points.'! *ompare the measured results and simulation results.


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al"#lated Res#lts:

Tas< @: Passive R Low Pass Filter

Fre#en"'

,)HD-(ra* /#) |H()|= 1

(1 )2+ 2

H()=20 log0

0(*B) =tan1(c)

:.:#fcG

:.#f*G

:.fc G

fc G

&fc G

+fc G3fc G

5fc G

#:fc G

#::fc G

Table @ ,R Low Pass Filter-

Tas< A: Passive R High Pass Filter

Fre#en"',)HD- (ra* /#) |H()|= 1

(1 )2+c

2 H()=20 log0

0(*B) =tan1(

c)

:.:#fcG

:.#f*G

:.fc G

fc G

&fc G

+fc G

3fc G

5fc G

#:fc G

#::fc G

Table A ,R High Pass Filter-


15/30


al"#lated Res#lts:

Tas< B: Passive RL Low Pass Filter

Fre#en"'

,)HD-(ra* /#) |H()|= 1

(1 )2+ 2

H()=20 log0

0(*B) =tan1(c)

:.:#fcG

:.#f*G

:.fc G

fc G

&fc G

+fc G3fc G

5fc G

#:fc G

#::fc G

Table B ,RL Low Pass Filter-

Tas< C: Passive RL High Pass Filter

Fre#en"'

,)HD-(ra* /#) |H()|= 1

(1 )2+c

2H()=20 log

0

0(*B) =tan1( c)

:.:#fcG

:.#f*G

:.fc G

fc G

&fc G

+fc G

3fc G

5fc G

#:fc G

#::fc G

Table C ,RL High Pass Filter-


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7e"tion C 9eas#rement Tables

@ame" HHHHHHHHHHHHHHHHHHHHHHHHHH )eg. @oHHHHHHHHHHHHHHHHHHHHHHH

Tas< @: Passive R Low Pass FilterAin (p-p! G #: AP-P

Fre#en"'

,)HD-(ra* /#) 6o#t,PP- H()=

0

0H()=20 log

0

0(*B) (*e+ree#)

:.:#fcG

:.#f*G

:.fc Gfc G

&fc G

+fc G

3fc G

5fc G

#:fc G

#::fc G

Table @ ,R Low Pass Filter-

Tas< A: Passive R High Pass FilterAin (p-p! G #: AP-P

Fre#en"'

,)HD-(ra* /#) 6o#t,PP- H()=

0

0H()=20 log

0

0(*B) (*e+ree#)

:.:#fcG

:.#f*G

:.fc G

fc G

&fc G+fc G

3fc G

5fc G

#:fc G

#::fc G


17/30


Table A ,R High Pass Filter-

7e"tion C 9eas#rement Tables

@ame" HHHHHHHHHHHHHHHHHHHHHHHHHH )eg. @o

HHHHHHHHHHHHHHHHHHHHHHH

Tas< B: Passive RL Low Pass FilterAin (p-p! G #: AP-P

Fre#en"'

,)HD-(ra* /#) 6o#t,PP- H()=

0

0H()=20 log

0

0(*B) (*e+ree#)

:.:#fcG

:.#f*G:.fc G

fc G

&fc G

+fc G

3fc G

5fc G

#:fc G

#::fc G

Table B ,RL Low Pass Filter-Tas< C: Passive RL High Pass Filter

Ain (p-p! G #: AP-P

Fre#en"'

,)HD-(ra* /#) 6o#t,PP- H()=

0

0H()=20 log

0

0(*B) (*e+ree#)

:.:#fcG

:.#f*G

:.fc G

fc G&fc G

+fc G

3fc G

5fc G

#:fc G


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#::fc GTable C ,RL High Pass Filter-

3ame: Reg. 3o

4ode Plot %or R Low Pass Filter:

agnit#de

4-

IType a uote from the

document or the summary of

an interesting point. Jou can

position the text box anywhere

in the document. ?se the

,rawing Tools tab to changethe formatting of the pull

uote text box.K

Fre#en"'


19/30


3ame: Reg. 3o

4ode Plot %or R High Pass Filter:

ase

egree-

e#en"'

agnit#de

4-

IType a uote from thedocument or the summary of




,rawing Tools tab to change

the formatting of the pull

uote text box.K

Fre#en"'


20/30


3ame: Reg. 3o

4ode Plot %or RL Low Pass Filter:

ase

egree-

e#en"'

agnit#de

4-








uote text box.K

Fre#en"'


21/30


3ame: Reg. 3o

4ode Plot %or RL High Pass Filter:

ase

egree-

e#en"'

agnit#de

4-








uote text box.K

Fre#en"'


22/30


2ppendix 2 ,R Low Pass Filter-

From the circuit diagram0

is given by0=

1

-C

R+ 1

-C

0

0

0=

1

1+-RC

;s we 2now that0

0=H()

H()= 1

1+-RC(1)

ase

egree-

e#en"'


23/30


|H()|= 11+(RC)

;t = c

|H()| G :.4:4 1

0.707= 1

1+(cRC)

0.7072=

1

1+(cRC)2

0.5= 1

1+(cRC)2

0.5+0.5 (cRC)2=1

0.5 (cRC)2=10.5

(cRC)2=

0.5

0.5

(cRC)2=1

c2=

1

(RC)2

c= 1

RC(2)

fc= 1

2 RC

2ppendix 4 ,R High Pass Filter-


is given by


24/30


0= R

R+ 1

-C

0

0

0=

1

1+ 1

-RC

;s we 2now that0

0=H()

H()= 11+

1

-RC

(5)

|H()|= 1

1+ 1

(RC)

;t = c

|H()| G :.4:4

1+ 1

( c RC)

0.707=1

1uaring both sides

1+ 1

( c RC)

0.7072=1


25/30


1+ 1

( c RC)

0.5=1

( c RC)

1+1

0.5

( c RC)2=1

0.5+0.5

( c RC)2=10.50.5

(cRC)2=

0.5

0.5

(cRC)2=1

c2=

1

(RC)2

c= 1

RC

fc= 1

2 RC


26/30



27/30


2ppendix ,RL Low Pass Filter-

From the circuit diagram 0 is given by

0= R

R+-L0

0

0=

R

R(1+-L

R )

;s we 2now that

0

0=H()

H()= 1

1+ -LR

|H( )|= 1

1+(L

R)

;t = c

|H()| G :.4:4

0.707= 1

1+(cL

R)


28/30


0.7072=

1

1+

(

cL

R

)

2

0.5= 1

1+( cLR)2

0.5+0.5( cLR)2

=1

0.5( cLR)2

=10.5

( cLR)2

=0.5

0.5

(cL

R)2

=1

c2=

R2

L2

c=R

L

f= R2L


29/30


2ppendix ,RL High Pass Filter-


is given by

0= -L

R+-L0

0

0

=-L

-L( R-L+1)

;s we 2now that

0

0=H()

H()= 1

1+

R

-L

|H( )|= 1

1+( R

L )

;t = c

|H()| G :.4:4

0.707= 1

1+( R

cL )


30/30


0.7072=

1

1+

(

R

cL

)

2

0.5= 1

1+( RcL )2

0.5+0.5

( R

cL

)

2

=1

0.5( RcL )2

=10.5

( RcL )2

=0.5

0.5

( RcL )

2=1

c2=

R2

L2

c=R

L

f= R

2L

passive low pass and high pass filter

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