ece 3042 experiment 6 active filter...

ECE 3042 Experiment 6 Active Filter Design

1. Design a 3rd order Butterworth low-pass filters having a dc gain of unityand a cutoff frequency, fc, of 10.28 kHz.

fc 10.28kHz:= K 1:= The transfer function is given on page 72 j 1−:=

TB f( ) K1

jffc⋅ 1+

⋅1

jffc⋅⎛⎜

⎝⎞⎟⎠

2j

ffc⋅+ 1+

⋅:= This is the product of a 1st order LPF & 2nd orderLPF.

1 103× 1 104× 1 105× 1 106×1 10 4−×

1 10 3−×

0.01

0.1

1

10

TB f( )

f

2 103× 6 103× 1 104×

0.6

0.8

1

1.2

1.4

TB f( )

f

To implement this with a circuit cascade the circuit on page 82 with that on page 83.For each the dc gain is unity (K) which means that RF is zero (a wire) and the resistorfrom the inverting input to ground is infinity (nothing there).

Start by picking two of the capacitors to be 0.01μF. For the Butterworth filter ωc & ωo arethe same.

So for the circuit on page 82 C 0.01μF:= R11

2 π⋅ fc⋅ C⋅:= R1 1.548 103

× Ω=This is a 1st order LPF

For the circuit shown on page 83, the 2nd order LPF, pick C1 0.01μF:= C2 0.1C1:=then Eq. 6.84 applies with Q=1 and ωo=ωc

Q 1:=ωo 2 π⋅ fc⋅:=

R11

2 Q⋅ ωo⋅ C2⋅1 1 4 Q2

⋅C2

C1−+

⎛⎜⎝

⎞⎟⎠

⋅:= R21

2 Q⋅ ωo⋅ C2⋅1 1 4 Q2

⋅C2

C1−−

⎛⎜⎝

⎞⎟⎠

⋅:=

R1 1.374 104× Ω= R2 1.745 103

× Ω= C1 1 10 8−× F= C2 1 10 9−

× F=

Now that all of the component values have been determined it's time to simulate it withSPICE

0.001

0.01

0.1

1

10

103 104 105

Butterworth Filter

Gai

n (L

inea

r)

Frequency (Hz)

The next step is to head to the lab and build the circuits. Use 741s, LF351s, LF347s.The resistors for your use are 5%. The caps are 20 %. Try to find 3 caps reasonablyclose to the design values.

φ f( )180π

arg TB f( )( )⋅:=τp f( )

1−2 π⋅

φ f( )f

⋅:= τg f( )1−

2 π⋅ fφ f( )d

d⎛⎜⎝

⎞⎟⎠

⋅:=

1 103× 1 104× 1 105×0

1 10 3−×

2 10 3−×τp f( )

τg f( )

f

2. Design a 3rd order unity dc gain Chebyshev LPF with a -3 frequency of 10.28 kHz and 0.5db ripple in the pass band.

db 0.5:= f3 10.28kHz:= K 1:= n 3:= t3 x( ) 4 x3⋅ 3 x⋅−:= j 1−:=

Eq. 6.47 must be solved to obtain the relationship between ωc & ω3which requires that Eq. 6.46 be solved which is a cubic polynomial g(x)ε 10

db

10 1−:=

g x( ) 4 x3⋅ 3 x⋅−1ε

−:= Since t3(0)=0 To solve this form the vector v

This is done with the Insert Matrix selection from the toolbar.The roots are now obtained with the polyroots(.) function.With MathCad the index on arrays in a matrix begin with 0.

v

1−

ε

3−

0

4

⎛⎜⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎟⎠

:=Since this is a cubic polynomial it will have at least one real rootand its the one required.

u polyroots v( ):= u

0.584− 0.522i−

0.584− 0.522i+

1.167

⎛⎜⎜⎝

⎞⎟⎟⎠

= x u2 0, := x 1.167=

fcf3x

:= fc 8.805 103×

1s

= The transfer function is Eq. 6.56 whichrequires h, a2, a1, & b1

h tanh1n

asinh1ε

⎛⎜⎝

⎞⎟⎠

⋅⎛⎜⎝

⎞⎟⎠

:= ε 0.349= h 0.531= θ113

π

2⋅:=

a2h

1 h2−

:= a11

1 h2−

sin θ1( )( )2−:= b1

12

11

h tan θ1( )⋅( )2+⋅:=

a2 0.626= a1 1.069= b1 1.706= The transfer function then becomes

TC f( ) K1

j f⋅a2 fc⋅

1+

⋅1

j f⋅a1 fc⋅

⎛⎜⎝

⎞⎟⎠

2 1b1

j f⋅a1 fc⋅

⋅+ 1+⎡⎢⎣

⎤⎥⎦

⋅:= y f( ) 20 log TC f( )( )⋅:=

For a check of the solution the magnitude of the transfer function in db will be plotted vs f

1 103× 1 104× 1 105×4−

3−

2−

1−

0

y f( )

f100 1 103× 1 104×1−

0.5−

0

0.5

1

y f( )

f Note that it is3 dB down at10.28 kHz

Equiripple box 3 db box

Now the circuit must be designed. This requires a 1st order lpf cascaded with a 3rd order lpf.This can be done by cascading the circuit shown in Fig. 6.9.a (page 83) with Fig. 6.11 (page83).

For the 1st order filter, since the dc gain is unity, K=1, pick RF=0 (a wire) and R1 infinity.

Pick C1 0.01μF:=

R11

2 π⋅ a2⋅ fc⋅ C1⋅:= R1 2.885 103

× Ω=

For the 2nd order filter, K=1, pick RF=0 & R3 open ckt.

fo fc a1⋅:= ωo 2 π⋅ fo⋅:= Q b1:=

Pick C1 0.1μF:= C2 0.01 C1⋅:=

R11

2 Q⋅ ωo⋅ C2⋅1 1

4 Q2⋅ C2⋅

C1−+

⎛⎜⎜⎝

⎞⎟⎟⎠

⋅:= R1 9.614 103× Ω= C1 1 10 7−

× F=

R21

2 Q⋅ ωo⋅ C2⋅1 1

4 Q2⋅ C2⋅

C1−−

⎛⎜⎜⎝

⎞⎟⎟⎠

⋅:= R2 297.455 Ω= C2 1 10 9−× F=

-3.5

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1000 104 105

Chebyshev

Gai

n

Frequency

-70

-60

-50

-40

-30

-20

-10

0

10

1000 104 105

Chebyshev

Gai

n

Frequency

φ f( )180π

arg TC f( )( )⋅:=τp f( )

1−

2 π⋅

φ f( )f

⋅:= τg f( )1−

2 π⋅ fφ f( )d

d⎛⎜⎝

⎞⎟⎠

⋅:=

1 103× 1 104× 1 105×0

1 10 3−×

2 10 3−×

3 10 3−×

τp f( )

τg f( )

f

6, Fig 6-14

Second Order Sallen Key BPF

fc 10.28 kHz⋅:= K 1:= Q 5:= j 1−:=fo fc:=

T f( ) K

1Q

j⋅ffo

⋅

jffo

⋅⎛⎜⎝

⎞⎟⎠

2 1Q

j⋅ffo

⋅+ 1+

⋅:= φ f( )180π

arg T f( )( )⋅:=

1 103× 1 104× 1 105×0.01

0.1

1

100−

50−

0

50

100

T f( ) φ f( )

f

R4 3 kΩ⋅:= R5 3 kΩ⋅:= C1 10 nF⋅:= C2 10 nF⋅:= ωo 2 π⋅ fo⋅:=

R1 1.8 kΩ⋅:= R2 1.8 kΩ⋅:= R3 1.8 kΩ⋅:= Ko 1R5

R4+:=

Given

KR2

R1 R2+

Ko R3⋅ C2⋅

R1 R2⋅

R1 R2+

⎛⎜⎝

⎞⎟⎠

C1 C2+( )⋅ R3 C2⋅ 1Ko R1⋅

R1 R2+( )−⎡⎢⎣

⎤⎥⎦

⋅+

⋅=

ωo1

R1 R2⋅

R1 R2+R3⋅ C1⋅ C2⋅

=

Q

R1 R2⋅

R1 R2+R3⋅ C1⋅ C2⋅

R1 R2⋅

R1 R2+

⎛⎜⎝

⎞⎟⎠

C1 C2+( ) R3 C2⋅ 1Ko R1⋅

R1 R2+−

⎛⎜⎝

⎞⎟⎠

⋅+

=

Find R1 R2, R3, ( )1.548 104

×

1.178 103×

2.189 103×

⎛⎜⎜⎜⎜⎝

⎞⎟⎟⎟⎟⎠

Ω=

0.01

0.1

1

103 104 105

Sallen Key BPFG

ain

Frequency

Second Order Infitite Gain Multiple Feedback BPF, page 87, Exp 6

fo 10.28 kHz⋅:= Q 5:= K 1:= ωo 2 π⋅ fo⋅:= j 1−:=

T f( ) K−

1Q

j⋅ffo

⋅

jffo

⋅⎛⎜⎝

⎞⎟⎠

2 1Q

j⋅ffo

⋅+ 1+

:=

1 103× 1 104× 1 105×0.01

0.1

1

T f( )

f

1 103× 1 104× 1 105×

100−

0

100

180 arg T f( )( )⋅

π

fC1 0.01 μF⋅:= C2 C1:= R1 10 kΩ⋅:= R2 240 Ω⋅:= R3 20 kΩ⋅:=

Given

R3 C1⋅

R1 C1 C2+( )⋅K=

1

R1 R2⋅ R3⋅ C1⋅ C2⋅

R1 R2+

ωo=

R3 C1⋅ C2⋅ R1 R2+( )⋅

R1 R2⋅( )C1 C2+

Q=

Find R1 R2, R3, ( )7.741 103

×

157.98

1.548 104×

⎛⎜⎜⎜⎝

⎞⎟⎟⎟⎠

Ω=

0.01

0.1

1

103 104 105

Infinite Gain Multiple Feedback BPF

Gai

n

Frequency

General Bi Quadratic Filter

T s( )

sωo

⎛⎜⎝

⎞⎟⎠

22 α⋅ γ−( )⋅

1Q

sωo

⎛⎜⎝

⎞⎟⎠

⋅ 2 β⋅ γ−( )⋅+ γ+

sωo

⎛⎜⎝

⎞⎟⎠

2 1Q

sωo⋅+ 1+

⎡⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎦

=

fo 10.28kHz:= N 2000:= i 0 N 1−..:= fstart 1kHz:= j 1−:=

fstop 100kHz:=

f i fstartfstopfstart

⎛⎜⎝

⎞⎟⎠

i

N 1−

⋅:=

Allpass

Q 3:= α 1:= β 0:= γ 1:=

T f( )

ffo

j⋅⎛⎜⎝

⎞⎟⎠

22 α⋅ γ−( )⋅

1Q

j f⋅fo

⎛⎜⎝

⎞⎟⎠

⋅ 2 β⋅ γ−( )⋅+ γ+

jffo

⎛⎜⎝

⎞⎟⎠

2 1Q

j f⋅fo

⋅+ 1+

:=

1 103× 1 104× 1 105×0.1

1

10

T fi( )

fi1 103× 1 104× 1 105×

100−

0

100

180arg T fi( )( )

π⋅

fi

Notch α 1:= β 0.5:= γ 1:= Q 3:= fo 10.28kHz:=

T f( )

ffo

j⋅⎛⎜⎝

⎞⎟⎠

22 α⋅ γ−( )⋅

1Q

j f⋅fo

⎛⎜⎝

⎞⎟⎠

⋅ 2 β⋅ γ−( )⋅+ γ+

jffo

⎛⎜⎝

⎞⎟⎠

2 1Q

j f⋅fo

⋅+ 1+

:=

1 103× 1 104× 1 105×

50−

0

50

180arg T fi( )( )

π⋅

f i1 103× 1 104× 1 105×

0.1

1

10

T fi( )

fi

Bandpass α 0:= β 0.5:= γ 0:= fo 10.28kHz:= Q 3:=

T f( )

ffo

j⋅⎛⎜⎝

⎞⎟⎠

22 α⋅ γ−( )⋅

1Q

j f⋅fo

⎛⎜⎝

⎞⎟⎠

⋅ 2 β⋅ γ−( )⋅+ γ+

jffo

⎛⎜⎝

⎞⎟⎠

2 1Q

j f⋅fo

⋅+ 1+

:=

1 103× 1 104× 1 105×0.1

1

10

T fi( )

fi

1 103× 1 104× 1 105×

50−

0

50

180arg T fi( )( )

π⋅

f i

Highpass α 0.5:= β 0:= γ 0:= fo 10.28kHz:= Q 3:=

T f( )

ffo

j⋅⎛⎜⎝

⎞⎟⎠

22 α⋅ γ−( )⋅

1Q

j f⋅fo

⎛⎜⎝

⎞⎟⎠

⋅ 2 β⋅ γ−( )⋅+ γ+

jffo

⎛⎜⎝

⎞⎟⎠

2 1Q

j f⋅fo

⋅+ 1+

:=

1 103× 1 104× 1 105×0.1

1

10

T fi( )

fi1 103× 1 104× 1 105×0

50

100

150

180arg T fi( )( )

π⋅

f i

Lowpass α 0.5:= β 0.5:= γ 1:= fo 10.28kHz:= Q 3:=

T f( )

ffo

j⋅⎛⎜⎝

⎞⎟⎠

22 α⋅ γ−( )⋅

1Q

j f⋅fo

⎛⎜⎝

⎞⎟⎠

⋅ 2 β⋅ γ−( )⋅+ γ+

jffo

⎛⎜⎝

⎞⎟⎠

2 1Q

j f⋅fo

⋅+ 1+

:=

1 103× 1 104× 1 105×0.1

1

10

T fi( )

fi1 103× 1 104× 1 105×

150−

100−

50−

0

180arg T fi( )( )

π⋅

fi

Third Order Elliptic Filter with 0.5 db ripple unity dc gain with stop band to cutoff ratio of 1.5

with a min attenuation in the stop band of 21.9 dB from page 79 in the lab manual

T s( )1

s0.76695ωc

1+

s1.6751 ωc⋅

⎛⎜⎝

⎞⎟⎠

21+

s1.0720 ωc⋅

⎛⎜⎝

⎞⎟⎠

2 12.3672

s1.0720 ωc⋅⋅+ 1+

⋅=

this requires that a first order filter be cascaded with a bi quad

for a notch at fp this means

fc 10.28kHz:= γ 1:= β12

:= fo 1.072 fc⋅:=

α

γ1.0721.6751

⎛⎜⎝

⎞⎟⎠

2+

20.705=:= Q 2.3672:=

T2 f( )

ffo

j⋅⎛⎜⎝

⎞⎟⎠

22 α⋅ γ−( )⋅

1Q

j f⋅fo

⎛⎜⎝

⎞⎟⎠

⋅ 2 β⋅ γ−( )⋅+ γ+

jffo

⎛⎜⎝

⎞⎟⎠

2 1Q

j f⋅fo

⋅+ 1+

:=

for the first order filterf1 0.7669 fc⋅:=

T1 f( )1

1 jff1⋅+

:=T f( ) T1 f( ) T2 f( )⋅:=

1 103× 1 104× 1 105×

0.2

0.4

0.6

0.8

T fi( )

fi

φ f( )180π

arg T f( )( )⋅:=

τg f( )1

2 π⋅−

fφ f( )d

d⎛⎜⎝

⎞⎟⎠

⋅:=

τp f( )φ f( )2 π⋅ f⋅

−:=

M f( ) 20 log T f( )( )⋅:=

1 103× 1 104× 1 105×30−

20−

10−

0

200−

100−

0

100

200

M fi( ) φ f(

fi

φ f( )180π

arg T f( )( )⋅:=τp f( )

φ f( )2 π⋅ f⋅

−:=

τg f( )1

2 π⋅−

fφ f( )d

d⎛⎜⎝

⎞⎟⎠

⋅:=

1 103× 1 104× 1 105×3−

2−

1−

0

1

2

4− 10 3−×

2− 10 3−×

0

2 10 3−×

4 10 3−×

6 10 3−×

M fi( )

fi

Third Order Bessel Filter f3 10.28kHz:=fc

f31.7557

:=

a2 2.3222:= a1 2.5415:= b1 0.69105:=

T f( )1

jf

a2 fc⋅⋅ 1+

1

jf

a1 fc⋅⋅⎛⎜

⎝⎞⎟⎠

2 1b1

j⋅f

a1 fc⋅⋅+ 1+

⋅:=

M f( ) 20 log T f( )( )⋅:= φ f( )180π

arg T f( )( )⋅:=

φ f( )180π

arg T f( )( )⋅:=τp f( )

φ f( )2 π⋅ f⋅

−:=

τg f( )1

2 π⋅−

fφ f( )d

d⎛⎜⎝

⎞⎟⎠

⋅:=

1 103× 1 104× 1 105×3−

2−

1−

0

1

2

2− 10−×

1− 10−×

0

1 10 3−×

2 10 3−×

M fi( )

fi

n 3=f3fc

1.7557= a1 2.5415:= b1 0.69105:=

a2 2.3222:=

T s( )1

sa2 ωc⋅

1+

1

sa1 ωc⋅

⎛⎜⎝

⎞⎟⎠

2 1b1

sa1 ωc⋅⋅+ 1+

⋅= 1st Order LPF2nd Order LPF

f3 10.28kHz:= fcf3

1.7557:= ωc 2 π⋅ fc⋅:=

C3 1nF:= R31

a2 ωc⋅ C3⋅1.171 104

× Ω=:=

Use Sallen Key

C1 0.01μF:= C2 0.1 C1⋅:=

R11

2 b1⋅ a1⋅ ωc⋅ C2⋅1 1 4 b1

2⋅

C2C1⋅−+

⎛⎜⎜⎝

⎞⎟⎟⎠

⋅ 1.47 104× Ω=:=

R21

2 b1⋅ a1⋅ ωc⋅ C2⋅1 1 4 b1

2⋅

C2C1⋅−−

⎛⎜⎜⎝

⎞⎟⎟⎠

⋅ 778.221 Ω=:=

5

5

4

4

3

3

2

2

1

1

D D

C C

B B

A A

0 0

00

Title

Size Document Number Rev

Date: Sheet of

Active Filters 1

Third Order Elliptic Filter

A

1 1Tuesday, March 11, 2008

Title


Date: Sheet of

Active Filters 1


A


Title


Date: Sheet of

Active Filters 1


A



V

R2

14.44k

R2

14.44k

C10.295nC10.295n

R3

14.44k

R3

14.44k

C2

1n

C2

1n

R4

68.4k

R4

68.4k

U1

OPAMP

U1

OPAMP

+

-

OUTC3

0.705n

C3

0.705n

R568.4kR568.4k

R8

20.2k

R8

20.2k

U2

OPAMP

U2

OPAMP

+

-

OUT

V11Vac0Vdc

V11Vac0Vdc

U3

OPAMP

U3

OPAMP

+

-

OUT

R7

14.44k

R7

14.44k

R1

14.44k

R1

14.44kC41nC41n

Date/Time run: 03/23/08 10:30:41** Profile: "SCHEMATIC1-sweep" [ G:\brewdoc\ece3042hwk\WA2_Sprg08_Filter\Elliptic\elliptic-pspicefiles\s...

Temperature: 27.0

Date: March 23, 2008 Page 1 Time: 10:33:44

(A) sweep (active)

Frequency

1.0KHz 3.0KHz 10KHz 30KHz 100KHzV(R2:2)

0V

0.2V

0.4V

0.6V

0.8V

1.0V

Goal CutOff Frequency=10.28k


(10.261K,945.407m)

(5.8374K,943.807m)

(17.219K,5.8725m)


Temperature: 27.0


(A) sweep (active)

Frequency

1.0KHz 3.0KHz 10KHz 30KHz 100KHzdb(V(R2:2))

-50

-40

-30

-20

-10

0

10

(10.286K,-519.469m)

(5.7033K,-503.150m)

(17.378K,-46.230)

(26.975K,-21.928)



Temperature: 27.0


(A) sweep (active)

Frequency

1.0KHz 3.0KHz 10KHz 30KHz 100KHz-(P(V(R2:2))/Frequency)*(PI/180)/(2*PI) G(V(R2:2))

0

20u

40u

60u

80u

100u

(1.6090K,25.867u)

(10.290K,73.578u)

(10.290K,33.617u)

Phase and Group Delays for 3rd Order Elliptic Filter

Group Delay

Phase Delay

5

5

4

4

3

3

2

2

1

1

D D

C C

B B

A A

0

00

Title


Date: Sheet of

Active Filters 1

Third Order Bessel Filter

A

1 1Wednesday, March 12, 2008

Title


Date: Sheet of

Active Filters 1


A


Title


Date: Sheet of

Active Filters 1


A



V

R3

11.71k

R3

11.71k

C1

0.01u

C1

0.01u

U1

OPAMP

U1

OPAMP

+

-

OUT

C21nC21n

U2

OPAMP

U2

OPAMP

+

-

OUTC31nC31n

V11Vac0Vdc

V11Vac0Vdc

R1

14.7k

R1

14.7k

R2

778.221

R2

778.221

Date/Time run: 03/23/08 11:04:29** Profile: "SCHEMATIC1-sweep" [ G:\brewdoc\ece3042hwk\WA2_Sprg08_Filter\Bessel\bessel-pspicefiles\schem...

Temperature: 27.0


(A) sweep (active)

Frequency

1.0KHz 3.0KHz 10KHz 30KHz 100KHzDB(V(U2:OUT))

-60

-50

-40

-30

-20

-10

0


(10.286K,-3.0162)

Date/Time run: 03/23/08 11:04:29** Profile: "SCHEMATIC1-sweep" [ G:\brewdoc\ece3042hwk\WA2_Sprg08_Filter\Bessel\bessel-pspicefiles\schem...

Temperature: 27.0


(A) sweep (active)

Frequency

1.0KHz 3.0KHz 10KHz 30KHz 100KHz(P(V(U2:OUT))/Frequency)*(PI/180)*(-1/(2*PI)) G(V(U2:OUT))

0

10u

20u

30u

40u

Third Order Bessel FilterGroup Delay

Phase Delay

(10.289K,25.407u)

(10.289K,26.885u)(1.5565K,27.188u)

Georgia Institute of Technology

School of Electrical and Computer Engineering

ECE 3042 Microelectronic Circuits Laboratory Verification Sheet

NAME:________________________________________ SECTION:___________________________

GT NUMBER:___________________________________ GTID:______________________________

Experiment 6: Op‐Amp Active Filters

Procedure Time Completed Date Completed Verification (Must demonstrate

circuit)

Points Possible

Points Received

1. Third‐Order Butterworth LPF

16

2. Third‐Order Chebyshev LPF

16

3. Second‐Order Band‐Pass

16

4. Second‐Order Notch

16

5. First‐Order All‐Pass 16

6. Second‐Order All‐Pass

20

Enter your critical frequency below:

fcrit

To be permitted to complete the experiment during the open lab hours, you must complete at least three procedures during your scheduled lab period or spend your entire scheduled lab session attempting to do so. A signature below by your lab instructor, Dr. Brewer, or Dr. Robinson permits you to attend the open lab hours to complete the experiment and receive full credit on the report. Without this signature, you may use the open lab to perform the experiment at a 50% penalty.

SIGNATURE:____________________________________ DATE:____________________________________

ECE 3042 Check‐off Requirements for Experiment 6 Make sure you have made all required measurements before requesting a check‐off. For all check‐offs, you must demonstrate the circuit or measurement to a lab instructor. All screen captures must have a time/date stamp. Do not follow the procedures in the lab manual. Only Bode magnitude plots are required—it is not necessary to measure the phase. Do not follow the lab report format for this experiment. Instead, display two Bode plots and their associated tables per page. 1. Third‐Order Butterworth Low‐Pass Filter

Bode gain magnitude plot over frequency range of 100Hz to 100khz. Measurement of dc gain and ‐3dB frequency. Table comparing these measured values to the design specifications. Show percent error.

2. Third‐Order Chebyshev Low‐Pass Filter Bode gain magnitude plot over frequency range of 100Hz to 100khz. Measurement of dc gain, dB ripple, and ‐3dB frequency. Table comparing these measured values to the design specifications. Show percent error.

3. Second‐Order Bandpass Filter Bode gain magnitude plot over frequency range of 100Hz to 100khz. Measurement of center frequency fo, ‐3dB bandwidth BW, and Q. Q is given by fo /BW. Table comparing these measured values to the design specifications. Show percent error.

4. Second‐Order Notch Filter

• Implement filter with the general biquad circuit from the class notes. Save this filter—it can be modified to obtain the second‐order all‐pass transfer function.

Bode gain magnitude plot over frequency range of 100Hz to 100khz. Measurement of center frequency fo, ‐3dB bandwidth BW, and Q. Q is given by fo/BW. Table comparing these measured values to the design specifications. Show percent error.

5. First‐Order All‐Pass Filter Bode gain magnitude plot over frequency range of 100Hz to 100khz. Measurement of dc gain. Scope screen capture showing measured fcrit, the frequency at which the phase shift between input and output is 90 deg. Connect input to ch1 and output to ch2. Display measured Vpp for each channel, the frequency, and the phase.

Table comparing these measured values to the design specifications. Show percent error. 6. Second‐Order All‐Pass Filter

Bode gain magnitude plot over frequency range of 100Hz to 100khz. Measurement of dc gain. Scope screen capture showing measured fcrit, the frequency at which the phase shift between input and output is 180 deg. Connect input to ch1 and output to ch2. Display measured Vpp for each channel, the frequency, and the phase.

Table comparing these measured values to the design specifications. Show percent error.

ece 3042 experiment 6 active filter...

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