ECE 3042
1.
Experiment 6 Active Filter Design
Design a 3rd order Butterworth low-pass filters having a dc gain of unity
and a cutoff frequency, fc, of 10.28 kHz.
fc := 10.28kHz
K := 1
1
TB( f ) := K⋅
j⋅
f
fc
1
⋅
+1
2
⎛j ⋅ f ⎞ + j ⋅ f + 1
⎜ f⎟
fc
⎝ c⎠
−1
This is the product of a 1st order LPF & 2nd order
LPF.
10
1.4
1
1.2
0.1
TB( f )
j :=
The transfer function is given on page 72
TB( f )
0.01
1
0.8
−3
1× 10
0.6
−4
1× 10
3
1× 10
4
5
1× 10
1× 10
3
3
2× 10
6
1× 10
4
6× 10
1× 10
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 resistor
from 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 are
the same.
1
3
So for the circuit on page 82
C := 0.01μF
R1 :=
R1 = 1.548 × 10 Ω
⋅
⋅
C
2
⋅
π
f
c
This is a 1st order LPF
For the circuit shown on page 83, the 2nd order LPF, pick
then Eq. 6.84 applies with Q=1 and ωo=ωc
Q := 1
R1 :=
⎛
1
2 ⋅ Q⋅ ωo⋅ C2
⋅⎜1 +
4
⎝
R1 = 1.374 × 10 Ω
2 C2 ⎞
1 − 4⋅ Q
⎟
C1 ⎠
R2 :=
3
R2 = 1.745 × 10 Ω
C1 := 0.01μF
C2 := 0.1C1
ωo := 2 ⋅ π⋅ fc
1
2 ⋅ Q⋅ ωo⋅ C2
⎛
⋅⎜1 −
⎝
−8
C1 = 1 × 10
2 C2 ⎞
1 − 4⋅ Q
F
⎟
C1 ⎠
−9
C2 = 1 × 10
Now that all of the component values have been determined it's time to simulate it with
SPICE
F
Butterworth Filter
10
Gain (Linear)
1
0.1
0.01
0.001
10
3
4
10
Frequency (Hz)
10
5
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 reasonably
close to the design values.
180
φ( f ) :=
π
⋅ arg( TB( f ) )
τp( f ) :=
−1 φ( f )
⋅
2⋅ π f
τg( f ) :=
−3
2× 10
τ p( f )
τ g( f )
−3
1× 10
0
3
1× 10
4
1× 10
f
5
1× 10
⎛ d φ( f ) ⎞
⎟
2 ⋅ π ⎝ df
⎠
−1
⋅⎜
2. Design a 3rd order unity dc gain Chebyshev LPF with a -3 frequency of 10.28 kHz and 0.5
db ripple in the pass band.
db := 0.5
f3 := 10.28kHz
K := 1
3
n := 3
t3( x) := 4⋅ x − 3⋅ x
j :=
−1
db
ε :=
10
−1
Eq. 6.47 must be solved to obtain the relationship between ωc & ω3
which requires that Eq. 6.46 be solved which is a cubic polynomial g(x)
3
1
10
g ( x) := 4⋅ x − 3⋅ x −
⎛
⎜
⎜
v := ⎜
⎜
⎜
⎝
Since t3(0)=0 To solve this form the vector v
ε
⎞
⎟
⎟
−3 ⎟
0 ⎟
⎟
4 ⎠
−1
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.
ε
Since this is a cubic polynomial it will have at least one real root
and its the one required.
⎛ −0.584 − 0.522i ⎞
u = ⎜ −0.584 + 0.522i⎟
⎜
⎟
1.167
⎝
⎠
u := polyroots ( v )
fc :=
f3
31
fc = 8.805 × 10
x
h
1−h
a1 :=
2
1−h
a2 = 0.626
TC( f ) := K⋅
ε = 0.349
1
2
− ( sin ( θ1) )
a1 = 1.069
1
⋅
2
b 1 :=
b 1 = 1.706
1
2
⎤
1 j⋅ f
+ 1 ⎡⎛ j⋅ f ⎞
⎢
+
⋅
+
1
⎥
a2⋅ fc
⎜
⎟
b 1 a1⋅ fc
⎣⎝ a1⋅ fc ⎠
⎦
j⋅ f
x = 1.167
2, 0
The transfer function is Eq. 6.56 which
requires h, a2, a1, & b1
s
1
1
h := tanh ⎛⎜ ⋅ asinh ⎛⎜ ⎞⎟ ⎞⎟
⎝n
⎝ ε ⎠⎠
a2 :=
x := u
h = 0.531
1
2
⋅ 1+
θ1 :=
1 π
⋅
3 2
1
(h⋅ tan (θ1)) 2
The transfer function then becomes
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
0
1
−1
0.5
y( f )
y( f ) − 2
0
−3
− 0.5
−1
100
3
−4
3
1× 10
4
1× 10
1× 10
4
1× 10
f
f
Equiripple box
3 db box
5
1× 10
Note that it is
3 dB down at
10.28 kHz
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 (page
83).
For the 1st order filter, since the dc gain is unity, K=1, pick RF=0 (a wire) and R1 infinity.
C1 := 0.01μF
Pick
R1 :=
1
3
R1 = 2.885 × 10 Ω
2 ⋅ π⋅ a2⋅ fc⋅ C1
For the 2nd order filter, K=1, pick RF=0 & R3 open ckt.
fo := fc⋅ a1
Pick
ωo := 2 ⋅ π⋅ fo
C1 := 0.1μF
Q := b 1
C2 := 0.01⋅ C1
2
⎛
⎞
4 ⋅ Q ⋅ C2 ⎟
⎜
R1 :=
⋅ 1+ 1−
C1 ⎟⎠
2 ⋅ Q⋅ ωo⋅ C2 ⎜⎝
1
R2 :=
1
2 ⋅ Q⋅ ωo⋅ C2
⎛
⎜
⋅⎜1 −
⎝
1−
2
⎞
C1
⎟
⎠
4 ⋅ Q ⋅ C2 ⎟
−7
R1 = 9.614 × 10 Ω
3
C1 = 1 × 10
R2 = 297.455 Ω
C2 = 1 × 10
−9
F
F
C hebyshev
0.5
0
-0.5
G ain
-1
-1.5
-2
-2.5
-3
-3.5
1000
4
10
Frequency
10
5
C hebyshev
10
0
-10
G ain
-20
-30
-40
-50
-60
-70
4
1000
180
φ( f ) :=
π
⋅ arg( TC( f ) )
10
Frequency
τp( f ) :=
−1 φ( f )
⋅
2⋅ π f
10
τg( f ) :=
−3
3× 10
τ p( f )
τ g( f )
−3
2× 10
−3
1× 10
0
3
1× 10
4
1× 10
f
5
1× 10
5
⎛ d φ( f ) ⎞
⎟
2 ⋅ π ⎝ df
⎠
−1
⋅⎜
Page 86, Fig 6-14
Second Order Sallen Key BPF
fc := 10.28 ⋅ kHz
K := 1
1
Q
T( f ) := K⋅
2
⋅j ⋅
Q := 5
fo := fc
1
−1
f
fo
φ( f ) :=
⎛j ⋅ ⎞ + ⋅j ⋅ + 1
⎜ f ⎟
Q fo
⎝ o⎠
f
j :=
f
180
π
⋅ arg( T( f ) )
1
100
50
T( f )
0.1
0
φ( f )
− 50
0.01
3
1× 10
− 100
5
1× 10
4
1× 10
f
R4 := 3 ⋅ kΩ
R5 := 3 ⋅ kΩ C1 := 10⋅ nF
R1 := 1.8⋅ kΩ
R2 := 1.8⋅ kΩ
R3 := 1.8⋅ kΩ
C2 := 10⋅ nF
ωo := 2 ⋅ π⋅ fo
Ko := 1 +
Given
K=
R2
R1 + R2
⋅
Ko⋅ R3⋅ C2
Ko⋅ R1 ⎤
⎛ R 1⋅ R 2 ⎞
⎡
⎜ + R ⎟ ⋅ ( C1 + C2) + R3⋅ C2⋅ ⎢1 −
⎥
2⎠
⎝ R1
⎣ ( R 1 + R 2) ⎦
R5
R4
ωo =
1
R1⋅ R2
R1 + R2
⋅ R3⋅ C1⋅ C2
R1⋅ R2
Q=
R1 + R2
⋅ R3⋅ C1⋅ C2
Ko⋅ R1 ⎞
⎛ R 1⋅ R 2 ⎞
⎛
⎜ + R ⎟ ( C1 + C2) + R3⋅ C2⋅ ⎜ 1 −
⎟
R1 + R2 ⎠
2⎠
⎝ R1
⎝
⎛ 1.548 × 104 ⎞
⎜
⎟
⎜
3
Find( R1 , R2 , R3) = 1.178 × 10 ⎟ Ω
⎜
⎟
⎜
3⎟
⎝ 2.189 × 10 ⎠
Sallen Key BPF
G ain
1
0.1
0.01
10
3
4
10
Frequency
10
5
Second Order Infitite Gain Multiple Feedback BPF, page 87, Exp 6
fo := 10.28 ⋅ kHz
Q := 5
1
Q
T( f ) := −K
⋅j ⋅
K := 1
ωo := 2 ⋅ π⋅ fo
j :=
−1
f
fo
2
⎛j ⋅ f ⎞ + 1 ⋅j ⋅ f + 1
⎜ f ⎟
Q fo
⎝ o⎠
1
100
180⋅ arg( T( f ) )
T( f )
0.1
π
0
− 100
0.01
3
1× 10
4
5
1× 10
R1 := 10⋅ kΩ
R2 := 240 ⋅ Ω
1× 10
1× 10
3
f
C1 := 0.01⋅ μF
f
C2 := C1
Given
R 3⋅ C 1
R1⋅ ( C1 + C2)
4
1× 10
=K
1
R1⋅ R2⋅ R3⋅ C1⋅ C2
= ωo
R1 + R2
R3⋅ C1⋅ C2⋅ ( R1 + R2)
(R1⋅ R2)
C1 + C2
=Q
⎛ 7.741 × 103 ⎞
⎜
⎟
Find( R1 , R2 , R3) = ⎜ 157.98 ⎟ Ω
⎜
4⎟
⎝ 1.548 × 10 ⎠
R3 := 20⋅ kΩ
5
1× 10
Infinite Gain M ultiple Feedback BPF
G ain
1
0.1
0.01
10
3
4
10
Frequency
10
5
General Bi Quadratic Filter
⎡⎛ s ⎞2
1
s ⎞
⎢
⋅ ( 2 ⋅ α − γ) + ⋅ ⎛⎜
⋅ ( 2 ⋅ β − γ) +
⎜
⎟
Q ωo ⎟
⎢ ⎝ ωo ⎠
⎝
⎠
T( s) = ⎢
2
⎢
⎛ s ⎞ + 1⋅ s + 1
⎜ω ⎟
⎢
Q ωo
⎣
⎝ o⎠
fo := 10.28kHz
N := 2000
i := 0 .. N − 1
fstop := 100kHz
i
⎛ fstop ⎞
f := fstart⋅ ⎜
⎟
i
⎝ fstart ⎠
N− 1
Allpass
Q := 3
α := 1
β := 0
2
⎤
γ⎥
γ := 1
⎛ f ⋅ j ⎞ ⋅ ( 2 ⋅ α − γ) + 1 ⋅ ⎛ j ⋅ f ⎞ ⋅ ( 2 ⋅ β − γ) + γ
⎜f ⎟
Q ⎜ fo ⎟
⎝ o ⎠
⎝ ⎠
T( f ) :=
2
⎛j f ⎞ + 1 ⋅ j ⋅f + 1
⎜ f ⎟
Q fo
⎝ o⎠
⎥
⎥
⎥
⎥
⎦
fstart := 1kHz
j :=
−1
10
100
T( f i)
1
180⋅
arg( T( f i) )
0
π
− 100
0.1
3
1× 10
4
5
1× 10
1× 10
3
4
1× 10
fi
1× 10
1× 10
fi
α := 1
Notch
β := 0.5
γ := 1
Q := 3
fo := 10.28kHz
2
⎛ f ⋅ j ⎞ ⋅ ( 2 ⋅ α − γ) + 1 ⋅ ⎛ j ⋅ f ⎞ ⋅ ( 2 ⋅ β − γ) + γ
⎜f ⎟
Q ⎜ fo ⎟
⎝ o ⎠
⎝ ⎠
T( f ) :=
2
⎛j f ⎞ + 1 ⋅ j ⋅f + 1
⎜ f ⎟
Q fo
⎝ o⎠
10
50
180⋅
T( f i)
arg( T( f i) )
π
1
0
− 50
0.1
3
1× 10
3
4
1× 10
1× 10
5
1× 10
4
1× 10
5
1× 10
fi
fi
Bandpass
α := 0
β := 0.5
γ := 0
fo := 10.28kHz
Q := 3
5
2
⎛ f ⋅ j ⎞ ⋅ ( 2 ⋅ α − γ) + 1 ⋅ ⎛ j ⋅ f ⎞ ⋅ ( 2 ⋅ β − γ) + γ
⎜f ⎟
Q ⎜ fo ⎟
⎝ o ⎠
⎝ ⎠
T( f ) :=
2
⎛j f ⎞ + 1 ⋅ j ⋅f + 1
⎜ f ⎟
Q fo
⎝ o⎠
10
50
T( f i)
180⋅
1
arg( T( f i) )
0
π
− 50
0.1
3
1× 10
4
5
1× 10
3
1× 10
1× 10
4
1× 10
fi
Highpass
α := 0.5
5
1× 10
fi
β := 0
γ := 0
fo := 10.28kHz
Q := 3
2
⎛ f ⋅ j ⎞ ⋅ ( 2 ⋅ α − γ) + 1 ⋅ ⎛ j ⋅ f ⎞ ⋅ ( 2 ⋅ β − γ) + γ
⎜f ⎟
Q ⎜ fo ⎟
⎝ o ⎠
⎝ ⎠
T( f ) :=
2
⎛j f ⎞ + 1 ⋅ j ⋅f + 1
⎜ f ⎟
Q fo
⎝ o⎠
10
150
T( f i)
1
0.1
3
1× 10
180⋅
4
1× 10
fi
5
1× 10
arg( T( f i) ) 100
π
50
0
3
1× 10
4
1× 10
fi
5
1× 10
α := 0.5 β := 0.5 γ := 1
Lowpass
fo := 10.28kHz
Q := 3
2
⎛ f ⋅ j ⎞ ⋅ ( 2 ⋅ α − γ) + 1 ⋅ ⎛ j ⋅ f ⎞ ⋅ ( 2 ⋅ β − γ) + γ
⎜f ⎟
Q ⎜ fo ⎟
o ⎠
⎝
⎝ ⎠
T( f ) :=
2
⎛j f ⎞ + 1 ⋅ j ⋅f + 1
⎜ f ⎟
Q fo
⎝ o⎠
10
0
T( f i)
1
180⋅
arg( T( f i) )
π
0.1
3
1× 10
− 50
− 100
− 150
4
5
1× 10
1× 10
3
1× 10
fi
4
1× 10
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
2
T( s) =
1
s
0.76695ωc
⋅
+1
s
⎞
⎛
⎜ 1.6751⋅ ω ⎟ + 1
c⎠
⎝
2
s
1
s
⎛
⎞
⎜ 1.0720⋅ ω ⎟ + 2.3672 ⋅ 1.0720⋅ ω + 1
c⎠
c
⎝
1× 10
5
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
β :=
1
fo := 1.072 ⋅ fc
2
2
γ+
α :=
⎛ 1.072 ⎞
⎜
⎟
⎝ 1.6751 ⎠ = 0.705
Q := 2.3672
2
2
⎛ f ⋅ j ⎞ ⋅ ( 2 ⋅ α − γ) + 1 ⋅ ⎛ j ⋅ f ⎞ ⋅ ( 2 ⋅ β − γ) + γ
⎜f ⎟
Q ⎜ fo ⎟
⎝ o ⎠
⎝ ⎠
T2 ( f ) :=
2
⎛j f ⎞ + 1 ⋅ j ⋅f + 1
⎜ f ⎟
Q fo
⎝ o⎠
for the first order filter
T1 ( f ) :=
f1 := 0.7669⋅ fc
1
1 + j⋅
f
T( f ) := T1 ( f ) ⋅ T2 ( f )
f1
0.8
T( f i)
φ( f ) :=
0.6
180
π
⋅ arg( T( f ) )
1 ⎛d
⎞
τg ( f ) := −
⋅ ⎜ φ( f ) ⎟
2 ⋅ π ⎝ df
⎠
0.4
0.2
3
1× 10
4
1× 10
fi
5
1× 10
φ( f )
τp ( f ) := −
2 ⋅ π⋅ f
M ( f ) := 20⋅ log( T( f )
)
200
0
100
− 10
M( f i)
0
− 20
− 100
− 30
3
1× 10
4
1× 10
fi
φ( f ) :=
180
π
⋅ arg( T( f ) )
1 ⎛d
⎞
τg ( f ) := −
⋅ ⎜ φ( f ) ⎟
2 ⋅ π ⎝ df
⎠
φ( f )
τp ( f ) := −
2 ⋅ π⋅ f
− 200
5
1× 10
φ( f
−3
2
6× 10
1
4× 10
0
2× 10
−3
−3
M( f i)
−1
0
−2
− 2× 10
−3
3
1× 10
− 4× 10
5
1× 10
4
1× 10
fi
Third Order Bessel Filter
a2 := 2.3222
f3 := 10.28kHz
a1 := 2.5415
f3
fc :=
1.7557
b 1 := 0.69105
−3
−3
1
T( f ) :=
j⋅
f
a2 ⋅ fc
1
⋅
+1
⎛j ⋅ f ⎞ + 1 ⋅j ⋅ f + 1
⎜ a ⋅f ⎟
b 1 a1 ⋅ fc
⎝ 1 c⎠
M ( f ) := 20⋅ log( T( f )
φ( f ) :=
180
π
2
)
⋅ arg( T( f ) )
1 ⎛d
⎞
τg ( f ) := −
⋅ ⎜ φ( f ) ⎟
2 ⋅ π ⎝ df
⎠
φ( f ) :=
180
π
⋅ arg( T( f ) )
φ( f )
τp ( f ) := −
2 ⋅ π⋅ f
2
2× 10
−3
1× 10
−3
1
0
M( f i)
0
−1
− 1× 10
−
− 2× 10
5
1× 10
−
−2
−3
3
1× 10
1× 10
4
fi
f3
n=3
fc
a1 := 2.5415
= 1.7557
b 1 := 0.69105
a2 := 2.3222
1
T( s) =
s
a2 ⋅ ωc
1
⋅
+1
⎛ s ⎞ + 1 ⋅ s +1
⎜ a ⋅ω ⎟
b 1 a1 ⋅ ωc
⎝ 1 c⎠
f3
fc :=
1.7557
f3 := 10.28kHz
C3 := 1nF
1st Order LPF
2nd Order LPF
2
R3 :=
1
a2 ⋅ ωc⋅ C3
ωc := 2 ⋅ π⋅ fc
4
= 1.171 × 10 Ω
Use Sallen Key
C1 := 0.01μF
C2 := 0.1⋅ C1
R1 :=
⎛
2 ⋅ b 1 ⋅ a1 ⋅ ωc⋅ C2 ⎜
⎝
2 C2 ⎞
⎟ = 1.47 × 104 Ω
1 − 4⋅ b1 ⋅
C1 ⎟
⎠
R2 :=
⎛
2 ⋅ b 1 ⋅ a1 ⋅ ωc⋅ C2 ⎜
⎝
2 C2 ⎞
⎟ = 778.221 Ω
1 − 4⋅ b1 ⋅
C1 ⎟
⎠
1
1
⋅⎜1 +
⋅⎜1 −
5
4
3
2
1
R7
D
D
14.44k
U1
+
C3
R8
0.705n
U3
+
V1
20.2k
C4
1n
1Vac
0Vdc
C
0
OUT
-
R4
R1
68.4k
14.44k
C2
OPAMP
V
R2
R3
14.44k
14.44k
OUT
-
1n
OPAMP
R5
68.4k
0
C1
0.295n
OPAMP
-
C
OUT
0
+
U2
0
B
B
Third Order Elliptic Filter
A
A
Title
Third Order Elliptic Filter
Size
A
Date:
5
4
3
Document Number
Active Filters
Tuesday, March 11, 2008
2
Rev
1
Sheet
1
of
1
1
** Profile: "SCHEMATIC1-sweep" [ G:\brewdoc\ece3042hwk\WA2_Sprg08_Filter\Elliptic\elliptic-pspicefiles\s...
Date/Time run: 03/23/08 10:30:41
Temperature: 27.0
(A) sweep (active)
1.0V
(10.261K,945.407m)
(5.8374K,943.807m)
0.8V
0.6V
Third Order Elliptic Filter
Goal CutOff Frequency=10.28k
0.4V
0.2V
(17.219K,5.8725m)
0V
1.0KHz
V(R2:2)
Date: March 23, 2008
3.0KHz
10KHz
Frequency
Page 1
30KHz
100KHz
Time: 10:33:44
** Profile: "SCHEMATIC1-sweep" [ G:\brewdoc\ece3042hwk\WA2_Sprg08_Filter\Elliptic\elliptic-pspicefiles\s...
Date/Time run: 03/23/08 10:30:41
Temperature: 27.0
(A) sweep (active)
10
(10.286K,-519.469m)
0
Third Order Elliptic Filter
(5.7033K,-503.150m)
-10
(26.975K,-21.928)
-20
-30
(17.378K,-46.230)
-40
-50
1.0KHz
db(V(R2:2))
Date: March 23, 2008
3.0KHz
10KHz
Frequency
Page 1
30KHz
100KHz
Time: 10:39:27
** Profile: "SCHEMATIC1-sweep" [ G:\brewdoc\ece3042hwk\WA2_Sprg08_Filter\Elliptic\elliptic-pspicefiles\s...
Date/Time run: 03/23/08 10:40:03
Temperature: 27.0
(A) sweep (active)
100u
Phase and Group Delays for 3rd Order Elliptic Filter
80u
(10.290K,73.578u)
Group Delay
60u
40u
(1.6090K,25.867u)
Phase Delay
20u
(10.290K,33.617u)
0
1.0KHz
3.0KHz
-(P(V(R2:2))/Frequency)*(PI/180)/(2*PI)
Date: March 23, 2008
10KHz
G(V(R2:2))
Frequency
Page 1
30KHz
100KHz
Time: 10:57:50
5
4
3
2
1
D
D
C1
0.01u
R3
U1
+
R1
11.71k
R2
U2
OUT
V1
1Vac
0Vdc
C3
1n
+
14.7k
-
778.221
OUT
OPAMP
C
-
0
OPAMP
C
V
C2
1n
0
0
B
B
Third Order Bessel Filter
A
A
Title
Third Order Bessel Filter
Size
A
Date:
5
4
3
Document Number
Active Filters
Wednesday, March 12, 2008
2
Rev
1
Sheet
1
of
1
1
** Profile: "SCHEMATIC1-sweep" [ G:\brewdoc\ece3042hwk\WA2_Sprg08_Filter\Bessel\bessel-pspicefiles\schem...
Date/Time run: 03/23/08 11:04:29
Temperature: 27.0
(A) sweep (active)
0
-10
(10.286K,-3.0162)
-20
-30
Third Order Bessel Filter
-40
-50
-60
1.0KHz
DB(V(U2:OUT))
Date: March 23, 2008
3.0KHz
10KHz
Frequency
Page 1
30KHz
100KHz
Time: 11:07:14
** Profile: "SCHEMATIC1-sweep" [ G:\brewdoc\ece3042hwk\WA2_Sprg08_Filter\Bessel\bessel-pspicefiles\schem...
Date/Time run: 03/23/08 11:04:29
Temperature: 27.0
(A) sweep (active)
40u
30u
(1.5565K,27.188u)
(10.289K,26.885u)
Phase Delay
20u
(10.289K,25.407u)
Third Order Bessel Filter
Group Delay
10u
0
1.0KHz
3.0KHz
10KHz
(P(V(U2:OUT))/Frequency)*(PI/180)*(-1/(2*PI))
G(V(U2:OUT))
Frequency
Date: March 23, 2008
Page 1
30KHz
100KHz
Time: 11:15:21
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 1. Third‐Order Butterworth LPF Verification (Must demonstrate circuit) 2. Third‐Order Chebyshev LPF 3. Second‐Order Band‐Pass 4. Second‐Order Notch 5. First‐Order All‐Pass 6. Second‐Order All‐
Pass Points Points Possible Received
16 16 16 16 16 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 9 Bode gain magnitude plot over frequency range of 100Hz to 100khz. 9 Measurement of dc gain and ‐3dB frequency. 9 Table comparing these measured values to the design specifications. Show percent error. 2. Third‐Order Chebyshev Low‐Pass Filter 9 Bode gain magnitude plot over frequency range of 100Hz to 100khz. 9 Measurement of dc gain, dB ripple, and ‐3dB frequency. 9 Table comparing these measured values to the design specifications. Show percent error. 3. Second‐Order Bandpass Filter 9 Bode gain magnitude plot over frequency range of 100Hz to 100khz. 9 Measurement of center frequency fo, ‐3dB bandwidth BW, and Q. Q is given by fo /BW. 9 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. 9 Bode gain magnitude plot over frequency range of 100Hz to 100khz. 9 Measurement of center frequency fo, ‐3dB bandwidth BW, and Q. Q is given by fo/BW. 9 Table comparing these measured values to the design specifications. Show percent error. 5. First‐Order All‐Pass Filter 9 Bode gain magnitude plot over frequency range of 100Hz to 100khz. 9 Measurement of dc gain. 9 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. 9 Table comparing these measured values to the design specifications. Show percent error. 6. Second‐Order All‐Pass Filter 9 Bode gain magnitude plot over frequency range of 100Hz to 100khz. 9 Measurement of dc gain. 9 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. 9 Table comparing these measured values to the design specifications. Show percent error.