User manual

page 32
Analog System Lab Kit PRO
experiment 4
To understand the working of four types of second order lters, namely, Low
Pass, High Pass, Band Pass, and Band Stop lters, and study their frequency
characteristics (phase and magnitude).
Secondorderlters(or biquardlters) areimportantsince theyarethebuilding
blocks in the construction of
d
d
2
1
1
1
1
10
10
1
10
210/
10
1000.1sinsin
N
N
N
N
N
RC
H
V
V
Q
ss
H
V
V
Q
ss
H
s
V
V
Q
ss
H
s
V
V
Q
ss
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
HQ
V
V
rad s
H
ttt
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$$
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~~
~
~
~
~
r
~r
yrr
=
=
++
=
++
=
++
+
=
=
=
=
=
=
=
=
=
=+
-
=
++
+
-
-
-
-
b
b
b
b
a
b
b
_
__
l
l
l
l
k
l
l
i
ii
orderlters,for
d
d
2
1
1
1
1
10
10
1
10
210/
10
1000.1sinsin
N
N
N
N
N
RC
H
V
V
Q
ss
H
V
V
Q
ss
H
s
V
V
Q
ss
H
s
V
V
Q
ss
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
HQ
V
V
rad s
H
ttt
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$$
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~~
~
~
~
~
r
~r
yrr
=
=
++
=
++
=
++
+
=
=
=
=
=
=
=
=
=
=+
-
=
++
+
-
-
-
-
b
b
b
b
a
b
b
_
__
l
l
l
l
k
l
l
i
ii
. When N is odd, the
d
d
2
1
1
1
1
10
10
1
10
210/
10
1000.1sinsin
N
N
N
N
N
RC
H
V
V
Q
ss
H
V
V
Q
ss
H
s
V
V
Q
ss
H
s
V
V
Q
ss
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
HQ
V
V
rad s
H
ttt
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$$
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~~
~
~
~
~
r
~r
yrr
=
=
++
=
++
=
++
+
=
=
=
=
=
=
=
=
=
=+
-
=
++
+
-
-
-
-
b
b
b
b
a
b
b
_
__
l
l
l
l
k
l
l
i
ii
order
ltercanberealizedusing
d
d
2
1
1
1
1
10
10
1
10
210/
10
1000.1sinsin
N
N
N
N
N
RC
H
V
V
Q
ss
H
V
V
Q
ss
H
s
V
V
Q
ss
H
s
V
V
Q
ss
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
HQ
V
V
rad s
H
ttt
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$$
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~~
~
~
~
~
r
~r
yrr
=
=
++
=
++
=
++
+
=
=
=
=
=
=
=
=
=
=+
-
=
++
+
-
-
-
-
b
b
b
b
a
b
b
_
__
l
l
l
l
k
l
l
i
ii
secondorderltersandonerstorderlter.When
d
d
2
1
1
1
1
10
10
1
10
210/
10
1000.1sinsin
N
N
N
N
N
RC
H
V
V
Q
ss
H
V
V
Q
ss
H
s
V
V
Q
ss
H
s
V
V
Q
ss
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
HQ
V
V
rad s
H
ttt
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$$
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~~
~
~
~
~
r
~r
yrr
=
=
++
=
++
=
++
+
=
=
=
=
=
=
=
=
=
=+
-
=
++
+
-
-
-
-
b
b
b
b
a
b
b
_
__
l
l
l
l
k
l
l
i
ii
is even, we need
d
d
2
1
1
1
1
10
10
1
10
210/
10
1000.1sinsin
N
N
N
N
N
RC
H
V
V
Q
ss
H
V
V
Q
ss
H
s
V
V
Q
ss
H
s
V
V
Q
ss
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
HQ
V
V
rad s
H
ttt
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$$
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~~
~
~
~
~
r
~r
yrr
=
=
++
=
++
=
++
+
=
=
=
=
=
=
=
=
=
=+
-
=
++
+
-
-
-
-
b
b
b
b
a
b
b
_
__
l
l
l
l
k
l
l
i
ii
secondorderlters.Pleaselistentotherecordedlecture
at [19]foradetailedexplanationofactivelters.
Secondorderltercanbeusedtoconstructfourdierenttypesoflters.Thetransfer
functionsforthedierentltertypesareshowninTable4.1,where
d
d
2
1
1
1
1
10
10
1
10
210/
10
1000.1sinsin
N
N
N
N
N
RC
H
V
V
Q
ss
H
V
V
Q
ss
H
s
V
V
Q
ss
H
s
V
V
Q
ss
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
HQ
V
V
rad s
H
ttt
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$$
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~~
~
~
~
~
r
~r
yrr
=
=
++
=
++
=
++
+
=
=
=
=
=
=
=
=
=
=+
-
=
++
+
-
-
-
-
b
b
b
b
a
b
b
_
__
l
l
l
l
k
l
l
i
ii
and
d
d
2
1
1
1
1
10
10
1
10
210/
10
1000.1sinsin
N
N
N
N
N
RC
H
V
V
Q
ss
H
V
V
Q
ss
H
s
V
V
Q
ss
H
s
V
V
Q
ss
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
HQ
V
V
rad s
H
ttt
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$$
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~~
~
~
~
~
r
~r
yrr
=
=
++
=
++
=
++
+
=
=
=
=
=
=
=
=
=
=+
-
=
++
+
-
-
-
-
b
b
b
b
a
b
b
_
__
l
l
l
l
k
l
l
i
ii
isthelowfrequencygainofthetransferfunction.Thelternamesareoften
abbreviated as LPF (Low-pass Filter), HPF (High-pass Filter), BPF (Band Pass Filter),
and BSF (Band Stop Filter). In this experiment, we will describe a universal active
lter,whichprovidesallthefourlterfunctionalities.Figure4.1showsasecond
orderuniversallterrealizedusingtwointegrators.Notethattherearedierent
outputs of the circuit that realize LPF, HPF, BPF and BSF functions.
4.1 Brief theory and motivation
Goal of the experiment
C
R
C
R
R
R
Q•R
V
I
R/H0
R
BPF
LPF
BSF
HPF
R
Figure 4.1: A Second-order Universal Active Filter
Figure 4.2: Magnitude and Phase response of LPF, BPF, BSF, and HPF lters
Table 4.1: Transfer functions of Active Filters
Low Pass Filter
d
d
2
1
1
1
1
10
10
1
10
2 10 /
10
100 0.1sin sin
N
N
N
N
N
RC
H
V
V
Q
s s
H
V
V
Q
s s
H
s
V
V
Q
s s
H
s
V
V
Q
s s
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
H Q
V
V
rad s
H
t t t
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$ $
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~ ~
~
~
~
~
r
~ r
y r r
=
=
+ +
=
+ +
=
+ +
+
=
=
=
=
=
=
=
=
=
= +
-
=
+ +
+
-
-
-
-
b
b
b
b
a
b
b
_
_ _
l
l
l
l
k
l
l
i
i i
High Pass Filter
d
d
2
1
1
1
1
10
10
1
10
2 10 /
10
100 0.1sin sin
N
N
N
N
N
RC
H
V
V
Q
s s
H
V
V
Q
s s
H
s
V
V
Q
s s
H
s
V
V
Q
s s
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
H Q
V
V
rad s
H
t t t
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$ $
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~ ~
~
~
~
~
r
~ r
y r r
=
=
+ +
=
+ +
=
+ +
+
=
=
=
=
=
=
=
=
=
= +
-
=
+ +
+
-
-
-
-
b
b
b
b
a
b
b
_
_ _
l
l
l
l
k
l
l
i
i i
Band Pass Filter
d
d
2
1
1
1
1
10
10
1
10
2 10 /
10
100 0.1sin sin
N
N
N
N
N
RC
H
V
V
Q
s s
H
V
V
Q
s s
H
s
V
V
Q
s s
H
s
V
V
Q
s s
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
H Q
V
V
rad s
H
t t t
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$ $
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~ ~
~
~
~
~
r
~ r
y r r
=
=
+ +
=
+ +
=
+ +
+
=
=
=
=
=
=
=
=
=
= +
-
=
+ +
+
-
-
-
-
b
b
b
b
a
b
b
_
_ _
l
l
l
l
k
l
l
i
i i
Band Stop Filter
d
d
2
1
1
1
1
10
10
1
10
2 10 /
10
100 0.1sin sin
N
N
N
N
N
RC
H
V
V
Q
s s
H
V
V
Q
s s
H
s
V
V
Q
s s
H
s
V
V
Q
s s
s
H
Q
Q
HQ
Q
HQ
kHz
Q
kHz
Q
f kHz
f kHz
H Q
V
V
rad s
H
t t t
2
1
2
1
1
1
1
1
2
1
1
4
1
2
4
200
0
03
2
2
0
01
0
2
2
0
0
0
4
th
i
i
i
i
p
p
0
0
0
0
0
2
2
0
2
02
0
0
2
2
0
0
04
0
0
2
2
0
2
2
0
0
2
0
0
0
0
0
0
0
$
$
$
$
$ $
$
$
2
~
~
~
~
~
~
~
~
~
~
~
~
~
~
z
~ ~
~
~
~
~
r
~ r
y r r
=
=
+ +
=
+ +
=
+ +
+
=
=
=
=
=
=
=
=
=
= +
-
=
+ +
+
-
-
-
-
b
b
b
b
a
b
b
_
_ _
l
l
l
l
k
l
l
i
i i