it is a lab manual, normally in various colleges filter designing is "Black-Sheep" on subjects. because many of the students failed in this exam. it is very helpful to them.

1. Shri Govindram Seksaria Institute of Technology
& Science, Indore
Department of Electronics & Instrumentation Engineering
Lab Manual 2013-14
Filter Design & Simulation
Submitted By:
Sandesh Agrawal, 0801EI111047, AB 37039
Vinay R.G. Dubey ,0801EI111055,AB 37047
Vikas Jain ,0801EI111054,AB 37046

2. Contents
1. Design a low pass 2nd
order Sallen-key filter and also find its transfer
function using IAM approach and also simulate it and give it’s Bode plot.
2. Design an all pass 1st
order filter and also find its transfer function using
IAM approach and also simulate it and give it’s Bode plot.
3. Design a high pass 2nd
order using Friend’s topology and also find its
transfer function using IAM approach and also simulate it and give it’s Bode
plot.

3. Experiment no.-01
Design a low pass 2nd
order Sallen-key filter and also find its transfer function
using IAM approach and also simulate it and give its Bode plot.
Solution:
Since, the OPAMP is in inverting mode we can write the inverting gain (β)
β = 1 + (Rb/Ra)
step 1: Numbering all the nodes and replacing the inverting opamp as follows:
So, Indefinite Admittance Matrix (IAM) will be of 5X5 size.

4. Since 5th
node is grounded, so deleting the corresponding row and column of
grounded node, we will get IAM of 4X4 size.
Now deleting the row corresponding to driven node (4th
). So IAM will be of 3X4
size.
1 2 3 4
1 G1 -G1 0 0
2 -G1 (G1+G2+sC1) -G2 -sC1
3 0 -G2 (G2+sC2) 0
Now the column corresponding to driven node will be deleted by adding it to the
column corresponding to driving node by multiplying it with β.
Now, constrained matrix will be:
1 2 3
1 G1 -G1 0
2 -G1 (G1+G2+sC1) -G2-βsC1
3 0 -G2 (G2+sC2)
Now, calculating the transfer function of above circuit taking 4th
node as output
and first node as input.
So, T(s) = V4/V1 = βV3/V1
T(s) = β Y(1,3)/Y(1,1)
Where Y(1,3) = value of determinant by deleting first row and third column
Y(1,1) = value of determinant by deleting first row and first column
T(s) = (-1)1+3-1
G1G2 (β)
(-1)1+1
[(G1+G2+sC1) (G2+sC2) – G2 (G2+βsC1)]
T(s) = -G1G2 (β)
s2
C1C2 + s[C2(G1+G2)+C1(1-β)] + G1G2]

5. Now consider the following example with unity gain feedback. And following
component values:
R1= 1/G1 = 2.74kΩ C1 = 47nF
R2 = 1/G2 = 19.6kΩ C2 = 10nF
Above circuit is simulated on Tina-TI simulation software and the result is
obtained as follows:
V+ 5
Cbypass 10n
R2 19.6k
Vout
+
Vin 0
Voffset 2.5
C2 47n
R1 2.74k
C1 10n
+
-
+
U1 OPA364
T
Time (s)
0 1000u 2m 3m 4m
Vin
-2
0
2
Vout
0
1
2
3
4
5

6. T
Vout
Input voltage (V)
-3 -2 -1 0 1 2 3
Voltage(V)
0
1
2
3
4
5
Vout
The Bode plot is plotted in TINA-TI also as follows:
Transfer characteristics as follows:
T
Vout
Frequency (Hz)
10 100 1k 10k 100k
Gain(dB)
-80
-60
-40
-20
0
Vout

7. Experiment no.-02
Design an all pass 1st
order filter and also find its transfer function using IAM
approach and also simulate it and give its Bode plot.
Solution:
The OPAMP is in differential mode.
Step 1: Numbering all the nodes.
So, Indefinite Admittance Matrix (IAM) will be of 5X5 size.
Since 5th
node is grounded, so deleting the corresponding row and column of
grounded node, we will get IAM of 4X4 size.
Now deleting the row corresponding to driven node (4th
). So IAM will be of 3X4
size.
1 2 3 4
1 2G -G -G 0
2 -G 2G 0 -G
3 -G 0 (G+sC) 0

8. 1kHz ALL- PASS FILTER
Now any column corresponding to driven nodes (2nd
or 3rd
) will be deleted by
adding it to the other driven column. Here we are deleting 3rd
column by adding it
to 2nd
column.
Now, constrained matrix will be:
1 2 4
1 2G -2G 0
2 -G 2G -G
3 -G (G+sC) 0
Now, calculating the transfer function of above circuit taking 4th
node as output
and first node as input.
So, T(s) = V4/V1
T(s) = Y(1,4)/Y(1,1)
Where Y(1,4) = value of determinant by deleting first row and fourth column
Y(1,1) = value of determinant by deleting first row and first column
T(s) = (-1)1+4
[G2
– sCG]
(-1)1+1
[G2
+ sCG]
T(s) = s – G/C
s + G/C
Now consider the following example with unity gain feedback. And following
component values:
R= 1/G = 15kΩ C = 10nF
V1 5
R1 15k
R2 15k
R3 15k
C110n
+
Vin 2.5
VoutC2 10n+
-
+
U1 OPA364
+2.5V offset

9. Above circuit is simulated on Tina-TI simulation software and the result is
obtained and the Bode plot is plotted in TINA-TI also as follows:
T
Frequency (Hz)
10 100 1k 10k 100k
Gain(dB)
-3
-2
-1
0
1
2
3
Frequency (Hz)
10 100 1k 10k 100k
Phase[deg]
-180
-135
-90
-45
0
Phase Response
Frequency Response
Note:
These curves are resolution-limited by the
computer monitor. In reality, they are
perfectly smooth.

10. Experiment no.-03
Design a high pass 2nd
order using Friend’s topology and also find its transfer
function using IAM approach and also simulate it and give its Bode plot.
Solution:
The OPAMP is in inverting mode.
Numbering all the nodes and replacing as follows:
So, Indefinite Admittance Matrix (IAM) will be of 5X5 size.
Since 5th
node is grounded, so deleting the corresponding row and column of
grounded node, we will get IAM of 4X4 size.
Now deleting the row corresponding to driven node (4th
). So IAM will be of 3X4
size.
1 2 3 4
1 aG1 -aG1 0 0
2 -aG1 G1 + sC1+sC2 -sC1 -sC2
3 0 -sC1 (G2+sC2) -G2

11. Now the column corresponding to driving node (3rd ).
Now, constrained matrix will be:
1 2 4
1 aG1 -aG1 0
2 -aG1 (G1+sC1+sC2) -sC2
3 0 -sC1 -G2
Now, calculating the transfer function of above circuit taking 4th
node as output
and first node as input.
So, T(s) = V4/V1
T(s) = Y(1,4)/Y(1,1)
Where Y(1,4) = value of determinant by deleting first row and fourth column
Y(1,1) = value of determinant by deleting first row and first column
T(s) = (-1)1+4-1
asC1G1
(-1)1+1
-[aG1G2 + 2s(C1+C2)G2 + s2
C1C2]
T(s) = -s(aG1/C2)
s2
+ s[2G2(C1+C2)/C1C2] + G1G2/C1C2
Now consider the following example with unity gain feedback. And following
component values:
R1= 1/G1 = 3.83kΩ C1 = 22nF R2 = 1/G2 = 20kΩ C2 = 15nF
V+ 5
Cbypass 10n
R23.83k
Vout
+
Vin 0
Voffset 2.5
C1 22n
R1 20k
C2 22n
C3 15n
+
-
+
U1 OPA364

12. Above circuit is simulated on Tina-TI simulation software and the result is
obtained as follows:
T
Vout
Frequency (Hz)
10 100 1k 10k 100k
Gain(dB)
-80
-60
-40
-20
0
Vout