filter design & simulation

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

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.

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.

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)

s2C1C2 + s[C2(G1+G2)+C1(1-β)] + G1G2]

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 19.6kVout

+

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

T

Vout

Input voltage (V)

-3 -2 -1 0 1 2 3

Vo

lta

ge

(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

Ga

in (

dB

)

-80

-60

-40

-20

0

Vout

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.




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

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.


1 2 4

1 2G -2G 0

2 -G 2G -G

3 -G (G+sC) 0



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


T(s) = (-1)1+4 [G2 – sCG]

(-1)1+1 [G2 + sCG]

T(s) = s – G/C

s + G/C


component values:

R= 1/G = 15kΩ C = 10nF

V1 5

R1 15k

R2 15k

R3 15k

C1 1

0n

+

Vin 2.5

Vout C2 10n+

-

+

U1 OPA364

+2.5V offset


obtained and the Bode plot is plotted in TINA-TI also as follows:

T

Frequency (Hz)

10 100 1k 10k 100k

Ga

in (

dB

)

-3

-2

-1

0

1

2

3

Frequency (Hz)

10 100 1k 10k 100k

Ph

ase

[d

eg

]

-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.

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:




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

Now the column corresponding to driving node (3rd ).


1 2 4

1 aG1 -aG1 0

2 -aG1 (G1+sC1+sC2) -sC2

3 0 -sC1 -G2



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


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


component values:

R1= 1/G1 = 3.83kΩ C1 = 22nF R2 = 1/G2 = 20kΩ C2 = 15nF

V+ 5

Cbypass 10n

R2 3

.83k Vout

+

Vin 0

Voffset 2.5

C1 22n

R1 20k

C2 22n

C3 15n

+

-

+

U1 OPA364


obtained as follows:

T

Vout

Frequency (Hz)

10 100 1k 10k 100k

Ga

in (

dB

)

-80

-60

-40

-20

0

Vout

filter design & simulation

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