Active Filters

Active filters design procedure Butterworth and Chebyshev interpolation filters
Here the design procedure for low pass filters, in order to get those filters works as high pass filters, resistors and capacitors should be swap. R1 with C1, R2 with C2, and R3 with C3.




1. Determinate filter order


for buterworth


for Chebishev where:
Fs= stop frequency [Hz]
Fc= cut frequency [Hz]





where
As magnitude at stop frequency [db]
Ac magnitude at cut frequency [db] usually 3db

Base on the result we might need to put two or more filters series, for example if we need to get 4th order we can put two second order filters in series, if we need to get fifth order filter we can put second and third order filter, and etc
2.Frequency Impedance Scaling

FSF = 2*3.14*Fc

3.Assign parameter Z (filter impedance) base on op amp parameters it should >> then output impedance, and << input impedance
4.Calculate Resistor and capacitors according follow formulas for low pass filter
R1=R2 =Z for second order
R1=R2=R3 = Z for third order

For high pass filter we need to re-calculate all capacitors equal 1/R what is give 1F and resistors, according to the formulas
‘R1=1/C1
‘R2=1/C2
‘R3=1/C3
Now find value of the component what we will place on schematic
R1= R1’*Z
R2=R2’*Z
R3=R3’*Z

Capacitors

In formula for low pass filter capacitors C1 in table becoming C1 on schematic C2 in table C2 in schematic, and C3 as well. But be sure when you pick values from the table you are using correct filter order
To create band pass or band stop filters you can put two series filters low pass with high pass and vice versa
Here the look up tables for both filters

Filter order

C1

C2

C3

2

1,414

0,7071

 

3.

3,546

1,392

0,2024

4

1,082

0,9241

 

4

2,613

0,3825

 

5

1,753

1,354

0,4214

5

3,235

0,3090

 

6

6 1,035

0,9660

 

6

1,414

0,7071

 

6

3,863

0,2588

 

7

1,531

1,336

0,4885

7

1,604

0,6235

 

7

4,493

0,2225

 

8

1,020

0,9809

 

8

1,202

0,8313

 

8

1,800

0,5557

 

8

5,125

0.1950

 

9

1,455

1,327

0,5170

9

1,305

0.7661

 

9

2,000

0,5000

 

9

5,758

0,1736

 

10

1,012

0,9874

 

10

1,122

0,8908

 

10

1,414

0,7071

 

10

2,202

0,4540

 

10

6,390

0.1563

 

Butterworth coefficients table

 

 

Filter order

C1

C2

C3

2

1,638

0,6955

 

3

6,653

1,825

0,1345

4

1,900

1,241

 

 

 

4,592

0,2410

 

5

4,446

2,520

0,3804

 

 

6,810

0,1580

 

6

2,553

1,776

 

 

 

3,487

0,4917

 

 

 

9,531

0,1110

 

7

5,175

3,322

0,5693

 

 

4,546

0,3331

 

 

 

12,73

0,08194

 

8

3,270

2,323

 

 

 

3,857

0,6890

 

 

 

 

5,773

0,2398

 

 

 

16,44

0,06292

 

9

6,194

4,161

0,7483

 

 

4,678

0,4655

 

 

 

7.170

0.1812

 

 

 

20.64

0,4980

 

10

4,011

2,877

 

 

 

4,447

0,8756

 

 

 

5,603

0,3353

 

 

 

8,727

0,1419

 

 

 

25,32

0.04037