its-fonsy / cheb_filter

Python script to make a Chebysev low pass filter

Low pass Chebyshev filter

Python script to implement a low pass Chebyshev filter with Tow-Thomas or Sallen & Key circuit.

Install and usage

With python3 already installed

git clone https://github.com/its-fonsy/cheb_filter.git
cd cheb_filter

To work correctly the script need Amax Amin fp fs G (in this order) as parameter when lunch. So an example of correct use would be

python -B cheb.py 1 20 15000 20000 5

the -B flag is for preventing python to generate the folder __pycache__.

Example of output

An example of the output would be

  Specs
  =====
  Amax = 1
  Amin = 20
  fp = 15000
  fp = 20000
  G = 5

  Calculate the order of the filter
  ===================================
  ε=0.5088471399095875

  Find the minimum order
    with N = 2 --> A is 3.6151629991213756
    with N = 3 --> A is 7.837518586503201
    with N = 4 --> A is 13.449096456182193
    with N = 5 --> A is 19.553801351470202
    with N = 6 --> A is 25.7896385433968
  The filter will be of order 6

  Calculate the poles
  =====================
  p1 = wp(-0.06218102379301138+0.993411202482326j)
  p2 = wp(-0.16988171626915632+0.7272274730251562j)
  p3 = wp(-0.23206274006216773+0.2661837294571697j)
  p4 = wp(-0.23206274006216773-0.26618372945716984j)
  p5 = wp(-0.16988171626915635-0.7272274730251561j)
  p6 = wp(-0.06218102379301145-0.9934112024823258j)

  Transfer Function
  =================
                                              5 ⍵p^6
  ----------------------------------------------------------------------------------------
  16.2831(s² + s‧⍵p‧0.1244 + 0.9907)(s² + s‧⍵p‧0.3398 + 0.5577)(s² + s‧⍵p‧0.4641 + 0.1247)

  Calculate w and Q for filters
  =============================
  w = 93810 with a Q = 8.0037
  w = 70384 with a Q = 2.1980
  w = 33282 with a Q = 0.7609

  Sallen and Key filters
  ======================
  For w=93810 and Q=8.00
    C1 = 3.9e-12 F
     R = 170752 ohm
    C2 = 9.993214080813776e-10 F --> commercial C2 = 1e-09 F

  For w=70384 and Q=2.20
    C1 = 6.2e-12 F
     R = 521276 ohm
    C2 = 1.1981586102873136e-10 F --> commercial C2 = 1.2e-10 F

  For w=33282 and Q=0.76
    C1 = 2.2000000000000003e-12 F
     R = 8974724 ohm
    C2 = 5.0945087072459805e-12 F --> commercial C2 = 5.1e-12 F

  Tow-Thomas filters
  ==================
  For w=93810 and Q=8.00
     C = 3.9e-09 F
     R = 2733 ohm -> commercial R = 2700 ohm
    R2 = 21876 ohm -> commercial R2 = 22000 ohm

  For w=70384 and Q=2.20
     C = 1.3e-09 F
     R = 10928 ohm -> commercial R = 11000 ohm
    R2 = 24021 ohm -> commercial R2 = 24000 ohm

  For w=33282 and Q=0.76
     C = 1.5000000000000002e-09 F
     R = 20030 ohm -> commercial R = 20000 ohm
    R2 = 15240 ohm -> commercial R2 = 15000 ohm

  Resistance to set the G
  =======================
  Opamp in inverting amplifier configuration
  R1 = 10000 ohm
  R2 = 50000 ohm

Components for Sallen-Key filter

Using the smart strategy when designing the filter the algorithm try to use two capacitance of commercial value. The resistor is calculated from those value.

Components for Tow-Thomas filter

The algorithm calculate all the value of both resistance for each commercial capacitor. Then it display the one with nearest value, for both resistance, the commercial one.

Circuits reference

TO BE DONE