Bessel filter design.ipynb

multiple-feedback-filter-demo.asc

Version 4
SHEET 1 1496 1228
WIRE -48 256 -160 256
WIRE 128 256 32 256
WIRE -336 272 -336 256
WIRE 384 272 272 272
WIRE 560 272 464 272
WIRE 32 336 16 336
WIRE 128 336 128 256
WIRE 128 336 96 336
WIRE 464 352 448 352
WIRE 560 352 560 272
WIRE 560 352 528 352
WIRE 64 416 64 400
WIRE -320 432 -336 432
WIRE -272 432 -320 432
WIRE -160 432 -160 256
WIRE -160 432 -192 432
WIRE -112 432 -160 432
WIRE 16 432 16 336
WIRE 16 432 -32 432
WIRE 32 432 16 432
WIRE 496 432 496 416
WIRE -336 448 -336 432
WIRE 128 448 128 336
WIRE 128 448 96 448
WIRE 160 448 128 448
WIRE 272 448 272 272
WIRE 272 448 240 448
WIRE 320 448 272 448
WIRE 448 448 448 352
WIRE 448 448 400 448
WIRE 464 448 448 448
WIRE 32 464 16 464
WIRE 560 464 560 352
WIRE 560 464 528 464
WIRE 608 464 560 464
WIRE 720 464 688 464
WIRE 784 464 720 464
WIRE 800 464 784 464
WIRE 16 480 16 464
WIRE 464 480 448 480
WIRE 448 496 448 480
FLAG -336 352 0
FLAG -336 256 vcc
FLAG 64 480 0
FLAG 64 400 vcc
FLAG 16 560 0
FLAG -336 528 0
FLAG -160 496 0
FLAG 496 496 0
FLAG 496 416 vcc
FLAG 448 576 0
FLAG 272 512 0
FLAG 720 528 0
FLAG 784 464 Vout
FLAG -320 432 Vin
SYMBOL voltage -336 256 R0
WINDOW 0 45 43 Left 2
WINDOW 3 46 73 Left 2
WINDOW 123 0 0 Left 2
WINDOW 39 0 0 Left 2
SYMATTR InstName V1
SYMATTR Value 3.3
SYMBOL res -288 448 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 0 56 VBottom 2
SYMATTR InstName R1
SYMATTR Value 100k
SYMBOL Opamps\\UniversalOpamp2 64 448 R0
SYMATTR InstName U1
SYMATTR Value2 Avol=10Meg GBW=100Meg Slew=100Meg
SYMBOL voltage -336 432 R0
WINDOW 123 36 90 Left 2
WINDOW 0 39 62 Left 2
WINDOW 3 36 120 Left 2
SYMATTR Value2 AC 1
SYMATTR InstName V2
SYMATTR Value SINE(1.25 1.25 50E3 0 0)
SYMBOL voltage 16 464 R0
WINDOW 0 43 68 Left 2
WINDOW 3 39 94 Left 2
SYMATTR InstName V3
SYMATTR Value 1.25
SYMBOL cap 96 320 R90
WINDOW 0 12 58 VBottom 2
WINDOW 3 -13 -3 VTop 2
SYMATTR InstName C2
SYMATTR Value 47p
SYMBOL res -128 448 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 0 56 VBottom 2
SYMATTR InstName R2
SYMATTR Value 18146
SYMBOL res -64 272 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 0 56 VBottom 2
SYMATTR InstName R3
SYMATTR Value 50k
SYMBOL res 144 464 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 0 56 VBottom 2
SYMATTR InstName R4
SYMATTR Value 10k
SYMBOL Opamps\\UniversalOpamp2 496 464 R0
SYMATTR InstName U2
SYMATTR Value2 Avol=10Meg GBW=100Meg Slew=100Meg
SYMBOL voltage 448 480 R0
WINDOW 0 45 63 Left 2
WINDOW 3 43 90 Left 2
SYMATTR InstName V4
SYMATTR Value 1.25
SYMBOL cap 528 336 R90
WINDOW 0 11 64 VBottom 2
WINDOW 3 -13 -5 VTop 2
SYMATTR InstName C4
SYMATTR Value 33p
SYMBOL res 304 464 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 0 56 VBottom 2
SYMATTR InstName R5
SYMATTR Value 24979
SYMBOL cap 256 448 R0
WINDOW 0 47 62 Left 2
WINDOW 3 48 89 Left 2
SYMATTR InstName C3
SYMATTR Value 398.90p
SYMBOL res 368 288 R270
WINDOW 0 32 56 VTop 2
WINDOW 3 0 56 VBottom 2
SYMATTR InstName R6
SYMATTR Value 10k
SYMBOL cap -176 432 R0
WINDOW 0 44 53 Left 2
WINDOW 3 45 79 Left 2
SYMATTR InstName C1
SYMATTR Value 98.093p
SYMBOL res 704 448 R90
WINDOW 0 0 56 VBottom 2
WINDOW 3 32 56 VTop 2
SYMATTR InstName R7
SYMATTR Value 100
SYMBOL cap 704 464 R0
WINDOW 0 52 20 Left 2
WINDOW 3 51 46 Left 2
SYMATTR InstName C5
SYMATTR Value 21.188n
TEXT -344 152 Left 2 !;tran 0 1.08E-3 1e-3 1E-6
TEXT -344 176 Left 2 !.ac oct 100 1 100E6

multiple_feedback_low_pass_fifth_order_filter_op_amp.png

multiple_feedback_low_pass_fifth_order_filter_op_amp_response.png

multiple_feedback_low_pass_second_order_filter_op_amp.png

rc_lowpass_filter.png

Hello! Thanks for the great design guide! Helped me understand what is going on as well as how to design the filter! Sadly some of the plots are not working great in the original. Most importantly the Group Delay plots do not work as intended because scipy seems to assume digital filters in its implementation of group_delay() making nonsensical results for those curves. Secondly, when the phase "wraps" above π or below -π there is a jump in the Phase graph. This is technically correct but makes it harder to interpret what is going on in the graph, especially when comparing Phase from different filters. In my Fork I implemented a Group Delay function that calculates it directly from the numerator and denominator polynomials. Also I implemented a corrected call to scipy's group_delay() that makes it work right. I used both together as a sanity check.
My Fork
Please check out this fork, as I can't make a pull request to a gist as far as I can tell. Note that some of the Matplotlib colors are confusing because I'm always plotting the two different ways to calculate the Group Delay, to confirm that they are both in fact working. This would not be helpful for the demo itself, I just left it as proof.
I think fixing your original gist is important because some external sites link to it (which is how I found it) and it was VERY helpful for getting the basics of designing such a filter! Maybe more people would benefit from a clearer version from the start!