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about LC ladder filter and activeRC filter

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linkern

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lc filter

Hi,all
I want design a 7th low pass filter use LC ladder method, then use signal flow to convert it into inverting intergrator and non-inverting intergrator format. I'm not very clear with the relationship about L & C value with the cut-off frequency.Also I want to realize the active inductor with gyrator-C .what's the relationship with the opamp(gain,bandwith) ,C and L
 

ladder filter

Your problem is not clear to me. You are mixing two design strategies:
By using a flow diagram and to convert it into an integrator realization you follow the "leap frog" approach. The other keyword "gyrator" corresponds with another filter topology: FDNR technique with BRUTON transformation.
(Hint: Active inductor realizations are not used for low pass filters) .
 

lc ladder

Hi,lvW
It seems I am puzzled by some papers/books.
I mean ,if I want to design a 7th LPF using leap frog approach ,the procedure should be like this:
1st: I draw a 7th LC ladder
2nd: change the LC ladder into flow diagram.The transformation from LC ladder filter to leapfrog
3rd: the parameter(or called impedance) are four kinds :noninverting lossy integrator,inverting lossy integrator,noninverting integrator and inverting integrator.
4th: find the relationship among the parameter(or called impedance), cut-off frequency, filter type(butterworth ,chebyshev ..)
5th: computer aided simulation

now the problem is I don't know the 4th step .
In past , I have done a six-order LPF, use 3 opamp , MFB structure . the fitler type is butterwoth .I find the parameters from books. Nowadays ,I 'm puzzled.

in the book: Continuous-time Active filter Design. Chapter 6.3 : methods of LC ladder simulation , it says : inductance substitution by a gyrator-C combination ..

I 'm very puzzled now:
 

lc ladder filter

As I have mentioned before:
Based on a passive LP ladder structure of 7th order there are TWO different design strategies:

1.) Conversion to design flow equations resulting in a leap frog structure (using several integrator stages with/without damping)
2.) Direct replacement of all passive elements with other parts. This requires application of the BRUTON transformation before.
As a result all floating inductances are replaced by resistors, as well as resistors by caps and capacitors by active FDNR´s.
 

    linkern

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lc filter simulator

hi,LvM
In the leapfrog design strategy.what's the relationship between the integrator's op's parameters(gain,bandwidth) and capacitor value to LC ladder's L ,C ,Rs & Rl.
Is there any papers/books on it ?
Thanks!
 

leapfrog structure

Sorry for the late answer - I was absent for some days.
There is a rather simple relation between the leap frog integrator time constants and the L- resp.C-values of a passive ladder structure.
The procedure is described in various filter books. Its not economic to repeat all design steps here in the forum. Most probably you are succesful also by google searching .
Godd luck.
 

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