- #1

Frank-95

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Hi all.

I would like to ask some explanation regarding how to obtain L and C values for a butterworth filter using the first Cauer topology. I will consider a normalized low pass filter.

https://en.wikipedia.org/wiki/Butterworth_filter

What I don't understand is this: how to pass from transfer function to L and C values?

For example: let's consider a second order filter, with 0 dB gain at DC (for simplicity). I have:

We find poles by putting the deniminator equal to 0. Hence it yields:

For

I thus have:

As shown also on wikipedia.

What I don't understand now is this: how can I calculate from here the values of capacitors and inductors of the LC ladder. There are formulas at wikipedia but they don't explain how they are obtained.

Any tip?

Thank you

I would like to ask some explanation regarding how to obtain L and C values for a butterworth filter using the first Cauer topology. I will consider a normalized low pass filter.

**(Link added by Mentor)**https://en.wikipedia.org/wiki/Butterworth_filter

What I don't understand is this: how to pass from transfer function to L and C values?

For example: let's consider a second order filter, with 0 dB gain at DC (for simplicity). I have:

**|H(jω)|**^{2}= 1 / [1 + (ω/ω_{c})^{2n}] ⇒ H(s)H(-s) = 1 /[1 + (-s^{2}/ω_{c}^{2})^{n}]We find poles by putting the deniminator equal to 0. Hence it yields:

**s**_{k}= jω_{c}e^{j(2k - 1)π/(2n)}For

**n = 2**and**k = 1, 2****s1 = jω**

s2 = jω_{c}e^{jπ/4}s2 = jω

_{c}e^{j3π/4}I thus have:

**H(s) = ω**_{c}/ [(s - s1) (s - s2)]As shown also on wikipedia.

What I don't understand now is this: how can I calculate from here the values of capacitors and inductors of the LC ladder. There are formulas at wikipedia but they don't explain how they are obtained.

Any tip?

Thank you

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