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How do I calculate the component values for a Butterworth filter?

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ElectricalEngineer

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I would like to calculate the component values for a Butterworth filter, but cannot seem to figure out how to apply the formulas to give me meaningful values.

I have read through a few books recommended, and they seem to all focus on the transfer function and how it related to amplitude over frequency, however, I would like to figure out how to calculate the values of each component to make this filter. I know of many calculators out there but for the purposes of this I prefer to do it by hand.

The specifications are just for a learning exercise but lets say we want a 4th order butterworth:

4 Pole
50Ohms impedance
146Mhz center frequency.

Can anyone point me in the right direction? I can't seem to figure out how to apply the formulas to get actual component values.

Thanks!
 

LvW

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The specifications are just for a learning exercise but lets say we want a 4th order butterworth:

4 Pole
50Ohms impedance
146Mhz center frequency.

Since you are speaking of a "center frequency" - are you going to design a bandpass?
More than that, because of the high frequency I assume that you want a passive RLC filter, right?

As you can see, some more informations are required for answering your question.
 

ElectricalEngineer

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Since you are speaking of a "center frequency" - are you going to design a bandpass?
More than that, because of the high frequency I assume that you want a passive RLC filter, right?

As you can see, some more informations are required for answering your question.

I am indeed looking for a bandpass filter, and yes passive type. Although if it makes anything easier 1MHz would be fine too. My end application if for a 2m amateur radio bandpass filter. I think that if we get in the 1MHz area the components would be small enough to not be relatively expensive to try out a few different filter types and get the math down while learning about analog filters which is my goal for this exercise.

Thanks for your time!
 

SunnySkyguy

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Passive RF voice or data filters shall be specified by many parameters of your choice.


  • Passband width, often @-3dB
  • Passband ripple (dB)
  • Passband Group delay ripple (affects data bit shift)
  • Bandstop or Rejection Bandwidth @ -X dB
  • Input Z
  • Output Current or power or input?

Then you decide on topology and values and order of filter, n , which is # of reactive filter parts , based on above specs.
ok?

but if none of this matters, and you just want Butterworth...

the easy way is the cookbook recipe online.
which way do you want?
 

BradtheRad

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A single LC tank, or LC series, may yield the Q you need. Select values which can be driven by the current you have available.

A large capacitor needs higher current to operate it, to provide sufficient voltage swings. A small inductor likewise needs higher current.

If you have small current available, then choose a high L:C ratio. Large inductor, small capacitor.
 

exp

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As already mentioned, this really depends on the architecture of the filter!

If you build a simple LC ladder filter, then you can use Elsie for example https://tonnesoftware.com/elsie.html

If you look in Schaumann's book you can also directly read off the component values:

TGzNF.jpg
 

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