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

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#### ElectricalEngineer

##### Junior Member level 1
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!

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?

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?

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.

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?

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.

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 http://tonnesoftware.com/elsie.html

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

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