How do I calculate component values for multi-pole analog filters?

[MajorEE]

I have been trying to figure out how to apply the mathematical functions for a passive filter so that I can get component values out of it, however, I have hit a roadblock and do not understand how they are calculated.

I understand the basic concept of reactance (1/2pifC & 2pifL) and how they chance impedance as the frequencies changes, and from my reading the formulas are based upon impedance and not really values themselves right?

For my application I chose the Butterworth band pass type because it has a more linear response. It really doesn't matter though as I chose this to be educational. (146MHz, 50Ohm, 4 pole)

If I grab the formula I found 2*sin(((2*1-6283)*pi)/(2*4)) where it is a 4 pole filter, 6283 is 1Khz -> rad/s and the "1" term is the component position. I thought these were the values I should be using based upon a paper i read on it that uses 1 rad/s and so forth to generate the values in Farads and Henries, however, as soon as I change the frequency it starts outputting negative numbers.

I have checked out books such as Electronic Filter Design Handbook, ARRL handbook, Analog and digital filter design, and countless whitepaper and videos such as the MIT one.

I am at a complete loss here, and am in way over my head. I'm looking to calculate the value of the components by hand to understand the actual math behind it, not just design the filter as I am aware of countless calculators available to do the calculations. Can anyone explain how to apply the formula to get component values, or point me in the right direction? I have seen plenty of plots of the function, but again cannot figure out how to connect the math to real world component values.

Thanks!

[KJDS]

First you need to create a low pass prototype filter.

Then transform that to a bandpass filter and also adjust the impedance to suit.

Here are the starting values for a butterworth filter

http://www.rfcafe.com/references/electrical/butter-proto-values.htm

The equations to denormalize the prototype filter are here

http://www.rfcafe.com/references/electrical/filter-denorm.htm

The creation of the original table is an entertaining task and is an exercise left for the reader.

[Cliff Matthews]

Ten years ago we could never have imagined saying "there's an app for that" but today there is https://play.google.com/store/search?q=Butterworth%20Filter&c=apps&hl=en

[dadler]

This book has sections that go over this process in detail (as KJDS has explained), at a level even I can understand. Basically convert everything to a low pass filter, and then transform them into the other filter types (swap caps vs inductors, do the math, etc). The book gives examples too.

http://www.amazon.com/Practical-Electronics-Inventors-Paul-Scherz/dp/0071771336

[notsob]

AADE in western australia  has a free filter design program, although he is offline due to ill health the download is still available

http://www.aade.com/filter32/download.htm

[rimpelbekkie]

Have you tried QUCS ?  http://qucs.sourceforge.net/ It's a circuit simulator which comes with a built-in filter generator.
It can generate a filter, for example: 3rd order Butterworth low pass filter, 1 MHz, 50 ohms in and output impedance.
Since qucs is a circuit simulator, in just a few steps you can simulate the bode plots. 

[LvW]

For my application I chose the Butterworth band pass type because it has a more linear response. It really doesn't matter though as I chose this to be educational. (146MHz, 50Ohm, 4 pole)

MajorEE - you will be not surprised to hear that - before designing a filter - the requirements have to be known.
Therefore my question: What means "4 pole"?
Because the poles (for pole-Q values above 0.5) are conjugate complex, are you speaking of two pole pairs (4th order bandpass) or four pole pairs (8th order bandpass)? 
Moreover, what bandwidth do you require?