# Practical Considerations of a Butterworth Filter

I'm trying to design/implement a low-pass filter for the amateur 2M band (144-148 MHz). To meet FCC regs, I need harmonics to be at least 40dB down, so I calculated a 7-stage Butterworth Filter with a 175MHz cutoff. This gave me the following component values:

• L1, L3 = 56.70371 nH
• L2 = 90.94568 nH
• C1, C4 = 8.094927 pF
• C2, C3 = 32.77569 pF

There seems to be a lot of information on the theory of operation of these filters both on here and on other sites, but I can't find as much on the practical implementation and component selection aspects. Given that, obviously, you can't buy components with those values, I'm picking "close" values, but I'm not sure to what extent that will affect the resulting filter. I now have:

• L1, L3 = 56 nH
• L2 = 91 nH
• C1, C4 = 8 pF
• C2, C3 = 33 pF

Is there any way I can calculate/simulate what the curve for this filter will look like? Mostly I just need to calculate it at 144-148 MHz, and 288-296 MHz (the 2nd order harmonic) to make sure I'm not attenuating my pass band and that I am attenuating the harmonics adequately.

Secondly, how can I determine the voltage and current ratings I need for the components? The transmitter is a mere 1W, which should be about 10V peak, and 200mA (50 ohm characteristic impedance) but I'm not sure if that holds true of the individual components in the filter.

Finally, is there anything else I need to know in actually implementing one of these? Specific types of capacitors to use or avoid (currently planning on SMD ceramics) and the same for the inductors?

Here is a calculator that you can use and it plots frequency/phase responses AND it seems you can tweak the values: -

Here is another one.

Here is another

And another

I can't underwrite any of them but there appear to be plenty to choose from OR get LTSpice (now that's my main recommendation).

1 - Get yourself a SPICE program. Even a limited-functionality version will be able to handle this sort of thing. You'll be able to enter the exact values.

2 - That said, don't bother. Your nominal values are as good as any. At the frequencies you're working, nothing will behave exactly as you think it will. Parasitics and construction techniques will be major modifiers of your filter response.

• That's unfortunate -- so how can I build a filter if I don't know how it will behave? Commented Apr 15, 2015 at 4:37
• LTSpice is free along with the natural learning curve but it will give you what you want. Commented Apr 15, 2015 at 7:37
• @David - You start with your nominal values. Then you start modifying, testing, modifying, etc. You'll want a variable RF generator and a power meter, to start with. Once you've got a circuit that seems right, package it in the box you're going to use for final use, and test again. Commented Apr 15, 2015 at 11:20
• @WhatRoughBeast - is there a range of components I should buy to try this? Seems like a real pain to have to keep reworking a board for "trial and error". I guess I'll also need to get a variable RF generator... Commented Apr 15, 2015 at 14:55

Consider simpler alternatives to butterworth. These are relatively narrow band signals, so the harmonics also have closely defined frequencies.

Form a lowpass filter with two notches at 2nd and 3rd harmonics - these can be combined in a Cauer (elliptic) filter of lower order - less complex, easier to build.

Or given a suitable power stage, it may be possible to eliminate the 2nd harmonic by design leaving only odd order (primarily 3rd) harmonics to worry about. Then a single notch at 432 MHz as part of a 3rd order Cauer filter will suffice. (At lower frequencies, a push-pull amplifier cancels out the even harmonics, I don't know if a similar approach works at 2m.)

• Wouldn't the notches on the Cauer filter require more precision in the components, not less? Also, I can't do anything about the design of the power stage, I'm using a commercial radio module whose 2nd order harmonics are only ~4dB down on the fundamental. Commented Apr 15, 2015 at 14:57
• Unless you're building quantities of these, you may end up tuning the filters anyway ( and a notch is fairly easy to tune). Simpler structure may still win even if it requires more precision.
– user16324
Commented Apr 15, 2015 at 15:03

I'm wondering why you picked the Butterworth configuration in the first place for such a tight requirement. Only advantage of Butterworth that I can see is the zero passband ripple. You can get very small to almost non-existent ripple with Cauer (elliptical) filters, for a simpler circuit order and maximal rolloff. One other zero passband ripple filter topology is Chebyshev Type 2, possibly simpler, but I haven't played with it, yet.

To answer your question as to the topology and implementation of the circuit of the components you've calculated, and without further information as to your source of calculations, the components could possibly be placed in a ladder topology (aka Cauer topology) - the capacitors in shunt (ie parallel), alternating with the inductors in series, with $C_1$ leading, like so:

You may want to try a filter design program called Elsie, that has been written for the amateur radio community by a US radio amateur.

The free version of the program calculates a range of filter topologies up to a certain order, and is packed with a lot of nice features like a well-written tutoria-style online help, plotting of performance and schematic, 5%-value component substitution, editing of circuit schematic, Monte Carlo simulation, etc.; too many to list here.

You're also missing out on the fun of experimenting as a radio amateur (I'm presuming you are one, by your first sentence) if you're not willing to try at least throwing up the circuit into a circuit simulation programme/s (already mentioned by @Andy Aka and others) to play around with topology and component values.

For an open source modelling and simulation programme, try SciLab.

73s

• Also have a look at the Filters pages on microwaves101.com Commented Jul 29, 2015 at 12:33

@WhatRoughBeast is right, at those parameter values parasitics will be a big deal. However, if you had rather think about doing things than actually do things here is an alternative.

You will need a model for your filter (state space or transfer function), which you had to have to design it (even if you didn't realize it). You can use Python with the Controls System Library to analyze your system. I wanted to mention this technique because 10 years ago this required a pricey Matlab license so I think free is a good deal here.

There is a lot of functionality in there, you could analyze parameter sensitivity, step functions, or whatever. So many options you may never get around to actually trying it(don't do this). You can also do all this in Spice, but the learning curve and design iteration time is steeper.

Here is a bode plot of 1/(s+1) low pass filter.

from control.matlab import *

num = [1]
den = [1,1]
G = tf(num,den)
bode(G)


• How does one translate this into an actual implementation? I'm not sure what you meant by "rather think about doing things than actually do things." Your suggestion seems to require transforming component values into an equation to model the filter, and I'm not sure how to do that either. Commented Apr 15, 2015 at 15:24
• Many filter design tools provide a transfer function in terms of the component values, it is a common way to describe circuits. Sorry, the "think about things" was just a joke...It is easy to overthink things when building and testing them is faster. butterworth tf
– Matt
Commented Apr 15, 2015 at 15:33