Corner Frequency Shortcut Calculation

[HaroldBrooks]

This may be old news already, and it's of small import, so I appologize if it's redundant.

I started finding it a bit tedious using the f = 1/（2*PI*R*C） equation to find a filter corner frequency, so through some very basic math, I found a constant ( 159155 ) That when divided by the multiplication of ( resistance * capacitance-(uf) ) gives you a very close appoximation of a filter corner frequency.

The constant is fairly easy to remember, and the shortcut requires no fidling with converting microfarads to Farads, as those really small numbers are sometimes prone to errors, with the resulting string of zeros.

So there are only two steps to the shortcut, divide 159155 by the product of R x C, and there you have it : F = 159155 / (R * C).

Here's a real world example : r = 47000 c = .022uf

159155 / (47000 * .022) = 153.92hz

All comments are welcome, and any potential improvements as well !!!

[eschertron]

To 7 digits, 1 million divided by ( 2 Pi ) is equal to 159155, so there's nothing wrong with your shortcut at all.

I have to ask, though, are you often caught doing this math on paper? I'm never too for from a scientific calculator that has a Pi key (even one on my phone!) so it hasn't been an issue. If I'm doing design work, I'll be on a computer with a spreadsheet to do the repetitive calculations for me.

[Helmholtz]

1 million divided by ( 2 Pi ) is equal to 159155, so there's nothing wrong with your shortcut at all.

Yes and 1 million equals 1/µ, so 159155 = 1/(2*3.14*µ).

[eschertron]

If you haven't already, I think you'd like reading Goedel, Escher, Bach It combines music, math, and fascination in deep and entertaining ways.

[Enzo]

One thing to learn about is "significant digits". if you have two values, like 1.6 and 3.9, and I divide one by the other, the calculator says 0.410256. But that is not the case. Your answer cannot have more significant digits that the original data. In this case two. So the answer is 0.41

[eschertron]

One thing to learn about is "significant digits". if you have two values, like 1.6 and 3.9, and I divide one by the other, the calculator says 0.410256. But that is not the case. Your answer cannot have more significant digits that the original data. In this case two. So the answer is 0.41

Absolutely true. And in our case here, since the physical components come with an 'acceptable error range', then the answer to the problem above becomes:
1/(2PiRC) = [10^6]/(2*Pi*[47000+470]*[.022+.0022]) = 138.54 as a low value, to
1/(2PiRC) = [10^6]/(2*Pi*[47000-470]*[.022-.0022]) = 172.75 as a high value, assuming 1% resistors and 10% capacitors.
So just because 1/2 = .50000000 (to infinity) and Pi = 3.141572.... to whatever precision my calculator takes it to, the number we wish to know is always going to be around 154Hz give-or-take.

Above I simply reported the value of 1M/2*pi(). Because of component limitations, we could use 159000 or even 160000 as our multiplier and still be accurate enough.

edit: because as Enzo always says, it's ... ah.. erm.. something about... rocket science?

[Enzo]

Rocket surgery, but close enough...

[HaroldBrooks]

If you haven't already, I think you'd like reading Goedel, Escher, Bach It combines music, math, and fascination in deep and entertaining ways.

Thanks Eschertron. Read that around 2007, great and very insightfull book ! I got to that book by being a big fan of J.S. Bach, and basically obsessed by his music.

The big Oratorios, the Violin / Harpsichord concertos are so advanced in their structure and art, they bring me to tears. If there were an IQ you could measure Bach by, I'm sure it would be 300+ right up there with Da Vinci. But there's even more, and I believe his inspiration is truly devine, and I'm not highly religious, but it's obvious and he was beyond human !

[HaroldBrooks]

Yes and 1 million equals 1/µ, so 159155 = 1/(2*3.14*µ).

Lol, sorry got my "wires" crossed, the quoted response should have been for you Helmholtz, but as you guys know, I thank you all for your help and fellowship !

I just accidently deleted my post to your quote !

But I was indicating that it's great on this website how we can talk about a shared passion, electronics ! I am new to all this, but always loved from the subject afar, now I have my hands on it (with insulating gloves of course...). I was an advid calculator and pocket computer collector for many years, but had to step back from that obsession, and open the door to a new one !

Guitar amps and stomp boxes. I am not a mathematician by any stretch, but I hear you are a physisist, and that's super cool, as I had two paths when I was young and perhaps could have been a scientist of some sort... but who knows. I became a finance guy and then a software developer in the end, now I am a consultant with a relaxed schedule.

My recently deceased Dad loved everything German, learned to speak fluent German, and was a clock builder, fabricator, and repair man of a very high order, but he was many things and a true Renisance man, and I owe a lot to his diversity in thought. My Mom's people were from Germany originally, and that was a strong attraction to my Father, to say the least.

What type of world would it be without numbers, art, and music ? I shudder to think !

Anyway, thanks for your help and insight Helmholtz !

[d95err]

You can simply google ”RC filter calculator” and you’ll find something like this:

http://www.learningaboutelectronics....calculator.php