Easier Calculation of some LC Resonant Circuits John L Stewart Feb 2023
Keeping track of all the zeroes can be confusing when calculating resonant frequency of LC circuits. Here is a simplification of the basic equation that can help.
This version is setup to cover capacitors from One nanofarad to several microfarads. And chokes from one mH to several Henries.
The basic resonance equation is 1 / 2*PI*root LC.
To an accuracy of better than one percent 1 / 2*PI is simply 0.159. The equation becomes 0.159 / root LC
Multiplying top & bottom of this by 10^3 (1000) results in the numerator (top) is now 159.
On the bottom (denominator), taking the root of the 10^-6 in the cap micro farad gets a 10^-3 (0.001).
That cancels the multiplier of 10^3 (1000) in the denominator. And the equation for resonance becomes simply 159 / root LC, where L is in Henries & C is in microF.
As a typical example a power supply filter might consist of a 5H choke & 40 microF cap. What is the resonant frequency?
Calc the root of 5*40, By eyeball looks like ~14. 14 squared is 196. Close enough. 14 fits into 159 a bit more than 14 times.
15 Hz is the resonant frequency, in this case all done without a calculator.
Keeping track of all the zeroes can be confusing when calculating resonant frequency of LC circuits. Here is a simplification of the basic equation that can help.
This version is setup to cover capacitors from One nanofarad to several microfarads. And chokes from one mH to several Henries.
The basic resonance equation is 1 / 2*PI*root LC.
To an accuracy of better than one percent 1 / 2*PI is simply 0.159. The equation becomes 0.159 / root LC
Multiplying top & bottom of this by 10^3 (1000) results in the numerator (top) is now 159.
On the bottom (denominator), taking the root of the 10^-6 in the cap micro farad gets a 10^-3 (0.001).
That cancels the multiplier of 10^3 (1000) in the denominator. And the equation for resonance becomes simply 159 / root LC, where L is in Henries & C is in microF.
As a typical example a power supply filter might consist of a 5H choke & 40 microF cap. What is the resonant frequency?
Calc the root of 5*40, By eyeball looks like ~14. 14 squared is 196. Close enough. 14 fits into 159 a bit more than 14 times.
15 Hz is the resonant frequency, in this case all done without a calculator.
Attachments
Thank you @jhstewart9 ,
very interesting and practical, just one typo on the last calculation, as the final text should be:
“14 fits into 159 a bit more than 10 times.
11 Hz is the resonant frequency, in this case all done without a calculator.”
very interesting and practical, just one typo on the last calculation, as the final text should be:
“14 fits into 159 a bit more than 10 times.
11 Hz is the resonant frequency, in this case all done without a calculator.”
In Radio it often is used a simplification as 25330/sqrt(L × C) to take picofarad and microhenry, values more realistic in higher frequencies. But I personally prefeer the original equation as is. Got from equating energies stored in the inductance and capacitance.
The root of 5*40 is 10 times the square root of two. Remember to factor your square roots out and just commit square roots of 2,3,and 5 to memory and you’re most of the way there, most of the time.
THX to Zintolo for his correction of the result of the example I used. Guess I should have used a 4-function Rechner. 😱
And to all the others for their helpful ideas.👍
And to all the others for their helpful ideas.👍
You folk are more intuned with the music of the spheres than I'm able to get. I do the 159 thing, da nada, then spend five minutes banging my head on the floor to do the exp thing. Calculators are less than useful. At least in slide rule days, you knew you had to pre-plan it. Math is not kind to linear minds.
All good fortune,
Chris
All good fortune,
Chris
Hey Chris, taking that pesky 10 to the minus 6 out from under the square root sign fixes that,
No more pain. suffering & agony solving many LC puzzles.😀👍
No more pain. suffering & agony solving many LC puzzles.😀👍