EEVblog Electronics Community Forum
Electronics => RF, Microwave, Ham Radio => Topic started by: eTobey on January 10, 2024, 12:17:10 pm
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Hi,
I simulated a simple filter, but when i calculate, i got a different result:
The Simulation peaks at 164.05kHz (Vout - not resonant frequency), but my calculation gets me 165.83kHz. Usually if one messes up the formula, the result goes off quite far. So i guess it is an issue of rounding? But 1% of error seems a bit too much to me.
In the simulation, i have not added any values other that the bare inductance, capacity and resistance.
Maybe it is another added value "behind the scenes" in the sim?
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Are you really correct when you subtsitute 1/wC and wL for ZC and ZL? The impedances are complex but your substitutions are not.
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I dont know ;D
Had another read:
It should be XL and XC. So it just applies to ideal components. But since i did not enter any other parasitic values in the fields of the components, it should be idealy simulated?
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The resonance happens when XL == XC. Start from this definition when you calculate the resonant frequency. The one in which you considered R is not correct.
R has nothing to do with the resonant frequency. R only alters how fast the oscillations get extinguished, therefore R has no place in the resonant frequency formula.
- R is responsible with the energy dissipated, the losses, but can not change the frequency.
- L and C are responsible with the frequency, but ideal L and C can not dissipate energy.
If it were only an ideal LC, and no R, then the oscillations will go on forever. With or without R (so dampened oscillations or not), the resonant frequency is the same, and dictated only by the values of L and C.
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The resonance happens when XL == XC. Start from this definition when you calculate the resonant frequency. The one in which you considered R is not correct.
See the significance of and equation determining wc in
https://en.m.wikipedia.org/wiki/RLC_circuit
as distinct from w0
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This is such a confusing topic, that this confusion spreads like a virus.
That peak i am referencing to, is not the resonant freqency, but rather the "Vout" peak.
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I dont know ;D
Had another read:
It should be XL and XC. So it just applies to ideal components. But since i did not enter any other parasitic values in the fields of the components, it should be idealy simulated?
My question was a rhetorical one. Look at your final equation. All the terms on the right hand side are positive yet summations and multiplications of them yield a negative number.
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Are you really correct when you subtsitute 1/wC and wL for ZC and ZL? The impedances are complex but your substitutions are not.
Yup, this is where your math went wrong. You left out i or j (your preference). Xl=1i*w*L and Xc = 1/(1i*w*C). Then you need to take the magnitude of the resulting complex expression.
The previously posted Wikipedia link gets it right. Specifically, look at this section: https://en.m.wikipedia.org/wiki/RLC_circuit#Sinusoidal_steady_state
The equation for Wc gives the same value you observed in simulation: Wc = sqrt(L/C-1/2*R^2)/L = sqrt(4u/160n-1/2*4^2)/4u = 1,030,776.4 rad/s = 164.0531 kHz
(Also, is this topic really RF specific? This is ECE101 stuff).
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Actually i found where my math got wrong:
Basic stuff: fraction calculation (see attachment).
I further more explored the unkown (at least for me) of the mathematical universe and found interesting things after realizing how far i got off track:
With the formula i got: w²CL+wCR-1=0 when trying to calculate w for "Vout max", i got a "complex frequency" with my calculator (Casio fx-991ES), where the length of the complex arrow (dont know the english term), is equal to the resonant frequency calculated with the formula for series resonance.
How in the world can this yield the same value? And what would be the phase of 66.4°?