Calculation of voltage with impedances - Differences calculation vs. simulation. - Page 1
Forum section: electronics / rf-microwave

author: eTobey
author_rank: Super Contributor
timestamp: January 10, 2024, 12:17:10 pm
content: 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?

author: wasedadoc
author_rank: Super Contributor
timestamp: January 10, 2024, 12:36:08 pm
content: Are you really correct when you subtsitute 1/wC and wL for ZC and ZL? The impedances are complex but your substitutions are not.

author: eTobey
author_rank: Super Contributor
timestamp: January 10, 2024, 01:26:46 pm
content: I dont knowHad 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?

author: RoGeorge
author_rank: Super Contributor
timestamp: January 10, 2024, 03:01:59 pm
content: 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.

author: tggzzz
author_rank: Super Contributor
timestamp: January 10, 2024, 03:22:18 pm
content: Quote from: RoGeorge on January 10, 2024, 03:01:59 pmSee the significance of and equation determining wcinhttps://en.m.wikipedia.org/wiki/RLC_circuitas distinct from w0

author: eTobey
author_rank: Super Contributor
timestamp: January 10, 2024, 05:34:57 pm
content: 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.

author: wasedadoc
author_rank: Super Contributor
timestamp: January 10, 2024, 07:49:25 pm
content: Quote from: eTobey on January 10, 2024, 01:26:46 pmMy 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.

author: Odysseus
author_rank: Regular Contributor
timestamp: January 10, 2024, 11:11:08 pm
content: Quote from: wasedadoc on January 10, 2024, 12:36:08 pmYup, this is where your math went wrong. You left outiorj(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_stateThe 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).

author: eTobey
author_rank: Super Contributor
timestamp: January 11, 2024, 09:06:39 am
content: 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°?