Author Topic: LC resonance mixed success  (Read 8304 times)

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Offline electrolustTopic starter

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Re: LC resonance mixed success
« Reply #25 on: June 05, 2017, 10:11:00 pm »
Not sure what you mean here about the ideal components, because RL is the ESR of the indcutor.  You did not seem to want to include non idealities for teh capacitor so i did not include that.

Sorry, yes you did say that.  I overlooked that and thought the RL was a parallel load in a generalized RLC parallel circuit.
« Last Edit: June 05, 2017, 10:20:16 pm by electrolust »
 

Offline The Electrician

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Re: LC resonance mixed success
« Reply #26 on: June 05, 2017, 10:41:14 pm »
The peak amplitude should occur at angular frequency:
w=sqrt((sqrt(2*Rs^2*C*L*RL^2+2*Rs*L^2*RL+Rs^2*L^2)-Rs*C*RL^2)/(Rs*C*L^2))

Reformatting:



I don't see how that's possible since it doesn't include terms for ESR and DCR.  Also, I mean I guess it could be wrong but StillTrying showed me and I was able to verify, that the Rs term has no affect on resonant frequency.  Without going through your formula, maybe the Rs terms cancel out, but the problem remains that it is only considering an ideal inductor and ideal capacitor.

What definition are you using for resonance?

For parallel circuits there can be more than one definition: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/parres.html#c1

You might also want to have a look at: https://en.wikipedia.org/wiki/RLC_circuit
 
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Offline electrolustTopic starter

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Re: LC resonance mixed success
« Reply #27 on: June 05, 2017, 11:00:12 pm »
Ah, thanks for that.  Do you know if AoE covers that detail?  At least in chapter 1, I don't think they do.  They seem to only talk about resonance in terms of min/max impedance.  I guess AoE is more of a 100-level text?
 Now that I understand the subject a bit more, I see that the wikipedia page is going to be a good jumping off point for me.

Wikipedia uses Kaiser as a reference, but ouch that book is expensive!
« Last Edit: June 05, 2017, 11:37:55 pm by electrolust »
 

Offline electrolustTopic starter

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Re: LC resonance mixed success
« Reply #28 on: June 08, 2017, 09:12:55 am »
So.  I [re]read wikipedia and the hyper-physics site.   Wikipedia in particular has a nice reference to a paper by Kenneth Cartwright, which is very approachable.  In summary, there are three resonant points.

f_0: series resonant point (X_C = X_L); works for parallel given low ESR
f_p: (phase = 0) = (power factor = 1)
f_m: max impedance

From the Cartwright paper I was easily able to construct a spreadsheet that allows me to calculate either f_m or C (given the other), for a given L+ESR.  The result is in very good agreement with Circuitlab and LTSpice.  And I can see both the f_p and f_m points on the plots.  Now I have a good enough grasp of this to properly consider the effect of R_s.

But I'm still at a loss as to why the minimum current does not occur at the f_m maximum impedance frequency.  It also is not at the f_p frequency.  Cartwright does not consider this at all; in his circuit he uses a 1A constant current source, which at least one good reason to do so is to remove the effect of R_s!

Why doesn't V=IZ apply?  Z is not plotted, V is plotted.  It occurs at f_m, max impedance.  Ergo, given V=IZ, V is at a maximum, Z is at a maximum, shouldn't I be at a minimum at this same frequency?

EDIT: Possible answer: V is not the total circuit voltage, it's the voltage at the divider point.  As Z (of L//C) changes, R_s remains constant.  This means the division ratio changes with frequency.  The shift in I_min away from f_m reflects that V is not changing at the same rate as Z!

Re-attaching a couple of relevant plots from a previous post.
« Last Edit: June 08, 2017, 10:40:49 am by electrolust »
 

Offline electrolustTopic starter

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Re: LC resonance mixed success
« Reply #29 on: June 09, 2017, 08:25:33 pm »
The peak amplitude should occur at angular frequency:
w=sqrt((sqrt(2*Rs^2*C*L*RL^2+2*Rs*L^2*RL+Rs^2*L^2)-Rs*C*RL^2)/(Rs*C*L^2))

Reformatting:



This doesn't work for me.  The numerator of the outer radical is negative and the denominator is positive.  So I can't take the square root of that.  It works.  I wasn't including factors for the prefix (10^ -3,-6,-9) in my calculation.

I'd love a better understanding of how this is derived.  I'm sure it's too involved to make a forum post so a text reference would be great.
« Last Edit: June 09, 2017, 08:52:54 pm by electrolust »
 

Offline electrolustTopic starter

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Re: LC resonance mixed success
« Reply #30 on: June 14, 2017, 08:31:55 pm »
quick bump
 


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