Looking for proof on difficult RLC problem

[Ratchit]

The Electrician,

Thanks for the posting of that link. As I suspected, multifrequency resonance needs parallel or series-parallel circuits. For the second circuit in the link, when Rl^2 = Rc^2 = L/C , then the circuit will be resonant at all frequencies. By resonance, I mean the reactance will cancel out at all frequencies.

Ratch

 

[Ratchit]

Winterstone,

Two definitions? Is each impedance maximum/minimum - according to your definition - always a resonance point? Or only in some specific cases?

As I said before, some definitions of resonance define it also as max impedance or voltage/current in phase. I don't think I agree with those definitions. Impedance and phase are conditions that may not always agree with resonance. I believe that resonance should only be defined as the cancellation of reactance.

Ratch

 

[The Electrician]

Two definitions? Is each impedance maximum/minimum - according to your definition - always a resonance point? Or only in some specific cases?
What about a Chebyshev filter response with gain peaking? Resonance?

What's wrong with having two definitions? This site gives three definitions:

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/parres.html

The first attached image gives some discussion from a circuit theory text:

The second image gives some discussion of phenomena associated with the series resonant circuit:

 

[Winterstone]

The Electrician - hello again and thanks for the additional information you gave.
I really must confess that I am surprised about the fact that - as stated in one of the referenced documents - there are three official definitions for resonance in the US.
I didn`t know that - up to now, although I am engaged in electronics since more than 30 years. A good example for "learning does never end".
Thanks and merry Christmas.
W.

 

[MrAl]

Hi again,


Winterstone:
I did comment when i mentioned that i thought you were talking about "physical resonance".

Ratchit:
"Which post did i say i accepted multi-frequency resonance for series circuits"
Well you said in post #14:
"Unless the OP can produce some documentation that shows multifrequency resonance for series circuits"
so it appeared that you implied that you would accept it if someone could produce some proof. No problem if you meant otherwise.

"We must be talking about cross topics here"
Yes and i mentioned that before when i noted that Winterstone was talking about what is
usually called "physical resonance". Physical resonance as i pointed out is when the
L and C reactances cancel and we're left with a pure resistance R. But the other points
are often referred to as resonance too, but more importantly that's what the OP asked for.
He was asking about the resonant peaks for each element not just physical resonance.


For proof that these peaks exist and are different, we analyze the circuit for the
three different AC voltages. The results are as follows...

Let D=sqrt(w^2*C^2*R^2+(1-w^2*C*L)^2)

then the three voltage amplitudes are:
vC=1/D
vL=w^2*L*C/D
vR=w*R*C/D

From my previous post, the three different angular frequencies that cause the peaks are computed:

for max across C:
w=sqrt((2*L-C*R^2)/(2*C*L^2))
for max across R:
w=sqrt(1/(L*C))
for max across L:
w^2=-2/(C^2*R^2-2*L*C), w=sqrt(2/(2*L*C-C^2*R^2)) {condition 2*L>R^2*C}

So we immediately see three different frequencies as well as three different amplitude
equations. Next we could insert each w into each respective amplitude equation and
we could calculate the three normalized peak voltages:

max across C:
vCmax=2*L/(R*sqrt(4*L*C-C^2*R^2))

max across L:
vLmax=-(2*L*abs(C*R^2-2*L))/(sqrt(4*C*L-C^2*R^2)*(C*R^3-2*L*R)), {condition 2*L>R^2*C}

max across R:
vRmax=1

It might be interesting to note that under certain conditions the max across C is the same as the max across L, but they occur with different w. For the example i gave before with L=1mH, C=10uf, and R=1, this can be observed.

 

[The Electrician]

Winterstone,



As I said before, some definitions of resonance define it also as max impedance or voltage/current in phase. I don't think I agree with those definitions. Impedance and phase are conditions that may not always agree with resonance. I believe that resonance should only be defined as the cancellation of reactance.

Ratch

If the circuit is a pure series RLC circuit, isn't "cancellation of reactance" the same thing as zero phase angle between the terminal voltage and current?

 

[MrAl]

Hi again,


I'll try to find that paper i was talking about earlier so you guys can take a look. It's been so long now since i read it, and i might have it stored on HD.

Winterstone:
Merry Christmas to you too, and have a Happy New Year.

The Rest:
Merry Christmas to you all too, if you celebrate, or just Happy Holidays if you dont.

 

[Winterstone]

Hi again to all,

as I have learned from "The Electrician" the American Standards Association defines in parallel three different definitions for "resonance".
Now - as every body knows, a definition can be "good" and make sense - or not.
In general, I don`t like a situation with more than one single definition for a technical term.
Therefore, I ask myself - as far as our discussion about the resonance is concerned - if it really make sense to have more than one definition, and I would like to forward this question to the forum.

I think - as far as mechanical systems are concerned - a system is under "resonance conditions" if it is excited with its characteristic frequency ("eigen frequency") leading to decaying oscillations with maximum amplitudes.
So - what happens if we excite any series or parallel RLC combination with a short pulse? I think it will respond with a kind of decaying oscillation at one single frequency only.
Why not define this frequency only as the systems resonant frequency? Is there any need for another definition?

 

[MrAl]

Hi again to all,

as I have learned from "The Electrician" the American Standards Association defines in parallel three different definitions for "resonance".
Now - as every body knows, a definition can be "good" and make sense - or not.
In general, I don`t like a situation with more than one single definition for a technical term.
Therefore, I ask myself - as far as our discussion about the resonance is concerned - if it really make sense to have more than one definition, and I would like to forward this question to the forum.

I think - as far as mechanical systems are concerned - a system is under "resonance conditions" if it is excited with its characteristic frequency ("eigen frequency") leading to decaying oscillations with maximum amplitudes.
So - what happens if we excite any series or parallel RLC combination with a short pulse? I think it will respond with a kind of decaying oscillation at one single frequency only.
Why not define this frequency only as the systems resonant frequency? Is there any need for another definition?

Hi again,


Words in any language often have more than one meaning. I tried to point this out three times now, when i described your interpretation as "physical resonance". That term distinguishes your interpretation from the others and it still has meaning so nothing is lost. In fact, something is gained because we now can identify other important characteristics about the circuit whereas before we were more limited (with only one definition). So we havent lost anything we've gained. You can call it anything you want i guess (like mechanical resonance perhaps) if it makes it more clear to you.

 

[Winterstone]

Hi again,
Words in any language often have more than one meaning. I tried to point this out three times now, when i described your interpretation as "physical resonance". That term distinguishes your interpretation from the others and it still has meaning so nothing is lost. In fact, something is gained because we now can identify other important characteristics about the circuit whereas before we were more limited (with only one definition). So we havent lost anything we've gained. You can call it anything you want i guess (like mechanical resonance perhaps) if it makes it more clear to you.

Hello again,
MrAl thanks for your response. l completely agree with you and I also did understand (at least I hope so) the contents of your last contributions to this discussion.
However, your last sentence meets the point: " You can call it anything you want.."
Of course, I am free to define something for myself - but I am afraid, this is not the best way to discuss with other people, which may use another definition.
That is the best way to create misunderstandings.
For my opinion, this thread is the best example because it has shown that there are different opinions about a common definition of the term "resonance".

It was my only intention, therefore, to express my concern about different definitions for the same subject and to hear what other forum members think about it - that`s all.

 

[Ratchit]

The Electrician,

If the circuit is a pure series RLC circuit, isn't "cancellation of reactance" the same thing as zero phase angle between the terminal voltage and current?

One would think so, but it is not for a parallel resonant circuit. See the figure description of the attachment.

Ratch

 

[MrAl]

Hello again,


One small note i'd like to add is that if anyone decides to look this up in any written material (like reference books, engineering handbooks, etc.) i think it would be best to find one that is copyright dated sometime after say 2008. Anything sooner than that might not reflect the most recent work done in the study of resonance.

 

[steveB]

Overall, I don't have a lot to add to this good discussion and I certainly don't have any new information after 2008 on questions of resonance. However, I wanted to make one general comment/clarification related to the parallel RLC circuit. Some of the references sited above seem to indicate a voltage driven parallel circuit, but this can be problematic.

A series RLC circuit can be driven by a voltage source without problem. Even if we add parasitic series resistance to the cap and coil, all resistances can be lumped into one equivalent series resistor, and the overall structure of the system is unaltered.

A parallel RLC circuit driven by a voltage source suffers from two key issues. First, a capacitor should never be directly driven by a perfect voltage source; although, this can be remedied by adding the series resistance to the ideal cap. It is also prudent to add a parasitic resistance to the coil. The second issue with this circuit is that driving parallel branches, with a ideal voltage source, perfectly isolates each branch. Hence, strictly there are three independent systems, and not one RLC system.

If a parallel RLC is driven with a current source, a single system with resonance is allowed.

I'm not sure if any of these comments directly affect anyones thinking, or any comments/conclusions mentioned above, but I thought I would just make this reminder because forgetting about it sometimes leads to misconceptions. More importantly, many references (confusingly) show the ideal parallel RLC circuit with an ideal voltage source driving it, which is not really a correct presentation.

 

[MrAl]

Hi Steve,


Yeah that makes sense. If we connect a voltage source across a parallel circuit we effectively short out the circuit as well as power it. Caps can take a voltage source though as long as it is sinusoidal. But that doesnt help if the circuit can not behave the way we want it too. In the past i've done parallel RLC circuits but they were powered from a source that always had at least some internal impedance, so their reactance was still measurable. Long time ago (very long time ago) i did a circuit with three RLC circuits connected together in a pi fashion where there was one parallel RLC connected to the other parallel RLC with a series RLC. Made a very sharp bandpass filter.

I mentioned the year 2008 because i believe new ideas have come up around that time, but if you have anything older it may still be of interest if it has some more information. I assumed you might have some more reference books laying around maybe dusty by now but maybe still useful. I looked in my engineering handbook but hey it's only one book and it didnt have a whole lot on resonance, just the basics really, and quite disappointing. It has a lot of information in it but every time i go to look for something it's not in there. Funny too as it is a very thick book. There's just too much information that needs to be known today

 

[Winterstone]

I mentioned the year 2008 because i believe new ideas have come up around that time..

Hello MrAl,

please, can you explain/elaborate this assertion (presumption?) a bit? Because I cannot remember any important "knowledge step" or fundamental new ideas (concerning resonance) at that time.

 

[MrAl]

Hello Winterstone,


Yes, that's about the time when the paper i was talking about earlier in this thread was published. I'll try looking around again later today hopefully or maybe tomorrow. Got a little busy at home for a while.