Impedance

LvW

Joined Jun 13, 2013
1,752
I did not say to remove anything from the website, but it is obvious that some of you, somehow missed the context of my postings and were defensive. Sorry if I could have written it differently. I am surprised about the discussion of this simple, and I think, self explanatory equation.
Ragwire, if this is such s "self-explanatory" equation - why didn`t you answer my simple question in post#12:
"Does this mean that the impedance Z is increasing continuously with frequency f?"

EDIT: Perhaps you should have answered that this "beautiful" equation applies for the case of resonance only (as mentioned in the referenced book).

But another question arises: What is the advantage of this equation ? Why do you like it so much?
I suppose, one could use this equation under the assumption that the Q of the tank circuit (Q=Fo/BW,3dB) could be measured because the losses of the inductor are not known.
However, knowing the definition Q=Rp/2*Pi*Fo*L (for the inductor) and assuming (as you did) a lossless capacitor you can derive the desired value of Zo=Z(F=Fo)=Rp directly from this Q measurement. Thus, we do not need "your" equation. (Note that in the above formulas Rp is the parallel loss resistance of the tank circuit and is NOT identical with Rp in the book page referenced by you.)
 
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Thread Starter

Ragwire

Joined Dec 9, 2013
36
Electrician (The) Great post, but the Q formula works for the internal coil resistance of a parallel resonant circuit as well as a series resonant circuit, no?

I was not talking about R/Xl for parallel resistance. I am sure studiot's method is accurate, as is your post here, but I find it simpler to use this formula for finding impedance for the single stage gain. I believe the same formula would work with any appropriate Q-factor entered--eg. the geometric mean of the individual Qs of a double tuned, secondary loaded circuit, a parallel resistance across a single tank circuit, etc.
The numbers all come out the same when I use it, no matter which method I have used. Correct me if I'm wrong.

Ragwire, if this is such s "self-explanatory" equation - why didn`t you answer my simple question in post#12:
"Does this mean that the impedance Z is increasing continuously with frequency f?"
I did, but I am not sure you read it correctly(?)

I don't understand your reference to "beautiful" or "my" equation? This is electronics. I prefer to keep emotion out of it. There seems to be a lot of it around here, and certainly, that pissed me off too.
 

LvW

Joined Jun 13, 2013
1,752
I don't understand your reference to "beautiful" or "my" equation? This is electronics. I prefer to keep emotion out of it. There seems to be a lot of it around here, and certainly, that pissed me off too.
OK - you are right. Cancel "beautiful". And with "your" equation I mean "equation as given by you". OK?
 

WBahn

Joined Mar 31, 2012
29,978
Well Q is always resistance over reactance, but the trick is which resistance and which reactance.

for instance see here for simple cases.

http://www.qsl.net/va3iul/Impedance_Matching/Impedance_Matching.pdf

Note also that I gave a reference to a more comprehensive source in post#11
I think that Q is most generally defined as the ratio of the resonant frequency to the half power bandwidth (with comparable adjustment for a notch filter).

The question of what the definition of the resonant frequency remains, however, since many places define it as being when the impedance is purely real and others as being where the impedance is max (or min, for a notch) even if there is still a reactive component there.
 

WBahn

Joined Mar 31, 2012
29,978
Now let me say this, (Italics will not turn off, by the way)
You might try just posting in the default font unless there is a specific reason to do otherwise. It makes it much easier to quote material and using a non-default font really don't accomplish anything.

I am surprised about the discussion of this simple, and I think, self explanatory equation.
The equation is not at all self-explanatory. It is valid for ONE frequency for ONE particular circuit topology. There is nothing in the equation that hints of that; instead, you need to supply that information supplementally, which you did only by inference spread out across more than one post.

Once again--it is a useful equation that fits in with all the other equations.
What "all the other equations"? You mean several pages of equations for each conceivable situation that would be needed by someone that lacks the necessary skills to analyze the circuits in those situations?

I've actually got a book that is pretty much exactly that. The author gave it to me as a gift because he gave me an acknowledgement for explaining a few equations to him on Usenet. I had no idea he was writing a book at the time and the help I gave him was pretty basic. But he was coming at it from just your perspective -- catalog every possible equation that might be useful so that people can just look up the formula they need and plug and chug.

WBahn: I feel that you are the one with the bruised ego becuase you never understood this equation, nor have heard of it,
What could possibly have lead you to conclude that I don't understand this equation? It is trivial to derive, which is what makes it of limited value to catalog. It falls into the category of equation that, if it is useful enough for what you do, you will tend to have it at the tip of your fingers all the time and, if not, you can derive it on a napkin about as quickly as you can look it up (though with smartphones and the internet, that is not so sure a statement, any more).

You might not have noticed that I'm the one that was defending you in terms of arguing that you were only talking about the impedance at the resonant frequency instead of trying to claim that that formula yielded the impedance at any frequency, which the very presence of 'f' in the equation tends to suggest.

yet you accuse me of not understanding it and attacked me with all sorts of things--for no reason at all.
I'm sorry that you are so thin skinned. By your own admission you apparently go around punching people that disagree with you (a practice you might want to reconsider, by the way, as it will inevitably end up with you either in jail or in the hospital).

I do not suffer fools gladly, and will not suffer you, either. Are you sure you are fit to teach?
Yep, pretty sure.
 
Electrician (The) Great post, but the Q formula works for the internal coil resistance of a parallel resonant circuit as well as a series resonant circuit, no?

I was not talking about R/Xl for parallel resistance. I am sure studiot's method is accurate, as is your post here, but I find it simpler to use this formula for finding impedance for the single stage gain. I believe the same formula would work with any appropriate Q-factor entered--eg. the geometric mean of the individual Qs of a double tuned, secondary loaded circuit, a parallel resistance across a single tank circuit, etc.
The numbers all come out the same when I use it, no matter which method I have used. Correct me if I'm wrong.
On page 237 of the Rider book the formula 2 ∏ Q L f appears, apparently in reference to figure 12-2 on that page. There is no Q determining resistance shown with the tank (parallel L and C; Rp is the plate resistance of a tube), so the reader doesn't know if Q is the Q of the inductor alone, or if it's the Q of the whole tank circuit. The Q of the inductor alone is ωL/R, if R is the series resistance of L. If R is in parallel with L and C, then the circuit Q is not ω L/R.

On page 240, figure 12-5, Rider finally shows a parallel circuit with a resistance R included. This circuit doesn't have R in series with just the inductor, so the circuit Q is not ωL/R. The formula 2 ∏ Q L f doesn't apply to this parallel circuit.

It's true that the formula 2 ∏ Q L f applies to the case of a high Q parallel circuit with the resistor in series with only the inductor (and not the case where R is in parallel with both L and C), but you wouldn't know that from what's shown in Rider's book. The parallel circuit he shows (in figure 12-5) is not the one for which the formula 2 ∏ Q L f applies, but the reader would most likely think that it does, since that's the only parallel circuit including a resistance that he shows, and he only gave (earlier) one formula, 2 ∏ Q L f.

The purpose of my long post is to point out that the phrase "parallel circuit" in this context is ambiguous; there's more than one topology with resistance to which that phrase applies, and different formulas for the resonance frequency and impedance at that frequency.

This ambiguity isn't present in the case of a series resonant circuit; there's only one topology.

Your post #1 suffered from this ambiguity about parallel resonant circuits, hence the warning about blindly using formulas which are not well explained, if at all.

The reason for so much math about parallel resonant circuits should be apparent.
 

Thread Starter

Ragwire

Joined Dec 9, 2013
36
I'm sorry that you are so thin skinned.
That's rich. You come here whining about not being able to find someplace that will feed you formulas because you don't want to be bothered having to thing, and when people don't trip over themselves to stroke your ego you go stomping and pouting away.
...Not surprising, since you want everything handed to you on a silver platter and this forum is reluctant to do that, instead encouraging people to actually learn something. So it is fundamentally not a match for your tastes.
And herein lies the problem. You were taught to be an equation monkey. You were fed equations and told when and how to use them. You don't understand where they come from or why they are valid in some circumstances and not in others. Hence, when you forget them, you have no fundamentals to fall back on and figure it out, you have to go hunting around for someone to feed you the equations all over again.
Are you kidding me? I don't have time for your kind. Don't talk to me anymore.
 

Thread Starter

Ragwire

Joined Dec 9, 2013
36
Electrician: I am at work and busy, but yes, I see your point that the write up in that book can be confusing. I believe the reader is assumed to know that the XL at resonance divided by the series resistance of the inductor of that tank circuit is the Q factor of the complete tank circuit. I believe this is why he is using the example in calculating gain of the single stage amplifier. Mr. Rider has written a more than a few electronics books, and included many of these booklets in the schematic diagram volumes he published, and I do not believe that the technique he is using is wrong.
 

WBahn

Joined Mar 31, 2012
29,978
Are you kidding me? I don't have time for your kind. Don't talk to me anymore.
Don't you think it's rather childish to make statements toward someone and then tell them not to respond? What's next, sticking your fingers in your ears and yelling, "La la la," over and over?
 

studiot

Joined Nov 9, 2007
4,998
LvW
For example, the question
* what is Q (are there different definitions?) , and
* if it really changes with frequency (as mentioned by you)
may be interersting to discuss.
Yes there are different definitions, including my OOps one in post#35

I'd like to thank all those who noticed my inadvertent inversion of Q there.

Say that again quickly Mr Bond.

But seriously yes, Q can be defined in different, but equivalent ways. WBahn has alluded to another and there are even versions for mechanical systems.

However.

What we are calling Q should really be awarded the symbol \({Q_0}\).

That is the Q at resonance.

We can then use the more general Q, for a general frequency ω.

The impedence equation for the tank circuit then becomes

\(Z = \frac{{{R_0}}}{{1 + j{Q_0}\left( {1 - \frac{{\omega _0^2}}{{{\omega ^2}}}} \right)}}\)

It should be noted that WBahn's √2 definition is the basis for one type of Q meter.

It is also woth noting that another approach is a graphical one, drawing phasors. This allows the highly visual demonstration of the point that the Electrician made, viz that theere can be two solutions to the parallel case.

At resonance do we mean max impedance, current or voltage (across the capacitor)
 
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Thread Starter

Ragwire

Joined Dec 9, 2013
36
Don't you think it's rather childish to make statements toward someone and then tell them not to respond? What's next, sticking your fingers in your ears and yelling, "La la la," over and over?
Once again a transfer of one's own behavior onto the expectation of others' behaviors. I think that is common with a narcissistic personality disorder.
Maybe you should look into it? I still will not spend time discussing any circuit theory with someone who appears to fly into an infantile, and insulting rage over not being able to read and understand my posts. You may or may not know your stuff, but I personally find your communication, social and comprehensive skills are so tragically lacking that you seem to already have in your mind what negative thing you are going to say or write before the other person could even ask a question. I must assume you do this to your students, and this is why I question your fitness to teach.

This entire topic has become a bore. I'm out.

Go ahead and write your next pissy little girl post. I will not read it.
 
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WBahn

Joined Mar 31, 2012
29,978
Once again a transfer of one's own behavior onto the expectation of others' behaviors. I think that is common with a narcissistic personality disorder.
Maybe you should look into it? I still will not spend time discussing any circuit theory with someone who appears to fly into an infantile, and insulting rage over not being able to read and understand my posts. You may or may not know your stuff, but I personally find your communication, social and comprehensive skills are so tragically lacking that you seem to already have in your mind what negative thing you are going to say or write before the other person could even ask a question. I must assume you do this to your students, and this is why I question your fitness to teach.

This entire topic has become a bore. I'm out.

Go ahead and write your next pissy little girl post. I will not read it.
Yeah, right. Here's to hoping, but, "Once again a transfer of one's own behavior onto the expectation of others' behaviors. I think that is common with a narcissistic personality disorder."
 
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t_n_k

Joined Mar 6, 2009
5,455
Also, for a parallel resonant circuit, there can be more than one definition of resonance.

One definition is that resonance is taken to be the frequency where the terminal impedance is a pure resistance (zero phase angle).

Another definition is the frequency where the impedance magnitude is a maximum.
Another is possibly excitation of the circuit at its natural frequency.
A quote from Ronald E. Scott's August 1964 book - "Linear Circuits" states on page 618: "The condition for resonance is thus the coincidence of the driving complex frequency with the complex frequency which represents the natural behavior of the circuit."
 

Thread Starter

Ragwire

Joined Dec 9, 2013
36
Yeah, right. Here's to hoping, but, "Once again a transfer of one's own behavior onto the expectation of others' behaviors. I think that is common with a narcissistic personality disorder."
Alright, I apologize if I overreacted. All I wanted to know was why it was so difficult to find a simple relationship on the web, as part of the the existing information/formulae. I am not a mathemetician, but I am not, nor have learned from, any "equation monkey" either. Your postings were rather harsh, and made untrue assumptions about me and my teachers. Naturally I was offended.

I would rather discuss technology than rant.
 

studiot

Joined Nov 9, 2007
4,998
I would rather discuss technology than rant.
Well then let's discuss it.

There is much technical material in this thread now.
My post#50 would be a good start.

Also my post#11 was meant to highlight the fact that incorporating a tank circuit in a valve based design, and taking measurements with a VTVM will face a load impedance of around 10M from the next stage, whilst using semiconductors the load figure will be perhaps 1000 times less at 10K.
This significantly affects calculations.

Also, How do you obtain your Q?

If by measurement you need to make it clear that you probably need an RF VTVM.

And thank you for the link to the pdf.

In return

There is a good section on Q meters in 'Basic electronic Test Instruments', by R Turner which is from that era or perhaps a decade later. Of course these employ RF VTVMs

I'm sorry I don't have any links to pdfs for this.
 
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