What's with the page of math on the impedance calculations for parallel resonant circuits? Why not just use the old (apparently, lost knowledge?) formula of Z = 2*pi*f*L*Q?
L is in Henries. Just multiply the right side of the old XL equation by the Q of the circuit. Q here is the ohms of inductive reactance at the resonant frequency divided by its internal series resistance. (Assuming a negligible resistive loss of the capacitor) this is a good approximation, I believe, for finding the Z, in ohms, across a resonating parallel LC circuit for figuring load and therefore gain of amplifier. This is the formula in John F. Rider's V.T.V.M. book, and was the way I was taught. I guess that the authors of the websites I've been to do not know the simple form equations?
My point is, if someone entering electronics wanted to find simple impedeance to do a stage gain calculation, they couldn't find the information out there anymore. They would have to make a study of it. I don't understand why common knowledge for problem has disappeared in favor of Master's level mathematics. Somehow, I find that disturbing.
We have a whole generation who have become computer cripples. Funny, the story on national news was how commercial pilots have no flying skills because of their dependence on automated controls.
What's with all this calculation stuff? What in the world are you looking at? f you have some specific criticism of some web page then A) reference that page and 2) state your issue. Otherwise your rant is best served in the "off-topic" area. (Wasn't it talking Barbi who once said "math is hard"?)
Because calculating this way is not as simple as this, or more people would do it that way. You are quoting a formula for an isolated stage. In reality stages are incorporated in a complete circuit and the Q factor is affected by preceding and succeeding stages. So in cascaded stages we need to use the so called 'loaded Q' value. Do you know how to calculate this?
They would do it if they knew about it. Why can't the easy formula for finding impedance of a single LC parallel circuit be seem found on the web? Is it an oversight, or is this just lost knowledge? I was hoping to see reference to it on this site, since it has been most useful to me in the past. I searched the internet, and finally found it in a 1947 textbook. If a page is going to discuss calculating coupled stage gains, they might well start with single impedance stage with a text (not formula) explanation, then quantify it with formulae, and then show the applicable changes for mutiple stages the same way. It would be a learning experience.
1. The issue: I was hoping to find a simple formula somewhere on the web for calculating or even approximating the impedance of a parallel resonant circuit with internal series resistance of the inductor. I didn't want to have to go brush up on j operators or complex numbers to arrive at a figure for ohms. 2. I was unable to find this on the internet, or on this site, or--in particular--this web page. http://www.allaboutcircuits.com/vol_2/chpt_6/2.html I found it disappointing that I had to refer to a 1947 text book. Later I found an online calculator for this problem, and the answer from my inputed data simply agreed with the result I had earlier found in the "lost" formula. I am suggesting an improvement would be to include some of these simpler solutions, where applicable, in this site. This website has been very useful to me in the past. Sorry if I was not clear. Do you understand now?
Despite your statement that AAC has been very useful to you in the past I see that your sign up date is listed as December 2013. Now all are welcome, from old hands(like yourself ?) to circuit newbies and we pride ourselves on a warm and friendly community in general. So welcome to AAC and let us discuss your topic in a manner appropriate to the above. So I have attached a simple tank circuit, resonant at about 100kHz, at fig(1) Would you lime to discuss what happens in terms of Q when this is incorporated into a real circuit, as at fig(2)? Incidentally you do not have to go back to 1947 to find discussion of this subject. There are plenty of modern books about it. Basic Electric Circuits by A Brookes devotes the whole of chapter 13 to it for instance.
Ragwire - are you sure about this equation? Did you proof or justify it ? For my opinion, the quality factor Q is a fixed quantity, right? Does this mean that the impedance Z is increasing continuously with frequency f? Or did I misinterprete anything?
I think this gets to the nub of the OP's question. People use math differently. For instance if I needed to calculate the volume of a cone, I would have little interest in finding "the formula" for that in some book. I would do the triple integral and prove the formula. Only then might I take a look to make sure the two approaches agree. To me, a formula presented without proof is next to useless. But not everyone sees it this way and many just want "the answer". Different sources are written for different users.
There is no problem with ragwire's equation. By definition, at resonance Q = R/ωL So R = Z =ωLQ since at resonance the impedance is resistive. Hence my comment about the equivalent parallel resistance (impedence) of my tank circuit in my previous post. I am glad we are now discussing the meat of the OP, however. The use of Q is quite interesting.
It is not mine. It is from a publication by John F. Rider. I am pretty sure this is the way I learned it in school--and had forgotten. Q is not fixed. In this case it is the inductive reactance, at whatever the resonant frequency of the tank circuit is, divided by that same inductor's DC resistance. In practical terms it usually falls between two hundred and three hundred in typical radio circuits, for example. True indeed. It may be difficult for those who do mathematics for mathematics' own sake to understand that 99% of us just want a result, and quickly, so we can get back to whatever we are trying to accomplish. I have no interest in re-inventing the wheel. I am just disappointed that it is so difficult in this day and age to find practical information that I worry what will happen when the last of the vintage books rots away.
Here is the online calculator where R is the DC coil resistance: http://www.thetaeng.com/calc_LC_tank.htm Feed some numbers into it. Feed the same numbers into Z = 2πfLQ No calculus required. (I got an A in calculus, but still...c'mon, right?) LOL
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. I went for over two decades without ever doing anything with a resonant circuit. Then one day it came up in talking to a customer during a meeting for a project they had and they said that the unloaded Q of the series LC circuit connecting their sensor to our chip had to be no more than a certain amount. They didn't know what the hell Q was, but they had been given that spec by the team that was making the sensor. So, recalling that Q was a metric for the quality of the circuit, meaning how frequency selective it was, and that the only rational definition of this that made sense was the ratio of the center frequency to the half-power bandwidth, I turned over the sheet of paper and in a couple minutes was able to tell them the Q for the interface pad we presently had, which did not meet their requirements, but was also able to offer, on the fly, some changes to the pad that would allow it to meet their requirement while still being comfortably within our layout and design rule constraints. That meeting would not have gone nearly as well if I had just been an equation monkey that had to go out somewhere and search for just the right formula to copy from a book or website.
I like that. Never heard of "calculator monkey" or "equation monkey" before. I have to add that to my vocabulary. It's like when I cringe when I see students reaching for a calculator to determine the single voltage step of an 8-bit DAC with a 2.56V reference.