How is this modulating?

[MrAl]

Hi,

You must be overlooking something here, because i did not do anything "wrong". If you think i did, then show what it was and prove it was wrong. I did EXACTLY as i intended to do, and verified with simulation data to at least 4 significant figures.

You also must state what you are calling Wo and Wn, because it does not mean anything unless you describe what it is. That's because different text's call them different things and refer to them differently sometimes. Even Wikipedia now notes what "w" it is talking about, and it must be described in terms of another circuit idea such as impedance or whatever.

So far unless you quit being so short and critical on your replies you wont get any real information across, unless you dont care to do that anyway which is what it is starting to look like. As you see i describe my formulas in complete detail so anyone that reads it can know right away what it stands for.

If after all this you still dont agree, then you can continue to argue with Wikipedia because they provide a formula which is the same as mine "w2".

BTW i recognize sqrt(a^2-w^2) but you typed it the other way around.

Also, are you still saying that in a three element parallel circuit RLC with no series R that R can change the resonant frequency?

 

[MrAl]

Hello again Einar,

My apologies on this topic here. I think we did not understand each other at first, and now i can better see what you were trying to get across. Also, what i see as sqrt(a^2-w^2) you typed as sqrt(w^2-a^2) and that threw me a little off too because i am used to seeing it as sqrt(a^2-w^2) and that way we can tell right away if the response is under damped, critically damped, or over damped. Your sqrt(w^2-a^2) could still be applied, but it has to be limited to the under damped case. In this case you are absolutely correct in stating it is the 'ring' frequency even though it takes a certain level of damping to see this happen. It's still a valid idea however so that's good and it's also good of you to point this out.

However, i still have reserves whether we should care too much about this or the over damped ring frequency because in the circuit and application we were talking about we care most about the actual electrical resonant frequency where we see a dip or valley in the response, and dont care too much about physical energy ni the circuit unless of course power comes under consideration. For the purely electrical signal i think we care only about the min or max response, and this is typically the nature by which these things are tuned in real life...ie they dont look for a ring frequency they look for a min or max in the response as they turn the capacitor screw

You've helped identify this third frequency however and i think that is very good of you to stick with it. I think we have all three now, and i just wish i could find that paper on the geometric oval relationship between the three (it's been a long time now since i read that paper). Maybe you have some info on this somewhere.

 

[EinarA]

Hi Al. After more thought and work I realize that eq 1 in post 39 is just an approximation of eq 3, but written for Rs, where eq 3 is for Rp. You can transform a series R into a parallel R with the formula: Rp=Rs*Q^2. This gives good results only with fairly high Qs, ten or more. Plugging this into either eq 1 or 2 and they turn out to be equivalent, but only for hi Q circuits. Tests with some actual circuits confirm this. However, adding either a series R or a parallel R made the peak frequency go up so eq 1,2 do not describe what is happening. It appears that your eq 3 does describe the effect correctly, but I haven't tried putting numbers in it yet.
None of this really applies to the oscillator circuit though because phase trumps amplitude. With excess gain the frequency will be that which makes the phase around the loop zero. I dug up an equation for the Fo of a Colpitts oscillator but it didn't predict the changes to Fo that Jim has given.
I am sorry that you find my brief posts frustrating but this one has taken about forty minutes; I am simply never going to be up to the long ones you make.