RE: A question about LCR circuits

To: tesla-at-poodle.pupman-dot-com
Subject: RE: A question about LCR circuits
From: Tesla List <tesla-at-stic-dot-net>
Date: Thu, 15 May 1997 09:11:25 -0500
Approved: tesla-at-stic-dot-net
Subject:      RE: A question about LCR circuits
       Date:  Thu, 15 May 1997 17:52:26 +1200
       From: "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
Organization: Wellington Polytechnic, NZ
         To:  tesla-at-pupman-dot-com


Hello Heinz,
              Perhaps the method I used is what is causing confusion.
The object was to find the value of Q which would prevent the circuit 
from ringing. Therefore, one equates the frequency to 0 Hz in order 
to find this out. The unforced ringing formula I started with is 
essentially that which you have outlined. The difference is that it 
applies for _all_ frequencies and is therefore entirely general. As 
you can see, it is not the popular equation incorporating L and C 
only. It takes the circuit series resistance into account. You are 
quite right that the "standard" formula is a good approximation for 
high Q's because high Q => low series resistance and we can safely 
ignore what little there is, particularly for the secondary coil.
If you plug typical secondary values into the general formula, you 
find that the R^2/4L^2 term is around 5 orders of magnitude less than 
the 1/LC term and can be disregarded for most purposes.

Hope this makes sense,
Malcolm

>   From:  Heinz Wahl <hwahl-at-jtc-campus.moric-dot-org>
>     To:  "'Tesla List'" <tesla-at-pupman-dot-com>
> 
> 
> Malcolm,
> 
> I know you didn't come out and say "the circuit cannot ring at and below
> DC" but you equated f=0, which I read as D.C. It
> might be easier to state that lower values of Q are easier to tune
> because they ring in a broader BW. However, if Q < 10 then
> you don't use the simple formula fr=1/(2pi sqrt(LC)) because the angle
> between Il and Vt = 84 degrees and changes more so
> below Q = 10. Of course at this point the circuit is so sloppy it'll
> resonate at any frequency but dampen rapidly. When Q falls
> below 10 try the formula fr= 1/(2pi sqrt(LC)) sqrt(1-(CRl^2/L)). I read
> ahead in the e-mail and see that you have performed
> and experiment in regard to this. 
> 
> Regards,
> 
> Heinz
> 
> 
> 
> Heinz,
>          Given the value of Q=0.5, take any LCR circuit and arrange 
> the values in it so that it equates. It certainly can't ring at any 
> frequency. 0.5 is the value for critical damping for any filter is 
> it not? This is standard filter theory according to the texts I've 
> read on the subject.
>     I did not say "the circuit cannot ring at and below DC" did I? I 
> said "a circuit with a Q <= 0.5 can't ring".
> 
> Malcolm
> 
> > If you equate f=0 your talking D.C.. "at and below which" your circuit
> > can't ring.
> > 
> > Heinz
> <snip>
> 
>