# RE: A question about LCR circuits

```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
>     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>
>
>

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