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 09:28:06 -0500
Approved: tesla-at-stic-dot-net
Subject:  Re: A question about LCR circuits
  Date:  Thu, 15 May 1997 05:37:26 +0000
  From:  John H. Couture" <couturejh-at-worldnet.att-dot-net>
    To:  Tesla List <tesla-at-pupman-dot-com>


At 05:33 AM 5/14/97 +0000, you wrote:
>Subject:      Re: A question about LCR circuits
>       Date:  Wed, 14 May 1997 09:25:41 +1200
>       From:  "Malcolm Watts" <MALCOLM-at-directorate.wnp.ac.nz>
>Organization:  Wellington Polytechnic, NZ
>         To:   tesla-at-pupman-dot-com
>
>
>Hello John,
>            You wrote in reply....
>
>>   From: "John H. Couture" <couturejh-at-worldnet.att-dot-net>
>>     To: Tesla List <tesla-at-pupman-dot-com>
>> 
>-------------------------------    Big Snip
>> 
>>   The critical damping point is when R = 2 sqrt(L/C) .
>
>i.e. 0.5=X/R  That is precisely the endpoint of my maths.
>
>>   When R is less than
>> this value the circuit will oscillate. When greater the circuit will be
>> aperiotic or will not oscillate.
>>   The circuit will oscillate with Q below .5 if the R is less than 
>>  2 sqrt(L/C) and X is less than R/2 .
>
>What you appear to be saying is: R < 2X  AND  2X < R  ??????  
>
>Malcolm
>
>----------------------------------------------------------

  Malcolm -

  I now know what you are trying to tell us. As you did not say in your
post
how all this related to Tesla coils, it was difficult to determine
exactly
what you meant regarding LCR circuits and resonant frequencies.

  The equation you used for resonant frequency 

         Fr = (1/6.283) sqrt(1/LC - R^2/(4L^2)

  is shown in my Tesla Coil Construction Guide page 5-1. In there I said
"
>From this equation it can be seen that a high resistance value will decrease
the resonant frequency and if large enough will cancel out the LC value
in
which case there will be no resonant frequency. This does not occur with
Tesla coils because the resistance is never high enough".   Note that I
did
not say the resonant frequency equated to zero. This is why your
derivation
confused me and apparently others.

  You show that   Q = sqrt(L/C)/R   Where did you find this equation? 
  As Z = sqrt(L/C)  this gives       Q = Z/R = cos A 
  Now I have often seen that   Q = X/R = Tan A   in the literature but
not
                Q = Z/R = cos A     
  The Q factor cannot equal both cos A and tan A.

  You indicate that the effective resistance (for Tesla coils?) is
easily
measured. Would you explain this test?

  I agree with you that my last sentences regarding critical damping and
Q
below 0.5 were confusing and in partial error. If my description of what
I
thought I said was followed you would always arrive at Q = 0.5 which is
what
you pointed out at the beginning of this dissertation.

  Tesla List appreciates that you are helping further the progress of
Tesla
coil understanding. Do not feel upset that it results in controversy
because
you are not alone. Many contributors to Tesla List including me run into
the
same difficulties.

  John Couture