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Re: A question about LCR circuits
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>
>
<snip>
> >Dividing each side by R^2 gives Q^2 = 1/4 which => Q = 1/2 = 0.5
> >(negative square root discarded).
> >
> >This is the value of Q, at and below which the circuit can no longer
> >ring. In other words, a circuit with this value of Q loses energy at
> >the same rate as it can take it up.
> >
> >Think that's all OK but comments welcomed as always,
> >Malcolm
> >
> >----------------------------------------------------------
>
> Malcolm -
>
> I do not believe that Q = ((L/C)/R = cos A where A equals the angle
> of
> the vector parameters R, X, and Z.
I am of the opinion that belief falls squarely in the realm of
metaphysics, not science.
> Also the R does not equal the DC or AC resistance. The R equals an
> effective resistance which is a higher value and difficult to determine.
ESR *by definition* is the resistance at the frequency of operation.
It is a standard concept used in the design of SMPS. It is the
resistance *measured at a particular frequency*. It is not at all
difficult to determine. In fact, the design of the compensation
network in a SMPS requires that this value be known, if only
approximately. It is *easily* measured.
> The Q = tan A = X/R is correct. The impedance of an RCL circuit is
> sqrt(L/C) only if the effective resistance is small enough to be
> neglected.
But I haven't neglected resistance have I? What does "R" stand for in
the formulae I used?
> The sqrt(L/C)/R = cos A cannot, therefore, equal X/R = tan A or the Q
> factor.
>
> When the circuit frequency drops to zero HZ the R is so large that it
> cancels out the 1/LC quantity and the Q factor approaches zero.
Please redo my maths and highlight the error.
> When the R is small enough to be neglected the Q factor approches
> infinity.
Agree.
>
> 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