Confused dude, and by orders of magnitude, dude

[Gene Zumchak]

Bill, Scott and Others:

    The time contant, tau, does not relate to frequency.  Tau comes from the
general solution of a first order differential equation:  dx/dt  + at = K.  The
solution is

x(t) = Ae^-(t/tau) + B    (read e to the minus t over tau)

The constants A and B are determined by initial and final conditions.  A
typical first order system is an uncharged capacitor connected to a voltage V
via a resistor R.  The solution for the voltage on the capacitor, Vc is as
follows:

    Vc = V ( 1 - e^-(t/RC) ) where the time constant tau in the general
solution is equal to the product RC.  This charging circuit is not an
oscillator and has no frequency associated with it.

    When t  = 1 tau in the above equation, the exponential evaluates to e^-1
which is .36879etc.  1 - .368 equals .632.  Accordingly, for the charging
capacitor example, the cap charges to 63.2% of the final value in one tau.  In
two time constants, .Vc reaches 86.5% of the final value, which incidentally is
reached only when the exponential in the above equation reaches zero which
happens at infinity (or in 2000 as I pointed out earlier).  In five time
constants, 99.33% of the final value is reached and 5 tau is accepted as good
enough for the final value.

    None of this has any bearing to voltage-controlled analog oscillators whose
frequencies are invariable dependent upon a capacitor linearly charged and/or
discharged with a current source.  The frequency depends upon the current, the
value of C and the thresholds between which the waveform oscillates.

Gene Z.



Bill Layer wrote:

> Hi Scott, All,
>
> >If the time constant of an RC circuit is one second, how can the frequency
> >be 1/6 hz?  Isn't that 1 hz?  Isn't freq the reciprocal of the time
> >constant?
>
> The time constant is 1 second, which means it requires 1 second to charge,
> and 1 second to discharge, to complete a full cycle.
>
> Since we have a complete cycle every 2 seconds, I would say the frequency
> is 0.5Hz. based on the values given.
>
> >
> >-- Scott Gravenhorst
> >-- FatMan: www.teklab.com/~chordman     | Linux Rex, Linux Vobiscum
> >-- NonFatMan: members.xoom.com/chordman | RedWebMail by RedStarWare
> >-- Al Gore: I'm the father of the internet.
> >
> >
> Bill Layer
> Sales Technician
> <b.layer at vikingelectronics.com>
>
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