Re: Resonant Voltage Formula

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: Ed Phillips <evp-at-pacbell-dot-net> 

"Tesla list wrote:
  >
  > Original poster: John <fireba8104-at-yahoo-dot-com>

  > As we all know a resonant circuit driven at it's resonant frequency
will
  > have a final voltage of Vin *  Q of the circuit. I wish to know if
there is
  > a formula or method for finding the voltage at X number of cycles.
This
  > also might be useful in the up and coming DRSSTC field.

For a - single LCR circuit - the amplitude of the oscillations follows:
Vpeak = Vmax(1-exp(-t/T))
where T=2*Q/w0 and t is the time.
but t=n*2*pi/w0 where n is the number of cycles.
Vpeak = Vmax(1-exp(-n*pi/Q))
Q cycles:   0.96 Vmax
Q/2 cycles: 0.80 Vmax
Q/4 cycles: 0.54 Vmax

Antonio Carlos M. de Queiroz"

	The quantiti [pi/Q] in "Vpeak = Vmax(1-exp(-n*pi/Q))" is known as the
"logarithmic decrement" of the waveform.  The smaller the value the
longer the decay time.  In "the good old days of spark gap transmitters"
the goal of all transmitter designers was to get the lowest possible
value of "decrement" since that resulted in the "narrowest wave" and
least interference to other services.  The log decrement is just equal
to the natural log of the ratio of two successive voltage peaks which,
for exponential decay, is constant with time.

Ed