Re: Pig Ballast -> description of complex conjugate of load (fwd)

---------- Forwarded message ----------
Date: Sun, 19 Jul 98 10:32:13 EDT
From: Jim Monte <JDM95003-at-UCONNVM.UCONN.EDU>
To: tesla-at-pupman-dot-com
Subject: Re: Pig Ballast -> description of complex conjugate of load

>Date: Sat, 18 Jul 1998 15:16:34 -0500 (CDT)
>From: Larry Bud Melman <gasman-at-althea.a-line-dot-net>
>To: Tesla List <tesla-at-pupman-dot-com>
>Subject: Re: Pig Ballast Question (fwd)
>	I have only a limited background in electronics and physics.
>Would you explain what the 'complex conjugate' of the load is?
>Sounds like you're talking about imaginary numbers...  :-)

  Yes, complex numbers...

  Starting with the facts that voltage across an inductor is
  directly proportional to its inductance and the rate that the
  current is changing and the current through a capacitor is
  directly proportional to its capacitance and the rate that the
  voltage is changing, you can eventually show for steady-state
  conditions with sinusoldal inputs that an inductor can be
  treated as an imaginary number j*w*L and a capacitor as -j/(w*C),
  where j is the square root of -1 (usually called i in math areas
  but j in engineering because i is already commonly used to denote
  current), w is the angular frequency, L is inductance, and C is
  capacitance.  Using these numbers, steady-state voltages and
  currents in circuits with resistors, inductors, and capacitors
  that have a sinusoidal input can be determined.

  As a simple example, suppose you have a 1nF capacitor in series
  with a 1k ohm resistor and you plug the unconnected ends of the
  capacitor and resistor into a typical 120 V RMS, 60 Hz wall outlet.
  Since w=2*pi*f, w=120*pi.  The reactance of the capacitor will
  be Z= -j/wC = -j/(120*pi*1E-9).  The voltage across the resistor can
  be found using a voltage divider VR = 120*(1000/(1000+Z)).  Similar
  calculations can be done for current.  Notice that VR and the others
  are complex numbers.  The magnitude of the number is the voltage and
  the phase is relative to the 120 volt input.

  Relating this to Tesla coils, ballasting, and power transfer, notice
  that wL is positive and -1/wC.  Suppose you are given an L, such as
  from a transformer.  By choosing C appropriately, you can cancel out
  the impedance from L.  This cancelling is the key to resonant
  charging and resonance in general for that matter.  Using the complex
  conjugate "removes" the reactive part of the load (either L or C) and
  allows more current and hence power to be delivered to that load.

  Jim Monte
>					Clay