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RE: Series or Parallel resonant ?

Hi Richie and All & Seasons Greetings,

Thanks for the acknowledgement on Secondary being Series resonant.

I chose to deal with the Sec issue first on the list.
Has anyone recognized the similarity in excitation of the Pri & Sec ?

Consider this for the Primary:
If it is parallel resonant it would be a 'trap' 
EXCITATION in parallel where the source generator current is minimum at
resonance, i.e. the Z of LC = Max. 
This is a condition of "antiresonance" or "rejection" !,
and is most associated with radio frequency procession for reception, etc..
reference: ARRL Handbook, 1995, Pg 6.35, Fig 6.67

This does not appear to be the case for the TC.
 
A charged Pri Tank Cap shock excites the Pri at a peak current followed by
Pri Ringdown as that energy transfers back and forth between the
electromagnetic field of the inductor and the electrostatic field of the
Capacitor less the 1st order resistive loss of the GAP ***, coupling that
energy resonantly to the Sec LC where the same process brings about a
Voltage Maximum and Sparks fly, dissipating that electromagnetic and
electrostatic stored energy (otherwise the energy is decrementally consumed
in resistive losses Pri & Sec (Pri losses coupled to Sec) - coupled Rgap,
unseen PRI/Sec corona and DC resistive leakage to ground (coil form,
coating, moisture/dust on surface), inductor series Rdc, Capacitor parallel
Rleakage (which may be represented by a resistance in series with the Cap
%%%), cycle by cycle)
++++++++++++++++

*** I propose the Gap in the Pri Tank circuit is a "generator source" (for
model)

The energy initially stored in Cap is first transferred to Lpri
 setting up LC decrement that appears to be sourced from this Rgen
resistance.

 Rgen = Rgap + inductor&wiring_Rdc + cap_RseriesEquiv(convert from
Rcap_parallel)

The equivalent Pri circuit then looks like Sec Series Resonance as Richie
drew.

A generator = switching of energy source in form of Pri tank "Pre-stored"
energy .

A square wave {implemented w/simple switch between energy source-Hi and
short-Low}
   is composed of a sinewave fundamental + all of the sinewave's odd
harmonics.

The Pri behavior behaves like Series Resonance.

  The circulating peak Current is maximum, 
  The junction between LC is at Maximum pk=pk due to

      Vpk =  Ipk*Ipk*Z   (where Z = XL = Xc (+ tiny Rdc) at resonance)
+++++++++++++

%%% Here is the revelation, (OK, just a derivation)

Cap, C
Xc = cap's reactance
Rp = resistance in Parallel with Cap (dielectric leakage, Requiv of Spark !)
Rs = ESR: resistance equivalent to Rp  (substitute for ckt modeling)

  Rs = Xc^2/Rp  = 1/(Rp*(2PiFC)^2)

Richie, as you now realize this has nothing to do with 1/4 wave theory !
(whew)
   just basic physics, electronic engineering.

asside: DF, dissipation factor, is Rs/Xc 
so corona/spark loading (decreasing Rp) decreases DF 
by increasing equivalent series resistance of the Sec which couples back to
Pri.

A power strike to ground drains energy from Csec then Lsec & coupled LCpri
 increasing Pri equiv series resistance easing gap quench !?

2nd asside: A Cap's Loss Angle causes additional parasitic R
 due to the electromagnetic properties of dielectric materials.
 Due to the very intense peak tank currents, may merit consideration.
++++++++++++++++++++++++

Well I hope I haven't confused the issue further.

Terry, 
Utilizing this relationship may aide PSPICE model refinement
to explain nonlinear sparking behavior (cause & effect).

Comment, Opinion welcome !

Regards, 
Dale
Redondo Beach, Calif

-----Original Message-----
From: Tesla List [mailto:tesla-at-pupman-dot-com]
Sent: Wednesday, December 15, 1999 11:27 AM
To: tesla-at-pupman-dot-com
Subject: Re: Series or Parallel resonant ?

Original Poster: "R.E.Burnett" <R.E.Burnett-at-newcastle.ac.uk> 

Hi Dale and all,

In a typical TC schematic the base of the secondary is grounded, and
the top of the secondary has capacitance back to ground.  So my initial
opinion was that this is best represented as a parallel resonant
network.  That is how it appears on paper anyhow.

However,  as you correctly pointed out,  voltage is actually induced
into the lower few turns of the secondary due to transformer action
with the primary circuit.  This changes the "equivalent circuit" such
that it appears as a series resonant circuit with a voltage source at
the base of the secondary inductor.   See below:
      ______________
     !              !  <--- Top of secondary
     !              !
     !              !
      )             !
      ) Ls        __!__  Cs
      )           _____
      )             !
     !              !
    _!_             !
   /   \            !
   \___/ Vac        !
     !              !
     !              !
     !______________!  <--- Ground

Vac is the voltage induced into the bottom hundred or so turns by
coupling with Lp.  Ls is the secondary inductance, Cs is the total
secondary capacitance.  This is obviously a SERIES RESONANT CIRCUIT.
Of course you are right,  it is me that is getting confused !

The situation is even more clear in the case of the extra coil in a
magnifier.  This coil is end fed from a stiff voltage source and also
behaves as a series resonant circuit.  In this case Vac represents
the output of the driver.

I agree that the primary circuit is parallel resonant when the spark
gap is in conduction.

You are the first person who has spotted this mistake.  Thankyou for
pointing it out, Dale.  I will correct the web page as soon as I can.

You lost me with the bit about secondary discharges being represented
as an equivalent Sec series resistance.  I am not too hot on the 1/4
wave theory of the secondary.  Although I have heard that loading at
the top of the secondary causes a rise in base impedance.

Any more comments on this topic ?

						Cheers,

						-Richie,

> Original Poster: Dale Hall <Dale.Hall-at-trw-dot-com> 
>
> One befuddlement:
> The Secondary is referred to as being parallel resonant.
> At parallel resonance, voltage is minimum across LC 
> and minimum current is sourced from a parallel generator.
>
> In a classic TC, Primary energy and its loss resistance
> is coupled as a low impedance series generator into the Secondary,
> effecting a Series Resonant condition.
> The generator current is maximum (requiring a low Z source),
> limited by Rdc_inductor+SeriesEquivCoupledPri&ArcLoad,
> the LC junction (top of Sec) voltage is maximum at resonance.
>
>  Discharges represent resistance in parallel with both Sec L & C,
>  that can be represented as an equivalent Sec series resistance.
>
> Comment ?  
> Am I confused ? perhaps series=parallel depending on how viewed ?
>
> The Primary LC is parallel resonance since energy is provided
> in parallel from precharged Pri Cap prior to a brief switch closure
> to transfer stored energy.
> When the switch is open the generator charges the Cap in 
> a dormant, not part of the resonant period, isolating its losses (?).

> Perhaps the confusion is due to the impulse excitation of TC's Vs
> continuous
> nature of the generator (signal source) so a comparison loses meaning ?
> Help ?
>
> Regards, Dale