Re: LCLR Resonance...

["Tesla list" <tesla@xxxxxxxxxx>]

Original poster: Harvey Norris <harvich@xxxxxxxxx>



--- Tesla list <tesla@xxxxxxxxxx> wrote:

> Original poster: "Rajesh Seenivasan"
> <rajeshkvs@xxxxxxxxxxx>
>
> Dear forum members,
>
> Yesterday, I tried to simulating the behavior of a
> LCLR circuit using
> PSPice. I connected a LCLR circuit to an AC source
> (sine wave
> generator). The analysis type was 'AC sweep'.
> Using PSpice, I plotted various graphs with
> Frequency on the x-axis
> and the following three parameters in Y-axis:
> 1. Current through Parallel Inductor (inductor in
> tank circuit)
> 2. Current through Parallel Capacitor (capacitor in
> tank circuit)
> 3. Current through Series inductor.
>
> My understanding is that at resonance:
> 1. The current through the tank circuit's L and C
> will be same.
> 2. The tank circuit's (either through L or C) will
> be IN PHASE with
> the input sine wave source.
Hi Raj; You mention some basic points here which
should be clarified.  Not specifically being a tesla
coil builder myself, nevertheless I was able to apply
the same principles of air core resonance to
investigate frequencies near 500 hz from common AC
alternators. In this instance to say that the tank
circuit's current will be in phase with (either
through L or C) is a very generalized statement that
may hold truth. On the parallel branches containing L
and C in the tank circuit, each current direction in
the branch sides is ALMOST opposite in time, therefore
direction, or almost 180 out of phase: but it is the
net difference in the non-perfect 180 timing that
enables the difference to be measured as a Q factor
and that net difference to be meaured as input current
to the branches. Since the currents at a node are
known to be simple additions of current quantites
entering and leaving a junction: this nevertheless
does not specify how the "timing" of those entering
and exiting currents can occur and how it subverts the
ordinary Kirchoff addition laws. In three phase one
has 1.7 Amps serving two one amp delivery lines 120
out of phase. As the phase angle between the branches
increases towards 180 degrees, less input current
enables a greater circulation. Typically the
understanding between series resonance causing voltage
rise; and parallel resonance causing amperage rise is
misunderstood in entirety because the fundamental
"source frequency" resonance laws have been
overlooked. The inductive reactive current of a air
core coil is actually never 90 degrees out of phase
with the source voltage, rather the ratio is
negotiated from the phase angle  established from X(L)
vs R. If the inductive reactance equals the
resistance, that is only a 45 degree phase angle, not
a 90 degree angle by simple virtue of the device being
called an inductor. The ratio exibited as the Q factor
X(L)/R, in turn predicting the voltage rise at series
resonance only applies to the ideal case, not the real
case in which a reduction of  predicted Q factor is
usually the case. It may be tempting to conclude that
in these cases of imperfect resonance that the current
will  never completely follow the source of its
voltage, and lag slightly behind, hence the lack of a
perfect q factor. A simple example of an inductor
showing a Q of 5 was found at ~500 hz. It will conduct
5 times more current, and show 5 times more voltage
inside the LC midpoint reference point to the outside
of the circuit, then is the voltage imposed upon it by
the alternator. If the C in the series is shorted, or
either the L, both reactors consume aproximately the
same current, 5 times less then at resonance. This is
the reactive current. If it is balanced as opposite
reactive currents in branches as a tank circuit the
original reactive current remains in the loop, but the
input current is reduced 5 times. Again the input
current is only due to the mistiming of opposite
currents between each side of the current loop, with
the net difference in time being that amount of
current being admitted into the loop acoording to
nodal laws of entering and leaving currents,(in
instantaneous time) More specifically is the confusion
regarding a tank circuit and a series resonant circuit
when the input is not given as a line coupled input as
wires leading into or out of the structure as a
schematic embodiment.  In series resonance the current
through L is closely in phase with the source voltage
at series resonance, but at parallel resonance the
current, and its associated magnetic field is closely
180 out of phase. However those definitions apply to
"line coupled" or wire connected circuits where the
definitive differences between series and parallel
resonance are clearly defined. If however the
quantites of L and C are simply connected together as
a loop, and then given an exterior influence through
air induction as the source of secondary currents as
an air core transformer, then since no exterior
currents are line connected to the LC loop, the
opposing currents in the loop will be almost perfectly
balanced and the outside of the circuit will show
practically no voltage input, but the inside reference
point to outside or ground will show a high voltage
gain. This definition itself however is lacking
because the distinction between inside and outside of
the circuit is never made until the addition of loads
whether they be attached to the exterior portions of
LC in series, or a pathway from the LC midpoint.
>
> Question:
> I noticed that at resonant frequency the current
> through the Series
> inductor was not IN PHASE with the input AC (sine
> wave) source.
If you are speaking of the tank circuit, the current
through the inductor should be more then 90 degrees,
towards 180 instead.

The
> phase difference between the AC source and the
> current through the
> series inductor was approximately 90 degrees. Is
> that true?
Shouldnt be. But one should note that at 60 hz the
reactive state of the inductor might not even be close
to 90 degrees to begin with. All depends on the size
of the inductor to begin with.
> Also, I have read in some SSTC articles that
> explains the use of PLL
> to auto-tune the coil.  Is it possible to use the
> current through the
> series inductor as the feedback signal? One thing I
> noticed is that
> at resonance, the series inductor current is not in
> phase with the ac
> sine wave source.
Note if the q factor obeys real conditions.
> I can use the current through the Tank circuit's L
> or C will be in
> phase at resonance and it can act as a feedback
> (either using an
> antenna or current transformer). But, I would like
> to use the series
> inductor's current to lock to the resonant
> frequency. Please let me
> know your suggestions.
>
> Thanks and regards,
> Raj.
>
>
>
>