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Guide 60HzMatch
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All,
I need feedback on the following possible entry for the Guide. (It is no
longer the Idiot's Guide. Just the Guide).
Critique style, tone, syntax, grammar, but especially home in on content,
useability, etc. For all I know, this may be totally wrong.
If you have ANY relevant material, please e-mail to me Re:Guide 60HzMatch.
*** Beginning of article
MATCHING THE IMPEDANCE OF THE TRANSFORMER AND THE CAPACITOR
This section discusses material that affects the efficiency of operation.
It also affects the quality of the spark produced at the spark gap.
By carefully matching the impedance of the transformer and the capacitor,
the efficiency of the circuit can be improved. Matching will allow us to:
a) Get maximum delivered power from the transformer.
b) Use the smallest capacitor necessary to store the power delivered by the
transformer.
The transformer secondary winding has a characteristic impedance at 50/60Hz
that will limit the maximum current that the transformer can deliver. You
can model the transformer as a perfect voltage source in series with an
inductor and a resistor. The resistance is caused by
the length and diameter of wire used in the construction of the
transformer's secondary. The inductor represents the inductance of the
transformer secondary, which causes its AC resistance at 50/60Hz. {Fig ??
Eq ??}
Methods for measuring actual transformer secondary impedance are given in
{Ref Transformer Sec ??}
The current available at any given instant from a given transformer is
limited by the transformer's instantaneous voltage and total effective
resistance at that instant.
If a capacitor and an inductor are connected in series, and if the
inductive reactance and the capacitive reactances are made to be equal,
then the effective total reactance equals ZERO. For a given inductance and
capacitor, this will occur at only one particular frequency, known as the
resonant frequency. {Eq ??}
Note: Some authors prefer to refer to this as the anti-resonant frequency,
because at this frequency the overall Series Circuit resistance is at its
Minimum. In a Parallel Resonant Circuit the resistance is Maximum at
Resonance.
Note: Do not confuse this 50/60Hz resonant frequency with the resonant
frequency of the RF portion of the Tank circuit, or the self-resonant
frequency of the secondary.
You might object that it doesn't LOOK like the transformer and capacitor
are in series, but they are. That is because we can consider the circuit AS
IF the transformer was a perfect voltage source in series with a resistor
and an inductive reactance, and the capacitor as if it were a perfect
energy storage device in series with a resistance and a capacitive
reactance.
At Resonance the circuit reverts to acting like a perfect voltage source, a
resistance, and a perfect energy storage device connected in series,
because at resonance the reactances cancel. At resonance the transformer is
able to transfer the maximum current possible to the capacitor.
If the Spark Gap were to fire at the instant the above mentioned Maximum
voltage was reached across the capacitor, then the system would be firing
at a point where optimum energy useage was being achieved.
It has been shown that for optimal efficiency (and operation) the power
capacitor's capacitive reactance should be equal to the inductive reactance
of the transformer. When this is done the capacitor's capacitance rating
will be the smallest value possible that will allow that particular
transformer to transfer the maximum possible charge within a given half
cycle. {Eq ??}
If the inductive reactance of the transformer is greater than the
capacitive reactance of the capacitor, then this results in a lower maximum
voltage appearing across the capacitor, with resultant reduction in the
total charge transferred to the capacitor during the charging time. The
capacitor is under-utilized. This means that the capacitor is actually
larger and more expensive than it has to be. The Tesla coil will work, but
efficiency is lower than it could be.
If the inductive reactance of the transformer is less than the capacitive
reactance of the capacitor, then the transformer will cause the capacitor
to reach its maximum voltage early in the charging cycle. In this case the
transformer is under-utilized. As we shall see later, this can create
excessive flame arcing at the Spark Gap. {Ref Spark Gaps}
{Prog ??: Transformer and Capacitor Matching}
Additional Remarks:
If RF chokes are introduced into the transformer circuit, then their
inductive reactance at 50/60Hz may have some effect on the total inductive
reactance, though it is generally small compared to the inductive reactance
of the transformer's secondary.
The RF impedance of chokes does not enter into this
discussion of matching, because in matching we are only concerned with the
charge cycle, not the discharge cycle.
The inductive reactance of a transformer's secondary may vary. This can be
due to such things as Saturation of the core, or the inclusion of
resistances and/or inductances in the PRIMARY circuit. This is especially
the case with pole pigs, as they are often fitted with things like arc
welders and heating coils for use as ballast. {Ref Pole Pigs Sec 112} The
use of a variac will affect the secondary's inductive reactance, because a
variac is actually an autotransformer. With some of the larger Tesla coils
it may be adviseable to measure the actual inductive reactance of the
composite secondary rather than trying to determine it with a formula,
since some of the factors entering into play are not readily known.
Neon transformers sometimes have Power Correction, Magnetic Shunts, and
other features that may affect the actual inductive reactance. {Ref
Transformers}
If a transformer has been modified by removing magnetic shunts, then the
current rating will be greater than that indicated by its original
nameplate. {Ref Modifying Transformers}
*** end of article
1) OK, what do you think about this as a possible entry in the Guide?
If you think an equation is necessary, useful, available, just say
so. If you know the equation, please supply it. Identify all
variables. I will attempt to normalize equations so they are
somewhat consistent.
What is wrong? If you can, write what you would propose to put in
its place.
What is missing? Be as explicit as you can.
2) I need the actual formula for computing transformer impedance.
Someone on the list said Ztrans=Etrans/Itrans. Is that right?
Does that mean that a Neon with a tag that says 12KV -at- 30ma
has Ztrans=12000/.030 ? That seems AWFULLY High!
That implies that a 12KV Neon produces 30ma when you short
out the secondary and its voltage drops to ZERO.
That further implies that the Neon WASTES 360 Watts
when the current is 30ma. Can't be, can it?
Isn't the 30ma the rated continuous current.. and isn't
12000 the OPEN circuit voltage with NO LOAD?
(Or have I misunderstood the tag rating?)
I am more familiar with regular transformers, where
the power rating is the product of the voltage at
rated current, and the rated current.
Shouldn't the circuit be loaded down
until it produces the 30ma and then measure the voltage...
Then the difference in voltage from 12000 would be the
voltage being dropped ACROSS the impedance at a draw of 30ma
and the formula would now be:
Ztrans=(E1-E2)/I where E1=open circuit voltage (12KV)
E2=voltage at terminals when load draws rated current (Say 11KV)
I=rated current (.030 Amps)
****
Thank you for reading this. I would appreciate any constructive criticism
you might have regarding this particular article, or the Guide itself.
Fr. Tom McGahee