RE: Resonant capacitor charging calculations QUESTION - answered?

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

Original poster: "Pete Komen by way of Terry Fritz <twftesla-at-qwest-dot-net>" <pkomen-at-zianet-dot-com>

I had the feeling that my thinking was wrong.  I was right about that, I was
wrong.  With some hints from the tutorial at
http://www.smpstech-dot-com/tutorial/t02top.htm, I think I have it.  If 300V is
considered the center of the capacitor voltage (see original example below),
then the energy given up by the cap in discharging from the -300v (gnd) to
the new zero line (300V) matches the energy gained from the inductor to the
+300V (or 600V) level.  So the final voltage of the cap is 2 times the input
DC voltage (ignoring loses).

The characteristic impedance of the series inductor and capacitor is given
by Z = SQRT(L/C).  In the above tutorial, V/Z gave the current at turn on
with no load for an L shaped filter section (inductor and cap in series with
the load paralleling the cap).  As a check on my figures in the original
message below, I calculated V/Z = 9.5 amps (rounded).

Anyhow, my assumptions were right, but my picture of what was going on was
wrong.  This newer view makes all the graphs of voltage and current into
nice symmetrical sine waves and feels right to me.

That leaves the question of what happens to the current in the primary of an
ignition coil while a cap is discharging through it and the secondary arcs.
I expect it to jump to a high value, but how high?  If I build this circuit,
I could try it at low voltage and watch what happens on a scope.  All I need
is time.

Regards,

Pete Komen

-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Thursday, January 24, 2002 4:06 PM
To: tesla-at-pupman-dot-com
Subject: Resonant capacitor charging calculations QUESTION

Original poster: "Pete Komen by way of Terry Fritz <twftesla-at-qwest-dot-net>"
<pkomen-at-zianet-dot-com>

I was considering building a capacitor discharge coil driver (and even
considering using that to power a mini-TC).  The books I have don't really
talk about the voltage, current, or energy in relation to time when an
inductor and capacitor are connected in series to a DC voltage source.  I
have been thinking about this problem and would like the assistance of you
all.

Given an inductor, a diode, and a capacitor in series switched on to a DC
voltage what is the maximum voltage attained across the capacitor.  What is
the maximum current?

For example: 5mH inductor and a 5uF capacitor with a diode in series
connected to a 300V source.

Assumptions:  (I am wondering if these are correct.)
1. The time, T1, when the cap charges to 300V is also the time of maximum
current.  Before that time there is still a voltage across the inductor
causing the current to increase.
2. The energy stored in the inductor (Energy = L* I**2 / 2) equals the
energy in the Cap at time T1.
3. The energy in the inductor ends up in the Cap.

The energy in the Cap at T1 is 300**2 * 5e-6 / 2 = 0.225 Joules.
Maximum energy in the cap is 2 * 0.225 Joules = 0.45 Joules.
Ending voltage in the Cap is SQRT(0.45 * 2 / 5e-6) = 424V (fraction dropped)
Maximum current   SQRT(0.225 * 2 / 0.005) =  9.5 amps (rounded)

The resonant frequency of this combination is 1 / (2 * PI * SQRT(L * C)) = f
= 1007 Hz (rounded).

The time to charge the Cap should be one-half cycle or a little less than
1/2 ms.

Now, to turn this around a little; if the inductor was the primary of an
ignition coil during discharge of the Cap through it, what happens to the
current through the primary when the secondary arcs?  If an SCR controls the
discharge, how much current must it handle?

I have some ignition coils that measure 5mH on the primary with the
secondary open and .7 with the secondary shorted.  The secondary measures 7K
ohms but gives no reading on the inductance scale.  Is the inductance
measurement on the primary with the secondary shorted meaningful?

Last question:  if the secondary of an ignition coil were to be used to
drive the primary of a mini-TC, would it need a spark gap?  Why not parallel
the ignition coil secondary with the mini-TC cap and primary winding?  The
very high impedance of the ignition coil secondary is overwhelmed by the low
impedance TC primary.  The tuning might change a very little but not much.

I would really appreciate any correction or discussion of all this.

Regards,

Pete Komen