Re: Parallel and Series LCR Circuit Qs

[Terry Fritz <twftesla-at-uswest-dot-net>]

Hi Ed,

At 11:59 AM 8/13/00 -0700, you wrote:

>> snip...
>> 
>> The peak current is about 600 amps!!  However, that is only a brief 1% duty
>> cycle pulse.  If you look at the continuous equivalent current (the RMS
>> value) it is far lower, about 12 amps on my coil.  The RMS value of primary
>> current is extremely useful for determining capacitor ratings and such.
>> One has to be a little carful about using the AC resistances with skin
>> effects in the calculations, but the RMS primary current value really can
>> tell you many things.  In this case, it tells the power lost to the gap and
>> that I need about four 3amp RMS cap strings for the primary cap...
>> 
>> RMS primary current equations are giving in the notes at:
>> 
>> http://users.better-dot-org/tfritz/site/MMCinfo/MMCPower4.html
>> 
>> Cheers,
>> 
>>         Terry
>
>	If I haven't slipped a decimal point. the actual RMS current in this
>example is 60 amps!  RMS is root mean square.  The square of 600 amps is
>360,000 amps^2.  Multiply this by 0.01 (the duty factor) and you get
>3600.  Take the (square) root of this and you get 60.
>
>Ed
>

You are basically correct, but I didn't explain...  The 1% duty cycle is
for the entire firing cycle.  The 600 amp "peak" current only exist for the
first portion of that cycle and then quickly falls away.  Thus the
equivalent RMS current is about 1/5th of 60 ARMS.  Of course, these are
just general numbers for an example.

I ran a model of this just to see for sure and the result is at:
http://1071737050/site/misc/PKvsRMS.gif

This is a 15/60 LTR coil that hits a peak primary current of 274.37 amps
and has an average RMS current of 7.696 amps.  Using your above reasoning
we can find the "sort-of-equivalent" duty cycle :-))  1/(274.37/7.696)^2 =
0.0787% "duty cycle"...

So really, I should have said 275 amps peak, 7.7 ARMS and 0.079% "duty cycle".

I should have let the model run longer.  The RMS current was still
increasing a bit and really levels out to about 8.7 ARMS given enough time.
 That gives a "duty cycle" of about 0.1%.

So the "firing cycle" may have about 1% duty cycle but the equivalent for
this purpose is about 0.1% duty cycle...  That could vary a bit so I am not
sure this would be a good "rule" for other than rough estimates.

Cheers,

	Terry