RE: Three Voltages and Series Resistor (was - Magnetic quenching.)

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

Original poster: "John H. Couture" <couturejh-at-mgte-dot-com> 


Ed, Jim, Robert, All -

This problem caught my attention so I dug further. I at first thought that
it would not be possible to find the unknown load reactance without using a
capacitor or inductor.
I found that only one resistor is needed and three voltage readings and no
capacitor or inductor.
This will also give you input watts without a wattmeter for your Tesla coil.

Here is a problem to work on -
Given 3 voltages (60 Hz) and a series resistor
Find the resistance and inductance of the load.

Volts across load & res   = 120
Volts across load (TC?)   = 108
Volts across resistor     = 15
Series resistor ohms      = 15

There is more than one way to solve this problem. In fact there is one
method that is very easy. Just find the sides of two right angle triangles.
One is the triangle with the load and series resistor and the other the
triangle with only the load.

I have simplified the problem somewhat by using a 15 ohm resistor and 15
volts across the resistor for a one amp current in the circuit. Try the
problem with a 10 ohm resistor and 20 volts across the resistor.

The load and resistor triangle -
    x= 100    y = 66.14    z = 120

The load triangle -
    x = 85   y = 66.14    z = 108

The load resistance is 85 ohms
The inductance is 66.14/377 = .17543 = 175.43 mh

Can you fill in the calc details? Find the power factor? Input Watts?
Can you solve the problem in another way?
I wonder how Ed's students would solve this problem now?
I wonder if I got it right?

John Couture

------------------------------


-----Original Message-----
From: Tesla list [mailto:tesla-at-pupman-dot-com]
Sent: Sunday, March 14, 2004 8:06 PM
To: tesla-at-pupman-dot-com
Subject: Re: Magnetic quenching.


Original poster: "Jim Lux" <jimlux-at-earthlink-dot-net>


----- Original Message -----
From: "Tesla list" <tesla-at-pupman-dot-com>
To: <tesla-at-pupman-dot-com>
Sent: Sunday, March 14, 2004 8:41 AM
Subject: Re: Magnetic quenching.


  > Original poster: Ed Phillips <evp-at-pacbell-dot-net>
  >
  > "With an AC voltmeter, a series resistor and a series capacitor or
  > inductor,
  > you can measure true power, apparent power, vars, watts, power factor
  > etc.
  > It's called the "three meter technique" when measuring RF impedances.
  > Requires a bit of math, but these days, that's no big deal.  You want a
  > capacitor or inductor that has a reactance that's not too huge compared
  > to
  > the load, but also not so small that there's a lot of measurement error.
  > (X=1/(377 * C) (in 60 Hz lands).... Say you're looking at 1 kW loads on
  > 120V
  > (i.e about 0.1 ohm).. you want a reactance that's probably in the area
  > of
  > 0.01 ohm.  That would be a HUGE capacitor (1/3 Farad!), so, an inductor
  > is
  > probably a better bet.  (X=377*L)  1mH=.377 ohm, 10 uH = .0038 ohm,
  > which is
  > in the right ball park."
  >
  > OK except for the numbers. Try ~ ohms instead of 0.1 ohm.


Ooops... Subconsciously, I was thinking of a really BIG coil... 100 kW+

So, you'd want an ohm or so.. Still a huge cap, but still a practical
inductor.


   I thought
  > the "three voltmeter method" was long forgotten, and never heard of its
  > use for RF.

Featured quite prominently in several of the ARRL Antenna Compendium series
of books, where the oldest articles describe the graphical approach, and the
newer ones are more software oriented.  Once I ran across it there, I
started looking in the literature and found it has been used for quite a
while.  There are some papers from authors at NBS and elsewhere that talk
about error analysis in detail, and so forth.  I also ran across some papers
that describe it in the context of measuring the admittance matrix of an
arbitrary (linear) N-port with only voltage probes (a process of great
interest to folks trying to build field deployed HF phased arrays)

   Actually, all it takes is a resistor and the load to be
  > measured - the reactance isn't needed. I worked out the arithmetic and
  > posted it here a while back.  The arithmetic is simple, and a graphical
  > construction works fine too.

How do you do it with no reactance and a scalar measurement? You can only
make two independent measurements with a single resistor in series, and you
need to determine three things (I, V, phase, or some combination of those).
  >
  > All this applies to LINEAR impedances.  I suspect that the results with
  > a TC load might be quite misleading, whereas a true electrodynamic
  > wattmeter is quite accurate.

Now that's an interesting aspect... The three meter technique does depend on
knowing the reactance of the standard component in series, and if you don't
know the power spectrum of the signal being measured, you can't really know
the reactance.

  >
  > Ed
  >
  >