On 7/22/2015 6:02 PM, Roger Hayter wrote:
wrote:

John S wrote:
If Maxwell can have a Demon, then so can I.

There is a 100W RF transmitter attached to an antenna, through
an ammeter, whose terminal impedance is 50+j0 at an arbitrary
frequency, Fo. The transmitter has a drive control, that is, the
amount of power can be adjusted by my Demon.

I have an RF voltmeter also attached to the antenna/transmitter
junction.

The goal is to measure the power into the antenna as frequency is
varied.

At Fo, my Demon adjusts the drive level to 50V at the antenna
terminal. The power into the antenna is 50W. So far, so good.

As we sweep the frequency, my Demon adjusts the drive control to
supply 50V at the terminal. So, let's plot just 3 points:

R X Z Amps Pwr 37.34 -48.86
61.49 0.813 24.68 50.56 0.06 50.56 0.989
49.44 68.44 48.44 83.84 0.596 24.34

My Demon is only watching the antenna's terminal voltage,
adjusting the drive to maintain 50V and has no idea about R and
X. I have included R, X and the resulting calculations (Z, Amps,
Pwr) from a simulated antenna for those who wish to verify that
the the resulting calculations are correct.

While the load current has changed from .8 amps through .99 amps
to .6 amps, the voltage has remained constant.

If you the only thing you know is that the terminal voltage set
my Demon has maintained the voltage at 50V and you can read the
current, what conclusion could you draw about the source
impedance? Well, since the voltage has remained unchanged while
the current varied, it would appear that, for all practical
purposes, the source impedance is zero because the dynamic source
impedance is dV/dI (0/dI = 0) at the antenna terminals.

I invite comments about this thought experiment.

Thanks folks, and I promise no bickering and name-calling from
me.

Yes, the source impendance of a regulated voltage source can be
concidered to be zero over it's linear range, i.e. it does not go
into limiting.

That the voltage is AC and the load is complex is irrelevant.

I am afraid that the "demon" described does not necessarily represent
a zero source impedance generator. To specify a constant voltage
gererator you do not have to invent a "demon" at all. You just have
to specify an AC voltage generator with whch is either ideal (a
theoretical construct) or has an arbitrarily low source impedance so
that the voltage is constant to any degree of precision you require.
This is quite possible to make in practice, and would be said to have
negligible source impedance in the above circuit.


You are quite correct, Roger. I'm trying find a way to describe a
theoretical source impedance such that it will make sense. Perhaps this
is the wrong approach. Let me try this:

120V, 60Hz comes into my house. I place a 1uF capacitor across the line.
It draws .054A. I look at the line voltage. It is still 120V. As far as
this experiment is concerned, the source (line) is so close to zero that
I do not need to include its value in my experiment.


But the experiment as specified could also be implemented with a
generator with as high a source impedance as desired but which had
an automatic level control operating at loop bandwidth much lower
than its working frequency.

To get a zero impedance generator you have to specify that the demon
works at the operating frequency.

Very well, I will state that it works at any desired frequency. It is
just a theoretical construct, after all.

Thanks, Roger. And
Cheers