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.

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.



--
Jim Pennino

On 7/22/2015 12:07 PM, 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.

Thanks, Jim. Your response is greatly appreciated.

On 7/22/2015 12:07 PM, 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.

Can we describe such a demon that works on current as well? My guess is
that you will agree that it can.

If so, can we have a demon that supplies a constant power? My bet is
that you will agree again.

This all depends on that hypothetical demon, of course. What do you
think? Can the thought experiment be set up differently or better?

John S wrote:
On 7/22/2015 12:07 PM, 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.

Can we describe such a demon that works on current as well? My guess is
that you will agree that it can.

It is called a constant current source.

Like constant voltage sources, there are the theoretical ones and the
practical ones you buy as a chip.

If so, can we have a demon that supplies a constant power? My bet is
that you will agree again.

Theoretical circuit analysis does not use constant power sources.

Constant power sources are sometimes used for things like S-parameter
analysis. They will always have a source impedance.

To build one you design a circuit that monitors the output current
and voltage then adjusts the output voltage to equal the desired power
divided by the output current. This of course will have practical limits
and while not trivial to design, not impossible.

Also it is of no use that I can think of.

This all depends on that hypothetical demon, of course. What do you
think? Can the thought experiment be set up differently or better?

What exactly IS the experiment?


--
Jim Pennino

On 7/22/2015 1:14 PM, wrote:
John S wrote:
On 7/22/2015 12:07 PM, 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.

Can we describe such a demon that works on current as well? My guess is
that you will agree that it can.

It is called a constant current source.

Yes, of course.

Like constant voltage sources, there are the theoretical ones and the
practical ones you buy as a chip.

True. And I thought by using a demon to describe the operation, I was
setting the stage for a theoretical discussion.

If so, can we have a demon that supplies a constant power? My bet is
that you will agree again.

Theoretical circuit analysis does not use constant power sources.

Constant power sources are sometimes used for things like S-parameter
analysis. They will always have a source impedance.

It does not matter because my theoretical Demon will adjust the power
into the load. At the load, the source will still appear as having no
source impedance because my Demon adjusts the parameters accordingly.

To build one you design a circuit that monitors the output current
and voltage then adjusts the output voltage to equal the desired power
divided by the output current. This of course will have practical limits
and while not trivial to design, not impossible.

We are not discussing practical limits. We are not discussing building a
circuit. We are discussing theory, just as Maxwell did. We are trying to
gain an understanding and an agreement on theoretical approaches to
problem solving starting at first principles.

Also it is of no use that I can think of.

Well, maybe not. That does remain to be seen, yes?

This all depends on that hypothetical demon, of course. What do you
think? Can the thought experiment be set up differently or better?

What exactly IS the experiment?

See the subject line, please.

John S wrote:
On 7/22/2015 1:14 PM, wrote:
John S wrote:
On 7/22/2015 12:07 PM, 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.

Can we describe such a demon that works on current as well? My guess is
that you will agree that it can.

It is called a constant current source.

Yes, of course.

Like constant voltage sources, there are the theoretical ones and the
practical ones you buy as a chip.

True. And I thought by using a demon to describe the operation, I was
setting the stage for a theoretical discussion.

You will not find the word "demon" in any theoretical electronics
discussion, so I'm not sure what you are getting at.

BTW, Maxwell's demon had to do with theromdynamics, not electricity.

If so, can we have a demon that supplies a constant power? My bet is
that you will agree again.

Theoretical circuit analysis does not use constant power sources.

Constant power sources are sometimes used for things like S-parameter
analysis. They will always have a source impedance.

It does not matter because my theoretical Demon will adjust the power
into the load. At the load, the source will still appear as having no
source impedance because my Demon adjusts the parameters accordingly.

To build one you design a circuit that monitors the output current
and voltage then adjusts the output voltage to equal the desired power
divided by the output current. This of course will have practical limits
and while not trivial to design, not impossible.

We are not discussing practical limits. We are not discussing building a
circuit. We are discussing theory, just as Maxwell did. We are trying to
gain an understanding and an agreement on theoretical approaches to
problem solving starting at first principles.

Maxwell's demon had to do with theromdynamics, not electricity.

The theoretical approaches to problem solving starting at first principles
has been settled for well over a hundred years.

Are you expecting to uncover something new?

Also it is of no use that I can think of.

Well, maybe not. That does remain to be seen, yes?

Well, since absolutely no one makes such a thing and none of the
many texts on electronics discusses such a thing, it would seem to
me that question is long settled.

This all depends on that hypothetical demon, of course. What do you
think? Can the thought experiment be set up differently or better?

What exactly IS the experiment?

See the subject line, please.

For ANY device, plot the voltage versus current curve for the device
in question over the range of interest.

The effective output impedance at any point is equal to the slope of
the curve.

Example: the slope of the V/I curve for a voltage regulator is zero
until the limits of the device are reached.


--
Jim Pennino

On 7/22/2015 2:14 PM, wrote:
John S wrote:
On 7/22/2015 12:07 PM, 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.

Can we describe such a demon that works on current as well? My guess is
that you will agree that it can.

It is called a constant current source.

Like constant voltage sources, there are the theoretical ones and the
practical ones you buy as a chip.

If so, can we have a demon that supplies a constant power? My bet is
that you will agree again.

The answer to your question is yes.


Theoretical circuit analysis does not use constant power sources.

Irrelevant. The question is not about what others do, it is about physics.


Constant power sources are sometimes used for things like S-parameter
analysis. They will always have a source impedance.

To build one you design a circuit that monitors the output current
and voltage then adjusts the output voltage to equal the desired power
divided by the output current. This of course will have practical limits
and while not trivial to design, not impossible.

No one asked how to build such an instrument. So you agree that the
answer to the question being asked is yes?


What exactly IS the experiment?

That was stated clearly.

--

Rick

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.


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.


--
Roger Hayter

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