On Jun 30, 5:55*pm, Roy Lewallen wrote:
Keith obviously understands the requirements for energy flow, but a
casual reader might draw the wrong conclusions. . .

Keith Dysart wrote:
. . .
This is quite incorrect. Energy flows must balance, otherwise energy
is being created or destroyed to sustain a difference in flow.

On the average, yes. But not moment-by-moment. Energy can be stored and
retrieved from storage, resulting in unequal energy flow (power) into
and out of a point. For a while. This was explicitly stated earlier when
discussing a capacitor, but I think it's important to make the
distinction here between instantaneous and average requirements. In
steady state, the average condition (energy flow balance) must be met
each cycle. That is, the total energy into a node over a cycle has to
equal the energy out of a node over a cycle.

. . .
Unfortunately wrong. Energy flows must balance as well. Otherwise,
energy is coming from nowhere to sustain the flow.

Ditto.

. . .
Yes, indeed. At that instant, zero energy is flowing from the inductor
to the capacitor. But very soon, energy will be flowing from the
capacitor to the inductor. The balance is that the energy flowing
out of the capacitor is always and exactly equal to the energy flowing
in to the inductor. That is the energy flow balance. The only way for
this not to be true is for energy to be created or destroyed.

Ditto.

. . .
Instead, think that at every instant, the energy flow between the
entities in the experiment must balance.

No, it doesn't, unless I'm misunderstanding the statement. At a given
instant, more energy can flow into a component (e.g., a capacitor or
inductor) than is flowing out, or vice-versa. But in steady state,
whatever flows in during one part of the cycle must flow out during the
remainder of the cycle.

I think you are misunderstanding, possibly because I am not expressing
as clearly as could be. I find it difficult to pick a vocabulary that
will not be confusing due to prior associations with the words. But
then words like 'entity' are too fuzzy.

The system I have in mind has ports through which energy can flow in
or out of the system and components inside the system which can
store energy. For such a system, the energy flowing in to ports
of the system minus the energy flowing out of ports must
equal the increase in energy being stored in the system.

This must be true at all times, or energy is being created or
destroyed; a bit of a no-no.

This system can be subdivided in to sub-systems for which this
energy flow balance must also hold.

As such, if the energy stored in one of the entities (e.g.
capacitor) is increasing, either net energy is flowing in to
the ports of the system, or the energy stored in some other
entity in the system is decreasing (or both). But the sum
of all the flows entering or leaving the ports, plus
the flows between the internal entities must balance on
a moment by moment basis.

Of course the expressions written to describe this will
be dependent on the details of the system. One must also
not forget to account for energy that leaves the system
as heat courtesy resistors. These can be thought of as
ports which only remove energy from the system.

The requirement for moment-by-moment balance is more stringent
than the requirement for average balance. The former inevitably
leads to the latter, but the converse is not true.

From Wikipedia, I have just learned that the concept I am attempting
to describe is known as a "Continuity equation".

Every time one of your instantaneous power curves crosses the zero
axis, power has been destroyed. Every time one of your instantaneous
power curves reaches a peak, power has been created.

I think you may be confused because you are only looking at the
flow in and out of a single entity. This is clearly not conserved.
Nor for that matter is the energy within that entity. It is the
total energy within the system that is conserved, just as it is
the total of the flows of energy between the entities within the
system that must be conserved.

Put more strictly: The sum of all the energy flows in to all of
the entities within the system must equal the energy flow in to
the system.

Again, only on an average or steady-state cycle-by-cycle basis. Great
inequalities can exist for shorter periods.

*. . .

Like Keith, I firmly believe that an instantaneous time-domain analysis
is essential in understanding what really happens to the energy in an AC
system. Averaging reduces the amount of information you have -- if all
you know is the average value of a waveform, you have no way of going
back and finding out what the waveform was, out of an infinite number of
possibilities. If averaging is to be done, it should be done after you
calculate and understand what's going on at each instant, not before you
begin the analysis.

But it's also essential to make absolutely clear what conditions must be
met every instant, such as p(t) = v(t) * i(t), and which must be met
only on the average, such as energy in = energy out.

Roy Lewallen, W7EL

On Jul 4, 8:08*pm, Keith Dysart wrote:
The system I have in mind has ports through which energy can flow in
or out of the system and components inside the system which can
store energy. For such a system, the energy flowing in to ports
of the system minus the energy flowing out of ports *must
equal the increase in energy being stored in the system.

This must be true at all times, or energy is being created or
destroyed; a bit of a no-no.

But you are not tracking energy - you are tracking power. As Roy has
said, there is no requirement that instantaneous power must balance.
Where are the stored energy terms in any of your instantaneous power
equations? How do you handle the difference in dimensions between
energy and power? The only condition for which NET power must balance
is during a time interval in which there is zero NET stored power,
e.g. during one cycle.

I have rev'ed my zero interference article to include the following
statement:

"Over a time period of many cycles, e.g. one second at MHz
frequencies, the net average energy and the net average power are
related by joules/second. Thus, if certain conditions are met, net
average power can be used to track the net average energy flow based
on the conservation of energy principle. However, at time intervals of
less than one cycle, as exists for instantaneous power, power cannot
be used to track energy because energy is often stored in a reactance,
is not moving at that instant, and is therefore technically not power.
In fact, unlike energy, power often appears and disappears. There are
special cases where average power in joules/second can be used to
track average energy in joules but instantaneous power is not one of
those special cases."
--
73, Cecil, w5dxp.com

On Jul 5, 8:33*am, Cecil Moore wrote:
On Jul 4, 8:08*pm, Keith Dysart wrote:

The system I have in mind has ports through which energy can flow in
or out of the system and components inside the system which can
store energy. For such a system, the energy flowing in to ports
of the system minus the energy flowing out of ports *must
equal the increase in energy being stored in the system.

This must be true at all times, or energy is being created or
destroyed; a bit of a no-no.

But you are not tracking energy - you are tracking power. As Roy has
said, there is no requirement that instantaneous power must balance.
Where are the stored energy terms in any of your instantaneous power
equations? How do you handle the difference in dimensions between
energy and power? The only condition for which NET power must balance
is during a time interval in which there is zero NET stored power,
e.g. during one cycle.

I have rev'ed my zero interference article to include the following
statement:

"Over a time period of many cycles, e.g. one second at MHz
frequencies, the net average energy and the net average power are
related by joules/second. Thus, if certain conditions are met, net
average power can be used to track the net average energy flow based
on the conservation of energy principle. However, at time intervals of
less than one cycle, as exists for instantaneous power, power cannot
be used to track energy because energy is often stored in a reactance,
is not moving at that instant, and is therefore technically not power.
In fact, unlike energy, power often appears and disappears. There are
special cases where average power in joules/second can be used to
track average energy in joules but instantaneous power is not one of
those special cases."
--
73, Cecil, w5dxp.com

Well, you are digging your hole deeper and deeper. You really should
take a pause and try to understand the significance of "Continuity
equations". Do seriously consider Kerchoff's current law as an
example.

....Keith

On Jul 5, 7:26*pm, Keith Dysart wrote:
You really should
take a pause and try to understand the significance of "Continuity
equations".

So you finally admit I was right all along, adopt my original
position, and claim it was yours all the while. Old trick - won't
work. I studied similar equations half a century ago when I studied
the conservation of energy principle. I told you long ago that your
P(t) = V(t)*I(t) equation did not contain all the energy in the
system.

I have never posted anything that disagrees with the continuity
equations. You are the one who chose to ignore the delta-dot-v terms
and have reversed your original position by introducing the continuity
equation. All you had in your equation previously was the de/dt term.

Do you still believe in the conservation of instantaneous power
principle?
--
73, Cecil, w5dxp.com

On Jul 6, 12:26*am, Keith Dysart wrote:
On Jul 5, 8:33*am, Cecil Moore wrote:



On Jul 4, 8:08*pm, Keith Dysart wrote:

The system I have in mind has ports through which energy can flow in
or out of the system and components inside the system which can
store energy. For such a system, the energy flowing in to ports
of the system minus the energy flowing out of ports *must
equal the increase in energy being stored in the system.

This must be true at all times, or energy is being created or
destroyed; a bit of a no-no.

But you are not tracking energy - you are tracking power. As Roy has
said, there is no requirement that instantaneous power must balance.
Where are the stored energy terms in any of your instantaneous power
equations? How do you handle the difference in dimensions between
energy and power? The only condition for which NET power must balance
is during a time interval in which there is zero NET stored power,
e.g. during one cycle.

I have rev'ed my zero interference article to include the following
statement:

"Over a time period of many cycles, e.g. one second at MHz
frequencies, the net average energy and the net average power are
related by joules/second. Thus, if certain conditions are met, net
average power can be used to track the net average energy flow based
on the conservation of energy principle. However, at time intervals of
less than one cycle, as exists for instantaneous power, power cannot
be used to track energy because energy is often stored in a reactance,
is not moving at that instant, and is therefore technically not power.
In fact, unlike energy, power often appears and disappears. There are
special cases where average power in joules/second can be used to
track average energy in joules but instantaneous power is not one of
those special cases."
--
73, Cecil, w5dxp.com

Well, you are digging your hole deeper and deeper. You really should
take a pause and try to understand the significance of "Continuity
equations". Do seriously consider Kerchoff's current law as an
example.

...Keith

do you not think that it is telling that there is a current law and a
voltage law, but not a basic power law included in basic circuit
theory? maybe there is a reason for that.

On Jul 6, 6:02*pm, K1TTT wrote:
On Jul 6, 12:26*am, Keith Dysart wrote:





On Jul 5, 8:33*am, Cecil Moore wrote:

On Jul 4, 8:08*pm, Keith Dysart wrote:

The system I have in mind has ports through which energy can flow in
or out of the system and components inside the system which can
store energy. For such a system, the energy flowing in to ports
of the system minus the energy flowing out of ports *must
equal the increase in energy being stored in the system.

This must be true at all times, or energy is being created or
destroyed; a bit of a no-no.

But you are not tracking energy - you are tracking power. As Roy has
said, there is no requirement that instantaneous power must balance.
Where are the stored energy terms in any of your instantaneous power
equations? How do you handle the difference in dimensions between
energy and power? The only condition for which NET power must balance
is during a time interval in which there is zero NET stored power,
e.g. during one cycle.

I have rev'ed my zero interference article to include the following
statement:

"Over a time period of many cycles, e.g. one second at MHz
frequencies, the net average energy and the net average power are
related by joules/second. Thus, if certain conditions are met, net
average power can be used to track the net average energy flow based
on the conservation of energy principle. However, at time intervals of
less than one cycle, as exists for instantaneous power, power cannot
be used to track energy because energy is often stored in a reactance,
is not moving at that instant, and is therefore technically not power..
In fact, unlike energy, power often appears and disappears. There are
special cases where average power in joules/second can be used to
track average energy in joules but instantaneous power is not one of
those special cases."
--
73, Cecil, w5dxp.com

Well, you are digging your hole deeper and deeper. You really should
take a pause and try to understand the significance of "Continuity
equations". Do seriously consider Kerchoff's current law as an
example.

...Keith

do you not think that it is telling that there is a current law and a
voltage law, but not a basic power law included in basic circuit
theory? *maybe there is a reason for that

Perhaps. What is your explanation?

....Keith

Keith Dysart wrote:

I think you are misunderstanding, possibly because I am not expressing
as clearly as could be. I find it difficult to pick a vocabulary that
will not be confusing due to prior associations with the words. But
then words like 'entity' are too fuzzy.

. . .

The problem I had was the use of "energy flow balance" which implied
equal energy flow into and out of any point at any time. Your more
detailed description explicitly includes stored and dissipated energy,
which as we've both said, makes it possible for energy flow into and out
of a point to be unequal at times, while obeying conservation of energy
by being equal on the average (when dissipated energy is accounted for
as removed from the system). The more detailed detailed description
should help alleviate misunderstandings some readers might have had.

. . .

From Wikipedia, I have just learned that the concept I am attempting
to describe is known as a "Continuity equation".

I can't recall ever having come across that term, but then I'm not a
physicist.

Roy Lewallen, W7EL