I apologize if my response seemed argumentative. It wasn't intended that
way. Certainly, sin^2(wt) has the same shape as the power waveform I
derived -- the only difference is its fixed D.C. term. And I certainly
agree that letting delta t approaching zero doesn't make any function of
t become zero at that point. And just as the analysis I've presented is
in your first year college electronics book, so is the point about delta
t in everyone's high school or first semester college calculus book. But
it's evident that some number of participants in this thread have either
forgotten, never seen, or never understood those basic principles. And
quite a few people either don't have any textbooks, don't understand
them, or are unwilling to open and read them. Hence the postings
containing information that you or I could find in moments.

Roy Lewallen, W7EL

Jim Kelley wrote:

You seem to be looking for an argument any way you can, Roy. ;-)
Sin^2(wt)/2 is the general form of any equation with the shape you
described in your previous post. Furthermore, instantaneous power can
be evaluated at any time t, irrespective of relative phase. The point
is simply that instantaneous power isn't necessarily zero as a result of
delta t's approaching zero.


Given that v = V * sin(wt + phiv)
i = I * sin(wt + phii)

Then p = v * i = VI * sin(wt + phiv) * sin(wt + phii)

The product of the sines can be transformed via a simple trig identity
to give

p = VI * 1/2[cos(phiv - phii) - cos(2wt + phiv + phii)]

The first term in the brackets is D.C. -- it's time-independent. The
second term is a pure sine wave. So the result is a pure sine wave with
a D.C. offset.

I've described the meaning and significance of the power waveform in at
least one earlier posting on this newsgroup. If anyone is interested who
can't find it on Google, I'll look it up and post the subject and date.


Yes. It's also in my first year college electronics book.

Thanks and 73,

AC6XG

I apologize if my response seemed argumentative. It wasn't intended that
way. Certainly, sin^2(wt) has the same shape as the power waveform I
derived -- the only difference is its fixed D.C. term. And I certainly
agree that letting delta t approaching zero doesn't make any function of
t become zero at that point. And just as the analysis I've presented is
in your first year college electronics book, so is the point about delta
t in everyone's high school or first semester college calculus book. But
it's evident that some number of participants in this thread have either
forgotten, never seen, or never understood those basic principles. And
quite a few people either don't have any textbooks, don't understand
them, or are unwilling to open and read them. Hence the postings
containing information that you or I could find in moments.

Roy Lewallen, W7EL

Cecil seemed to indicate that he thought delta t going to zero meant that
t was perpetually zero. I know he knows better than that.
73,
Tom Donaly, KA6RUH

Tdonaly wrote:
Cecil seemed to indicate that he thought delta t going to zero meant that
t was perpetually zero.

If delta-t ever gets to zero, time stands still. All you can allow
delta-t to do is to approach zero. Once it reaches zero the ballgame
is over. Limit delta-t to a minimum of a yoctosecond and everything
will be perfectly OK.
--
73, Cecil http://www.qsl.net/w5dxp



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Tdonaly wrote:
Cecil seemed to indicate that he thought delta t going to zero meant that
t was perpetually zero.

If delta-t ever gets to zero, time stands still. All you can allow
delta-t to do is to approach zero. Once it reaches zero the ballgame
is over. Limit delta-t to a minimum of a yoctosecond and everything
will be perfectly OK.
--
73, Cecil http://www.qsl.net/w5dxp


Are you trying to start an argument? I wrote "going to zero," not
"at zero." Besides, what the hell is a yoctosecond? All this was
argued over and discussed in the 18th century. You and Richard
Harrison are beginning to sound like Bishop Berkeley.
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:
"You and Richard Harrison are beginning to sound lke Bishop Berkeley."

We are in good company. Terman says on page 84 of his 1955 opus:
"In these equations Zo = sq rt Z/Y is termed the "characteristic
impedance" of the line. In the case of radio-frequency lines, Zo can
nearly always be assumed to be a pure resistance, as discussed on page
88."

When Terman says SWR = Emax / Emin, it makes no difference whether you
use instantaneous values or rms values, so long as you are consistent,
the ratio is the same.

Some complained that nobody provided a trustworthy VSWR related to
power. Bird Electronic Corporation does:

VSWR = 1+sq rt (reflected pwr/forward pwr) over 1-sq rt (reflected
pwr/forward pwr).

Millions of conversions have proved this VSWR from measured powers
relation.

Best regards, Richard Harrison, KB5WZI