Energy Brain Teaser
 

With as little effort as possible, determine Pfor2 and Pref2.

Given: Pfor1 = 100 watts, Pref1 = zero watts
[(Z02-Z01)/(Z02+Z01)]^2 = 0.5

100w---Z01 ohm line---+---Z02 ohm line---unknown load
Pfor1-- Pfor2--
--Pref1 --Pref2
--
73, Cecil http://www.w5dxp.com

Energy Brain Teaser
 

On Mar 31, 6:23 am, Cecil Moore wrote:
With as little effort as possible, determine Pfor2 and Pref2.

Given: Pfor1 = 100 watts, Pref1 = zero watts
[(Z02-Z01)/(Z02+Z01)]^2 = 0.5

100w---Z01 ohm line---+---Z02 ohm line---unknown load
Pfor1-- Pfor2--
--Pref1 --Pref2
--
73, Cecil http://www.w5dxp.com

If EITHER line has loss, the problem statement is incomplete, at best.

If the lines are lossless, Pfor2=175W, and Pref2 is obvious.

And it's a REALLY weird way to state the impedances. It looks like
someone was interested in the impedances of the lines after thinking
to make some measurements of VOLTAGE and maybe CURRENT along those
lines and couldn't quite figure out how to get there.

How do we KNOW that Pfor1 is 100 watts and Pref1 is zero?

How do we KNOW that line 1 and line 2 each have UNIFORM impedance?

Simply stating it as a brainteaser doesn't make it relevant to the
problems hams are faced with in line-matching situations. In most
cases, hams ASSUME they know the impedance of the line they are
measuring, whether they realize it or not. That is, they'll use a
bridge to make a measurement, and the bridge is calibrated for use at
a certain impedance (commonly 50 ohms). If the line isn't that
impedance, the measurement will be in error. Just because someone
measured 100W forward and 0W reflected on line 1 doesn't make it so,
and honestly, that's a much more interesting problem to me than this
easy "brainteaser."

Cheers,
Tom

Energy Brain Teaser
 

K7ITM wrote:
On Mar 31, 6:23 am, Cecil Moore wrote:
With as little effort as possible, determine Pfor2 and Pref2.

Given: Pfor1 = 100 watts, Pref1 = zero watts
[(Z02-Z01)/(Z02+Z01)]^2 = 0.5

100w---Z01 ohm line---+---Z02 ohm line---unknown load
Pfor1-- Pfor2--
--Pref1 --Pref2


If the lines are lossless, Pfor2=175W, and Pref2 is obvious.

Yes, assume the lines are lossless, but I don't think
that is the correct answer.

And it's a REALLY weird way to state the impedances.

Yes, to get people to think outside the box. Since the
Z0s are unknown, the voltages and currents are also
unknown, yet there exists a solution to the problem.
This is the typical kind of problem that my EE professors
used to give to the classes at Texas A&M to try to get
us to use our gray matter.

How do we KNOW that Pfor1 is 100 watts and Pref1 is zero?

Given.

How do we KNOW that line 1 and line 2 each have UNIFORM impedance?

Given.

Just because someone
measured 100W forward and 0W reflected on line 1 doesn't make it so,

Just because 100 watts forward and zero watts reflected
were measured by an ideal directional wattmeter calibrated
for a characteristic impedance of Z01, doesn't make it so???
Now that *is* an interesting diversion.
--
73, Cecil http://www.w5dxp.com

Energy Brain Teaser
 

Cecil Moore wrote:
K7ITM wrote:

And it's a REALLY weird way to state the impedances.

Yes, to get people to think outside the box.

Cecil,

It is really rare when one of these threads is *inside* the box.

8-)

73,
Gene
W4SZ

Energy Brain Teaser
 

Gene Fuller wrote:
It is really rare when one of these threads is *inside* the box.
8-)

Gene, can you solve the problem?
--
73, Cecil http://www.w5dxp.com

Energy Brain Teaser
 

On Mar 31, 8:51 am, Cecil Moore wrote:
K7ITM wrote:
On Mar 31, 6:23 am, Cecil Moore wrote:
With as little effort as possible, determine Pfor2 and Pref2.

Given: Pfor1 = 100 watts, Pref1 = zero watts
[(Z02-Z01)/(Z02+Z01)]^2 = 0.5

100w---Z01 ohm line---+---Z02 ohm line---unknown load
Pfor1-- Pfor2--
--Pref1 --Pref2

If the lines are lossless, Pfor2=175W, and Pref2 is obvious.

Yes, assume the lines are lossless, but I don't think
that is the correct answer.

And it's a REALLY weird way to state the impedances.

Yes, to get people to think outside the box. Since the
Z0s are unknown, the voltages and currents are also
unknown, yet there exists a solution to the problem.
This is the typical kind of problem that my EE professors
used to give to the classes at Texas A&M to try to get
us to use our gray matter.

How do we KNOW that Pfor1 is 100 watts and Pref1 is zero?

Given.

How do we KNOW that line 1 and line 2 each have UNIFORM impedance?

Given.

Just because someone
measured 100W forward and 0W reflected on line 1 doesn't make it so,

Just because 100 watts forward and zero watts reflected
were measured by an ideal directional wattmeter calibrated
for a characteristic impedance of Z01, doesn't make it so???
Now that *is* an interesting diversion.
--
73, Cecil http://www.w5dxp.com

In general, in real-world ham problems, it is far from given that we
know that the impedance of a line is really uniform. We don't even
know the impedance for certain. There have been any number of
postings here in the past where someone can't figure out what the
impedance of some unknown line is, and I'm sure there are far more
instances of people ASSUMING that RG-8-type line is 50.00 ohms. It
practically never is. (But it also practically never MATTERS for
typical ham applications.) WHY should I believe you know how to
measure the impedance of a line, and that you know how to calibrate a
bridge to that impedance? I'm NOT saying that you DON'T know how,
only that I need convincing. I've seen plenty of evidence of those
who haven't a clue about either around here, so I prefer to start from
the point of view that any reported measurements of "forward and
reverse power" are likely to be flawed.

Since you "know" that the meter is calibrated for the impedance of the
line, you must know the impedance of the line. Why didn't you just
give the line impedance? Is it possible to determine the forward and
reverse powers by measurement of a real TEM line of unknown impedance
without measuring everything you need to know to find the line
impedance (and in fact to do so nearly trivially)?

Yeah, I shouldn't try to work these things in my head before
breakfast. Pfor2=200.

Cheers,
Tom

Energy Brain Teaser
 

K7ITM wrote:
In general, in real-world ham problems, it is far from given that we
know that the impedance of a line is really uniform. We don't even
know the impedance for certain. There have been any number of
postings here in the past where someone can't figure out what the
impedance of some unknown line is, and I'm sure there are far more
instances of people ASSUMING that RG-8-type line is 50.00 ohms. It
practically never is. (But it also practically never MATTERS for
typical ham applications.) WHY should I believe you know how to
measure the impedance of a line, and that you know how to calibrate a
bridge to that impedance? I'm NOT saying that you DON'T know how,
only that I need convincing. I've seen plenty of evidence of those
who haven't a clue about either around here, so I prefer to start from
the point of view that any reported measurements of "forward and
reverse power" are likely to be flawed.

Well, let me do you one better. It is far from given that
you exist. Please prove that you exist before we go any
farther. (I have rarely heard such a strange argument
against mental exercises as you presented above.)

Seems you would be completely opposed to exercises using
lossless lines, huh? I can hear it now: "It is far from
given that a transmission line can be lossless." Yes, it
is, but textbooks are filled to overflowing with such
examples.

Since you "know" that the meter is calibrated for the impedance of the
line, you must know the impedance of the line. Why didn't you just
give the line impedance?

Then someone could have converted to voltage, wasted a
lot of time, and avoided the new experience of dealing
100% with power. I'm glad you woke up and figured it out.
See how easy that was? BTW, congratulations on being the
only one (so far) to figure it out.
--
73, Cecil http://www.w5dxp.com

Energy Brain Teaser
 

On Mar 31, 1:19 pm, Cecil Moore wrote:
K7ITM wrote:
In general, in real-world ham problems, it is far from given that we
know that the impedance of a line is really uniform. We don't even
know the impedance for certain. There have been any number of
postings here in the past where someone can't figure out what the
impedance of some unknown line is, and I'm sure there are far more
instances of people ASSUMING that RG-8-type line is 50.00 ohms. It
practically never is. (But it also practically never MATTERS for
typical ham applications.) WHY should I believe you know how to
measure the impedance of a line, and that you know how to calibrate a
bridge to that impedance? I'm NOT saying that you DON'T know how,
only that I need convincing. I've seen plenty of evidence of those
who haven't a clue about either around here, so I prefer to start from
the point of view that any reported measurements of "forward and
reverse power" are likely to be flawed.

Well, let me do you one better. It is far from given that
you exist. Please prove that you exist before we go any
farther. (I have rarely heard such a strange argument
against mental exercises as you presented above.)

Seems you would be completely opposed to exercises using
lossless lines, huh? I can hear it now: "It is far from
given that a transmission line can be lossless." Yes, it
is, but textbooks are filled to overflowing with such
examples.

Since you "know" that the meter is calibrated for the impedance of the
line, you must know the impedance of the line. Why didn't you just
give the line impedance?

Then someone could have converted to voltage, wasted a
lot of time, and avoided the new experience of dealing
100% with power. I'm glad you woke up and figured it out.
See how easy that was? BTW, congratulations on being the
only one (so far) to figure it out.
--
73, Cecil http://www.w5dxp.com

Actually, Cecil, I don't exist. I am purely a figment of your
imagination. So--why are you bothering to respond to me? Ah, never
mind. I see that you didn't, actually.

Since I'm just a figment of your imagination, there is no way I can be
awake, asleep, or anything else.

I'm sure I'm not the only one to have "figured it out;" I'm just the
only one fool enough to bother posting a reply. But since I don't
exist, I'm obviously not a fool, either.

Cheers,
Tom