Transmitter Output Impedance
 

On Sat, 14 May 2011 11:30:50 -0700 (PDT), K7ITM wrote:

FWIW, I've built audio amplifiers with output transistors with f-sub-t
around 50MHz. Those transistors certainly would provide decent power
gain at the lower frequency HF ham bands. They were used in the audio
amp to achieve very low distortion across the audio spectrum (a very
few PPM at full rated power output).

Hi Tom,

An Answer to one of my questions (and by inference two of them)!

The inference is there is NO transition frequency where source Z
becomes trivial/meaningful. Hence, statements alleging correlations
at one end of the spectrum must be observed at the other end.

If this is disputed, we (or at least I) would certainly like to see
what that transition frequency is.

One big difference between (typical) audio amplifiers and (typical) RF
power amplifiers is in the use of negative feedback. In an audio
amplifier, voltage-derived negative feedback yields a very low
amplifier output impedance. In almost all RF power amplifiers, little
or no negative feedback is used, so the output impedance is generally
much higher than with an audio amplifier running similar power and
supply voltage to the output devices.

Well, at the RF finals deck, before the Z transformer, there is slight
to no difference in output impedance. Both are sub-Ohm.

But again, the source impedance of a transmitter is seldom important
in the application of the amplifier.

This seems at odds with other writers - if it is an AF amplifier. And
yet none seem to be able to describe the transition frequency for
identical designs (such as yours above, or as close to it as
practicable) where it DOES become important (higher output power, as
if any Ham would snub that advantage if (s)he could snip out the Z
transformer in the rig).

One still unanswered question remains that if a low output Z is so
beneficial to achieving higher output power (a claim that none seem
ready to dispute), then why the step up in Z from the finals deck to
the output connector? I have read an explanation from Wim, but it
fails as an argument for AF where a similar mismatch between source
and load is observed - and yet this mismatch is the greatest quality
for an amplifier since sliced bread.

AF - RF A curious tennis match here where what going over the net in
this game is a golf ball in one direction, and a basketball in the
other.

What's important are things like
the optimal load impedance and the rated power output. I'd put things
like distortion specs for a linear amp far above source impedance in
importance. If you (the lurking reader) think source impedance is
important, please explain in detail _why_.

The self-same NEGATIVE feedback, lacking in retail rigs, would
accomplish any form of improvement at the cost of what H.W. Bode
called "noise gain." The dollar cost is not inconsequential. Not
much more detail is needed for the average Ham.

For the better than average Ham, the increase in NEGATIVE feedback,
goes directly to lowering:
Gain,
Power out (as a function of following gain),
Bandwidth (as a function of following gain),
Distortion,
Power supply disturbance,
Noise,
Input Z (or through clever design, raising it),
Output Z (or through clever design, raising it),
while increasing cost in near or GREATER proportion.

Every Ham knows the adage that there is no such thing as a free lunch,
and the marketplace enforces that without exception.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

On Mon, 25 Apr 2011 18:07:59 -0700, Jim Lux
wrote:

ON9CVD made some simple measurements using a couple of resistors and
foudn that a TS440 has a Zout somewhere around 15-40 ohms (depending on
frequency and output power).
http://sharon.esrac.ele.tue.nl/~on9c...impedantie.htm

Let's see here, a reported source Z as low as 15 (let's just call it
20) Ohms with 100W into 50 Ohms. I have read an explanation that this
is impossible (or improbable) for RF from a retail HF rig (such as a
TS440), but achievable at AF.

Meanwhile, back at the tennis match....

73's
Richard Clark, KB7QHC

Transmitter Output Impedance
 

On 14 mayo, 21:36, Richard Clark wrote:
On Sat, 14 May 2011 11:30:50 -0700 (PDT), K7ITM wrote:
FWIW, I've built audio amplifiers with output transistors with f-sub-t
around 50MHz. *Those transistors certainly would provide decent power
gain at the lower frequency HF ham bands. *They were used in the audio
amp to achieve very low distortion across the audio spectrum (a very
few PPM at full rated power output).

Hi Tom,

An Answer to one of my questions (and by inference two of them)!

The inference is there is NO transition frequency where source Z
becomes trivial/meaningful. *Hence, statements alleging correlations
at one end of the spectrum must be observed at the other end.

If this is disputed, we (or at least I) would certainly like to see
what that transition frequency is.

One big difference between (typical) audio amplifiers and (typical) RF
power amplifiers is in the use of negative feedback. *In an audio
amplifier, voltage-derived negative feedback yields a very low
amplifier output impedance. *In almost all RF power amplifiers, little
or no negative feedback is used, so the output impedance is generally
much higher than with an audio amplifier running similar power and
supply voltage to the output devices.

Well, at the RF finals deck, before the Z transformer, there is slight
to no difference in output impedance. *Both are sub-Ohm.

But again, the source impedance of a transmitter is seldom important
in the application of the amplifier. *

This seems at odds with other writers - if it is an AF amplifier. *And
yet none seem to be able to describe the transition frequency for
identical designs (such as yours above, or as close to it as
practicable) where it DOES become important (higher output power, as
if any Ham would snub that advantage if (s)he could snip out the Z
transformer in the rig).

One still unanswered question remains that if a low output Z is so
beneficial to achieving higher output power (a claim that none seem
ready to dispute), then why the step up in Z from the finals deck to
the output connector? *I have read an explanation from Wim, but it
fails as an argument for AF where a similar mismatch between source
and load is observed - and yet this mismatch is the greatest quality
for an amplifier since sliced bread.

Richard, who made that claim regarding that low output Z is so
beneficial? I didn't, so I also did not explain it. I only said that
many PAs don't operate under conjugated match (or even were not
designed to operate under it). This is valid for audio also.

AF - RF * A curious tennis match here where what going over the net in
this game is a golf ball in one direction, and a basketball in the
other.

What's important are things like
the optimal load impedance and the rated power output. *I'd put things
like distortion specs for a linear amp far above source impedance in
importance. *If you (the lurking reader) think source impedance is
important, please explain in detail _why_.

The self-same NEGATIVE feedback, lacking in retail rigs, would
accomplish any form of improvement at the cost of what H.W. Bode
called "noise gain." *The dollar cost is not inconsequential. *Not
much more detail is needed for the average Ham.

For the better than average Ham, the increase in NEGATIVE feedback,
goes directly to lowering:
Gain,
Power out (as a function of following gain),
Bandwidth (as a function of following gain),
Distortion,
Power supply disturbance,
Noise,
Input Z (or through clever design, raising it),
Output Z (or through clever design, raising it),
while increasing cost in near or GREATER proportion.

Every Ham knows the adage that there is no such thing as a free lunch,
and the marketplace enforces that without exception.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

On Mon, 25 Apr 2011 18:07:59 -0700, Jim Lux
wrote:

ON9CVD made some simple measurements using a couple of resistors and
foudn that a TS440 has a Zout somewhere around 15-40 ohms (depending on
frequency and output power).
http://sharon.esrac.ele.tue.nl/~on9c...impedantie.htm

Let's see here, a reported source Z as low as 15 (let's just call it
20) Ohms with 100W into 50 Ohms. *I have read an explanation that this
is impossible (or improbable) for RF from a retail HF rig (such as a
TS440), but achievable at AF. *

Meanwhile, back at the tennis match....

I just see such a series of postings as seperating myths from facts,
but maybe we have different fantasy....


73's
Richard Clark, KB7QHC

Wim
PA3DJS

Transmitter Output Impedance
 

On May 14, 12:36*pm, Richard Clark wrote:
On Sat, 14 May 2011 11:30:50 -0700 (PDT), K7ITM wrote:
FWIW, I've built audio amplifiers with output transistors with f-sub-t
around 50MHz. *Those transistors certainly would provide decent power
gain at the lower frequency HF ham bands. *They were used in the audio
amp to achieve very low distortion across the audio spectrum (a very
few PPM at full rated power output).

Hi Tom,

An Answer to one of my questions (and by inference two of them)!

The inference is there is NO transition frequency where source Z
becomes trivial/meaningful. *Hence, statements alleging correlations
at one end of the spectrum must be observed at the other end.

If this is disputed, we (or at least I) would certainly like to see
what that transition frequency is.

One big difference between (typical) audio amplifiers and (typical) RF
power amplifiers is in the use of negative feedback. *In an audio
amplifier, voltage-derived negative feedback yields a very low
amplifier output impedance. *In almost all RF power amplifiers, little
or no negative feedback is used, so the output impedance is generally
much higher than with an audio amplifier running similar power and
supply voltage to the output devices.

Well, at the RF finals deck, before the Z transformer, there is slight
to no difference in output impedance. *Both are sub-Ohm.

But again, the source impedance of a transmitter is seldom important
in the application of the amplifier. *

This seems at odds with other writers - if it is an AF amplifier. *And
yet none seem to be able to describe the transition frequency for
identical designs (such as yours above, or as close to it as
practicable) where it DOES become important (higher output power, as
if any Ham would snub that advantage if (s)he could snip out the Z
transformer in the rig).

One still unanswered question remains that if a low output Z is so
beneficial to achieving higher output power (a claim that none seem
ready to dispute), then why the step up in Z from the finals deck to
the output connector? *I have read an explanation from Wim, but it
fails as an argument for AF where a similar mismatch between source
and load is observed - and yet this mismatch is the greatest quality
for an amplifier since sliced bread.

AF - RF * A curious tennis match here where what going over the net in
this game is a golf ball in one direction, and a basketball in the
other.

What's important are things like
the optimal load impedance and the rated power output. *I'd put things
like distortion specs for a linear amp far above source impedance in
importance. *If you (the lurking reader) think source impedance is
important, please explain in detail _why_.

The self-same NEGATIVE feedback, lacking in retail rigs, would
accomplish any form of improvement at the cost of what H.W. Bode
called "noise gain." *The dollar cost is not inconsequential. *Not
much more detail is needed for the average Ham.

For the better than average Ham, the increase in NEGATIVE feedback,
goes directly to lowering:
Gain,
Power out (as a function of following gain),
Bandwidth (as a function of following gain),
Distortion,
Power supply disturbance,
Noise,
Input Z (or through clever design, raising it),
Output Z (or through clever design, raising it),
while increasing cost in near or GREATER proportion.

Every Ham knows the adage that there is no such thing as a free lunch,
and the marketplace enforces that without exception.

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

On Mon, 25 Apr 2011 18:07:59 -0700, Jim Lux
wrote:

ON9CVD made some simple measurements using a couple of resistors and
foudn that a TS440 has a Zout somewhere around 15-40 ohms (depending on
frequency and output power).
http://sharon.esrac.ele.tue.nl/~on9c...impedantie.htm

Let's see here, a reported source Z as low as 15 (let's just call it
20) Ohms with 100W into 50 Ohms. *I have read an explanation that this
is impossible (or improbable) for RF from a retail HF rig (such as a
TS440), but achievable at AF. *

Meanwhile, back at the tennis match....

73's
Richard Clark, KB7QHC

I don't get why you're so hung up on some transition frequency between
"RF" and "audio" amplifiers. You're looking at it in the wrong
dimension. Think instead of the loads they drive. Speakers (the
usual load for audio power amplifiers) work best when driven by a
voltage source, so audio amplifiers are designed to look like voltage
sources. With antenna systems, it doesn't much matter what the source
impedance of the driving amplifier is -- as long as the transmitted
bandwidth is small compared with 1/(transmission line time delay)
[question to ponder: why would I care about that?] -- so RF
amplifiers of the sort we normally use are simply not designed with an
eye toward providing any particular output impedance.

You're probably well aware that there are times when I'm personally
extremely concerned about providing an RF source that has a well-
controlled output impedance (pretty much always 50 ohms, just because
of how it's used, but could just as well be 75 ohms, or 100 ohms
balanced, or some other specific impedance). That's not the case for
the lion's share of ham applications, not even in sources used for
simple impedance measurements. There are a few situations in which a
ham might legitimately care about transmitter/amplifier output
impedance, but they are relatively rare. I'm willing to listen to
arguments to the contrary, but have yet to see any convincing ones.

Be careful what you say about the effects of negative feedback added
around an amplifier... (That could be a reasonable topic in another
group, but not in this thread, and probably not even in this group.)

Cheers,
Tom

Transmitter Output Impedance
 

On 5/15/2011 5:02 PM, K7ITM wrote:

Be careful what you say about the effects of negative feedback added
around an amplifier... (That could be a reasonable topic in another
group, but not in this thread, and probably not even in this group.)

Cheers,
Tom

Tom -

Because it is difficult to achieve stability or proper operation due to
phase shifts at RF?

John

Transmitter Output Impedance
 

On Sun, 15 May 2011 15:02:54 -0700 (PDT), K7ITM wrote:

I don't get why you're so hung up on some transition frequency between
"RF" and "audio" amplifiers. You're looking at it in the wrong
dimension.

Transition time, 1/f?

The point is the poor attempts to build a design argument against one
(RF) with the other (AF). Your response of using RF transistors for
AF application in nearly identical topologies suited the point: there
is NO transition frequency.

Think instead of the loads they drive. Speakers (the
usual load for audio power amplifiers) work best when driven by a
voltage source, so audio amplifiers are designed to look like voltage
sources. With antenna systems, it doesn't much matter what the source
impedance of the driving amplifier is -- as long as the transmitted
bandwidth is small compared with 1/(transmission line time delay)
[question to ponder: why would I care about that?]

Everything to that last point was fine. I can well read the stylistic
irony and I wouldn't project that it was a curious hang up.

-- so RF
amplifiers of the sort we normally use are simply not designed with an
eye toward providing any particular output impedance.

And yet challenges abound when one (Z) is chosen for any particular
design quality.

You're probably well aware that there are times when I'm personally
extremely concerned about providing an RF source that has a well-
controlled output impedance (pretty much always 50 ohms, just because
of how it's used, but could just as well be 75 ohms, or 100 ohms
balanced, or some other specific impedance).

All perfectly reasonable choices, and driven by engineering and
application decisions too.

That's not the case for
the lion's share of ham applications, not even in sources used for
simple impedance measurements.

?????

There are a few situations in which a
ham might legitimately care about transmitter/amplifier output
impedance, but they are relatively rare. I'm willing to listen to
arguments to the contrary, but have yet to see any convincing ones.

The length of any source Z thread more than proves your point about
its care. Which is to say, few care (there we agree across the
population of Hams), and there are those few who are vehement about
not caring.

Be careful what you say about the effects of negative feedback added
around an amplifier... (That could be a reasonable topic in another
group, but not in this thread, and probably not even in this group.)

I'm quite careful about the effects of negative feedback added around
an amplifier. Dare I say that we can be thankful there are none
vehement about not caring about that too?

73's
Richard Clark, KB7QHC

Transmitter Output Impedance
 

On Sun, 15 May 2011 02:27:26 -0700 (PDT), Wimpie
wrote:

Richard, who made that claim regarding that low output Z is so
beneficial?

Wim, I offered a corrected thread reference, asked you if you had a
threaded newsreader to respond in-thread, and here we are in another
branch.

I only said that
many PAs don't operate under conjugated match (or even were not
designed to operate under it).

You are being humble, you've written much more than that.

This is valid for audio also.

Valid for diesel engine design, I suppose, too. Unfortunately,
introducing distraction to the Subject line brings increasingly
distractive responses.

However, I enjoy distraction and I can wrap it back to topic:

For instance, AF transmitters were used during WWI for (literal,
through the) ground communications. Shall we expand on that history
that IS relevant to Transmitter Output Impedance?

References:
http://www.qsl.net/vk3gjz/EarthComs/Artillery%20LOI.pdf
http://www.qsl.net/vk3gjz/EarthComs/GroundComs.pdf
and more....

I dare say that these links, and more, can return the discussion back
to Source Z matching that is intuitive, uses very real resistance, and
no appeals (at least back then) to reactance.

73's
Richard Clark, KB7QHC

Transmitter Output Impedance
 

On 4/25/2011 7:35 PM, Sal M. Onella wrote:
This group has presented members with valuable lessons in antennas and
transmission lines, like how to measure, how to match, etc.

Something I haven't seen is a discussion of the source impedance of
the transmitter. My curiosity was piqued today as I took some baby
steps into EZNEC. A particular antenna had such-and-such VSWR if fed
with a 50-ohm cable and a different value if fed with a 75-ohm cable.

While this is hardly news, it got me wondering whether a 75-ohm cable
will load the transmitter the same. Doesn't seem like it.

My point: Using 75-ohm cable to improve the match at the antenna
won't help me ... IF ... I suffer a corresponding loss due to
mismatch at the back of the radio. My HF radios, all solid state,
specify a 50 ohm load. As necessary, I routinely use an internal
autotuner and either of two external manual tuners. (I'm aware of the
published 1/12 wavelength matching method.)

Wisdom in any form would be appreciated. Thanks.

"Sal"
(KD6VKW)

Hey, Sal -

Lots of good stuff he

http://www.vk1od.net/

Fun reading.

Cheers & 73,
John

Transmitter Output Impedance
 

On May 19, 7:33*pm, John KD5YI wrote:
On 4/25/2011 7:35 PM, Sal M. Onella wrote:









This group has presented members with valuable lessons in antennas and
transmission lines, like how to measure, how to match, etc.

Something I haven't seen is a discussion of the source impedance of
the transmitter. *My curiosity was piqued today as I took some baby
steps into EZNEC. *A particular antenna had such-and-such VSWR if fed
with a 50-ohm cable and a different value if fed with a 75-ohm cable.

While this is hardly news, it got me wondering whether a 75-ohm cable
will load the transmitter the same. *Doesn't seem like it.

My point: *Using 75-ohm cable to improve the match at the antenna
won't help me *... IF ... I suffer a corresponding loss due to
mismatch at the back of the radio. *My HF radios, all solid state,
specify a 50 ohm load. As necessary, I routinely use an internal
autotuner and either of two external manual tuners. *(I'm aware of the
published 1/12 wavelength matching method.)

Wisdom in any form would be appreciated. *Thanks.

"Sal"
(KD6VKW)

Hey, Sal -

Lots of good stuff he

http://www.vk1od.net/

Fun reading.

Cheers & 73,
John


John, I have always had great respect for VK1OD, but in the URL you
presented above I must take Dave to task for asserting that Cecil's
concept is suspect, simply because he didn't include attenuation in
the analysis of the lines.

Correct me if I'm wrong, but seems to me that a competent engineer
begins an analysis assuming lines and components are lossless. Then,
if the losses are going to be significant, he factors in the effects
of attenuation. If the losses are insignificant he ignores them.

In Cecil's paper he is not ignoring attenuation because he doesn't
understand its significance, he is ignoring it only because in
beginning the analysis it isn't significant. Cecil doesn't deserve
that unfortunate treatment.

Walt

Transmitter Output Impedance
 

On May 19, 7:33*pm, John KD5YI wrote:
On 4/25/2011 7:35 PM, Sal M. Onella wrote:









This group has presented members with valuable lessons in antennas and
transmission lines, like how to measure, how to match, etc.

Something I haven't seen is a discussion of the source impedance of
the transmitter. *My curiosity was piqued today as I took some baby
steps into EZNEC. *A particular antenna had such-and-such VSWR if fed
with a 50-ohm cable and a different value if fed with a 75-ohm cable.

While this is hardly news, it got me wondering whether a 75-ohm cable
will load the transmitter the same. *Doesn't seem like it.

My point: *Using 75-ohm cable to improve the match at the antenna
won't help me *... IF ... I suffer a corresponding loss due to
mismatch at the back of the radio. *My HF radios, all solid state,
specify a 50 ohm load. As necessary, I routinely use an internal
autotuner and either of two external manual tuners. *(I'm aware of the
published 1/12 wavelength matching method.)

Wisdom in any form would be appreciated. *Thanks.

"Sal"
(KD6VKW)

Hey, Sal -

Lots of good stuff he

http://www.vk1od.net/

Fun reading.

Cheers & 73,
John


Wim, in your calculation of PA output resistance via load pull, you
state:

"...load pulling with 51.2 Ohms and 44.6 Ohms:
V_out (51.2 Ohms) = 71.5V, I_out = 1.396A
V_out (44.6 Ohms) = 66.5V, I_out = 1.491A
Delta_V = 5.0V, Delta_I = 0.095A,
Hence Rout = 52.6 Ohms."

The following is what I obtained through actual measurement via load
pull:

Vout (51.2 ohms = 76.9v, Iout = 1.502a
Vout (44.6 ohms) = 71.6v, Iout = 1.605a
Delta V 5.3v, Delta I = 0.1034a
Hence Rout = 51.2 ohms

Wouldn't you agree that my measurement method and procedure are pretty
well on track?

Walt

Transmitter Output Impedance
 

On 5/19/2011 9:30 PM, walt wrote:
On May 19, 7:33 pm, John wrote:
On 4/25/2011 7:35 PM, Sal M. Onella wrote:









This group has presented members with valuable lessons in antennas and
transmission lines, like how to measure, how to match, etc.

Something I haven't seen is a discussion of the source impedance of
the transmitter. My curiosity was piqued today as I took some baby
steps into EZNEC. A particular antenna had such-and-such VSWR if fed
with a 50-ohm cable and a different value if fed with a 75-ohm cable.

While this is hardly news, it got me wondering whether a 75-ohm cable
will load the transmitter the same. Doesn't seem like it.

My point: Using 75-ohm cable to improve the match at the antenna
won't help me ... IF ... I suffer a corresponding loss due to
mismatch at the back of the radio. My HF radios, all solid state,
specify a 50 ohm load. As necessary, I routinely use an internal
autotuner and either of two external manual tuners. (I'm aware of the
published 1/12 wavelength matching method.)

Wisdom in any form would be appreciated. Thanks.

"Sal"
(KD6VKW)

Hey, Sal -

Lots of good stuff he

http://www.vk1od.net/

Fun reading.

Cheers& 73,
John


John, I have always had great respect for VK1OD, but in the URL you
presented above I must take Dave to task for asserting that Cecil's
concept is suspect, simply because he didn't include attenuation in
the analysis of the lines.

Correct me if I'm wrong, but seems to me that a competent engineer
begins an analysis assuming lines and components are lossless. Then,
if the losses are going to be significant, he factors in the effects
of attenuation. If the losses are insignificant he ignores them.

In Cecil's paper he is not ignoring attenuation because he doesn't
understand its significance, he is ignoring it only because in
beginning the analysis it isn't significant. Cecil doesn't deserve
that unfortunate treatment.

Walt

I do not disagree, Walt, and I do understand why Cecil chose his approach.

John

Transmitter Output Impedance
 

On 20 mayo, 04:46, walt wrote:
On May 19, 7:33*pm, John KD5YI wrote:



On 4/25/2011 7:35 PM, Sal M. Onella wrote:

This group has presented members with valuable lessons in antennas and
transmission lines, like how to measure, how to match, etc.

Something I haven't seen is a discussion of the source impedance of
the transmitter. *My curiosity was piqued today as I took some baby
steps into EZNEC. *A particular antenna had such-and-such VSWR if fed
with a 50-ohm cable and a different value if fed with a 75-ohm cable.

While this is hardly news, it got me wondering whether a 75-ohm cable
will load the transmitter the same. *Doesn't seem like it.

My point: *Using 75-ohm cable to improve the match at the antenna
won't help me *... IF ... I suffer a corresponding loss due to
mismatch at the back of the radio. *My HF radios, all solid state,
specify a 50 ohm load. As necessary, I routinely use an internal
autotuner and either of two external manual tuners. *(I'm aware of the
published 1/12 wavelength matching method.)

Wisdom in any form would be appreciated. *Thanks.

"Sal"
(KD6VKW)

Hey, Sal -

Lots of good stuff he

http://www.vk1od.net/

Fun reading.

Cheers & 73,
John

Wim, in your calculation of PA output resistance via load pull, you
state:

"...load pulling with 51.2 Ohms and 44.6 Ohms:
V_out (51.2 Ohms) = 71.5V, I_out = 1.396A
V_out (44.6 Ohms) = 66.5V, I_out = 1.491A
Delta_V = 5.0V, Delta_I = 0.095A,
Hence Rout = 52.6 Ohms."

The following is what I obtained through actual measurement via load
pull:

Vout (51.2 ohms = 76.9v, Iout = 1.502a
Vout (44.6 ohms) = 71.6v, Iout = 1.605a
Delta V 5.3v, Delta I = 0.1034a
Hence Rout = 51.2 ohms

Wouldn't you agree that my measurement method and procedure are pretty
well on track?

Walt

Hello Walt,

If you would read again my posting (you removed my source
description), I didn't refer to your actual measurements, but referred
to your measurement method applied to my source example (my source
example is 100Vp in series with -j50 Ohm).

I hope this makes clear the differences.

Wim
PA3DJS
www.tetech.nl

I was taught that by convention, i.e. by definition, the missing power
was never generated in the first place - always seemed like a copout
to me. :-)