RadioBanter

RadioBanter (https://www.radiobanter.com/)
-   Antenna (https://www.radiobanter.com/antenna/)
-   -   FIGHT! FIGHT! FIGHT! (https://www.radiobanter.com/antenna/94364-fight-fight-fight.html)

J. Mc Laughlin May 24th 06 02:35 AM

FIGHT! FIGHT! FIGHT!
 
Dear Richard:

Last week's lab job in both Electronics I and II (at different levels)
explored just this issue.
How great it is to have really good scopes and a spectrum analyzer in a
student tab.

73 Mac N8TT

--
J. Mc Laughlin; Michigan U.S.A.
Home:
"Richard Clark" wrote in message
...
On Tue, 23 May 2006 19:11:00 -0400, "J. Mc Laughlin"
wrote:

Dear Richard:

I have had occasion to note to students that some of what they call music
would not be noticeably modified by being amplified by a amplifier having

a
great deal of distortion.

Your point is right on target.


Hi Mac,

My point may have been on target, but the specifics left an escape for
those quick enough to pick up on it. In fact, I would speculate that
most audio (as do RF) amplifiers exhibit the gain characteristic of
f(x) = y = mx + b
and this is called class AB. When you build an amp employing two of
them in a push-pull configuration the constants b negate each other
and the 2mx remains.

Of course, the push-pull configuration is built to nullify the
distortion of this "linear" curve.

The single power supply Op Amp also suffers from
f(x) = y = mx + b
with the output floating at half the supply voltage - this has got to
be an application killer if it goes straight to the speakers without
removing the b with a capacitor.

73's
Richard Clark, KB7QHC




Cecil Moore May 24th 06 04:15 AM

FIGHT! FIGHT! FIGHT!
 
Richard Clark wrote:
Appeals of authority that are pegged to Cecil are like trying to tread
water with a concrete life preserver. Your logic is blighted by a
forced conclusion that has nothing to do with the obvious observation
that antennas, as transmission lines, are quite evidently non-linear
in their characteristic Z. This has been demonstrated and is historic
from sources that even Terman's accepts.


There exist transmission lines with a changing Z0 along their
lengths. Those transmission lines are linear systems.
--
73, Cecil http://www.qsl.net/w5dxp

Richard Harrison May 24th 06 05:01 AM

FIGHT! FIGHT! FIGHT!
 
Richard Clark wrote:
"Demanding that "new frequencies" must exist AND then saying that they
must be of such-and-such a magnitude to qualify is a hoot."

Glad you got a kick out of that. It is not original.

In analog microwave systems, often an baseband intermod monitor is used
to alarm the operator that nonlinearity has arrived in his system. New
frequencies have appeared and have reached a preset arbitrary amplitude
sufficient to trigger an alarm. Nothing is perfect so there will always
be some intermod. This requires setting a level of these intermod
products which will trigger the alarm. This is a standard procedure.

Best regards, Richard Harrison, KB5WZI


Richard Clark May 24th 06 06:44 AM

FIGHT! FIGHT! FIGHT!
 
On Tue, 23 May 2006 23:01:52 -0500, (Richard
Harrison) wrote:

Richard Clark wrote:
"Demanding that "new frequencies" must exist AND then saying that they
must be of such-and-such a magnitude to qualify is a hoot."

Glad you got a kick out of that. It is not original.


Hi Richard,

All that was missing from your response was the chuckle, and the
number at which distortion begins.

How is it if you are not laughing, that neither are you illuminating
to this specific point that is presumable a serious issue? Such a
shortfall doesn't inspire much confidence in your logic, which perhaps
sank with that concrete life jacket.

C'mon, is 10% distortion to be mandated as linear, and 11% distortion
non-linear? Need we push this to Cecil's Limit of perception - ±59%?

Choose your own numbers, or find a true authority to quote a
quantitative response.

73's
Richard Clark, KB7QHC

Richard Harrison May 24th 06 03:00 PM

FIGHT! FIGHT! FIGHT!
 
Richard Clark wrote:
"Choose your own numbers, or find an authority to quote a quantitave
response."

If you can`t detect it, it might as well not exist. If you do detect it,
it`s up to you to correct it or not.

How many antennas have troubled you with new frequencies?

Best regards, Richard Harrison, KB5WZI


Cecil Moore May 24th 06 03:34 PM

FIGHT! FIGHT! FIGHT!
 
Richard Harrison wrote:
How many antennas have troubled you with new frequencies?


Half a century ago, I installed a ceramic capacitor
across the feedpoint of my dipole to change the
resonant frequency. I'm sure it generated some new
frequencies when it blew up and caught on fire. :-)
--
73, Cecil http://www.qsl.net/w5dxp

chuck May 24th 06 04:35 PM

FIGHT! FIGHT! FIGHT!
 
Roy Lewallen wrote:
I'm sure that somewhere in one of your texts you can find the definition
of linear as applied to networks. Once you do, though, a little thought
is required to discover that y = mx + b doesn't satisfy the criteria for
network linearity.

To be linear, a network has to satisfy superposition. This means that:

If y1 is the response to excitation x1 and y2 is the response to
excitation x2, then the response to x1 + x2 must be y1 + y2.

Let's try that with your function.

The response to x1 is:

y(x1) = mx1 + b

The response to x2 is:

y(x2) = mx2 + b

The sum of y(x1) and y(x2) is:

y(x1) + y(x2) = m(x1 + x2) + 2b

But response to x1 + x2 is:

y(x1 + x2) = m(x1 + x2) + b

These are not equal as they must be to satisfy superposition and
therefore the requirements for linearity.

Roy Lewallen, W7EL

Richard Harrison wrote:
Roy Lewallen, W7EL wrote:
"But of course you realize that the function y = mx + b doesn`t meet the
requirements of a linear function when applied to network theory."

Works for me.

Linear means the graph of the function is a straight line.

f(x) = y = mx + b is called linear because its graph is a straight line.

A straight line is the shortest distance between two points.

In y = mx + b, m is a constant determining the slope of the line. x is
is the independent variable. b is the offset or point along the x-axis
where the line crosses.

y then is a linear function of x because its slope is always mx, but
displaced in the x-direction by a constant value, namely b.

y is linear the same as IR is linear, or by substitution, E is linear in
Ohm`s law where E=IR. For any value of I, voltage = IR and the graph of
I versus E is a straight line with a slope equal to R.

Resistance is a common factor in network theory.

Best regards, Richard Harrison, KB5WZI


Not that it means anything, but the linearity requirement is met when
b = 0, which, of course, is a subset of the family of equations of the
form y = mx + b.

73,

Chuck
NT3G

Richard Clark May 24th 06 04:46 PM

FIGHT! FIGHT! FIGHT!
 
On Wed, 24 May 2006 09:00:52 -0500, (Richard
Harrison) wrote:

Richard Clark wrote:
"Choose your own numbers, or find an authority to quote a quantitave
response."

If you can`t detect it, it might as well not exist. If you do detect it,
it`s up to you to correct it or not.


Hi Richard,

So the long and short of it is that you cannot supply us with any
quantifiable information and that you rely solely on impression.

Your explanation sounds like you are practicing psychiatry, not
technology. Given the repetition of the same vague answers would give
rise to the commonplace observation:
the definition of insanity is doing the same thing
over and over, expecting a new outcome.

73's
Richard Clark, KB7QHC

[email protected] May 24th 06 05:04 PM

FIGHT! FIGHT! FIGHT!
 
A good target number for antenna linearity would be one that does not
limit system dynamic range. Our best receivers have a dynamic range of
around 120 dB as measured by the minimum discernable signal on the low
end, and the point where two-tone third order distortion products are
detectable on the high end.

140 dB seems reasonable for an antenna and would theoretically be
measured the same way as receiver dynamic range, though setting up a
noise-free environment, and coupling large distortion-free signals to a
test antenna is a challenge, and is probably one reason we don't see
these measurements. The other reason is that there is good evidence
that a properly built antenna does not limit system dynamic range.
That is, it is very linear in the superposition sense.

By the way, generating new frequencies is not necessarily a violation
of superposition (though it usually is). Consider a system undergoing
a constant Doppler shift.

73,
Glenn AC7ZN


Richard Harrison May 24th 06 10:51 PM

FIGHT! FIGHT! FIGHT!
 
Richard Clark wrote:
"Your explanation sounds like you are practicing psychaitry, not
technoligy."

I think quantification is valuable if the measured value is accurate and
if the value makes a difference.

Antennas are used with transmitters of megawatts of power. These have
limitations by regulations on maximum noise and harmonic content. It
depends on the jurisdiction, but maximum noise and distortion must be at
least 50 dB below the fully modulated level in some locales. I`ve often
used the H.P. noise and distortion analyzer to measure off the air to be
sure we complied with the regulation. It never occurred to me that our
antenna system had a part in noise and distortion production. I expected
curvature in a tube`s characteristics or a failed component to cause a
rise in noise and distortion. Not once do I recall our antenna system
causing distortion anywhere except in the edges of pattern nulls.*This
is normal.

Receiving antennas on the other hand deliver a satisfactory signal
having only microwatts of power. As one responder noted the dynamic
range is enormous. This is not really an issue for concern among
amateurs. Antennas are in general distortion free.

Best regards, RIchard Harrison, KB5WZI


Richard Clark May 24th 06 11:45 PM

FIGHT! FIGHT! FIGHT!
 
On Wed, 24 May 2006 16:51:16 -0500, (Richard
Harrison) wrote:

Not once do I recall our antenna system
causing distortion anywhere except in the edges of pattern nulls.


Hi Richard,

So in this exception, I would make one compelling correlation to your
own observation. That distortion of the pattern was a product of
non-linear behavior in the characteristic Z of the antenna. That
alone seems to be evident. It happens so frequently that we need
complex tools (NEC) to juggle the outcome.

We have non-linear behavior, distortion, and it didn't demand
harmonics, did it? Such non-linearity AND distortion were in all
likelihood trivial, and yet it was noticeable. Now, if no one
complained about pattern nulls being lost, would the non-linearity go
away? ;-)

Cecil would shrug off 59% worth of distortion to define it linear.

73's
Richard Clark, KB7QHC

Cecil Moore May 25th 06 12:18 AM

FIGHT! FIGHT! FIGHT!
 
Richard Clark wrote:
Cecil would shrug off 59% worth of distortion to define it linear.


Richard, seems you suffer from the same affliction as Howard
Hughes, repeating the same psychotic nonsense over and over.
--
73, Cecil http://www.qsl.net/w5dxp

Sal M. Onella May 25th 06 04:50 AM

FIGHT! FIGHT! FIGHT!
 

"Richard Harrison" wrote in message
...

snip

Antennas are in general distortion free.

Yes, but "bad times" can make them non-linear. Consider the bolted joints
that get
corroded and semi-conductive over time, with rain and temperature changes to
help.

Nearby RF sources can generate distortion products in my antennas if I
haven't
kept up my maintenance.



Steve N. June 1st 06 08:17 PM

FIGHT! FIGHT! FIGHT!
 

wrote in message
oups.com...
... By the way, generating new frequencies is not necessarily a violation
of superposition (though it usually is). Consider a system undergoing
a constant Doppler shift.

73,
Glenn AC7ZN


Glenn,
boy! I can't read all these posts, so I was trying to see where you were
going and asking by just skimming, primarily your posts.

The above caught my eye. Doppler is not "generating new frequencies" as a
non linearity does. A non-linear system will produce harmonics with one
exitation frequency and produce the common mixing / IM with multiple
exitation (superimposed) frequencies. I think trying to mix relativistic
effects in with the stationary world is an unnecessary complication of a
linearity discussion.
If I have time I'll try to follow the thread to see what you're really
after...but. If it takes mega watts to see some non linearity in an
antenna, who cares? and more importantly how will you know whree it is
occuring since things like the junction of two connectorc can produce enough
IM to mask other, smaller sources. If you tried an experiment looking
for IM / Mixing you might try to use a receiver becaue a receiver could be a
very sensitive detector...but you'd have to have a pretty good receiver.
Something like a kW LO and mixer to have a really good intercept.
I'm not sure of the point here... Do antennas cause IM?
Sounds like a deadend arena to me.

73, Steve, K9DCI



[email protected] June 2nd 06 04:14 PM

FIGHT! FIGHT! FIGHT!
 
Thanks, Steve,

Good post. You do need to read a little mo by mentioning Doppler
shifts, I was illustrating that a linear system can generate new
frequencies without violating the law of superposition. No
relativistic effects needed he a two-tone train whistle will not
distort in the superposition sense under Doppler shift, but it can
generate new (or different) frequencies. My point was that generation
of new frequencies is not necessarily a valid test for nonlinearity.


My position on antennas is the same as yours. Earlier posts were
confusing as the term 'linearity' was being applied to antennas in two
ways. One in the electrical superposition sense (by me) and the other
in current distribution along the antenna element. Electrically,
antennas are very linear (I believe) even when their current
distribution along the element length is not.

I stopped posting when I realized we were discussing two different
things.

73,
Glenn AC7ZN



Steve N. wrote:
wrote in message
oups.com...
... By the way, generating new frequencies is not necessarily a violation
of superposition (though it usually is). Consider a system undergoing
a constant Doppler shift.

73,
Glenn AC7ZN


Glenn,
boy! I can't read all these posts, so I was trying to see where you were
going and asking by just skimming, primarily your posts.

The above caught my eye. Doppler is not "generating new frequencies" as a
non linearity does. A non-linear system will produce harmonics with one
exitation frequency and produce the common mixing / IM with multiple
exitation (superimposed) frequencies. I think trying to mix relativistic
effects in with the stationary world is an unnecessary complication of a
linearity discussion.
If I have time I'll try to follow the thread to see what you're really
after...but. If it takes mega watts to see some non linearity in an
antenna, who cares? and more importantly how will you know whree it is
occuring since things like the junction of two connectorc can produce enough
IM to mask other, smaller sources. If you tried an experiment looking
for IM / Mixing you might try to use a receiver becaue a receiver could be a
very sensitive detector...but you'd have to have a pretty good receiver.
Something like a kW LO and mixer to have a really good intercept.
I'm not sure of the point here... Do antennas cause IM?
Sounds like a deadend arena to me.

73, Steve, K9DCI



Cecil Moore June 3rd 06 03:34 PM

FIGHT! FIGHT! FIGHT!
 

wrote
Electrically,
antennas are very linear (I believe) even when their current
distribution along the element length is not.

I stopped posting when I realized we were discussing two different
things.


In a linear system, there only needs to be a straight line function
between the input and output. The actual signals on the input wouldn't
be very useful if only straight line functions were allowed on that
input. The current distribution along an antenna element length only
ever approximates a straight line. The only requirement for that
current to obey the rules for a linear system is that it be a
linear function of the source current and it is at every point.
--
73, Cecil http://www.qsl.net/w5dxp



[email protected] June 4th 06 11:38 PM

FIGHT! FIGHT! FIGHT!
 

Cecil Moore wrote:

In a linear system, there only needs to be a straight line function
between the input and output. The actual signals on the input wouldn't
be very useful if only straight line functions were allowed on that
input. The current distribution along an antenna element length only
ever approximates a straight line. The only requirement for that
current to obey the rules for a linear system is that it be a
linear function of the source current and it is at every point.


I mostly agree with your definition of linearity. Roy's point that an
offset in the straight line violates superposition is an example of a
straight line violating superposition. Also consider the throwing of
two dice. If the dice act independently they can be considered a
linear system with two outputs (the numbers that show on the dice)
which obeys the law of superposition. If, however, the dice collide
when thrown, they now influence each other, the system becomes
nonlinear, and the law of superposition is violated. It's pretty hard
for me to attach a straight line function to dice.

Mixers are especially interesting beasts when viewed in the light of
superposition. They are obviously highly nonlinear, yet we regularly
speak of mixer linearity. Here is the trick: when the local oscillator
is included in the input signal set, the mixer is highly nonlinear as
the LO influences every signal that comes in drastically, in the sense
of generating new frequencies.

But it is convenient to think of the local oscillator as just an
internal parameter of the mixer, and to not include it in the input
signal set. Under this assumption all the RF input signals
substantially obey the law of superposition (that is, they do not
influence each other) and discussing mixer linearity has enough meaning
that we can characterize it through standard tests. Note also that
under this assumption the output frequencies do not match the input
frequencies in general, yet the law of superposition holds over a wide
dynamic range.

Cecil's point that doubling antenna current will double the current at
each point in the antenna (I'm rephrasing) has a dual in mixers:
doubling any signal will double all the mixer's ouputs due to that
signal alone, and not any other outputs.


73,
Glenn Dixon AC7ZN


Cecil Moore June 5th 06 03:36 AM

FIGHT! FIGHT! FIGHT!
 
wrote:
Cecil's point that doubling antenna current will double the current at
each point in the antenna (I'm rephrasing) has a dual in mixers:
doubling any signal will double all the mixer's ouputs due to that
signal alone, and not any other outputs.


Yep, as long as system linearity is maintained.
--
73, Cecil http://www.qsl.net/w5dxp



Steve N. June 5th 06 10:29 PM

FIGHT! FIGHT! FIGHT!
 

wrote in message
oups.com...
Thanks, Steve,

Good post.


Thanks.

You do need to read a little mo by mentioning Doppler
shifts, I was illustrating that a linear system can generate new
frequencies without violating the law of superposition.


Hi Glenn,
I got that. Perhaps my use of "relativitistic effects" was inappropriate.
I still maintain that Doppler shift is not an example of (at least what I
would call) "creating new frequencies" because an electronis system did not
cause said shift. A system is linear or non-linear, but a system can't
"make Doppler happen". It is a frequency change, yes, but an "electronic
system" can't cause it. It occurs for reasons other than "system
characteristics". Yes, a space craft can be considered part of a system in
teh general sense, but not as I believe an "electronic system" should be
thought of when discussing such things. Perhaps symmantics in your view,
but not mine. I think it is a fundamental, but, perhaps can't explain
adequately why.
What a thread. usually when a thread gets this long it digresses far
outside the original intent.


...Earlier posts were
confusing as the term 'linearity' ...electrical superposition sense
... and ... current distribution along the antenna element.


So you *were* questioning the linearity of antennas as we understand the
term?

73, Steve


73,
Glenn AC7ZN



Steve N. wrote:
wrote in message
oups.com...
... By the way, generating new frequencies is not necessarily a

violation
of superposition (though it usually is). Consider a system undergoing
a constant Doppler shift.

73,
Glenn AC7ZN


Glenn,
boy! I can't read all these posts, so I was trying to see where you

were
going and asking by just skimming, primarily your posts.

The above caught my eye. Doppler is not "generating new frequencies" as

a
non linearity does. A non-linear system will produce harmonics with one
exitation frequency and produce the common mixing / IM with multiple
exitation (superimposed) frequencies. I think trying to mix

relativistic
effects in with the stationary world is an unnecessary complication of a
linearity discussion.
If I have time I'll try to follow the thread to see what you're really
after...but. If it takes mega watts to see some non linearity in an
antenna, who cares? and more importantly how will you know whree it is
occuring since things like the junction of two connectorc can produce

enough
IM to mask other, smaller sources. If you tried an experiment

looking
for IM / Mixing you might try to use a receiver becaue a receiver could

be a
very sensitive detector...but you'd have to have a pretty good receiver.
Something like a kW LO and mixer to have a really good intercept.
I'm not sure of the point here... Do antennas cause IM?
Sounds like a deadend arena to me.

73, Steve, K9DCI





K7ITM June 6th 06 01:18 AM

FIGHT! FIGHT! FIGHT!
 
I haven't been following this thread lately, but happened on this
particular posting...

Seems to me you want to say "Linear TIME INVARIANT system" to get to
not generating new frequencies. Certainly I can build a system that is
linear but not time-invariant and generate new frequencies with that
system. A simple one is a signal going into a potentiometer, coming
out the wiper, in which the wiper is rotated continuously. It's
linear, but not time invariant, and obviously any input will be
amplitued modulated at the rate of the time variation.

Is a double-balanced mixer with LO a linear system (for input signals
in the intended amplitued range)? Increasing the input amplitude by
1dB causes the output amplitude to increase by 1dB, though the output
is not at the same frequency as the input. If the response of the
DBM/LO system to input x1 is y1, and to x2 is y2, then is (y1+y2) the
response to input (x1+x2)? Is a DBM/LO system time-invariant: if I
apply stimulus x1 at time t1 do I get the same response as if I apply
it at time t2 (where the response is also shifted by t2-t1)?

Perhaps this will be useful food for thought...

Cheers,
Tom

Steve N. wrote:
wrote in message
oups.com...
Thanks, Steve,

Good post.


Thanks.

You do need to read a little mo by mentioning Doppler
shifts, I was illustrating that a linear system can generate new
frequencies without violating the law of superposition.


Hi Glenn,
I got that. Perhaps my use of "relativitistic effects" was inappropriate.
I still maintain that Doppler shift is not an example of (at least what I
would call) "creating new frequencies" because an electronis system did not
cause said shift. A system is linear or non-linear, but a system can't
"make Doppler happen". It is a frequency change, yes, but an "electronic
system" can't cause it. It occurs for reasons other than "system
characteristics". Yes, a space craft can be considered part of a system in
teh general sense, but not as I believe an "electronic system" should be
thought of when discussing such things. Perhaps symmantics in your view,
but not mine. I think it is a fundamental, but, perhaps can't explain
adequately why.
What a thread. usually when a thread gets this long it digresses far
outside the original intent.


...Earlier posts were
confusing as the term 'linearity' ...electrical superposition sense
... and ... current distribution along the antenna element.


So you *were* questioning the linearity of antennas as we understand the
term?

73, Steve


73,
Glenn AC7ZN



Steve N. wrote:
wrote in message
oups.com...
... By the way, generating new frequencies is not necessarily a

violation
of superposition (though it usually is). Consider a system undergoing
a constant Doppler shift.

73,
Glenn AC7ZN


Glenn,
boy! I can't read all these posts, so I was trying to see where you

were
going and asking by just skimming, primarily your posts.

The above caught my eye. Doppler is not "generating new frequencies" as

a
non linearity does. A non-linear system will produce harmonics with one
exitation frequency and produce the common mixing / IM with multiple
exitation (superimposed) frequencies. I think trying to mix

relativistic
effects in with the stationary world is an unnecessary complication of a
linearity discussion.
If I have time I'll try to follow the thread to see what you're really
after...but. If it takes mega watts to see some non linearity in an
antenna, who cares? and more importantly how will you know whree it is
occuring since things like the junction of two connectorc can produce

enough
IM to mask other, smaller sources. If you tried an experiment

looking
for IM / Mixing you might try to use a receiver becaue a receiver could

be a
very sensitive detector...but you'd have to have a pretty good receiver.
Something like a kW LO and mixer to have a really good intercept.
I'm not sure of the point here... Do antennas cause IM?
Sounds like a deadend arena to me.

73, Steve, K9DCI




K7ITM June 6th 06 07:56 AM

FIGHT! FIGHT! FIGHT!
 
I recall a prof or two arm-waving over that one. However, I think if
you formulate your definition of linearity properly, the transfer
function y=mx+b will still satisfy linearity. Specifically, if the
_response_ is the _change_ that occurs in the output going from x=0 to
x=x1, then the response for x1 is (m*x1+b)-(m*0+b) = m*x1, and of
course for x2, it's m*x2. The response for x=x1+x2 is m*(x1+x2), which
is exactly the sum of the responses for x1 and x2.

Similarly, for a mixer/LO system with RF input and IF output, if the
mixer is unbalanced and lets LO get through, it is still a linear
system if the change in output when go from zero input to input x1(t)
plus the change in output when you go from zero input to input x2(t) is
equal to the change in output when you go from zero input to input
(x1(t)+x2(t)).

But note that a mixer/LO system is NOT time invariant, because the
output for x1(t+delta) is in general NOT the same as the output shifted
in time by delta for input x1(t).

You can most certainly find text books that define linearity
differently than I did above. I find the definition above to be a more
useful one, however, and it seems to be the one generally accepted in
practice, even if it's not stated accurately in words.

Cheers,
Tom



Roy Lewallen wrote:
Richard Harrison wrote:
Richard Clark, KB7QHC wrote:
"Who. in your estimation, does qualify to discuss it?"

If it`s about antennas, I nominate Kraus. If it`s about mathematics,
many marhematicians qualify.

In algebra, y = mx + b, (the point slope formula), is called linear
because it is the graph of a straight line.
. . .


But of course you realize that the function y = mx + b doesn't meet the
requirements of a linear function when applied to network theory.

Roy Lewallen, W7EL



Roy Lewallen June 6th 06 08:25 AM

FIGHT! FIGHT! FIGHT!
 
It's not clear to me whether you're proposing an alternative definition
for linearity or for superposition. I've never seen superposition
defined as other than that the sum of responses to individual
excitations be equal to the response to the sum of the excitations --
that's the definition in Pearson & Maler's _Introductory Circuit
Analysis_, Van Valkenburg's _Network Analysis_, and the rather old
edition of the _IEEE Standard Dictonary of Electrical and Electronic
Terms_ I have. Do you have a reference that gives the definition you
propose for superposition?

If on the other hand the alternative definition is only for linearity,
we'd then be faced with the possibility of having a linear (and
time-invariant) circuit which doesn't satisfy superposition. That's not
a pleasant circumstance to ponder.

Roy Lewallen, W7EL

K7ITM wrote:
I recall a prof or two arm-waving over that one. However, I think if
you formulate your definition of linearity properly, the transfer
function y=mx+b will still satisfy linearity. Specifically, if the
_response_ is the _change_ that occurs in the output going from x=0 to
x=x1, then the response for x1 is (m*x1+b)-(m*0+b) = m*x1, and of
course for x2, it's m*x2. The response for x=x1+x2 is m*(x1+x2), which
is exactly the sum of the responses for x1 and x2.

Similarly, for a mixer/LO system with RF input and IF output, if the
mixer is unbalanced and lets LO get through, it is still a linear
system if the change in output when go from zero input to input x1(t)
plus the change in output when you go from zero input to input x2(t) is
equal to the change in output when you go from zero input to input
(x1(t)+x2(t)).

But note that a mixer/LO system is NOT time invariant, because the
output for x1(t+delta) is in general NOT the same as the output shifted
in time by delta for input x1(t).

You can most certainly find text books that define linearity
differently than I did above. I find the definition above to be a more
useful one, however, and it seems to be the one generally accepted in
practice, even if it's not stated accurately in words.

Cheers,
Tom


[email protected] June 6th 06 11:37 AM

FIGHT! FIGHT! FIGHT!
 

Steve N. wrote:

So you *were* questioning the linearity of antennas as we understand the
term?


No. I was claiming antennas were very linear in the electrical
superposition sense.

73,
Glenn


[email protected] June 6th 06 12:48 PM

FIGHT! FIGHT! FIGHT!
 

Roy Lewallen wrote:
It's not clear to me whether you're proposing an alternative definition
for linearity or for superposition.

Lest anyone think that the addition of an offset term (the b in y=mx+b)
violating superposition is merely of academic interest, analyze a
direct conversion receiver. At my shack I have a Softrock 40, which
tunes about thirty KHz of the 40 meter band. At the center of the
spectrum (which corresponds to the mixer converting to very low
frequencies and DC) is a 1/f bump that the designers have attributed to
mixer 1/f noise. But it is not noise at all. When tuned in, it is
full of strong signals and strange sounds. These are distortion
products, and are caused mainly by the b term in the detector used on
the receiver.

They wipe out about 3% of the receivable band.

Sometimes the b term is benign, but not in this case.

73,
Glenn Dixon AC7ZN


K7ITM June 6th 06 04:52 PM

FIGHT! FIGHT! FIGHT!
 
I would not propose to change the definition for either linearity or
superposition, at least as I saw them a moment ago in one text, the
"Linear Circuit Analysis" chapter of "The Electrical Engineering
Handbook," Richard C. Dorf, editor. Rather I propose we think more
carefully about just what "response" to a stimulus means. If you say
that in the system y=mx+b that b is the response to zero input (x=0)
then you will conclude that the system is nonlinear. On the other
hand, if the "response" to a "stimulus" only has meaning as the
_change_ (or difference) in output for a given _change_ (or difference)
in input, then it is a linear system.
Roy Lewallen wrote:
It's not clear to me whether you're proposing an alternative definition
for linearity or for superposition. I've never seen superposition
defined as other than that the sum of responses to individual
excitations be equal to the response to the sum of the excitations --
that's the definition in Pearson & Maler's _Introductory Circuit
Analysis_, Van Valkenburg's _Network Analysis_, and the rather old
edition of the _IEEE Standard Dictonary of Electrical and Electronic
Terms_ I have. Do you have a reference that gives the definition you
propose for superposition?

If on the other hand the alternative definition is only for linearity,
we'd then be faced with the possibility of having a linear (and
time-invariant) circuit which doesn't satisfy superposition. That's not
a pleasant circumstance to ponder.

Roy Lewallen, W7EL

K7ITM wrote:
I recall a prof or two arm-waving over that one. However, I think if
you formulate your definition of linearity properly, the transfer
function y=mx+b will still satisfy linearity. Specifically, if the
_response_ is the _change_ that occurs in the output going from x=0 to
x=x1, then the response for x1 is (m*x1+b)-(m*0+b) = m*x1, and of
course for x2, it's m*x2. The response for x=x1+x2 is m*(x1+x2), which
is exactly the sum of the responses for x1 and x2.

Similarly, for a mixer/LO system with RF input and IF output, if the
mixer is unbalanced and lets LO get through, it is still a linear
system if the change in output when go from zero input to input x1(t)
plus the change in output when you go from zero input to input x2(t) is
equal to the change in output when you go from zero input to input
(x1(t)+x2(t)).

But note that a mixer/LO system is NOT time invariant, because the
output for x1(t+delta) is in general NOT the same as the output shifted
in time by delta for input x1(t).

You can most certainly find text books that define linearity
differently than I did above. I find the definition above to be a more
useful one, however, and it seems to be the one generally accepted in
practice, even if it's not stated accurately in words.

Cheers,
Tom



Richard Harrison June 7th 06 01:57 AM

FIGHT! FIGHT! FIGHT!
 
K7ITM wrote:
"If you say that in the system (y = mx + b) that b is the response to
zero input (x=0) then you will conclude the system is nonlinear."

Why? the factor (b) is a constant, a value to be added to (mx) to total
a value for (y).

(mx) is a straight line. Every value of (b) produces a straight lline
parallel with lhe line y=mx when b=0. Factor (b) is merely the offset
value of the sloped line in the x direction.

y=mx+b is listed in math books as a defining example of a linear
equation. (When plotted, a linear equation produces a straight line.)
y=mx+b has a special name: "The point slope formula". Perfectly
descriptive, too.

To clarify everything, graph a few values for yourself.

Best regards, Richard Harrison, KB5WZI


Cecil Moore June 7th 06 04:38 AM

FIGHT! FIGHT! FIGHT!
 
Richard Harrison wrote:
(mx) is a straight line. Every value of (b) produces a straight lline
parallel with lhe line y=mx when b=0. Factor (b) is merely the offset
value of the sloped line in the x direction.


Why must superposition preserve 'b' (as someone has
asserted?)
--
73, Cecil http://www.qsl.net/w5dxp

K7ITM June 7th 06 03:53 PM

FIGHT! FIGHT! FIGHT!
 

Richard Harrison wrote:
K7ITM wrote:
"If you say that in the system (y = mx + b) that b is the response to
zero input (x=0) then you will conclude the system is nonlinear."

Why? the factor (b) is a constant, a value to be added to (mx) to total
a value for (y).


Because, from 3.3, 'Network Theorems,' in "The Electrical Engineering
Handbook,"
Ed. Richard C. Dorf, Boca Raton: CRC Press LLC, 2000 (you can find it
online),

"The superposition condition: If the input to the system, e1, causes a
response, r1, and if an input to the system, e2, causes a response, r2,
then a response, r1 + r2, will occur when the input is e1 + e2."

If you take the response to x0=0 to be b, then the response to, say,
x1=1 must be m+b, and to x2=2 must be 2*m+b. Then for superposition,
and therefore for linearity, the response to (x1+x2)=3 must be
m+b+2*m+b = 3*m+2*b, which it is not: it is 3*m+b. I do not suggest a
change in the definition of superposition or of homogeneity (which
seems to be simply a subset of superpostion anyway) or of linearity. I
only suggest that "response" be interpreted as the change in output
which occurs when you go from input a to input b. I've generally not
seen "response" to be very well defined in those texts which define
linearity, though it's quite possible I've missed it. In the PDF file
for all of Chapter 3 of the book quoted above, it is certainly not.

I guess I'd prefer, basically, to say that the following relationship
defines a linear system (MIMO even) -- but it is NOT sufficient to
describe all linear systems:

dx/dt = Ax + Bu
y = Cx + Du
where u is a vector of independent input variables, y is a vector of
dependent output variables, x represents state variables for the
system, and A, B, C and C are matrices of coefficients which are
constant in a time-invariant system, but which may be variable with
time in a system which is time variant.

Cheers,
Tom



(mx) is a straight line. Every value of (b) produces a straight lline
parallel with lhe line y=mx when b=0. Factor (b) is merely the offset
value of the sloped line in the x direction.

y=mx+b is listed in math books as a defining example of a linear
equation. (When plotted, a linear equation produces a straight line.)
y=mx+b has a special name: "The point slope formula". Perfectly
descriptive, too.

To clarify everything, graph a few values for yourself.

Best regards, Richard Harrison, KB5WZI




All times are GMT +1. The time now is 07:54 AM.

Powered by vBulletin® Copyright ©2000 - 2025, Jelsoft Enterprises Ltd.
RadioBanter.com