RadioBanter - Calculating loss on a mismatched line

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- - Calculating loss on a mismatched line (https://www.radiobanter.com/antenna/74096-calculating-loss-mismatched-line.html)

On Thu, 7 Jul 2005 18:46:36 -0400, "Walter Maxwell"
wrote:

Well, Owen, if you believe the expressions I presented in Reflections 2 are
approximate, then why do I get the correct answers?

It seems to me that the method requires that rho is not greater than
one (otherwise the denominator (1-rho2**2) becomes negative, which is
a nonsense). This hints that it does not apply in the general case
where rho *can* be greater than 1, and is therefore probably limited
to cases of distorionless line (Xo=0).

To avoid publishing "ugly" maths here, I have put a page up at
http://www.vk1od.net/temp/reflection.htm with a bunch of expressions
for conditions on the modelled line, including functions for power
flow at an arbitrary point, Loss calculated from powerflow at two
points and loss based on your loss formula + matched line loss.

The graphs show the loss from point x to the load, x is 0 at the load
and negative toward the source.

The algorithms produce quite different results. If I ignore Xo (ie
force Zo to be real), then both algorithms produce the same results.

Have I made a mistake in the maths, or in modelling the scenario?

Owen
--

"Owen" wrote in message
...
On Thu, 7 Jul 2005 18:46:36 -0400, "Walter Maxwell"
wrote:

Well, Owen, if you believe the expressions I presented in Reflections 2
are
approximate, then why do I get the correct answers?

It seems to me that the method requires that rho is not greater than
one (otherwise the denominator (1-rho2**2) becomes negative, which is
a nonsense). This hints that it does not apply in the general case
where rho *can* be greater than 1, and is therefore probably limited
to cases of distorionless line (Xo=0).

To avoid publishing "ugly" maths here, I have put a page up at
http://www.vk1od.net/temp/reflection.htm with a bunch of expressions
for conditions on the modelled line, including functions for power
flow at an arbitrary point, Loss calculated from powerflow at two
points and loss based on your loss formula + matched line loss.

The graphs show the loss from point x to the load, x is 0 at the load
and negative toward the source.

The algorithms produce quite different results. If I ignore Xo (ie
force Zo to be real), then both algorithms produce the same results.

Have I made a mistake in the maths, or in modelling the scenario?

Owen

Thanks for responding, Owen, but I'm going to be otherwise occupied until
Saturday, so the fact that I don't respond immediately doesn't mean that I'm
ignoring you.

Walt

On Wed, 6 Jul 2005 21:23:52 -0400, "Walter Maxwell"
wrote:

If you like, I am saying your approach is valid for lossless lines, it
is also valid for all distortionless lines, but I think it is not
accurate for lines in the general case because it isn't correct if
Xo!=0.

Owen

Owen, if X = 0 there is no attenuation, but you're saying my material is
invalid if X is not 0? I'm sorry, but I'm confused.

Walt, it has just occurred to me that I am using the "actual" Zo, not
the nominal Zo, and I think your rho calc is based on the nominal Zo,
as it will be measured with an instrument presumably calibrated for
nominal Zo.

I have compared the loss calculated by your method (with rho based on
nominal Zo, Zo=Ro+j0) and my method and they are very similar (though
not the same). I have added a function to calculate the loss using
your formula based on nominal Zo and plotted it, along with the
difference to the power based loss calc. They are at
http://www.vk1od.net/temp/reflection.htm .

If your method is based on nominal Zo, rather than the actual Zo, it
is likely to be an approximation, though on this example, it is pretty
close and probably is quite adequate for most practical lines at HF
and above. (The error increases as frequency is reduced (Zo departs
more from nominal Zo).)

Having resolved the apparent inconsistency... I am still in search of
a derivation of the Michaels formula.

Owen
--

Owen, I tried to send this as a reply to you, but your email address was
rejected, so I had to send this to the group. My response appears below your

Walt

"Owen" wrote in message
...
On Wed, 6 Jul 2005 21:23:52 -0400, "Walter Maxwell"
wrote:

If you like, I am saying your approach is valid for lossless lines, it
is also valid for all distortionless lines, but I think it is not
accurate for lines in the general case because it isn't correct if
Xo!=0.

Owen

Owen, if X = 0 there is no attenuation, but you're saying my material is
invalid if X is not 0? I'm sorry, but I'm confused.

Walt, it has just occurred to me that I am using the "actual" Zo, not
the nominal Zo, and I think your rho calc is based on the nominal Zo,
as it will be measured with an instrument presumably calibrated for
nominal Zo.

I have compared the loss calculated by your method (with rho based on
nominal Zo, Zo=Ro+j0) and my method and they are very similar (though
not the same). I have added a function to calculate the loss using
your formula based on nominal Zo and plotted it, along with the
difference to the power based loss calc. They are at
http://www.vk1od.net/temp/reflection.htm .

If your method is based on nominal Zo, rather than the actual Zo, it
is likely to be an approximation, though on this example, it is pretty
close and probably is quite adequate for most practical lines at HF
and above. (The error increases as frequency is reduced (Zo departs
more from nominal Zo).)

Having resolved the apparent inconsistency... I am still in search of
a derivation of the Michaels formula.

Owen

----- Original Message -----
From: "Owen"
Newsgroups: rec.radio.amateur.antenna
Sent: Friday, July 08, 2005 6:08 PM
Subject: Calculating loss on a mismatched line

Hi Owen,

I'm trying to understand your Mathcad presentations, but I've run into some
roadblocks concerning terminology, some of which I'm not familiar with. I
confess my questions prove my ignorance, but that's ok if one's trying to
learn. However, I was using nominal Zo.

First, Xo!=0. I don't know what this means.
Second, what does MML stand for in English?
Third, in 'functions for V, I, Z, etc at z'. Where is 'z'? I cannot find any
reference to it.
Fourth, 'exp'. Exponent? If so, of what? e?
Fifth, I understand 'x' as distance along the line from the termination, but
what is 'y'?
Sixth, what is AppLoss? Approximate? Apparent? Applied?
Seventh, 'DLoss'. What is 'D'? Dielectric? Again, what is the 'y' term? An
ordinate value?
Eighth, in the LineLoss(x,y) = 10log... the identical right-hand terms in
both numerator and denominator, the identical functions of 'e^^ x e^^. what
is the meaning of the bar above the second appearance of 'e'? And above
gamma(x)?

I want to understand your math presentation, Owen, especially when I see
that Loss(x,0 - W2DUloss(x,0) is so small I want to understand what makes
the difference. So I'd appreciate it if you'd set me straight on the points
I made above.

Walt

On Sat, 9 Jul 2005 23:17:18 -0400, "Walter Maxwell"
wrote:

I'm trying to understand your Mathcad presentations, but I've run into some
roadblocks concerning terminology, some of which I'm not familiar with. I
confess my questions prove my ignorance, but that's ok if one's trying to
learn. However, I was using nominal Zo.

Not at all, you are far more eminent that I on this topic, and I
appreciate your review. I am learning from all this.

Apologies for the difficulty in understanding my notation. Some of it
breaks into psuedo programming code.

First, Xo!=0. I don't know what this means.

Not equals.

Second, what does MML stand for in English?

MLL? Matched Line Loss (dB/m)

Third, in 'functions for V, I, Z, etc at z'. Where is 'z'? I cannot find any
reference to it.

These quantities are a function of z, where z is a position on the
line. The convention that I have used for displacement is that it is
negative towards the generator. When it matters, displacement is in
metres. The z is just used in definition of some functions in Matchcad
(where you see :=), I have used x for position variable in the graphs.

Fourth, 'exp'. Exponent? If so, of what? e?

exp(x) is e to the power of x (For clarity, I shouldn't have written
it that way, it works, but Mathcad understands the meaning of e
superscript x as e to the power of x, as you will see in some of the
expressions, and it is easier to read.)

Fifth, I understand 'x' as distance along the line from the termination, but
what is 'y'?

In some of the functions, I have written them to calculate some
quantity between two arbitrary points x and y. They are used in the
definition of fuctions (where you see :=). Most of the graphs use 0
for y so they are plotted wrt the load position

Sixth, what is AppLoss? Approximate? Apparent? Applied?

Approximate Loss, and it was incorrectly based on Zo rather than
nominal Zo.

Seventh, 'DLoss'. What is 'D'? Dielectric? Again, what is the 'y' term? An
ordinate value?

DLoss was equivalent to AppLoss.

Eighth, in the LineLoss(x,y) = 10log... the identical right-hand terms in
both numerator and denominator, the identical functions of 'e^^ x e^^. what
is the meaning of the bar above the second appearance of 'e'? And above
gamma(x)?

The bar above the variable is the complex conjugate operator.

I want to understand your math presentation, Owen, especially when I see
that Loss(x,0 - W2DUloss(x,0) is so small I want to understand what makes
the difference. So I'd appreciate it if you'd set me straight on the points
I made above.

Walt, in the models at http://www.vk1od.net/temp/LineLoss.htm , I now
know why there is such a gap between DLoss and LineLoss. You will
recognise AppLoss / DLoss is your Appendix 8 expression, but my rho
function was based on the modelled complex value of Zo (characteristic
impedance), not the nominal value of Zo.

In the second lot at http://www.vk1od.net/temp/reflection.htm ,
AppLoss is equivalent to DLoss and it is based on nominal Zo, W2DULoss
you will see calculates the rho term (though not identified) using
nominal Ro.

Comparing the results with loss calcuated from P(x)/P(y) (the ratio of
the real power at points x and y), the conclusion is that using your
expression with actual Zo is not at all accurate, using it with
nominal Zo is very close. If I force Zo to be real for all modelling,
the results of all methods is exactly the same (within rounding errors
of the order of 10 to the power of -14)

Some of your questions are just about the Mathcad notation (though
that is not too dissimilar to normal handwritten math notation), but
some of it is my expression and usage. Again my apologies for
confusing with too little explanation. I appreciate your review and
comments Walt.

Owen
--

"Owen" wrote in message
...
On Sat, 9 Jul 2005 23:17:18 -0400, "Walter Maxwell"
wrote:

I'm trying to understand your Mathcad presentations, but I've run into
some
roadblocks concerning terminology, some of which I'm not familiar with.
I
confess my questions prove my ignorance, but that's ok if one's trying
to
learn. However, I was using nominal Zo.

Not at all, you are far more eminent that I on this topic, and I
appreciate your review. I am learning from all this.

Apologies for the difficulty in understanding my notation. Some of it
breaks into psuedo programming code.

First, Xo!=0. I don't know what this means.

Not equals.

Second, what does MML stand for in English?

MLL? Matched Line Loss (dB/m)

Third, in 'functions for V, I, Z, etc at z'. Where is 'z'? I cannot
find any
reference to it.

These quantities are a function of z, where z is a position on the
line. The convention that I have used for displacement is that it is
negative towards the generator. When it matters, displacement is in
metres. The z is just used in definition of some functions in Matchcad
(where you see :=), I have used x for position variable in the graphs.

Fourth, 'exp'. Exponent? If so, of what? e?

exp(x) is e to the power of x (For clarity, I shouldn't have written
it that way, it works, but Mathcad understands the meaning of e
superscript x as e to the power of x, as you will see in some of the
expressions, and it is easier to read.)

Fifth, I understand 'x' as distance along the line from the
termination, but
what is 'y'?

In some of the functions, I have written them to calculate some
quantity between two arbitrary points x and y. They are used in the
definition of fuctions (where you see :=). Most of the graphs use 0
for y so they are plotted wrt the load position

Sixth, what is AppLoss? Approximate? Apparent? Applied?

Approximate Loss, and it was incorrectly based on Zo rather than
nominal Zo.

Seventh, 'DLoss'. What is 'D'? Dielectric? Again, what is the 'y' term?
An
ordinate value?

DLoss was equivalent to AppLoss.

Eighth, in the LineLoss(x,y) = 10log... the identical right-hand terms
in
both numerator and denominator, the identical functions of 'e^^ x e^^.
what
is the meaning of the bar above the second appearance of 'e'? And above
gamma(x)?

The bar above the variable is the complex conjugate operator.

I want to understand your math presentation, Owen, especially when I
see
that Loss(x,0 - W2DUloss(x,0) is so small I want to understand what
makes
the difference. So I'd appreciate it if you'd set me straight on the
points
I made above.

Walt, in the models at http://www.vk1od.net/temp/LineLoss.htm , I now
know why there is such a gap between DLoss and LineLoss. You will
recognise AppLoss / DLoss is your Appendix 8 expression, but my rho
function was based on the modelled complex value of Zo (characteristic
impedance), not the nominal value of Zo.

In the second lot at http://www.vk1od.net/temp/reflection.htm ,
AppLoss is equivalent to DLoss and it is based on nominal Zo, W2DULoss
you will see calculates the rho term (though not identified) using
nominal Ro.

Comparing the results with loss calcuated from P(x)/P(y) (the ratio of
the real power at points x and y), the conclusion is that using your
expression with actual Zo is not at all accurate, using it with
nominal Zo is very close. If I force Zo to be real for all modelling,
the results of all methods is exactly the same (within rounding errors
of the order of 10 to the power of -14)

Some of your questions are just about the Mathcad notation (though
that is not too dissimilar to normal handwritten math notation), but
some of it is my expression and usage. Again my apologies for
confusing with too little explanation. I appreciate your review and
comments Walt.

Owen

Thank you, Owen, for kicking aside the roadblocks preventing me from
understanding your math presentation. I get it now, and realize I was a
knothead for being confused.

It is now perfectly clear why one can't get the true answer using my
expressions for calculating loss on the line when using only the nominal Zo
and not the actual Zo when there is loss. I should have known that
intuitively, and why it escaped me is puzzling.

Studying your math approach let me see the light, and for that I thank
you. And thank you also for taking the time to teach me.

Walt

PS--I note from your telephone numbers in your email to me that you are
not located in the US. Also, the name Duffy sounds somewhat British. Are you
in the UK?

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