I did this. And the more difficult problem of:

Z o---Lm---+---C---+---GND
| |
+---R---+
| |
+---Lw--+

The expresion of which takes up a couple of lines on notebook paper alone.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

On Tue, 22 Jul 2008 23:46:42 -0500, "Tim Williams"
wrote:

I did this. And the more difficult problem of:

Z o---Lm---+---C---+---GND
| |
+---R---+
| |
+---Lw--+

The expresion of which takes up a couple of lines on notebook paper alone.

Tim

I find it easier (and less error prone) to use jw = s (Laplace
notation) until the very end, when you need to split amplitude and
phase.

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

Democrats are so cute. Â*Stupid as bricks, but cute.

On Tue, 22 Jul 2008 23:46:42 -0500, "Tim Williams"
wrote:

I did this. And the more difficult problem of:

Z o---Lm---+---C---+---GND
| |
+---R---+
| |
+---Lw--+

The expresion of which takes up a couple of lines on notebook paper alone.

Tim

I spent the day programming, and programming has absolutely nothing to
do with math.

John

On Tue, 22 Jul 2008 23:46:42 -0500, "Tim Williams"
wrote:

I did this. And the more difficult problem of:

Z o---Lm---+---C---+---GND
| |
+---R---+
| |
+---Lw--+

The expresion of which takes up a couple of lines on notebook paper alone.

Tim

The circuit you analyze in the PDF looks like the same one you asked about
in sci.electronic.basics in November or 2005. Didn't that have something
to do with induction heating?

You've definitely improved your skills with complex algebra in the
meantime. However, in the PDF file, on the first page, around the middle
you show 5 algebraic manipulations. The third one is in error.

You have:


jwL + R
= -----------
1 + jwRC

but it should be:

R
= jwL + ----------
1 + jwRC

The circuit you show in this post at the beginning can be analyzed as shown
in the attachment.

"The Phantom" wrote in message
...
On Tue, 22 Jul 2008 23:46:42 -0500, "Tim Williams"
wrote:

I did this. And the more difficult problem of:

Z o---Lm---+---C---+---GND
| |
+---R---+
| |
+---Lw--+
^ ^ ^ ^ ^ ^ ^ ^ ^ ^

The circuit you analyze in the PDF looks like the same one you asked about
in sci.electronic.basics in November or 2005. Didn't that have something
to do with induction heating?

Excellent memory! In fact the one quoted above is specifically my induction
heater output network... the one in the PDF is a simpler network, notably
differing in that Lw -- infinity. If Lw cancels with most of C (which it
does at resonance, except for the amount that Lm takes for itself), then
what's in the PDF is an acceptable model. But that's limited to resonance
only, which is kind of boring.

On the other hand, it works for anywhere you want to look at a
series-resonant tank with R || C...

You've definitely improved your skills with complex algebra in the
meantime. However, in the PDF file, on the first page, around the middle
you show 5 algebraic manipulations. The third one is in error.

Yup, I noticed that just this evening. Transcription error. I had it right
on paper, and I believe correct in ASCII as well. So, blame it on LaTeX...
LaTeX made me do it. :^)

I believe I also have the correct form of the four-element network. I fixed
the error where I was getting a few hundred negative ohms on the complex
plane. :^)

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

On Wed, 23 Jul 2008 14:04:16 -0700, John Larkin
wrote:

I spent the day programming, and programming has absolutely nothing to
do with math.

Curiously, I spent the day plumbing, which ended up involving the Law of
Sines for some strange reason.

The revised addition.

Typo fixed, plus a subtle typo nobody else noticed. ;-)

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

"Tim Williams" wrote in message
...
I did this. And the more difficult problem of:

Z o---Lm---+---C---+---GND
| |
+---R---+
| |
+---Lw--+

The expresion of which takes up a couple of lines on notebook paper alone.

"The Phantom" wrote in message
...
The circuit you show in this post at the beginning can be analyzed as
shown
in the attachment.

Bah, a triple-decker, with j's on all levels. Didn't your mother teach you
anything about math? ;-) (Probably not, mine isn't big on math...)

Here's the simplified version. It makes pretty plots that make sense, even
giving real-world values.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

On Thu, 24 Jul 2008 03:30:41 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
.. .
The circuit you show in this post at the beginning can be analyzed as
shown
in the attachment.

Bah, a triple-decker, with j's on all levels.

What's wrong with j's on all levels? If you can deal with j's in the
numerator, you should be able to deal with them in the denominator too.
That way you have a very compact expression, and avoid the possibility of
making an error in deriving the cumbersome expression you get when you
rationalize it (multiply the numerator and denominator by the conjugate of
the denominator).

Didn't your mother teach you
anything about math? ;-) (Probably not, mine isn't big on math...)

Here's the simplified version.

My expression agrees with this. It's identical, except that I left mine in
factored form, which makes it a less cumbersome expression.

It makes pretty plots that make sense, even
giving real-world values.

Tim

"R.L. Horn" wrote in message
...
Curiously, I spent the day plumbing, which ended up involving the Law of
Sines for some strange reason.

That Chebyshev guy was working on turning linear (pistion) motion into
circular (wheel) motion when he came up with those functions of his.

Anyone have a reference for a more detailed explanation of what Chebyshev was
up to? My knowledge of him comes primarily from a couple of brief footnotes
in engineering texts. I asked our ME at work if he'd every heard of the guy,
and he said no.

---JOel

"Tim Williams" wrote in message
...
Yup, I noticed that just this evening. Transcription error. I had it right
on paper, and I believe correct in ASCII as well. So, blame it on LaTeX...
LaTeX made me do it. :^)

If you want to use LaTeX but not bang your head against the wall nearly as
much (at least until you become quite proficient at it), you might want to
look at Scientific Workplace by McKichan Software (www.mackichan.com) -- it's
a WYSIWYG editor that still keeps everything in TeX internally so you can keep
using (most) LaTeX packages with it, style files, etc.

Some other options are MathType, which lets you enter the equation via WYSIWYG
and then generates the LaTeX for you, or something like Ekee which previews
LaTeX equations graphically (http://rlehy.free.fr/).

LaTeX/TeX is slowly dying, which is sort of a mixed blessing: While rather
brittle and difficult to use (far more so than need be in this day and age),
it still has many good features and ideas that regular word processors don't
(or don't implement as well). The hard-core TeXer keep
supporting/revising/updating it, but I suspect that it's still going to die
out almost entirely within a decade. (Where I did my graduate work only a
couple of departments -- ECE, math, etc. -- were still recommending it for
theses, but other than individual professor's requirements, I don't think it
was ever *required* so long as you could generate a PDF for the library
meeting the formatting standards proscribed.)

The biggest problem with, e.g., Microsoft Office and OpenOffice is that they
tend to start becoming brittle themselves when working on large documents.

---Joel

On Thu, 24 Jul 2008 05:32:10 +0000 (UTC), "R.L. Horn"
wrote:

On Wed, 23 Jul 2008 14:04:16 -0700, John Larkin
wrote:

I spent the day programming, and programming has absolutely nothing to
do with math.

Curiously, I spent the day plumbing, which ended up involving the Law of
Sines for some strange reason.

And a higher sense of accomplishment, no doubt.

John

"The Phantom" wrote in message
...
What's wrong with j's on all levels?

I was told to "simplify" expressions so that no radicals, imaginary factors,
fractions, etc. are on the bottom.

Too bad this leads to less than simple expressions, like for such purposes
as this!

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

John Larkin wrote:
On Thu, 24 Jul 2008 05:32:10 +0000 (UTC), "R.L. Horn"
wrote:

On Wed, 23 Jul 2008 14:04:16 -0700, John Larkin
wrote:

I spent the day programming, and programming has absolutely nothing to
do with math.
Curiously, I spent the day plumbing, which ended up involving the Law of
Sines for some strange reason.

And a higher sense of accomplishment, no doubt.

John

Higher math, higher sense of accomplishment. What's not to like? Beats
working for a living. I just finished a section showing that the SNR
of a focused-beam measurement is proportional to the square of the
Strehl ratio--thereby showing how optical aberrations affect the actual
data.

Cheers,

Phil Hobbs

On Fri, 25 Jul 2008 00:33:41 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
.. .
What's wrong with j's on all levels?

I was told to "simplify" expressions so that no radicals, imaginary factors,
fractions, etc. are on the bottom.

Same here. Makes splitting into net real and imaginary parts rather
obvious.


Too bad this leads to less than simple expressions, like for such purposes
as this!

Tim

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

Liberals are so cute. Â*Stupid as bricks, but cute.

"FatBytestard" wrote in message
...
ANY application that needs to deal with ANY overtly large file is going
to tax ANY system.

I've used both Word and LaTeX for large (100 pages), and I guarantee you that
LaTeX is much more stable in such situations.

LaTeX isn't exactly "user friendly" and has plenty of its own warts, but it's
very predictable, stable, and bug-free.

There was even an editorial back in the early 2000's in one of the IEEE
journals (I believe) where the editor lamented how Word was getting less and
less stable -- for large document usage -- with each subsequent release after
Office 2000. I've been told that Microsoft was making stability something of
a priority for Office 2007, though (but haven't used it myself).

Since spreadsheet and database apps are specifically meant to deal with
files so large, if opened on an appropriate system, one will experience
no problems.

Get a clue: Of all Word documents, how many do you think are 100 pages?
Maybe 0.01%? Guess how much priority fixing bugs related only to such
documents receives?

There's a good reason that very few books are published using Word as the
final typesetting program of choice.

---Joel

On Fri, 25 Jul 2008 10:18:15 -0400, Phil Hobbs
wrote:

John Larkin wrote:
On Thu, 24 Jul 2008 05:32:10 +0000 (UTC), "R.L. Horn"
wrote:

On Wed, 23 Jul 2008 14:04:16 -0700, John Larkin
wrote:

I spent the day programming, and programming has absolutely nothing to
do with math.
Curiously, I spent the day plumbing, which ended up involving the Law of
Sines for some strange reason.

And a higher sense of accomplishment, no doubt.

John

Higher math, higher sense of accomplishment. What's not to like? Beats
working for a living. I just finished a section showing that the SNR
of a focused-beam measurement is proportional to the square of the
Strehl ratio--thereby showing how optical aberrations affect the actual
data.

Cheers,

Phil Hobbs

And I find that the more hairy electronics I design, the less real
math I do. Square roots now and then, logs rarely, calculus pretty
much never. Simulate and fiddle, now and then.

Electronic design is largely qualitative. Of course, one has to
understand Fourier transforms and correlations and physics and stuff,
but not actually have to do them much.

John

On Fri, 25 Jul 2008 00:33:41 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
.. .
What's wrong with j's on all levels?

I was told to "simplify" expressions so that no radicals, imaginary factors,
fractions, etc. are on the bottom.

Too bad this leads to less than simple expressions, like for such purposes
as this!

What software are you using for plotting these expressions?


Tim

"The Phantom" wrote in message
...
What software are you using for plotting these expressions?

Simple stuff I can just plug into a function plotter I wrote in QBasic.
Obviously, any capture consists of a 640x480 bitmap.

For this I've been poking around with Octave, which is an open source,
mostly compatible version of Matlab. Gnuplot, which comes with it, can
save as .ps I think, and at any rate it makes prettier pictures with
antialiasing.

For example, here's C = 20uF, M = 30uH, W = 1uH, R = 2 ohms. Imaginary is
up, real to the right. Resonance is at the imaginary minima.

http://webpages.charter.net/dawill/I...etworkPlot.gif

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

"The Phantom" wrote in message
...
What software are you using for plotting these expressions?

Simple stuff I can just plug into a function plotter I wrote in QBasic.
Obviously, any capture consists of a 640x480 bitmap.

For this I've been poking around with Octave, which is an open source,
mostly compatible version of Matlab. Gnuplot, which comes with it, can
save as .ps I think, and at any rate it makes prettier pictures with
antialiasing.

For example, here's C = 20uF, M = 30uH, W = 1uH, R = 2 ohms. Imaginary is
up, real to the right. Resonance is at the imaginary minima.

http://webpages.charter.net/dawill/I...etworkPlot.gif

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

On Fri, 25 Jul 2008 00:33:41 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
.. .
What's wrong with j's on all levels?

I was told to "simplify" expressions so that no radicals, imaginary factors,
fractions, etc. are on the bottom.

If you go back and look at the thread from Nov 2005, you will see that at
one point you said:

"Ah, well then. Imaginary numbers are fine for imagining things, but I
need real numbers, that exist in the real world."

Apparently the plotting routine you were using at that time couldn't deal
with the complex constant j. But now you are able to deal with it in the
numerator. Whatever you're doing with j in the numerator, you can do the
same with j in the denominator.

When it comes to plotting functions, there's no need to '"simplify"
expressions so that no radicals, imaginary factors, fractions, etc. are on
the bottom.'

In fact, doing all the algebra to "simplify" increases the possibility of
making a mistake. If you just plot the simplest expression, such as the
first one in my attachment, the one with "j's on all levels", the plot
should be the same, and with no extra algebraic simplification necessary.


Too bad this leads to less than simple expressions, like for such purposes
as this!

Tim

"The Phantom" wrote in message
...
In fact, doing all the algebra to "simplify" increases the possibility of
making a mistake. If you just plot the simplest expression, such as the
first one in my attachment, the one with "j's on all levels", the plot
should be the same, and with no extra algebraic simplification necessary.

Ya, in fact at one point I tested the formula by comparison with that.
Since Octave handles complex numbers natively, that's no problem. But I
want to come up with an expression for the resonant frequency (that's got to
be a bitch, I haven't even worked it yet but I forsee a quartic...eugh!), so
I can plug it back in to get Z at resonance in terms of R, M, W and C only.

And besides, I need mathematical practice, unfortunately I don't need quite
this much of it...

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

On Sat, 26 Jul 2008 09:35:54 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
.. .
In fact, doing all the algebra to "simplify" increases the possibility of
making a mistake. If you just plot the simplest expression, such as the
first one in my attachment, the one with "j's on all levels", the plot
should be the same, and with no extra algebraic simplification necessary.

Ya, in fact at one point I tested the formula by comparison with that.
Since Octave handles complex numbers natively, that's no problem. But I
want to come up with an expression for the resonant frequency (that's got to
be a bitch, I haven't even worked it yet but I forsee a quartic...eugh!), so
I can plug it back in to get Z at resonance in terms of R, M, W and C only.

The imaginary part of the impedance of this circuit:

Z o---Lm---+---C---+---GND
| |
+---R---+
| |
+---Lw--+

for the example values you gave, C = 20uF, M = 30uH, W = 1uH, R = 2 ohms,
is never zero. So even if you solve the quartic, you will find the
solution gives a value for w (omega) which is complex. You will have to
use a different definition of resonance frequency. The phase angle of the
impedance never becomes zero, although it does reach a minimum.


And besides, I need mathematical practice, unfortunately I don't need quite
this much of it...

Tim

On Sat, 26 Jul 2008 15:25:52 -0700, The Phantom
wrote:

On Sat, 26 Jul 2008 09:35:54 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
. ..
In fact, doing all the algebra to "simplify" increases the possibility of
making a mistake. If you just plot the simplest expression, such as the
first one in my attachment, the one with "j's on all levels", the plot
should be the same, and with no extra algebraic simplification necessary.

Ya, in fact at one point I tested the formula by comparison with that.
Since Octave handles complex numbers natively, that's no problem. But I
want to come up with an expression for the resonant frequency (that's got to
be a bitch, I haven't even worked it yet but I forsee a quartic...eugh!), so
I can plug it back in to get Z at resonance in terms of R, M, W and C only.

The imaginary part of the impedance of this circuit:

Z o---Lm---+---C---+---GND
| |
+---R---+
| |
+---Lw--+

for the example values you gave, C = 20uF, M = 30uH, W = 1uH, R = 2 ohms,
is never zero. So even if you solve the quartic, you will find the
solution gives a value for w (omega) which is complex. You will have to
use a different definition of resonance frequency. The phase angle of the
impedance never becomes zero, although it does reach a minimum.


And besides, I need mathematical practice, unfortunately I don't need quite
this much of it...

Tim

What "quartic" ?:-) I keep harping at you guys to use Laplace
notation to avoid getting balled-up with "j".

...Jim Thompson
--
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona 85048 Skype: Contacts Only | |
| Voice480)460-2350 Fax: Available upon request | Brass Rat |
| E-mail Icon at http://www.analog-innovations.com | 1962 |

Liberals are so cute. Â*Stupid as bricks, but cute.

"The Phantom" wrote in message
...
The imaginary part of the impedance of this circuit:
...
is never zero.

Ya- so I'll have to differentiate, which means squaring the denominator too.
Plenty to loathe, but at least it equals zero so I don't need the stinkin'
denominator. I guess that w^5 term will become the quartic, but y'know,
there's only w^3 and w^1 imaginary terms, which are pretty easy to factor.
Think I'll go do some scratching...

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

"Tim Williams" wrote in message
...
Plenty to loathe, but at least it equals zero so I don't need the stinkin'
denominator. I guess that w^5 term will become the quartic, but y'know,
there's only w^3 and w^1 imaginary terms, which are pretty easy to factor.
Think I'll go do some scratching...

Gnaw, that's not even right... I still need to invoke the quotient rule.
But that doesn't matter, because of the four(!) resonance-related nodes in
the graph, the one I'm actually interested in is output voltage maxima. And
that formula is pretty simple as (parallel resonant formula) /
(series-parallel formula), except that leaves seven terms in the
denominator, six of which are imaginary. That's a long conjugate. And then
I need to find omega such that Re = 0 or Im = local extrema.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

On Sun, 27 Jul 2008 04:34:53 -0500, "Tim Williams"
wrote:

"Tim Williams" wrote in message
...
Plenty to loathe, but at least it equals zero so I don't need the stinkin'
denominator. I guess that w^5 term will become the quartic, but y'know,
there's only w^3 and w^1 imaginary terms, which are pretty easy to factor.
Think I'll go do some scratching...

Gnaw, that's not even right... I still need to invoke the quotient rule.
But that doesn't matter, because of the four(!) resonance-related nodes in
the graph, the one I'm actually interested in is output voltage maxima.

Are you saying that you want to find the voltage maximum across the C-R-Lw
combination with a voltage source with zero internal impedance applied to
the left side of Lm?

And
that formula is pretty simple as (parallel resonant formula) /
(series-parallel formula), except that leaves seven terms in the
denominator, six of which are imaginary. That's a long conjugate. And then
I need to find omega such that Re = 0 or Im = local extrema.

Tim

On Sun, 27 Jul 2008 13:29:51 -0700, The Phantom wrote:

On Sun, 27 Jul 2008 04:34:53 -0500, "Tim Williams"
wrote:

"Tim Williams" wrote in message
...
Plenty to loathe, but at least it equals zero so I don't need the stinkin'
denominator. I guess that w^5 term will become the quartic, but y'know,
there's only w^3 and w^1 imaginary terms, which are pretty easy to factor.
Think I'll go do some scratching...

Gnaw, that's not even right... I still need to invoke the quotient rule.
But that doesn't matter, because of the four(!) resonance-related nodes in
the graph, the one I'm actually interested in is output voltage maxima.

Are you saying that you want to find the voltage maximum across the C-R-Lw
combination with a voltage source with zero internal impedance applied to
the left side of Lm?

If this is what you want, it can be derived as shown in the attachment.

The attached .gif file is tall, but it can be viewed with Firefox.


And
that formula is pretty simple as (parallel resonant formula) /
(series-parallel formula), except that leaves seven terms in the
denominator, six of which are imaginary. That's a long conjugate. And then
I need to find omega such that Re = 0 or Im = local extrema.

Tim

"The Phantom" wrote in message
...
Are you saying that you want to find the voltage maximum across the C-R-Lw
combination with a voltage source with zero internal impedance applied to
the left side of Lm?

Yes. In practice there will be 1-2V drop at up to 100A peak (it's
exponential, so dV/dI is small), out of 160V, which is just about nothing (
20 mohm, on par with the physical Lm itself).

If this is what you want, it can be derived as shown in the attachment.

The attached .gif file is tall, but it can be viewed with Firefox.

Comes through fine.

So, you multiply top by its conjugate and bottom by its conjugate? Can you
do that? I don't think I've ever seen that. For sure, you can mutliply by
the denominator's conjugate, but you have to do it top and bottom. Your
plots appear to agree with mine though.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

"Tim Williams" wrote in message
...
So, you multiply top by its conjugate and bottom by its conjugate? Can
you do that?

Yes, easy to prove.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

On Mon, 28 Jul 2008 01:32:01 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
.. .
Are you saying that you want to find the voltage maximum across the C-R-Lw
combination with a voltage source with zero internal impedance applied to
the left side of Lm?

Yes. In practice there will be 1-2V drop at up to 100A peak (it's
exponential, so dV/dI is small), out of 160V, which is just about nothing (
20 mohm, on par with the physical Lm itself).

If this is what you want, it can be derived as shown in the attachment.

The attached .gif file is tall, but it can be viewed with Firefox.

Comes through fine.

So, you multiply top by its conjugate and bottom by its conjugate? Can you
do that? I don't think I've ever seen that. For sure, you can mutliply by
the denominator's conjugate, but you have to do it top and bottom. Your
plots appear to agree with mine though.

The magnitude of a complex number is the square root of the sum of the real
part squared plus the imaginary part squared. This can also be calculated
as the square root of the (number times its conjugate). The magnitude is a
pure real number; it has no imaginary part.

So, when we have a numerator and denominator (a rational function), we can
find the magnitude of the numerator and denominator separately, and divide
the two magnitudes.

When you multiply numerator and denominator by the conjugate of the
denominator, you're just getting rid of the j's in the denominator; the
function is still complex, and its value is unchanged.

When you multiply the numerator by its conjugate, you're calculating its
magnitude (the modulus in complex variable textbooks), squared. Similarly
for the denominator. You have to be sure to take the square root after
multiplying by conjugates.


Tim

Interesting, Re(Vo/Vin) = 0 is near resonance, but it's not exactly
resonance. For Re = 0, I get omega = sqrt[(Lm + Lw) / c*Lm*Lw], no R term.
In the limit as R -- infinity, this is correct, and it's pretty damn close
for useful values of R (1-10 ohms, other values as given).

And I suppose d(Im)/dw = 0 (imaginary extrema) gives yet another point that
isn't quite resonance. Hmm, that damn quotient rule again.

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

"The Phantom" wrote in message
...
On Sun, 27 Jul 2008 13:29:51 -0700, The Phantom wrote:

On Sun, 27 Jul 2008 04:34:53 -0500, "Tim Williams"
wrote:

"Tim Williams" wrote in message
...
Plenty to loathe, but at least it equals zero so I don't need the
stinkin'
denominator. I guess that w^5 term will become the quartic, but
y'know,
there's only w^3 and w^1 imaginary terms, which are pretty easy to
factor.
Think I'll go do some scratching...

Gnaw, that's not even right... I still need to invoke the quotient rule.
But that doesn't matter, because of the four(!) resonance-related nodes
in
the graph, the one I'm actually interested in is output voltage maxima.

Are you saying that you want to find the voltage maximum across the C-R-Lw
combination with a voltage source with zero internal impedance applied to
the left side of Lm?

If this is what you want, it can be derived as shown in the attachment.

The attached .gif file is tall, but it can be viewed with Firefox.


And
that formula is pretty simple as (parallel resonant formula) /
(series-parallel formula), except that leaves seven terms in the
denominator, six of which are imaginary. That's a long conjugate. And
then
I need to find omega such that Re = 0 or Im = local extrema.

Tim

On Mon, 28 Jul 2008 06:31:29 -0500, "Tim Williams"
wrote:

Interesting, Re(Vo/Vin) = 0 is near resonance, but it's not exactly
resonance. For Re = 0, I get omega = sqrt[(Lm + Lw) / c*Lm*Lw], no R term.
In the limit as R -- infinity, this is correct, and it's pretty damn close
for useful values of R (1-10 ohms, other values as given).

And I suppose d(Im)/dw = 0 (imaginary extrema) gives yet another point that
isn't quite resonance. Hmm, that damn quotient rule again.

See the attachment for the expression for the imaginary part minimum. It
is much more complicated than the other two, but it also has the property
that as R -- infinity its limit is sqrt[(Lm + Lw) / c*Lm*Lw].


Tim

John Larkin wrote:


And I find that the more hairy electronics I design, the less real
math I do. Square roots now and then, logs rarely, calculus pretty
much never. Simulate and fiddle, now and then.

Electronic design is largely qualitative. Of course, one has to
understand Fourier transforms and correlations and physics and stuff,
but not actually have to do them much.

John


Yeah, but you're down there in the boiler room.

Cheers,

Phil Hobbs

"The Phantom" wrote in message
...
And I suppose d(Im)/dw = 0 (imaginary extrema) gives yet another point
that
isn't quite resonance. Hmm, that damn quotient rule again.

See the attachment for the expression for the imaginary part minimum. It
is much more complicated than the other two, but it also has the property
that as R -- infinity its limit is sqrt[(Lm + Lw) / c*Lm*Lw].

Hmm, fortune produced a quadratic (in omega^2) in the expression, but seeing
no obvious way to simplify it, I left it at the incredibly awful
substitution in the quadratic formula. I'm somewhat relieved, though still
mortified, to see a similarly awful expression produced by Mathematica(?).
:^)

I wanted to have the derivation for resonance, but sadly it looks like
maxima of the modulus is the only way to go, outside of real = 0, which
turns out to be only an approximation, and it's just too complicated (and
involves a cubic) to write down. I guess I'll have to be satisfied to say
"steps --". :-/

Tim

--
Deep Friar: a very philosophical monk.
Website: http://webpages.charter.net/dawill/tmoranwms

"FatBytestard" wrote in message
...
It sucks for DTP. THAT is the reason. Word is not designed for huge
documents

Agreed!

like excel, access, publisher, and powerpoint are.

Access is a toy compared to something like SQL Server. While Microsoft has
never attempted to position Access as a "high end" database, you see an
unfortunately large number of people trying to press it into service as one.
It's often the usual case of where companies would rather have an employee
spend some hundreds of hours per year fighting with Access to get the job done
rather than just ponying up the money for SQL Server (or some other heavy-duty
database) proper -- salaries are easier to budget for than software upgrades.

Excel seems to have some surprisingly low "maximums," like 64k rows, but it's
been suggested to me that this may be done on purpose because it's difficult
to argue that you shouldn't be using a real databse by the time you hit 64k
row. So I'll reserve judgement there...

I haven't used Publisher and only used PowerPoint a few times, so I'll refrain
from commenting on them as well.

Perhaps in the future, you should be more specific.

Fair point.

---Joel

"The Phantom" wrote in message
...
In fact, doing all the algebra to "simplify" increases the possibility of
making a mistake.

Gee, Phantom, don't you remember those many days of algebra class in
middle/high school where all you did was practice simplifying algebraic
expressions? :-)

Or didn't you grow up in the U.S. in the '50s-'70s? :-)

On Mon, 28 Jul 2008 12:13:02 -0500, "Tim Williams"
wrote:

"The Phantom" wrote in message
.. .
And I suppose d(Im)/dw = 0 (imaginary extrema) gives yet another point
that
isn't quite resonance. Hmm, that damn quotient rule again.

See the attachment for the expression for the imaginary part minimum. It
is much more complicated than the other two, but it also has the property
that as R -- infinity its limit is sqrt[(Lm + Lw) / c*Lm*Lw].

Hmm, fortune produced a quadratic (in omega^2) in the expression, but seeing
no obvious way to simplify it, I left it at the incredibly awful
substitution in the quadratic formula. I'm somewhat relieved, though still
mortified, to see a similarly awful expression produced by Mathematica(?).
:^)

I wanted to have the derivation for resonance, but sadly it looks like
maxima of the modulus is the only way to go, outside of real = 0, which
turns out to be only an approximation, and it's just too complicated (and
involves a cubic) to write down.

I'm not sure what you mean by this. You said in another post, and I got
the same result, that:

"For Re = 0, I get omega = sqrt[(Lm + Lw) / c*Lm*Lw], no R term."

Are you talking about Re[Z} rather than Re[Vo/Vin]?

I guess I'll have to be satisfied to say
"steps --". :-/

Tim

On Mon, 28 Jul 2008 10:50:34 -0700, "Joel Koltner"
wrote:

"The Phantom" wrote in message
.. .
In fact, doing all the algebra to "simplify" increases the possibility of
making a mistake.

Gee, Phantom, don't you remember those many days of algebra class in
middle/high school where all you did was practice simplifying algebraic
expressions? :-)

And making mistakes? I remember it all too well!


Or didn't you grow up in the U.S. in the '50s-'70s? :-)

Oh, yes. My algebra teacher was an overweight woman named Mrs. Pouncy. We
kids used to make fun of her by saying "more bouncy to the pouncy".

"The Phantom" wrote in message
...
And making mistakes? I remember it all too well!

I make a lot more mistakes now (with algebraic manipulations) given thatm I do
the only, say, every few weeks rather than every day or so.

Oh, yes. My algebra teacher was an overweight woman named Mrs. Pouncy. We
kids used to make fun of her by saying "more bouncy to the pouncy".

My 8th grade teacher was a rather short fellow named Mr. Stubbe... who of
course was referred to as Mr. Stubble.