EMRFD Message Archive 3986

Message Date From Subject
3986 2010-01-15 12:01:51 Stephen Wandling Toroids: Phase, Sense & Direction
I am reminded by Dom posting his Flea toroid transformer picture, that I
still have a few questions about toroids. The first is in regards to
terminology:

1.) If I wind one winding on a toroid by putting the wire down through
the core, and a second winding by coming up through the core (both
windings proceeding in a CW direction around the core), I have changed
the __________?

2.) If I wind two windings on a core by putting the wire down through
the core, but one proceeds in a CW direction and the other in a CCW
direction, I have changed the __________?

3.) If, in "1" above, I reverse how start/finish of the second winding
is connected to the circuit, I have changed ________?

And my remaining question is:

4.) Compared to "1" above, is "2" equal in effect to "3"?

Thanks

72
Stephen
VE7NSD
3987 2010-01-15 15:28:36 aa7hq@comcast.net Re: Toroids: Phase, Sense & Direction
stephen, i have not the slightest idea of the word or words you are looking for in the question about
"I have changed the __________?". the reason is that the meaning of the word 'WINDING' to
you is not related to the physics of the problem. the problem has to do with describing in
circuit theory terms a field theory problem. the voltage in a circuit is related to the rate of change of flux
linkages. the number of flux linkages is computed by an integral over a closed path.
i have been personally and professionally interested in ideas of this kind for almost seventy
years. i believe that if you think a winding is just a wire through a hole in a toroid,
(or any similar simplification of the kind), you will never understand the problem you want to
understand.

i urge you to review ideas about flux lines, their density, their directions, and integrations
over closed paths.

furthermore, there are hundreds of good discussions of this problem, and if you learn the truth
you will be tickled pink!!! this is stuff worth knowing! many many people would like to
help you. nobody wants to praise you for avoiding mathematics no matter how cleverly you
describe your difficulties. good luck!


----- Original Message -----
3991 2010-01-16 01:15:33 Stephen Wandling Re: Toroids: Phase, Sense & Direction
Edward,

I often have questions and the urge to ask them, and sometimes I get
answers that assist me and sometimes I don't. You are obviously
knowledgeable about things such as "describing in circuit theory terms a
field theory problem", but I am not. I am aware that the physics of my
questions can not be avoided, but my hope was that answers in terms I
can understand might be available. You seem to be suggesting that they
are not.

If you believe that a winding is not a wire through a hole in a toroid
core, then I suspect you might have trouble assisting me with my simple
questions. Your statement that "nobody wants to praise you for avoiding
mathematics", is simply perplexing. Have I stepped on religious toes here?

72
Stephen
VE7NSD

aa7hq@comcast.net wrote:
> stephen, i have not the slightest idea of the word or words you are looking for in the question about
> "I have changed the __________?". the reason is that the meaning of the word 'WINDING' to
> you is not related to the physics of the problem. the problem has to do with describing in
> circuit theory terms a field theory problem. the voltage in a circuit is related to the rate of change of flux
> linkages. the number of flux linkages is computed by an integral over a closed path.
> i have been personally and professionally interested in ideas of this kind for almost seventy
> years. i believe that if you think a winding is just a wire through a hole in a toroid,
> (or any similar simplification of the kind), you will never understand the problem you want to
> understand.
>
> i urge you to review ideas about flux lines, their density, their directions, and integrations
> over closed paths.
>
> furthermore, there are hundreds of good discussions of this problem, and if you learn the truth
> you will be tickled pink!!! this is stuff worth knowing! many many people would like to
> help you. nobody wants to praise you for avoiding mathematics no matter how cleverly you
> describe your difficulties. good luck!
>
>
> ----- Original Message -----
>
3992 2010-01-16 07:26:18 aa7hq@comcast.net Re: Toroids: Phase, Sense & Direction
stephen, please accept my apologies for disturbing you. i made a mistake in thinking i could help you,
and i shall not bother you again.


----- Original Message --
3994 2010-01-16 07:50:35 k5nwa Re: Toroids: Phase, Sense & Direction
If I ask a simple questi
3995 2010-01-16 08:06:58 Nick Kennedy Re: Toroids: Phase, Sense & Direction
This is an area that's relatively simple once you grasp it, yet difficult
(especially for me) to describe in words. I don't believe a lot of physics
or math are needed but some simple rules of thumb (literally) apply. There
are certain principles that can be applied, and different ones work better
for different people.

If I actually understand the questions, they all boil down to determining
the relative polarity of the ends of different coupled windings. The words
that would go in the blanks would typically be "dotted end", "relative
polarity", "polarity", "sense" or similar terms describing the same
relation.

I think a few principles and rules are useful in visualizing or determining
relative polarity. It's interesting to convince yourself how they are all
consistent with one another.

1. Current flowing into the dotted end of one winding causes current to flow
out of the dotted end(s) of other windings.
2. Voltages at dotted ends all have the same instantaneous polarity.
3. Current induced in a secondary winding flows in the direction which
produces flux opposing the flux in the primary winding.

Using number 3, you might want to apply the right hand rule. Curl your
fingers in the direction of current flow in the windings and your thumb will
point in the direction of the flux.

In the above, for our purposes, it doesn't really matter if you are using
conventional current or electron / military current since we're interested
in *relative* polarity of windings only. If fact, it wouldn't matter if
your used your right or left hand for the same reason, if you're consistent.

Speaking of dotted ends, they are relative. You assign one arbitrarily and
the others are then determined in relation to that one by those basic
principles.

Now think of an example or two. The easiest might be a bifilar winding
transformer. You have two twisted wires, a red and a green, and wind them
onto a toroid (or rod, for that matter). You decided to say the red end at
the "start" end of the winding is a dotted end. Where's the dot go on the
green winding? I think (I hope) that in this case it's pretty easy to say
that current flowing into that red wire must produce current flowing out of
the green wire at the same end since that's what would produce flux in the
opposite direction. So the dot on the green winding is at the same end,
right next to the dot on the red winding.

Next, think of two windings on a toroid (or rod, or even B&W coil stock)
where the second is just a continuation of the first. To be more clear,
imagine that you made one winding of 100 turns, then cut it in the middle to
make two windings. Now, assign the dot marking to the beginning of the
winding. Is the dot on the second winding at the far end or is it at the
middle, where it faces the first winding? It comes down to the same
reasoning that the dot is where the two windings meet. Current flows out of
this dot, so flux produced by this coil opposes that produced by the first
one.

Both examples are simple (right?) and really reduce to the same thing. The
only complication I could think to add would be to take the above example,
but for the second coil, reverse the direction of winding. Now using the
right hand rule you see that current has to flow in the opposite direction
as it did in the above example, so the dot is at the far end.


73,

Nick, WA5BDU


3999 2010-01-16 21:10:38 Andy Re: Toroids: Phase, Sense & Direction
> 2.) If I wind two windings on a core by putting the wire down through
> the core, but one proceeds in a CW direction and the other in a CCW
> direction, I have changed the __________?

This change does not affects the polarity.

Except for physical limitations, one could wind multiple turns of wire
on a toroid and have the turns lie exactly on top of one another. The
magnetics are virtually the same. By spreading the turns out either
toward the left or right (CW or CCW going around the toroid), there is
little change in the coupling between current and magnetic flux in the
core. The wire is still wound in the same direction around the core.

> 4.) Compared to "1" above, is "2" equal in effect to "3"?

No.

Andy
4001 2010-01-17 13:54:54 Stephen Wandling Re: Toroids: Phase, Sense & Direction
I've been a little slow in responding to the numerous responses I have
received, both on and off list and on the GQRP list, where I also posted
it. I find much of this difficult for my brain to process. My note
pads are littered with many transformers, marked with 'dotted ends',
left-hand rule diagrams, etc.

On my point #2 below, if the start of the first winding is designated as
dotted, and if the second winding begins just to the 'right' of this
dotted end, then the dotted end of the second winding should be adjacent
to the dotted end of the first winding? Whereas, it seems to me that if
the second winding had proceed CW, like the first winding, then its
dotted end would be adjacent to the non-dotted end of the first
winding? To me, this seems to produce two possible secondaries that are
reversed in phase?

I am still pondering your comment on my #4.

Thanks for the response.

72
Stephen
VE7NSD

Andy wrote:
>> 2.) If I wind two windings on a core by putting the wire down through
>> the core, but one proceeds in a CW direction and the other in a CCW
>> direction, I have changed the __________?
>>
>
> This change does not affects the polarity.
>
> Except for physical limitations, one could wind multiple turns of wire
> on a toroid and have the turns lie exactly on top of one another. The
> magnetics are virtually the same. By spreading the turns out either
> toward the left or right (CW or CCW going around the toroid), there is
> little change in the coupling between current and magnetic flux in the
> core. The wire is still wound in the same direction around the core.
>
>
>> 4.) Compared to "1" above, is "2" equal in effect to "3"?
>>
>
> No.
>
> Andy
>
>
> ------------------------------------
>
> Yahoo! Groups Links
>
>
>
>
>
4002 2010-01-17 17:36:59 Brent G DeWitt Re: Toroids: Phase, Sense & Direction
Hi Stephen,

I admit to having difficulty understanding what answers you are requesting. Would it be possible to re-phrase the questions with multiple-choice answers available?

Respectfully,

Brent, AB1LF



> ----- Original Message -----
>
4003 2010-01-17 18:18:13 Stephen Wandling Re: Toroids: Phase, Sense & Direction
Hi Brent,

Thank you for asking this question. As I have been sorting through all
of the on and off list replies, I have come to realize that I was asking
two questions, one being terminology and the other being technical, and
using one set of examples. I don't think this has helped my situation
one bit. :-)

*Terminology*: I was hoping that there were some commonly accepted terms
that I could substitute instead of "holding the core in the right hand
and putting the winding down through the core and proceeding in a CW
direction". Or with one winding wound as above and the other in a CW
direction wound with the wire coming UP through the toroid might be
called ________? So, as my subject line was trying to say, I was
wondering if Phase or Sense or some other term is commonly used instead
of wordy Directions.

*Technical*: This is the area where Nick Kennedy (I will respond to you
soon, Nick!) and some others have provided much useful input, although I
don't think they all agree. The "dot convention" is very useful, if one
knows how to correctly apply it. I am familiar with the Right Hand
Rule, and know that with my thumb in the direction of current flow, my
fingers are in the 'direction' of the lines of flux, "*on a straight
wire*". But, when you wrap that wire around a core and add another wire
around that core, it becomes quite difficult for me to sort out the
effects between the two windings. Possibly I have some sort of dyslexic
problem? Or, do others have similar difficulties?

I know you asked for multiple-choice questions, but hopefully, from
reading the above, you will see that I don't have sufficient knowledge
to create such question types.

Anyway, thanks for the opportunity to further explain my original
question(s). Hopefully, it hasn't further muddied the waters! ;-)

72
Stephen
VE7NSD

Brent G DeWitt wrote:
> Hi Stephen,
>
> I admit to having difficulty understanding what answers you are requesting. Would it be possible to re-phrase the questions with multiple-choice answers available?
>
> Respectfully,
>
> Brent, AB1LF
>
>> ----- Original Message -----
>>
4004 2010-01-17 19:31:44 Brent G DeWitt Re: Toroids: Phase, Sense & Direction
Hello again Stephen!



I don't know if it will help at all, but I personally find it useful to view
the core "edge-wise" or perpendicular to the aperture, when I think of
windings. For my mindset, counting turns becomes much easier.



Brent



4005 2010-01-17 20:46:57 Andy Re: Toroids: Phase, Sense & Direction
Stephen,

> On my point #2 below, if the start of the first winding is designated as
> dotted, and if the second winding begins just to the 'right' of this
> dotted end, then the dotted end of the second winding should be adjacent
> to the dotted end of the first winding? Whereas, it seems to me that if
> the second winding had proceed CW, like the first winding, then its
> dotted end would be adjacent to the non-dotted end of the first
> winding? To me, this seems to produce two possible secondaries that are
> reversed in phase?

Be careful here. We have different meanings of CW. Maybe I misunderstood
your meaning. I took it to mean how the winding progresses around the
toroid, when viewing the toroid from above.

Let me try a different approach. Let's start with a ferrite bar rather than
a toroid, around which you wind your wire. (When you are done winding,
imagine bending the rod into a toroid. Bending it into a toroid doesn't
change any of the mutual polarities ... are you OK with that?)

Back to the straight bar. Put it in front of you, left to right. Take a
wire and start wrapping, first going away from you over the rod, then down,
then back towards you under the rod, and so on. Keep wrapping in that
direction. The end of wire you started from has the "dot".

As you wrap this winding, space each next turn slightly to the left of the
one before it. This winding will "grow" towards your left.

Now take a second piece of wire and do the same exact thing, only this time,
space each turn slightly to the right of the one before it. This winding
grows from its start or "dot" end towards your right.

Now you have two windings, which wind around the rod in the same direction
(as we will see next), but "grow" in opposite directions.

Move the rod to look at it end-on, so that the end that was towards the
right, directly faces you. Note that BOTH windings wrap in a clockwise
direction around the rod, starting from their "dot" ends.

That clockwise direction determines the coupling between the current and
the flux inside the winding, where the rod is. It is the same for both
windings. It makes no difference whether the first winding progresses away
from you in this view and the second one goes towards you. Both windings
wrap clockwise around the rod. That's what matters.

Thus, the "dot" conventions are correct. (Are you still with me?)

Put the rod back down in front of you like it was before. Now imagine
bending it into a toroid by taking the ends and bending them away from you,
until they meet.

Looking at this from above, winding 1 is going in a CW direction around the
torus, starting from its dot end. Winding 2 is going in a CCW direction,
starting from its dot end.

I think this is what you were asking in your original question #2. You
talked about making "two windings on a core by putting the wire down through
the core", meaning they both wrapped around the core material in the same
direction; but that one of them grew in a CW direction (i.e., towards the
left if that winding is on the side of the toroid closer to you), and the
other in a CCW direction (i.e., towards the right). Both windings have the
same polarity.

So the direction *around the torus* that the windings grow, or were wrapped,
makes no difference. What matters is the direction you go *through the
hole* in the toroid. Two windings that are wound going down through the
hole, both start from their "dot" ends (or alternatively, both end at their
"dot" ends).

Hopefully I haven't muddied up things even more for you!

Andy
4006 2010-01-17 21:07:47 Andy Re: Toroids: Phase, Sense & Direction
> ... I am familiar with the Right Hand
> Rule, and know that with my thumb in the direction of current flow, my
> fingers are in the 'direction' of the lines of flux, "*on a straight
> wire*". But, when you wrap that wire around a core and add another wire
> around that core, it becomes quite difficult for me to sort out the
> effects between the two windings. ...

The right hand rule still applies to the coil, showing you the lines of flux
close to any piece of wire. When your fingers wrap around a small section
of wire, the fingers that are inside the coil show the direction of flux
lines inside the coil, where the core usually is. You can do that to any
small piece of wire, on any part of the coil, and get the same flux
direction on the inside of the coil.

On the outside of the coil, the flux lines go in the opposite direction (to
complete the magnetic flux path), as also indicated by your fingers when
they are on the outside of the coil next to any small section of the coil's
wire.

With a toroid, you can always get the polarity relationship of a given
winding by pointing your thumb in the direction of the current that passes
through the toroid's hole. Your fingers show the direction of flux lines
around the hole, through the toroid's core.

There is a second way of applying the right hand rule to coils: If your
fingers wrap around the coil, fingers pointing in the direction of
conventional current flow, then your thumb shows the direction of flux lines
*inside* the coil. That can be used on toroids too.

Andy
4007 2010-01-18 13:06:36 victor Re: Toroids: Phase, Sense & Direction
A very simple rule to find the "dotted" ends of windings in a toroid follows:
Holding the toroid horizontal edge-wise, each winding will have one end coming from the top side of the toroid and the other winding end coming from the bottom. All the winding ends coming from the top are the "dotted ones".
That is all the definitions needed.
All CW and CCW windings directions are really not needed for defining the "Dotted" ends of windings.
Victor - 4Z4ME

4011 2010-01-18 15:14:53 Stephen Wandling Re: Toroids: Phase, Sense & Direction
Victor,

Thank you for the response. I am always attracted to simple rules, and
in my experience they do often exist.

I have taken your rule and applied it to the dotted transformer winding
graphic provided by Eduardo and Joan for their Pulga.
http://ea3fxf.googlepages.com/flea [See the second graphic on this
page] As you can see their dots are
4015 2010-01-18 20:07:19 Bill Noyce Re: Toroids: Phase, Sense & Direction
Victor's simple rule is correct. Another way to think of it ... most
powdered-metal cores actually have different colors on their two faces. For
example, a type 2 core is mostly red, with one charcoal-colored face. The
wires that exit the core on the red face all have one polarity (for example,
they're all dotted) and the wires that exit the core on the charcoal face
all have the opposite polarity (un-dotted in this example). Other details
of how the wire is wrapped don't affect this.

I would have to day the diagram you refer to does not properly use the dot
convention. To me, that raises the question of whether the dots are
correctly placed in the schematic, if the picture shows a core that works
correctly.

Building a Pulga is on my list, but I haven't gotten close to starting yet
...
-- Bill, AB1AV

4016 2010-01-18 20:34:51 Stephen Wandling Re: Toroids: Phase, Sense & Direction
Thanks Bill, I was afraid that was the case. I will let Eduardo and
Joan know. Actually, the schematic for the Pulga did not use the dot
convention, and they added the transformer drawing after I was pulling
my hair out to get the rig to work.

And I am pleased to hear confirmation of "Victor's Rule". I will just
forget about CW/CCW and winding Up or Down.

And of course that opens up the next obvious learning experience: how
does one 'use' the dot information in design? Maybe I could ask, where
should the dots go on the Pulga (flea) transformer:
http://ea3fxf.googlepages.com/flea to make it work?

72
Stephen
VE7NSD

Bill Noyce wrote:
> Victor's simple rule is correct. Another way to think of it ... most
> powdered-metal cores actually have different colors on their two faces. For
> example, a type 2 core is mostly red, with one charcoal-colored face. The
> wires that exit the core on the red face all have one polarity (for example,
> they're all dotted) and the wires that exit the core on the charcoal face
> all have the opposite polarity (un-dotted in this example). Other details
> of how the wire is wrapped don't affect this.
>
> I would have to say the diagram you refer to does not properly use the dot
> convention. To me, that raises the question of whether the dots are
> correctly placed in the schematic, if the picture shows a core that works
> correctly.
>
> Building a Pulga is on my list, but I haven't gotten close to starting yet
> ...
> -- Bill, AB1AV
>
>
4018 2010-01-18 22:11:04 victor Re: Toroids: Phase, Sense & Direction
Stephen,
The drawing of the inductor in the Pulga is wrong. If you look at the inductor connected to C3, in the inductor drawing the end connected to C3 is dotted, however in the Spice schematic the other end - the one connected to ground is the dotted one - so there is a difference between the inductor drawing and the Spice schematic.
Victor - 4Z4ME

4019 2010-01-18 22:35:11 Stephen Wandling Re: Toroids: Phase, Sense & Direction
Victor,

I too was puzzled by the 'differences' I could see between the schematic
and the Spice circuit. It was explained to me that the Spice model does
accurately represent the AC circuit. If you look, you will see that in
the Spice model and in the schematic, the dotted end of the winding does
attach to the 'junction' of C2 and C3 in both. In the Spice model, the
'junction' is ground.

But, I definitely encourage the review of this circuit to assist me in
understanding how to apply the dot convention to actual circuits.

Thanks Victor.

72
Stephen
VE7NSD

victor wrote:
> Stephen,
> The drawing of the inductor in the Pulga is wrong. If you look at the inductor connected to C3, in the inductor drawing the end connected to C3 is dotted, however in the Spice schematic the other end - the one connected to ground is the dotted one - so there is a difference between the inductor drawing and the Spice schematic.
> Victor - 4Z4ME
>
>
4020 2010-01-18 22:37:54 victor Re: Toroids: Phase, Sense & Direction
Stephen,
For your second question how to use the dotted inductor end information the answer is simple.
In most cases it matters only when using feedback. It can be positive or negative feedback.
For example in the "Pulga" it is positive feedback as it is an oscillator or regenerative receiver.
The rule is that positive voltage on the one dot will generate positive voltage on the other dot ends.
If we follow the loop voltages on the Pulga Spice schematic, we start by assuming a positive voltage at Q1 collector, it generates a negative voltage on the secondary winding on C3 (a non-dotted winding end!), this voltage level is reduced by C1/C2 capacitive voltage divider (without changing its phase) and then passes through the Xtal because it is connected in series with the signal path and at its series resonance it is a short circuit (almost..), so the voltage that reaches Q1 base is negative. Q1 inverts the signal phase (Common emitter amplifier inverts signal phase) and we return to Q3 collector with positive voltage signal, the same polarity we assumed at the analysis start, proving that we indeed get positive feedback.
Victor - 4Z4ME

4022 2010-01-18 23:13:36 Stephen Wandling Re: Toroids: Phase, Sense & Direction
Victor,

Thank you for this. You are the master of simplicity! For whatever
reason I can follow your voltage linkages, but I have a lot of trouble
if someone uses current to explain the same thing.

Am I correct in assuming that you still think the dot does not belong on
the winding end that connects to the junction of C2 & C3?

I ask this because I was also told that the signal from the capacitive
voltage divider is phase shifted by passing though the crystal. But,
you say the series crystal acts like a short circuit. Did I get some
incorrect information?

72
Stephen
VE7NSD

victor wrote:
> Stephen,
> For your second question how to use the dotted inductor end information the answer is simple.
> In most cases it matters only when using feedback. It can be positive or negative feedback.
> For example in the "Pulga" it is positive feedback as it is an oscillator or regenerative receiver.
> The rule is that positive voltage on the one dot will generate positive voltage on the other dot ends.
> If we follow the loop voltages on the Pulga Spice schematic, we start by assuming a positive voltage at Q1 collector, it generates a negative voltage on the secondary winding on C3 (a non-dotted winding end!), this voltage level is reduced by C1/C2 capacitive voltage divider (without changing its phase) and then passes through the Xtal because it is connected in series with the signal path and at its series resonance it is a short circuit (almost..), so the voltage that reaches Q1 base is negative. Q1 inverts the signal phase (Common emitter amplifier inverts signal phase) and we return to Q3 collector with positive voltage signal, the same polarity we assumed at the analysis start, proving that we indeed get positive feedback.
> Victor - 4Z4ME
>
>
4023 2010-01-18 23:50:32 victor Re: Toroids: Phase, Sense & Direction
Stephen,
In this circuit the oscillator oscillates in the Xtal series frequency so the Xtal does not affect the signal phase.
The correct connecti
4032 2010-01-19 08:08:08 Andy Re: Toroids: Phase, Sense & Direction
Stephen,

I completely agree with Victor's simple rule.

I also noticed the difference between the hand-drawn diagram and the
SPICE schematic. I'm assuming that they actually simulated the SPICE
version, so it should be correct.

It's OK when you flip ALL the polarities (or all but the antenna
winding in this case since its polarity doesn't matter).

I skipped through the link to the discussion about the circuit, and
saw there were a number of comments about the dots and polarities. I
couldn't figure out whether or not the hand drawing, as shown, was
supposed to be the "corrected" version. But one of the authors did
make the important comment that, in the end, it doesn't matter how you
draw it; if the circuit doesn't work when you build it, just reverse
the connections to one of the windings! That makes me suspect that
they were confused and weren't sure if they had it right.

Andy
4035 2010-01-19 13:17:26 Stephen Wandling Re: Toroids: Phase, Sense & Direction
Ok Victor. I have sent a note to Eduardo, one of the creators of the
Pulga, about their drawing of the Pulga transformer. Thank you again
for your clear and simple explanations.

I understand why you say the transformer drawing is incorrect, but I am
still a bit confused on why you don't think the schematic and the Spice
diagram are the same. I am only able to say that they are because a
respected designer informed me they were:
> Although the component designation of C1 and C2 are reveresed between
> the fig 5 schematic and the spice model, the values are in the correct
> locations. C1 in fig 5 is effectively at ground due to C4 on the
> supply bus.
He speaks of figure 5 because he was looking at my Pulga page:
http://www.qrpedia.com/book/200812/flea-catalonias-answer-pixie

Comments?

72
Stephen
VE7NSD

victor wrote:
> Stephen,
> In this circuit the oscillator oscillates in the Xtal series frequency so the Xtal does not affect the signal phase.
> The correct connecti
4036 2010-01-19 13:40:00 victor Re: Toroids: Phase, Sense & Direction
Stephen, the hand drawn schematic shows a toroid with three windings. On two winding (one connected to the transistor and the other to the antenna) the dots appear on the winding ends that come out from the toroid on the top side of the toroid while at the third winding the end that is dotted comes out at the bottom of the toroid, so there is a contradiction between the way that dotted winding ends must be marked (according to electromagnetic theory) and the way it is drawn.
If we change the third winding (connected to the capacitors)drawing so that the end that is dotted will start from above the toroid all will be correct.
Victor - 4Z4ME