We have repaired many switch mode ballasts for a medical fluorescent lighting system. There is a coil on these ballasts that often develops an open or shorted winding. It is a simple open bobbin unit that is quickly rewound.
It is used to provide feedback to the oscillator (approx 200Khz) and it carries only about 150ma The curiosity is that the primary winding is 4 strands of #36 magnet wire, loosly twisted together and connected at the ends and wound first on the core. The other winding is a single strand wound over the first with a kapton tape layer in between the windings. We have tried replacing the 4 stranded winding with an equivalent wire gauge and the ballast still works.
All of the ballasts, including several production revisions, use the quad wire for this winding.
What would have been the advantage or thinking in this design?
Len
Coil Question

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 Location: Redding, CA
 Contact:
Exitation Inductance
Lenp:
The frequency of operation is a hint. By winding the primary with 4 strands of wire side by side, the exitation inductance is reduced. From an inductance standpoint, it's like four inductors of the same impedance in parallel. This allows a faster rise time of the switching waveform thus reducing switching losses in the transistors driving the oscillator.
While the single winding with an equivalent sized wire will work, you might want to check the rise and fall time of the oscillator with each primary. The parallel primary should show a faster rise and fall time.
The frequency of operation is a hint. By winding the primary with 4 strands of wire side by side, the exitation inductance is reduced. From an inductance standpoint, it's like four inductors of the same impedance in parallel. This allows a faster rise time of the switching waveform thus reducing switching losses in the transistors driving the oscillator.
While the single winding with an equivalent sized wire will work, you might want to check the rise and fall time of the oscillator with each primary. The parallel primary should show a faster rise and fall time.
Hi there,
With any kind of power converter the name of the game is efficiency.
The four strands of wire provide a lower AC resistance than a single
strand of equivalent gauge wire because of the skin effect in wire
operating with an AC current.
The effective conduction area of any wire is reduced more and more
as the operating frequency is increased because only a part of
the wire is used for conduction (towards the outer surface). As
frequency is increased, less and less of the wire is available for
conduction, meaning the wires resistance increases.
Using four wires means there are four different cases each which
conducts to a depth in the wire equal to the skin depth at that
frequency.
To get an idea how this trick works, assume that the wire they
chose was the size such that one radius equals the skin depth
(which would provide for the least waste of copper).
This means compute the total area of all four wires.
Next, compute the outer shell area of the larger wire and compare
to the area obtained from using all four wires.
When the area of the larger wires shell equals the area of the
four smaller wires you have selected the correct larger wire diameter
in order to keep the efficiency roughly the same using only one wire.
With a little thought the following relationships are determined:
Without skin effect, the area of the larger wire would have to be
four times as large as one smaller wire, which means the radius
would have to be twice as large as the smaller wire. This only
works for DC however.
With skin effect, the area of the larger wires outer *shell* has to be
four times the area of one smaller wire. This of course means
that the larger wires radius has to be more than two times that of
one smaller wire. This is true for AC current.
To form this into two equations:
a1=4*pi*r1^2 total area of all four small wires
a2=pi*r2^2pi*(r2r1)^2 total area of larger wires shell
Now with r1 equal to the smaller wires radius,
when a1=a2 then r2 will be the correct value.
To do this set a1=a2 and solve for r2 in terms of r1:
4*pi*r1^2=pi*r2^2pi*(r2r1)^2
Solving,
r2=2.5*r1
From this we can conclude the proper size for the larger wire is
a wire with radius 2.5 times that of the smaller wire.
Since diameter=2*radius, this means the diameter of the larger wire
should also be 2.5 times that of the smaller wire, which makes it
easy to select the larger wires gauge.
Example
Say we have four small wires each with diameter 0.005 inches (AWG=36).
To replace this with a single larger wire the diameter should be
2.5 times that of the smaller wire, or 0.0125 inches. The nearest AWG
is AWG=28, so the four 36 gauge wires could be replaced with one
single 28 gauge wire.
Note had we not considered the skin effect in this example we would
have selected a wire gauge whos diameter was only twice that of the
smaller wire, resulting in a wire whos AWG=30 which is too small.
Note that the above formula works when there are 4 wires to be replaced
with 1 wire. To solve for the more general case where there are N wires
to be replaced results in the following formula:
d2=d1*(N+1)/2
where
d1 is the diameter of one of the small wires
d2 is the diameter of the large wire
N is the number of smaller wires to be replaced with one large wire of diameter d2
.
With any kind of power converter the name of the game is efficiency.
The four strands of wire provide a lower AC resistance than a single
strand of equivalent gauge wire because of the skin effect in wire
operating with an AC current.
The effective conduction area of any wire is reduced more and more
as the operating frequency is increased because only a part of
the wire is used for conduction (towards the outer surface). As
frequency is increased, less and less of the wire is available for
conduction, meaning the wires resistance increases.
Using four wires means there are four different cases each which
conducts to a depth in the wire equal to the skin depth at that
frequency.
To get an idea how this trick works, assume that the wire they
chose was the size such that one radius equals the skin depth
(which would provide for the least waste of copper).
This means compute the total area of all four wires.
Next, compute the outer shell area of the larger wire and compare
to the area obtained from using all four wires.
When the area of the larger wires shell equals the area of the
four smaller wires you have selected the correct larger wire diameter
in order to keep the efficiency roughly the same using only one wire.
With a little thought the following relationships are determined:
Without skin effect, the area of the larger wire would have to be
four times as large as one smaller wire, which means the radius
would have to be twice as large as the smaller wire. This only
works for DC however.
With skin effect, the area of the larger wires outer *shell* has to be
four times the area of one smaller wire. This of course means
that the larger wires radius has to be more than two times that of
one smaller wire. This is true for AC current.
To form this into two equations:
a1=4*pi*r1^2 total area of all four small wires
a2=pi*r2^2pi*(r2r1)^2 total area of larger wires shell
Now with r1 equal to the smaller wires radius,
when a1=a2 then r2 will be the correct value.
To do this set a1=a2 and solve for r2 in terms of r1:
4*pi*r1^2=pi*r2^2pi*(r2r1)^2
Solving,
r2=2.5*r1
From this we can conclude the proper size for the larger wire is
a wire with radius 2.5 times that of the smaller wire.
Since diameter=2*radius, this means the diameter of the larger wire
should also be 2.5 times that of the smaller wire, which makes it
easy to select the larger wires gauge.
Example
Say we have four small wires each with diameter 0.005 inches (AWG=36).
To replace this with a single larger wire the diameter should be
2.5 times that of the smaller wire, or 0.0125 inches. The nearest AWG
is AWG=28, so the four 36 gauge wires could be replaced with one
single 28 gauge wire.
Note had we not considered the skin effect in this example we would
have selected a wire gauge whos diameter was only twice that of the
smaller wire, resulting in a wire whos AWG=30 which is too small.
Note that the above formula works when there are 4 wires to be replaced
with 1 wire. To solve for the more general case where there are N wires
to be replaced results in the following formula:
d2=d1*(N+1)/2
where
d1 is the diameter of one of the small wires
d2 is the diameter of the large wire
N is the number of smaller wires to be replaced with one large wire of diameter d2
.
LEDs vs Bulbs, LEDs are winning.

 Posts: 2276
 Joined: Wed Nov 24, 2004 1:01 am
 Location: ASHTABULA,OHIO
 Contact:
MrAl
No argument on your dissertation on Skin Effect. However in the broad spectrum of ac, 200khz is a very low frequency. Theoretically ,Skin effect could occur at one Hz, although its effect would be infinitesimal. I have worked with RF power circuits up in the uhf range where Skin Effect is a definate reality, therefore requiring inductors of up to 1/4" tubing to overcome this. I don't have any argument with Skin effect reducing available conduction area at 200 Khz, but I have to question as to what degree at this low frequency. Also, from an economic standpoint one unit length of #28 wire should be cheaper than four unit lenths of # 36 wire per coil as copper costs seem to be a smaller percentage of overall costs( related to a pound of wire) as these wires get finer and finer. Do you have any info on formulas relating current penetration depth Vs. frequency?
I have seen only vague references to this subject in the past, so I am not fully informed on this subject.
No argument on your dissertation on Skin Effect. However in the broad spectrum of ac, 200khz is a very low frequency. Theoretically ,Skin effect could occur at one Hz, although its effect would be infinitesimal. I have worked with RF power circuits up in the uhf range where Skin Effect is a definate reality, therefore requiring inductors of up to 1/4" tubing to overcome this. I don't have any argument with Skin effect reducing available conduction area at 200 Khz, but I have to question as to what degree at this low frequency. Also, from an economic standpoint one unit length of #28 wire should be cheaper than four unit lenths of # 36 wire per coil as copper costs seem to be a smaller percentage of overall costs( related to a pound of wire) as these wires get finer and finer. Do you have any info on formulas relating current penetration depth Vs. frequency?
I have seen only vague references to this subject in the past, so I am not fully informed on this subject.

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 Joined: Fri Aug 22, 2003 1:01 am
 Location: Izmir, Turkiye; from Rochester, NY
 Contact:
http://en.wikipedia.org/wiki/Skin_effect for some numbers.
Were the wires actually loosely twisted together, or were they bifilar wound on the core? Four small wires laid sidebyside would take more length on the core than same number of turns of the larger wire. Also makes a less bumpy surface to put the secondary on to. If the manufacturer's winding machine only handles one gauge of wire at a time, it saves making a batch with primaries only, changing wire, then running batch again for secondaries. Just guessing of course, we'd have ask the engineers and managers who made the decision to find the real reason.
Interpulating from example table on Wikipedia page, at 200KHz No. 36 (5 mils or about 0.13 mm) wire is smaller than skin depth, two gauge sizes larger, the diameter would be greater then skin depth.
If they keep burning out, the manufacturer should have used one size larger than 36. (IMO)
Cheers,
Were the wires actually loosely twisted together, or were they bifilar wound on the core? Four small wires laid sidebyside would take more length on the core than same number of turns of the larger wire. Also makes a less bumpy surface to put the secondary on to. If the manufacturer's winding machine only handles one gauge of wire at a time, it saves making a batch with primaries only, changing wire, then running batch again for secondaries. Just guessing of course, we'd have ask the engineers and managers who made the decision to find the real reason.
Interpulating from example table on Wikipedia page, at 200KHz No. 36 (5 mils or about 0.13 mm) wire is smaller than skin depth, two gauge sizes larger, the diameter would be greater then skin depth.
If they keep burning out, the manufacturer should have used one size larger than 36. (IMO)
Cheers,
Dale Y
Hi again,
Robert:
You are right in that we should use a little more accuracy to figure
out the proper size wire, but this would require much more thought
and computations.
But, 200kHz is either a low frequency or a high frequency, depending
on what field you are working in. For example, when working with
RF, 200kHz is usually considered a 'low' frequency, but when dealing
with electrical power transfer or conversion, 200kHz is a very high
frequency. If you dont agree, consider that the skin depth of a
copper wire at 60Hz is roughly 1/4 inch, and that's only 60Hz.
At 200kHz i think it's around 0.006 inches, which is getting comparable
to the size of 36 AWG wire (0.005 inches).
Also, think about this for a minute...
The wave in question is not a sine wave anyway, it's a square wave.
The square wave is rich in odd harmonics, many of the lower ones
still transfer much energy. The third harmonic is at 600kHz, of which the
skin depth is around 0.003 inchs, which is comparable to the radius of
a AWG 36 wire. Since there is still plenty of energy in this harmonic
we would have to ensure the AC resistance of the wire isnt too high
at this frequency, as well as the 3th, 5th, and maybe 7th and 9th too.
This of course means it sounds like the designers might have taken
all this into consideration to come up with the wire size.
Having thought about that, it makes sense to select a larger wire
who's outer skin shell has the same area as the four wires do.
The worst that could happen is that we used a wire that was slightly
bigger than we needed.
Also, if we wanted to get more accurate we would have to consider
the effects to greater detail, taking into account the effect of each
harmonic in turn.
Another method i guess would be to compare the AC resistance at each
harmonic in the smaller wire with the AC resistance at each harmonic
in the larger wire and try to get 1/4 the resistance (or better) in the
larger wire at each frequency. When we select the wire with diameter
that meets this critereon, we have our solution.
BTW, 200kHz is a frequency that Magnetics, Inc. says Litz wire
should be used (in power converters).
Robert:
You are right in that we should use a little more accuracy to figure
out the proper size wire, but this would require much more thought
and computations.
But, 200kHz is either a low frequency or a high frequency, depending
on what field you are working in. For example, when working with
RF, 200kHz is usually considered a 'low' frequency, but when dealing
with electrical power transfer or conversion, 200kHz is a very high
frequency. If you dont agree, consider that the skin depth of a
copper wire at 60Hz is roughly 1/4 inch, and that's only 60Hz.
At 200kHz i think it's around 0.006 inches, which is getting comparable
to the size of 36 AWG wire (0.005 inches).
Also, think about this for a minute...
The wave in question is not a sine wave anyway, it's a square wave.
The square wave is rich in odd harmonics, many of the lower ones
still transfer much energy. The third harmonic is at 600kHz, of which the
skin depth is around 0.003 inchs, which is comparable to the radius of
a AWG 36 wire. Since there is still plenty of energy in this harmonic
we would have to ensure the AC resistance of the wire isnt too high
at this frequency, as well as the 3th, 5th, and maybe 7th and 9th too.
This of course means it sounds like the designers might have taken
all this into consideration to come up with the wire size.
Having thought about that, it makes sense to select a larger wire
who's outer skin shell has the same area as the four wires do.
The worst that could happen is that we used a wire that was slightly
bigger than we needed.
Also, if we wanted to get more accurate we would have to consider
the effects to greater detail, taking into account the effect of each
harmonic in turn.
Another method i guess would be to compare the AC resistance at each
harmonic in the smaller wire with the AC resistance at each harmonic
in the larger wire and try to get 1/4 the resistance (or better) in the
larger wire at each frequency. When we select the wire with diameter
that meets this critereon, we have our solution.
BTW, 200kHz is a frequency that Magnetics, Inc. says Litz wire
should be used (in power converters).
LEDs vs Bulbs, LEDs are winning.

 Posts: 2276
 Joined: Wed Nov 24, 2004 1:01 am
 Location: ASHTABULA,OHIO
 Contact:
MrAl
After following up on Dales info sources and reading your last post, its beginning to make a lot more sense. Had no idea that skin effect was that severe at lower frequencies, but remember that Skin effect shows no partiality to intended use  only frequency of the current in use. Since skin effect is caused by the self indutance of the conductor, its apparent that this condition becomes more intense as we scale up in frequency.I do remember from years ago, that as a rule of thumb, 1" of wire at 150 Mhz had about 50 ohms of impedance from its own inductive reactance and reduced conduction area. Hmmm  I wonder what the penetration depth is is at 450 Mhz!
After following up on Dales info sources and reading your last post, its beginning to make a lot more sense. Had no idea that skin effect was that severe at lower frequencies, but remember that Skin effect shows no partiality to intended use  only frequency of the current in use. Since skin effect is caused by the self indutance of the conductor, its apparent that this condition becomes more intense as we scale up in frequency.I do remember from years ago, that as a rule of thumb, 1" of wire at 150 Mhz had about 50 ohms of impedance from its own inductive reactance and reduced conduction area. Hmmm  I wonder what the penetration depth is is at 450 Mhz!

 Posts: 2276
 Joined: Wed Nov 24, 2004 1:01 am
 Location: ASHTABULA,OHIO
 Contact:
With regards to my former example of 1/4" tubing used in a UHF tank coil (450 Mhz). This was in a 50 watt transmitter employing vacuum tubes and pulling about 100 ma of plate current. Doing rough math in my head that would equate to a circular mil area of 80 with a current capacity of 115 ma  comparible to #31 wire. WOW
Re: Exitation Inductance
I didn't want to let this pass unchallenged. It sounds logical until you realize that the mutual coupling between the four inductors is unity, so the net inductance is identical to the inductance of a single winding.radionut8888 wrote:Lenp:
The frequency of operation is a hint. By winding the primary with 4 strands of wire side by side, the exitation inductance is reduced. From an inductance standpoint, it's like four inductors of the same impedance in parallel. This allows a faster rise time of the switching waveform thus reducing switching losses in the transistors driving the oscillator.
While the single winding with an equivalent sized wire will work, you might want to check the rise and fall time of the oscillator with each primary. The parallel primary should show a faster rise and fall time.
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