Monday, November 28, 2016

On the winding of power chokes and transformers: Part 2 - A filament transformer

Having wound the choke described in the previous installment about chokes - (link) - I decided to proceed with the next logical step in the project:  Winding a filament transformer.
Figure 1:
The completed filament transformer, before varnishing,
ready for testing.
Click on the image for a larger version.

With the lower voltage requirements, the filament transformer is the next-easiest since being a step down transformer, fewer turns are required overall and the wire sizes will be larger.

The first step was to figure out my voltage and current requirements - but this was already known in the form of the filament requirements of the tubes to be used:  Two center-tapped windings, each capable of 11 volts at 11 amps.  To calculate the necessary winding parameters (e.g. number of turns, size of wire, etc.) I will refer again to the two links noted in the previous installment, included below:

  1. Turner Audio (link) - These pages contain much practical advice on power and audio transformers and chokes.  (Refer to the link "Power Transformers and Chokes" (link) and related pages linked from that page.)
  2. Homo-Ludens - Practical transformer winding (link) - While mostly about power transformers, this page also contain practical advice based on hands-on experience of winding, re-winding and reverse-engineering/rebuilding transformers.  There is also another linked page "Transformers and Coils" (link) that has additional information on this topic.
While there are enough equations and general information spread across both pages to provide the necessary information if you want to crunch numbers with equations, of particular interest is a spreadsheet found on the Homo-Ludens "Practical transformer winding" web page that allows one to "play" with various configurations.  For this spreadsheet we will need to input what we already know, such as:
  • Input voltage:  120 VAC (nominal) at 60 Hz.  Since we want to have multiple taps to fine-tune the voltage, we'll also calculate for 115 and 125 volts.
  • Output voltage:  11 volts under load.  A rule of thumb is to add 5% to this to accommodate various losses so this would be (11 * 1.05 = 11.025) or approximately 11.5 volts.
  • Output current:  22 amps - the total sum of the two 11 amp filament windings.  They will be "split" in later calculations.
  • Core size:  E150.  The Edcor core and bobbin that will be used has a stack height of 38mm and a center leg that is 38mm across.
  • Set a design goal for wire sizes corresponding with a current density of 0.4 mm2/amp, a rather conservative number.
  • Let us initially set a "fill factor" of 0.4 - more on this parameter, later.
  • Core material information:  The Edcor laminations use M-6 GOSS (Grain-Oriented Silicon Steel) which is a material that is capable of safely handling higher magnetic flux than "generic" iron cores.  This has two important implications:
    • The saturation flux of this material is in the area of 1.7 Tesla.  This is a very "soft" number, dependent largely on how much core heating one is able to tolerate in the intended application.
    • The iron loss (in watts/kg at 1 Tesla) for the M-6 material is quite low - approximately 0.5 watts/kg@1T (at 50 Hz) versus 2 watts/kg@1T for "generic" transform iron.  The spreadsheet expects a 50 Hz value here regardless of the actual frequency.
A few words about the wire size:

The value of 0.4mm2/amp target that I chose is fairly conservative based on the recommendations found in several sources:
  • The Turner Audio site suggests a value of (3 amps/mm2) = 0.33mm2/amp as a general number.
  • The Homo-Ludens site suggests a value of 0.35mm2/amp for "medium-sized" transformers (50-300 watts) wire such as this and smaller/heavier (0.25 and 0.5mm2/amp) conductors for very small and large transformers, respectively.
  • Various vintages of the ARRL Amateur Radio Handbook note that a value of 1000 cma (0.506mm2/amp) as being "conservative" with a value of 700 cma (0.354mm2/amp) being suggested.
  • Interestingly, the 1936 Jones Radio Handbook notes recommends a 1000 cma
    (0.506mm2/amp) value for typical amateur use and increasing this to 1500 cma (0.759mm2/amp) for transformers that would be intermittently subjected to significant overload and/or were in hot, poorly ventilated environments.  These recommendations are understandably based on the use of older materials such as paper insulation and the more fragile varnished/enameled wire of the day.
  • If one peruses the Edcor site one can glean bits of data here and there and they mention a design goal of 500 cma (circular-mill amperes) which converts to 0.253mm2/amp.  (Reference:  Tek Note 43 - link.)  When I read this I presumed that this recommendation may have been intended for small, low-power transformers, but I noted this posting - link in their forum where a current of 200mA is mentioned being used with 30 AWG wire which calculates to 0.254mm2/amp.
Even more about flux density:
  • As noted, for inexpensive, generic cores of unknown properties Turner Audio suggests a maximum flux of 0.9 Telsa while the Homo-Ludens site suggests that 1.0 Tesla is "probably OK" for the vast majority of cores of unknown provenance.  The later site recommends that if these cores are being re-used that one counts the number of turns on the original primary (if it is being re-wound) and use this, along with the core's cross-sectional size to estimate the original flux density.
  • The M-6 material is capable of much better performance (e.g. lower loss) than "generic" iron - likely being usable at 1.6-1.7 Tesla, but Edcor mentions in Tek Note 43 (linked above) that their design goal is 1.4 Tesla - value with which both the Turner Audio and Homo-Ludens sites agree as being appropriate for this material.  Based on typical curves for M-6 material, this would seem to be a reasonable compromise between higher core losses, fewer turns (e.g. higher flux) and more turns with higher copper losses, lower core losses (lower flux).
 Based on the above I decided to use 1.4 Tesla in my design.

Comment:

If you are keeping the original primary winding, wind a few dozen turns of hookup wire and carefully measure the resulting, unloaded voltage.  Comparing this with the applied primary voltage and taking the number of temporary turns that were wound the number of turns on the primary could be quite accurately determined and from there, along with the stack height and center leg size, it should be possible calculate the approximate magnetic flux of the original device.
Crunching the numbers:

Inputting the above to the spreadsheet one can see that it does not actually care about the output current, but rather is tells you the highest possible load current and volt-amp capacity based on the core size and flux density that you specify and the most important information that it gives is the number of turns for the primary:  It is up to you to scale back the "worst case" numbers that it gives you to better suit your needs and make sure that everything will fit in the available space.

For example, given the information that we already have, the spreadsheet calculates that with the entered parameters one could expect to pull well over 26 amps at 11.5 watts - about 292 volt-amps using the wire targets along with what is calculated to be able to fit given the calculated wire sizes and the inputted fill factor.  In reality, we will need closer to (11.5 volt * 22 amps =) 253 volt-amps so we would be safe in downsizing our wire to about 83% of the calculated cross-sectional area.  Assuming the worst case loading of the primary - which occurs at the lowest primary voltage, 115 VAC, we can calculate that our maximum primary current will be (253 volt-amps / 115 volts) = 2.2 amps.
  • If we consult a wire table to see which size most closely matches our 0.4mm2/amp criteria (e.g. 0.4mm2/amp * 2.2 amps = 0.84mm2) we find:
    • 17 AWG wire at 1.04mm2.  This is (1.04mm2 /amp / 2.2 amps) = 0.472 mm2.
    • 18 AWG wire at 0.823mm2.  This is (0.823mm2/amp / 2.2 amps) = 0.37 mm2.
    • 19 AWG wire at 0.653mm2.  This is (0.653mm2/amp / 2.2 amps) = 0.30 mm2.
As we can see, either 17 or 18 AWG would be fine for the primary, both sizes being quite close to our design goal:  17 AWG will run a bit cooler with lower loss while 18 AWG will take up a bit less space on the bobbin.  19 AWG does fit within the Edcor guidelines but is much smaller than target - but would still probably be OK if one tolerated a bit of extra heat and voltage drop.

Based on the 1.4 Tesla flux values we can see that at 115 Volts we would need 223 turns on our primary to achieve the target of 11.5 volts and since the ratio of primary-secondary turns is exactly the same as our voltage ratio, we can calculate:
  • 115 volts / 11.5 volts = 10:1 ratio
What this means is that for our 223 turns on the 11.5 volt primary, we would need (223 / 10) = 22.3 turns.  Since it is awkward to wind a fractional turn, let's round down to 22 turns - an even number that also makes it easy to locate the center tap point.  By increasing the number of turns slightly we must now recalculate the 115 volt primary winding using the same ratio as above:
  • Doing this, we will need (10 * 22) = 220 turns.  This reduction in turns from 223 increases the flux density on the core, but only by a few percent so we can ignore it.
Let us now calculate the number of turns for 120 and 125 volts:
  • 120 volts / 11.5 volts = 10.435:1 ratio.  22 turns * 10.435 = 229 turns, rounded down.
  • 125 volts / 11.5 volts = 10.870:1 ratio.  22 turns * 10.870 = 239 turns, rounded down.
Since we need two filament windings, each capable of of 11 amps, we calculate the appropriate wire size for each:
  • For 11 amps, we calculated a minimum wire cross-sectional area of (0.4 mm2/amp * 11 amps) = 4.4 mm2.  Consulting the table, we find:
    • 10 AWG wire at 5.26mm2.  This is (5.26mm2/amp / 11 amps) = 0.48 mm2
    • 11 AWG wire at 4.17mm2.  This is (4.17mm2/amp / 11 amps) = 0.38 mm2
    • 12 AWG wire at 3.31mm2.  This is (3.31mm2/amp / 11 amps) = 0.30 mm2
    • 13 AWG wire at 2.62mm2.  This is (2.62mm2/amp / 11 amps) = 0.23 mm2
From all of the above we can see the 11 AWG wire is very close to our 0.4mm2/amp target - and still above the recommendations of the two web sites listed above while 12 AWG appears to be suitable if one goes with the Edcor guidelines.  It should also be noted that because these primary windings are on the "outside" layer (the reason to be noted later) they can more readily dissipate heat via convection than a winding deep inside the bobbin.

Comment: 
Instead of using 11 AWG, I could have used four parallel strands of 17 AWG as they would have a total of (1.04 * 4) = 4.16mm2 cross-sectional area - although handling multiple conductors at once can be quite awkward.  One might do this if larger wire was not on-hand, but also to take advantage of the fact that 17 AWG is more flexible than 11 AWG.  When paralleling conductors care must be taken to make sure that all are wound identically to prevent the differences in their intercepted magnetic fields which can cause "bucking", resulting in heating.

Will it fit?

As it turned out I had suitably large quantities of 10, 11 and 17 AWG on hand so I decided to calculate the volume that would be taken up by the three sets of windings.  Based on online drawings of the Edcor E150 nylon bobbin - and actual measurements with a set of calipers - I came up with the following:
  • According to the drawing the interior width is 53.28mm but the actual, measured size was 52.7mm.
  • The indicated window "height" (e.g. the available space on one of the four sides into which the windings must fit) is 16.935mm, but the actual, measured size was 16.5mm.
First we calculate how many turns of 17 AWG will fit on a layer.  The wire that I used (polyimide coating, rated for operation to 200C) has a diameter with insulation of 1.224mm which means that (52mm / 1.224mm/turn) = 43.05 turns may fit in a layer.  Rounding down and accounting for about 1 turn of "fudge factor" (e.g. wire laying with a slight amount of space between adjacent turns, a slight bit of wastage at the ends where the next layer starts) we can reasonably expect 41-42 turns per layer.

Knowing that we will need 239 turns for the 125 volt winding this comes out to (239 turns / 42 turns/layer) = 5.7 layers so there should be no problem keeping it down to just 6 layers with a little bit of room to spare. Between layers I was laying down one layer of 0.05mm polyimide (Kapton (tm)) tape which means that for each layer I was taking up (1.224mm (wire) + 0.05mm (insulation)) = 1.274mm, and for 6 layers the total would be 7.644mm.  Between the primary and secondary we need to put at least 0.5mm of additional insulation, bringing that up to a total of around 8.144mm of height out of the available 16mm.

Now taking the 11 AWG secondary we note that the diameter of the wire with insulation is 2.393mm which means that (52mm / 2.393mm/turn) = 21.99 turns will fit on a single layer - and this number is a bit "soft" in that we may be able to squeeze the full 22nd turn in if the nylon bobbin will flex just a little. Using the above numbers we can see that each layer will take (2.393mm (wire) + 0.5mm (insulation)) = 2.893 mm - and since we have two identical windings that turns out to be 5.786mm, total.

All together, including a final 0.5mm thick layer of insulation, the height of the windings will be 13.93mm - about 84% of the available space and based on this I decided not to try the equations for 10 AWG. Out of curiosity I recalculated the above for 12 AWG we get (52mm / 2.139mm/turn) = 24.31 turns fitting on a single layer with each layer+insulation being 13.442mm - about 81% so this would have been fine but because since I had 11 AWG on hand I decided to proceed with that size.

It was noted in the aforementioned Edcor Tek Note 43 that a reasonable design goal is around a 70% filling of the bobbin but that at 90% the numbers are re-crunched to see if smaller wire may be used and/or a larger core is required:  Both of our numbers, above, come in below that 90% margin so we should be pretty safe if we are neat and careful.

Calculating winding volume using "Fill factor":

"Fill factor" is the ratio between the volume occupied by the wire itself and the combined volume of the wires and insulation.  Because a circle that is 1mm diameter occupies about 79% of the volume of a square that is 1mm on a side we lose over 20% off the bat in our packing efficiency - and this is made only worse by the fact that we need to add insulation between layers and also that we cannot pack the wires perfectly side-by-side.  A bit less easy to calculate is the fact that at the ends of the bobbin where we transition layers, we tend to lose a portion of each turn at each end.

On the Turner Audio pages it was noted that a "Fill factor" of around 0.3 was common with older transformers with (thick!) paper insulation between each winding and closer to 0.45 with modern insulation was practical while the Homo-Ludens site mentions that a fill factor of around 0.5 is practical if it is wound with care (e.g. neat, side-by-side windings) and one uses thin, modern insulation.

How does our transformer "stack up" when using this method?

We know from above that the window size is (52.705mm * 16.51mm) = 870mm2, so let us calculate how much of the bobbin our wire is expected to take up:
  • 17 AWG is 1.224mm diameter so its cross-sectional area is 1.177mm2, so (1.177mm2/turn * 249 turns) = 293mm2.
  • 11 AWG is 2.393mm diameter so its cross-sectional area is 4.498mm2(4.498mm2/turn * 22) turns (total for both windings) = 99mm2.
  • The total of the copper alone is (293 + 99) = 392mm2, not including fill factor.  Using this number with various fill factors we get:
    • Fill factor of 0.3:  392 / 0.3 = 1307mm2150% of the available space - we must do better!
    • Fill factor of 0.4:  392 / 0.4 = 980mm2.  113% of the available space - getting closer.
    • Fill factor of 0.45:  392/0.45 = 871mm2. 100.1% - this is almost exactly how how much room we have.
    • Fill factor of 0.5:  392/0.5 = 784 mm2.  90% - we should be fine if we can do this.
According to this method of calculation we will need to achieve a fill factor of about 0.45 in order to have the turns actually fit. Will the fact that the thin (0.05mm) insulation between layers is thin enough that overlaying windings will take up less "height" if they can fall in the grooves between wires somewhat?  Can this fill factor actually be achieved?

Let's find out.
Figure 2:
The prepared bobbin, at the start of the wind, covered with an initial layer
of polyimide tape.
Click on the image for a larger version.

Winding the transformer:

While it might seem customary to wind the primary first, this is not always the best strategy.  It is often the case that the thinnest wire is wound first as the corners of the bobbin are their sharpest when the diameter is small, making it easy to handle and allowing slightly better packing efficiency and, thus, a better "fill factor."  In this case, because the primary used thinner wire (17 AWG) than the secondary (11 AWG), I wound the primary first.

In preparation for the start of winding I placed a layer of 0.05mm polyimide tape onto the nylon bobbin as a foundation and to give the wire a bit of a surface to "bite" into - and to provide just a little more protection even though it is unlikely that the transformer could ever survive the sorts of conditions that would melt or arc over the bobbin in the first place!

Figure 3:
The three primary voltage taps.
As may be seen, the lower voltage taps (115, 120 volts) consists of a loop
of wire that is brought out of the winding.  The locations of these taps
is staggered somewhat to space apart where they emerge from the side
of the bobbin:  The slight, fractional-turn deviation from the calculated tap
location causes an insignificant voltage change on a winding with this
many turns.  With the taps emerging at a right angle, away from the
"corners" of the bobbin they will add wire height only to the portion
that faces the end bells of the transformers, not on the "sides" between
the winding and the steel laminations which would be on the top
and bottom of this picture.  This method of bring out the taps
also prevents the taps from significantly reducing the number of turns
that will fit on the layer which can keep the number of layers down
to that calculated.
Click on the image for a larger version.
Because 17 AWG wire is actually quite large I "drilled" a hole through the nylon with the conical tip of a hot soldering iron (easier and safer to do than with a drill - particularly when there are already windings present on the bobbin that could be damaged by the bit) and brought the wire straight out the side of the bobbin.  Winding excess length around the screws of the bobbin that were placed there for the purpose of keeping this wire out of the way, I proceeded to place the first layer.

Winding very carefully I laid the turns side-by-side and pushed them closer together to reduce the space after every few turns.  At the end of the first layer I temporarily taped the wire to the side of the bobbin to keep it from unraveling and put an even layer of 0.05mm polyimide tape over the first layer to both insulate and secure the windings before starting the next layer.

Because the first layer was wound very neatly, the second and subsequent layers usually fell into the grooves between the windings of the previous layer with this thin insulating tape which can make it easier to keep these layers nice and neat.  At the ends of the winding there can be a bit of "mechanical confusion" as there is inevitably a sort of "half turn" of spacing between the wire and bobbin that cannot be effectively filled.  As one continues to add layers, this gap on the ends tends to gradually become deeper and care must be taken to make sure that as the wire (inevitably) falls into this gap that it falls atop insulation rather than the previous wire as to minimize the possibility of the wire being chafed and shorted with vibration and thermal cycling.

Figure 4:
A side view of from where the primary taps emerge.  It is important
that the taps be labeled at the time of winding to avoid later
confusion and the possible need to reverse engineer what was done!  Small
pieces of Nomex paper insulation are visible, used to mechanically
separate the overlaying conductors.
Click on the image for a larger version.
At turns 220 and 229 the winding was paused to make the 115 and 120 volt taps.  This was done by making a loop of wire approximately in the middle of the face of the winding, bringing the two wires of the loop together so that they carefully lay side-by-side and bringing it out the side of the bobbin through a hole that was labeled with a permanent marker.  Underneath this loop was placed both some polymide tape and some Nomex (tm) paper insulation to prevent the pressure of the wires of these taps from impinging directly on the insulation of the turns below it and shorting some turns.  At the very end of the winding the tail end of the wire was brought directly out through a labeled hole.

Over the top of the taps was placed an additional layer of polyimide tape and the entire primary was then covered with about 0.5mm of a combination of Nomex paper and polyimide tape to provide a durable insulation between it and the secondary.  Up along the sides of the bobbin a few millimeters of extra insulating tape was added to increase the "creep" distance - an important safety factor when high voltages are concerned.

Once this was done it was time for the secondary windings.  Because 11 AWG is quite large, it takes a bit of brute force to handle.  Using a pair of strong needle-nose a fairly sharp right-angle bend was made in the wire so that it could pass through the slightly oversized hole that I had melted into the side of the bobbin without taking up too much extra space and the winding proceeded with the wire being bent carefully around each corner of the bobbin.

Figure 5:
The completed bobbin, overtaped with taps coming out several sides.
The thin center-tap winding of the outer filament winding (yellow-orange
wire) is easily visible with the purple center tap of the inner filament winding
being seen in the background.  Since the center tap carries only the tubes'
cathode currents, the center taps need only carry a few hundred milliamps
at most.
Click on the image for a larger version.
As it turns out, only about 21 and a fraction turns of the required 22 turns would actually fit across the bobbin so a new layer was started that had just one turn - but this extra turn was lined up with the partial final layer of the primary so its total height was less than it would otherwise have been.  Carefully making a fairly sharp bend in the wire and passing it through a labeled hole in the bobbin, I then located - by counting from each end - the exact location of the 11th turn - the center-tap.  There I carefully scraped the insulation off the top of the wire and, with a very hot soldering iron it was tinned and a short piece of PTFE (Teflon (tm)) covered wire was was attached and brought out through a labeled hole in the side of the bobbin.

While this method of connecting the center-tap is a bit kludgy, the use of magnet wire with a high-temperature polyimide insulation and the underlying polyimide tape between layers minimizes the possibility that the wire itself will be damaged in the process of soldering - and careful visual inspection and tugging on the added tap wire indicated that the connection was quite secure and that the wire itself and insulation in neighboring turns were still intact.  The use of a very hot iron may seem counter-intuitive, but having a lot of heat and thermal mass means that one can thoroughly heat the wire rather quickly to make a proper, alloyed solder connection.  Because the center tap is low-current, needing to carry only a few hundred milliamps of cathode current from the tube, the tap wire is quite small - about 24 AWG.  If I do this technique again I will insert a piece of tape as a "cradle" at the tap point during winding to add extra insulation around the location of the tap and the adjacent turns.

Figure 6:
A side view of the completed bobbin.
Before the transformer's end bells are installed, wires will be attached to
the primary winding's connections and the heavy filament wires will be protected
with an additional layer of insulation where they are brought out.
Click on the image for a larger version.
The first primary completed, it was covered with a layer of 0.05mm polyimide tape, a layer of 0.05mm Nomex paper and another two layers of 0.05mm polyimide tape.

To avoid cluttering the bobbin with too many holes that were too close to each other, the second primary was started nearly 1/4 turn away from the first primary (at nearly the next corner) and since the first had taken a bit more than one layer, I had to "offset" the start of the winding slightly, crossing over the top single-turn top winding of the first primary.  Understandably, this was done with care, bending a slight loop in the wire to go up and over with plenty of insulating tape and a piece of Nomex paper slid underneath to protect the adjacent wires.

The winding proceeded from there, but since it could not start at the end of the bobbin there were now several turns at the end in an "extra" layer that required yet another careful "crossing of the wires" with plenty of insulation.  Upon securing the winding the exact middle of the secondary was located - a task made slightly more difficult by some of the turns being overlaid on a new layer and the center tap was carefully made in the same manner as before.

The winding being done, the second secondary was covered with several layers of polyimide tape and, using a clamp and two pieces of wood, the windings on the two sides of the bobbin that were not facing outwards were squeezed together, slightly reducing the height and increasing the spacing where it passed through the core.

Figure 7:
The "primary side" of the transformer with the solder
joints having been doubly-insulated with heat-
shrinkable tubing.
Click on the image for a larger version.
The results:

As it turned out, the windings - including the unintended partial layer on the secondaries - completely filled up the bobbin, but there was easily a millimeter or two clearance between the windings and the laminations.

In testing the transformer unloaded using a variable transformer I ended up with the following results:
  • 115 volt primary tap at 115.0 volts:  11.49 and 11.48 VAC on windings 1 and 2, respectively
  • 120 volt primary tap at 120.0 volts:  11.49 and 11.49 VAC
  • 125 volt primary tap at 125.0 volts:  11.52 and 11.51 VAC
  • Accuracy of center-tap voltage:  Better than 50 millivolts on each winding.
  • The magnetization current (no load) was approximately 300 mA on each tap at its rated voltage, decreasing somewhat with the higher-voltage taps.  It should be noted that the magnetization current is about 90 degrees out of phase with the reflected load current so it won't count too very much against us when the transformer is actually under load.
Figure 8:
The "secondary" side of the transformer.  The heavy
(11 AWG) wires are first insulated with PTFE
insulation and where they emerge from the metal
bell are covered with colored heat-shrinkable tubing
to identify the windings.
One of the reasons for the primary taps is to allow "fine tuning" of the filament voltage:  Putting taps on the relatively low-current primary is much easier than providing several pairs of equal-spaced taps on the center-tapped, high-current secondary!

As it turns out the actual heater voltage of the tubes that will be used is 10.5 volts, but it is common practice to purposely add a bit of series resistance to reduce the "cold filament" inrush current when the power is first applied - something that will likely involve a drop of a few hundred millivolts through additional resistance:  Anyway, it is much easier to drop a small bit of voltage than add it!

What if we did need more filament voltage than our 11 volt (loaded) target?  The worst-case scenario would be to run the 115 volt tap at 125 volts (yielding 12.5 unloaded volts on the secondaries) which would increase the magnetic flux of the core to an estimated 1.48 Tesla - still within the "safe" range for the M-6 core material!

Lessons learned:

The entire reason for doing this task is to learn something, so here are a few comments:
  • The "tack" method of attaching the center tap wire to the secondaries seems to work OK, but I can see that it was not done very carefully, it could easily go wrong for a number of reasons:
    • Damaging the insulation of adjacent turns and causing immediate or future problems with shorting.  The use of high-temperature polyimide wire allowed this to be done safely, but in the future I would lay the tap point in a "cradle" of polyimide tape to provide additional protection to the adjacent turns.
    • A faulty solder joint due to inadequate breaking of the insulation on the top surface of the wire and/or insufficient heat to make the joint.
    • This method of attaching a comparatively thin conductor is only appropriate where the current through the center tap will be quite small.  In this case, only the cathode current of the tubes - a few hundred milliamps at most - is all that need be conveyed.
  • I did not end up with much additional room on the bobbin when the winding and final insulation layers were completed.  Were I to design and build this transformer again and I were willing to buy whatever sized wire I needed I would probably have used 18 AWG for the primary.
  • 12 AWG would have probably been just fine for the secondaries, particularly with the use of modern, high temperature wire and insulation and the fact that the two secondaries are on the "outside" of the bobbin.  The use of 12 AWG would have also easily allowed each layer of 22 turns to be would with a little bit of room to spare.
  • Had I used 18 and 12 AWG wire for the primary and secondaries, respectively, there would have easily been enough room to add yet another secondary winding such as a 6.3 volt winding for tube filaments or even yet another low-current winding for bias, control logic, or whatever.
Overall, I'm pleased with the results.

Final comments:

The transformer has yet to be encapsulated in insulating varnish and shims have not been inserted between the core laminations and the bobbin, so it hums a lot more now than it will when it is complete.  It will not be until after the initial testing of the (yet to be constructed) amplifier that this will be done as it will still be possible to make slight modifications to the transformer (e.g. change the number of turns, add extra, low-current windings, etc.) in its present state.

In static (no load) testing the transformer was operated with 130 volts applied to the 115 volt tap resulting in an estimated 1.54 Tesla core flux, a 28C (50F) temperature rise was observed.  When 115 volts was applied to the same tap - a situation more representative of core losses (not including the resistive losses in the winding) that might be observed in actual use the temperature rise was just 19C (30F).


How long did it take to wind this thing?  With all of the materials and components lined up it took less than two hours to wind this transformer - being very careful - and about another hour to stack the cores and do initial testing using a variable transformer supply.

The next installment will describe the design and construction of the high voltage plate transformer.

[End]

Monday, November 14, 2016

"TDOA" direction finder systems - Part 1 - how they work, and a few examples.

Next to using a directional antenna, one of the simpler ways to determine the direction of a received signal is to use what is often referred to as the "TDOA" system which stands for Timed Direction Of Arrival.

One method of implementation involves the use of two separate antennas, switched at an audible rate, and connected to a narrowband FM receiver.  In its simplest form the antenna switch signal could be produced by anything from a 555 timer to an oscillator made from logic gates to one made using an op-amp:  All that is necessary is that the duty cycle of the driving (square) waveform me "near-ish" 50% (+/- 30% is probably ok...) and be of sufficient level to adequately drive the switching diodes on the antenna.

See the diagram below for an explanation of how this system works:
Figure 1:
A diagram showing how the "TDOA" system works.
Click on the image for a larger version.

In short, if both antennas - which are typically half-wave dipoles - are exactly the same distance from the signal source, the RF waveform on each of the two antennas will have arrived at exactly the same time.  If we electronically switch between the two antennas, nothing will happen because both signals are identical.

If one of the two dipoles in our DF antenna is closer to the transmitter than the other, switching the between the two antennas will cause the receiver to see a "jump" in the RF waveform:  Switching from, say, A to B will cause it to jump forward while switching from B to A will cause it to switch backward.

The switching, causing the RF waveform to "jump", is seen by the FM receiver as phase shift in the received signal - and being an FM receiver, it detects this as a "glitch" in the audio as depicted in Figure 2:
 
Figure 2:
Example of the "glitches" seen on the audio of a receiver connected to a TDOA system that switches antennas.

Because the discontinuity in the RF waveform caused by the antenna switch is abrupt, the "glitch" in the audio waveform is transient and occurring only when the antenna is switched.  You might notice something else in Figure 2 as well:  If we assume that a the first glitch is from switching from antenna "A" to antenna "B" and that it causes the glitch to be positive-going,  the switch from antenna "B" back to antenna "A" is going to be negative-going. Ideally, the glitches are going to be equal and opposite but sometimes - such as the case in Figure 2, they are not exactly the same and this is usually due to multipath distortion at the DF antenna array.

At this point, several things may have already occurred to you:
  • If switching from antenna "A" to antenna "B" causes a positive glitch and vice-versa, we know that the antenna array is not broadside to the transmitter.
  • If we rotate the antenna so that switching from antenna "B" to antenna "A" now causes a positive glitch and from "B" to "A" causes a negative one, we can reasonably assume that if antenna "A" were closer to the transmitter before we rotated it, that the direction of the transmitter is somewhere in between the two antenna positions.
  • If the two antennas are equidistant from the transmitter, the glitches will go away entirely.  At this point, the antenna will be oriented directly broadside to the transmitter, indicating its bearing.
  • The magnitude of the glitches provides some indication of the error in pointing:  If the antennas are equidistant with the two-element array perfectly broadside to the transmitter, the amplitude of the glitches will be pretty much nonexistent, but if the antenna is 90 degrees off (e.g. with the boom "pointed" at the transmitter as one would a normal Yagi antenna) the glitches - and the audible tone - will be at the highest possible amplitude.
Detecting the glitches by ear:

If the antennas are switched at an audible rate, these glitches will be clearly audible as a tone superimposed on the received signal.  While it is not possible to determine the phase relationships of these glitches by ear to determine whether the transmitter is to the left or right of our signal, by sweeping it back and forth and mentally noting where the "null" (e.g. the point at which the tone disappears) is, we can infer the direction of the transmitter by doing so - and that is exactly how the simplest of these TDOA systems work.

For an example of a simple TDOA system using a 555 timer, see the following web page:

WB2HOL 555 Time Difference-of-Arrival RDF - link

This circuit is about as simple as it gets:  A 555 timer that generates a square-ish wave.  It is up to the user to move the antenna back and forth, note the null and infer from that the direction of the signal.

It should be noted that in this case the transmitter could be behind the user, but with a bit of skill and practice one can resolve this 180 degree ambiguity - particularly if one is fairly close to the transmitter - by noting how the apparent bearing changes with respect to the relative locations of the user and the transmitter.

Detecting the glitches electronically:


To electronically determine if the signal is to the left or right of our position we must be able to determine if the glitch that occurs when switching from on antenna to the other is positive-going or negative-going and to do this, we need some simple circuity and one way to do this is to include a "window" detector - that is, a detector that "looks" at the receive audio for a brief instant, just after the antenna switch occurs and here are two circuits that do just that:

WB2HOL's Simple Time Difference-of-Arrival RDF - link
and
The WA7ARK TDOA units - link  (Some of the circuits on this page are described below. )

In looking at the WA7ARK pages, we find two units that indicate left/right in different ways:
  1. In the "Aural" unit, a 565 chip - which is a PLL (Phase Locked Loop) - is used to both generate the signal for switching the antennas and also to determine if the signal indicated is to the left or right by changing the pitch of the tone.
  2. In the "Metered" unit described below, an approach is taken very similar to that of the WB2HOL Simple Time Difference-of-Arrival RDF circuit in that a "snapshot" of the audio is taken an the appropriate time to determine the polarity of the glitches and display this as a left/right indication on a meter movement.
In both of these circuits one still hears the tone, but there is an additional input to the user - the pitch of the tone in the case of #1 and the movement of the meter for #2 - to indicate that the transmitter is left/right of the current antenna orientation.  Having this additional information also helps the user more-easily resolve the 180 degree ambiguity because, if the transmitter is behind, the left-right indications will be reversed.

Finding the glitches:

At this point in the discussion I would like to redirect your attention back to Figure 2, above.  You'll notice that these glitches are really quite brief:  They don't last very long at all - and most of the space between glitches is empty - at least if there is no other audio on the transmitted signal.

What about if the signal being received is heavily modulated with voice or noise?  That glitch can be easily lost amongst the clutter - but we have advantage:  We can know precisely when that glitch is going to occur and look for it only then, ignoring everything else.  In selectively looking for that glitch, much of the effect of modulation on that signal that would serve to "dilute" the signal that we want is reduced and this method is used in the "Metered" version of the WA7ARK circuit, reproduced below:
Figure 3:  The WA7ARK "Metered" circuit.
The "X" and "Y" taps are always "5" apart (0 and 5, 2 and 7, etc.) and are selected either with an oscilloscope or
experimentally, using a "clean" signal from a known-good receiver.
Click on the image for a larger version.
This circuit works as follows:
  • U3C, an op amp, is wired as an oscillator with the frequency selected as being in the neighborhood of 10 kHz.  The precise frequency really isn't critical, but it should be stable:  Just make sure that you don't use a ceramic capacitor for C4.
  • U2 is a 4017 CMOS divide-by-10 counter.  The "Cout" pin has a square wave at 1/10th of the frequency of the U3C oscillator (approximately 1 kHz) and this signal, buffered by U3D, drives the switched antennas.
  • The FM receiver is connected via J1 and this contains the audio with the "glitches" in it.
  • For every 10 count made by U2, there are two glitches:  One occurs when the square wave output from U3D goes from high-to-low, and another when it goes from low-to-high.  During that time, the "0-9" outputs of U2 go high, one-at-a-time, representing each of its 10 counts and is high for only 10% of the total time.
  • As shown in the diagram, we select two of the 0-9 outputs of U2, 5 counts apart from each other.  We pick the output that goes high at the same instant that the "glitch" from the receiver's audio arrives.
  • Being driven by U2, U1 contains electronic switches that are activated by the two, brief signals from U2 that we have selected to go high when the glitches arrive.  When activated, the appropriate switch inside U1 is closed at a time that coincides with the glitch and this brief signal changes the charges on C2 and C3, the voltage correlating with both the amplitude and polarity of the glitch.
  • U3A and U3B buffer the voltages on C2 and C3 and feed it to a zero-centered meter:  The more the charges on C2 and C3 differ from each other, the more the meter swings away from the center.  Since the voltages on C2 and C3 are derived from the glitches that occur, the meter indication tells us not only whether the signal is to the left or right of us, but also something about how far to the left/right it is!
By using a "windowed" detector driven by the relatively brief pulses from U2, we are only looking at our receive audio for 2/10ths of the time (e.g. 20%) and ignoring what is happening during the other 80% of the time and since our meter is connected across these two points it is also only going to react to energy that is consistently "equal and opposite" - as that of the "glitches" depicted in Figure 2.

Because we are looking at only the 20% of the time during which a glitch is coming in, we not only better-reject other audio that might be being transmitted on that signal, but by virtue of some filtering provided by capacitors C2, C3 and resistor R3, we are averaging out the noise and other modulation as well, further improving our effective sensitivity and reducing our susceptibility to effects of noise and modulation on our received signal!

In actual use, one would determine the optimal taps for "X" and "Y" on U2 in the diagram above - either with an oscilloscope, or experimentally by adjusting the taps using a clean tone - no modulation received using an antenna like that described below for the highest meter indication.  For calibration, one would simply set the volume on the receiver to cause full-scale deflection when the antenna was pointing "away" (e.g. 90 degrees rotated from the two elements being broadside to the transmitted signal).  If necessary, you may make R4 variable, placing a 1k resistor in series with a 10k-25k potentiometer.

The antenna:

Up to this point the antenna has been mentioned only in passing.  The simplest antenna - and one that works well for practically any of the simple TDOA systems (of the "left/right" variety) you are likely to find - is depicted below:
Figure 4:
A typical TDOA switch antenna.
The only critical points are that dimensions "L2" and "L3" be equal to each other and cut according
to the lengths calculated using the notes on the drawing above or using the example below.
Click on the image for a larger version.
Note:  The antennas depicted on the WB2HOL pages, linked above, will also work.

While the antenna depicted in Figure 4 looks like a 2-element Yagi, it is not.  What's more, it is important to realize that while you would line up the elements of a Yagi to point it at the signal being sought, this antenna - when "pointed" toward the transmitter - will have its elements oriented broadside to the transmitter.  In other words, if you are facing the transmitter and you are holding the antenna centered in front of you, one of its elements will be to your right and the other will be at the same distance, but on your left.



A few notes about construction:
  • The two elements must not be spaced farther than 1/2 wavelength apart at the highest frequency for which you plan to use the antenna.  If they are spaced farther than 1/2 wavelength apart, you'll get nonsensical readings!  Spacing them about 1/4 wavelength apart on 2 meters (144 MHz) results in a fairly compact and manageable antenna.
  • Make sure that the two pieces of coax depicted by "L2" are of the same type and length - an electrical 1/2 wavelength apart:  Note that the "velocity factor" of coax will mean that the coax's physical length will be significantly shorter than its electrical length.
  • For D1 and D2, use identical diodes.  Preferably, a PIN switching diode will work, but a 1N914 or 1N4148 will work in a pinch with somewhat degraded performance.  Reportedly, 1N4007 diodes (the 1000 volt version in the 1N400x family of diodes) work fairly well on 2 meters for this purpose.
  • For 2 meters, typical values might be:
    • L1 = 16 inches (42cm)
    • L2 = 13.5 inches (34cm) for cable with a solid polyethylene dielectric.
    • L3 = 38 inches (97cm) total consisting of two pieces of half that length. 
 How the antenna switching works:

If you look at Figure 3 you will see J2, which is connected to the DF antenna and J3, which is connected to the receiver and separating the two is C7, a 47pF capacitor:  C7 is too small to effectively pass our audio-frequency antenna switching signal and is thus able to prevent it from entering the front end of our receiver.

Our switching signal - a square wave - is coupled to the antenna via C6 and this capacitor is large enough that it allows the square wave to pass, but since it is AC coupled, it causes our positive-going square wave from U3D to become bipolar, centered about zero going both positive and negative with respect to ground.  R9 is used not only to limit the level of the square wave being fed to the diodes, but it also isolates the RF signal present at J2/C7 from the rest of the circuit.

The now-bipolar square wave travels down the coax to our antenna along with the RF and when it is positive-going, D1 (in Figure 4) conducts and reverse-biases D2, shutting it off, but when it is negative-going, D2 conducts and D1 is reverse-biased:  It is only when a diode is conducting that it is transparent to RF and in this way, we can alternately select either the left or the right element.

When using the antenna:
  • The above antenna only works well for vertically-polarized signals since the antenna must be held with the elements vertical to get left/right indications.
  • Remember that you do NOT use this as you would a Yagi.  The tone will disappear when the elements are vertical and the plane of the two elements are broadside to the distant transmitter.  In other words, if you are holding the antenna up to your chest, one element will be near your left arm and the other will be near your right.
  • If you "point" the boom at the transmitted signal as if it were a normal Yagi, you will get the loudest tone.
  • Because this is FM - and with FM, signal strength doesn't matter once the signal is full-quieting - the loudness of the tone will tell you nothing about the strength of the received signal.  Again, the loudest tone indicates that the antenna is about 90 degrees off the bearing of the transmitter and the tone disappearing tells you that the antenna is perfectly oriented broadside to the transmitter.
  • Remember that if the transmitter is behind you, the left-right indications (if the unit has the capability) will become reversed.
  • The presence of multipath and reflections can easily confuse a system like this.  Remember to note the trend of the bearings that you are getting rather than relying on a single bearing that might suddenly indicate a wildly different different direction:  If you do get vastly different reading, move to a different location and re-check.  Unless you are very near the transmitter - which probably means that you can disconnect the antenna cable from the radio and still hear the transmitter - a small change in location should not cause a large change in bearing:  If it does, suspect a reflection.

A few comments about some inexpensive imported radios and their suitability for use with these types of circuits:

In recent years there are a number of very inexpensive radios - mostly with Chinese names - that have appeared on the market in the sub-$100 price range - some $50 or below - and the question arises:  Are these suitable of direction-finding?

The quick answer is "possibly not."

Many of these radios use an "all-in-one" receiver chip which has several issues:
  • These radios tend to overload very easily in the presence of strong signals.  If one is very close to the transmitter being sought they can do strange things such as experiencing phase shifts.  If one is attempting to use one of these radios with an "Offset Mixer" (a different article...) then it can simply become impossible!
  • Many of these radios also have an audio filter that kicks in when the signal is weak and noisy that cannot be disabled.  This low-pass filter - which is apparent when the hiss or audio suddenly sounds somewhat muffled - causes a different audio delay.  While this will likely have little effect with the simplest TDOA circuit where one is simply listening to a tone, it will likely "break" fancier ones that provide left-right indications.
If you have one of these inexpensive radios and can't seem to make the circuit work, try a different radio - preferably one from one of the mainstream amateur radio brands - during your troubleshooting!


In the next part - to be posted some time in the future - we'll talk about how one might implement what we have learned about the circuits, above, in software.

Monday, October 24, 2016

On the winding of power chokes and transformers: Part 1 - A power choke

There is a follow-up to this post linked here that discusses the design and building of a filament transformer.

There are projects that homebrewers undertake that seem not to make sense when one considers the amount of time that it takes to do that thing - but then again, this is often the case when one builds projects at home, from "scratch".  The case in point for this discussion is the winding of power transformers and chokes.

Figure 1:
The finished choke with a rating of about 50 Henries at
200 milliamps, described below.
Click on the image for a larger version.
I am not an expert in the design and build of power transformers and coils so what follows is, among other things, the documentation of the learning experience:  No doubt I will make mistakes along the way, but analysis of these mistakes and observations will (hopefully) be enlightening.

Why?

For some reason I have decided to go "old school" and, along with a friend (Bryan, W7CBM) we will each construct a two-channel single-ended triode audio amplifier using some old WWII vintage tubes (the details on this amplifier to be detailed in a later post.)  To be clear, I'm not of the sort that really believes that the "tube sound" is best for various intangible reasons - in fact, I'm expecting that if it works better than expected, its performance will be worse than practically any other modern audio amplifier that I have in the ways that matter to most people (e.g. power efficiency, noise, hum, distortion, frequency flatness, phase - just name it!)

As it is often the case with a project like this, practicality is somewhat irrelevant:  It is the experience of doing something that you have never done before - and learning from it - that will be the reward whether or not the project is ultimately successful.  To be sure there will not likely be a cost savings in doing this and there certainly will not a time savings!

Diving into this project we decided to do something that I'd not done for many years:  Wind my own power transformers and chokes.  As for the audio output transformers for this audio project we decided to forgo that task and get "store bought", proven transformers given our current level of experience.

Where to find useful information:

Interestingly, scant useful and credible information seems to be available on the GoogleWeb on this topic, but two sources that are useful are:
  1. Turner Audio (link) - These pages contain much practical advice on power and audio transformers and chokes.  (Refer to the link "Power Transformers and Chokes" (link) and related pages linked from that page.)
  2. Figure 2:
    The NZ-1 "Hand Shake" winder (e.g. "hand cranked") winding
    machine, before it was mounted to a firm base.
    Click on the image for a larger version.
  3. Homo-Ludens - Practical transformer winding (link) - While mostly about power transformers, this page also contain practical advice based on hands-on experience of winding, re-winding and reverse-engineering/rebuilding transformers.  There is also another linked page "Transformers and Coils" (link) that has additional information on this topic.

A few other bits and pieces of information have been found but the above two seem to be some of the best, both written by people who have years of practical experience - and the pages include additional references to other sources.

Rummaging through some old amateur radio and electronics books I have been able to divine other details as well, but much of this information is rather generic and doesn't speak much about the use and capabilities of modern types of wire, insulation or core materials.


Getting the gear together:

Figure 3:
 A simple wire spool holder made from pieces of "1x2"
(actually 0.75" x 1.5")  poplar.  While it works, the variable
feed rate of the wire due to winding it onto a square bobbin
can cause the momentum of the supply spool's rotation to
occasionally "overspool" some wire.  I hope to (soon) 
add additional wire features (e.g. guides, wire-unspool
prevention, etc.) to prevent the wire from getting
tangled as it is unreeled during winding.
Click on the image for a larger version.
Before laying a large number of turns on a transformer bobbin, one must have a minimum of gear on-hand.  Starting out with nothing, I decided to buy an inexpensive ($40, delivered) Chinese-made "NZ-1 Hand Shake" (probably a mistranslation of "Hand Crank") coil winding machine (seen in Figure 2) via EvilBay.

Made mostly from cast steel, this device is about as simple as it can get:  It has some gears that provide an 8:1 ratio for the hand crank (e.g. one revolution of the crank = 8 turns on the coil), a 5-digit turns counter (0-99999) and a spindle on which one would mount the bobbin, and it seems to be built "well enough" for the purpose, likely to last many hundreds of thousands of revolutions.  This device has no wire-handling capability (e.g. nothing to hold the spool, guide the wire or provide tension) so those pieces would have to be constructed and/or improvised.

Figure 4:
 A simple bobbin holder made from scraps of "1x2"
poplar wood and paneling.  The left and middle pieces
are pinned to each other using finishing nails and
are clamped together when mounted on the winder.
"Face identification" marks allow one to keep track
and note the configuration of the wires and the visible
screw on the middle block - and its mate on the back-
side - allow wires attached to the various windings
to be kept out of the way.  To the right, in the background,
are two blocks that are used to help compress the
windings onto the bobbin as they bulge out when
many layers are added.
Click on the image for a larger version.

After the NZ-1 arrived I bolted it to a block of wood and for wire handling of the supply spool I made the simple wooden "A" frame holder seen in Figure 3, placing it on the workbench behind the winding machine. 

By default, the crank is connected to a lower shaft that, via gears, results in eight turns on the coil with one turn of the crank. For practical reasons, winding a core like this needs a bit more precision and control and a 1:1 ratio is desired and the obvious place to relocate the crank is the upper shaft with the pulley, visible in Figure 2 on the upper-right corner of the winding machine.

While the shaft size is the same, attaching the crank at this point caused the crank's handle to hit the lower shaft to which the crank is usually connected!  Fortunately I could attach the crank to the very end of the shaft and have it just barely clear the lower shaft where the crank would normally be attached for the 8:1 ratio:  At some point I'll have made a metal piece made that will extend the shaft by a half inch (approximately 1cm) or so.

Also very important is the bobbin holder shown in Figure 4 constructed from scraps of paneling and "1x2" pieces of poplar.  Because the core size is "E150" - which stands for 1.50 inches, two pieces 1x2 wood (which are really 0.75"x1.5" or approximately 19x38mm) fit very nicely within the bobbin.  Glued to the end of the bobbin holder on one side is a scrap of paneling as an end-stop while on the other side, oriented by two finishing nails used as pins, are two more pieces of 1x2 glued together as the "other" end stop.  Both the bobbin and the removable end stop are marked to provide a means of orienting the four faces of the bobbin and the removable piece also sports two screws around which wires that are brought out from the bobbin may be wound to keep them out of the way.

Two more blocks of wood, cut to the internal length of the bobbin, are also available to compress the "bulge" with a clamp that inevitably forms as wire is wound.  Through the center of the bobbin holder was drilled a hole of the size appropriate to allow it to be slipped over the shaft of the winding machine.  When mounted on the  the bobbin holder is held in by compression of the nut and it does not easily turn on its own.

While not the most elegant of solutions, this arrangement seems to work - provided that one takes care to prevent "overfeeding" of the wire and subsequent possible tangling of off-spooled wire caused by the inconsistent feed rate as one winds onto a square bobbin and the supply wire occasionally tries to wind itself around the piece of "allthread" on which the spool hangs!

The most important aspects of this (minimal) arrangement are:
  1. A means of automatically counting the turns laid down.  While inductors are somewhat less critical in terms of keeping track of turns with absolute accuracy, when winding transformers you do not want to lose count at all!
  2. The bobbin itself being mounted on a stable, rotating platform about its winding axis.
  3. Being able to manually gauge the tension and guide the wire into the bobbin.
While it would have been pretty easy to make a simple 1:1 gear ratio winding machine from parts laying about, the $40 price for the NZ-1 was hard to beat!
The goal:

Because a choke is "simpler" to wind than a transformer, I decided to start with that.

The design goal of the choke was to provide at least 10 Henries of inductance with a current capacity of at least 200mA.  The general rule of thumb for a modest-sized transformer or choke is to size the wire to 0.3 to 0.4 mm2 per amp (from references 1 and 2, above) which would imply that for 200mA the minimum wire would need a cross-sectional area of around 0.06mm2 which corresponds to #29 AWG.

Now we need to figure out (approximately) how many turns can fit on our bobbin.

The E150 bobbin that I would be using has an inside dimension of 41.5mm on a side and an outside dimension of 75.4mm on a side with a "width" of 53.3mm and based on this we calculate that the area of the bobbin's window is approximately 53mm wide and 17mm high, or about 901mm2.

Because the cross sectional area of #29 AWG wire, based on a 0.33mm diameter with insulation, is 0.086mm2 this implies that we could theoretically put around 10477 pieces of wire (or turns) in this 109mm2 space.  Practically speaking, this is simply not possible since there is always going to be some "wastage" based on the fact that we will be laying round wires next to each other and there will be gaps in between.  Typically, one would scale this calculation by a "fill factor" to accommodate such wastage with this factor typically being around 0.4 (e.g. 4191 turns) or as high as 0.5 (5239 turns) if one winds extremely carefully and neatly - and assuming no added insulation:  Less careful winding can easily result in "fill factors" lower than 0.4.

Breaking this down differently we can calculate that across the width of the bobbin we should (theoretically) be able to put (53mm/0.33mm = 161) turns on each layer, but taking into account the practicalities of being able to get wire to lie snugly next to its neighbor we can more reasonably expect to achieve around 95% of this for wire of this rather small size, - about 153 turns per layer, maybe slightly more if we are fastidious.

Since our bobbin window is 17mm "tall" we could theoretically expect to be able to stack 51 layers of 0.33 thick wire, but this also assumes both "perfect" stacking efficiency and the lack of any inter-layer insulation.  If we presume that each layer contains a 0.33mm thickness of wire and 0.05mm thickness of insulation - a total of 0.38mm - we can then recalculate that it would take about (17/0.38) 44 layers of windings to fill the bobbin - again, assuming perfect stacking and no need for additional insulation.

For practical reasons we would want to fill our bobbin to only 70-90% "fullness" in order to be able to add the final covering insulation and connecting wires, so this would take our maximum down to between 30 and 39 layers - again, assuming that we didn't need extra insulation anywhere.

If we take an average of 153 turns per layer we could reasonably expect be able to put between 4590 and 5957 turns on this bobbin.  Taking a median per-turn length of wire on the bobbin to be around 234 mm based on the size of the bobbin itself we can estimate that we'll need between 1074 and 1394 meters, or between 28 and 37% of our 5 pound spool.

Comment:
At this point in the design I should have referred more closely to link #1, above, to determine the amount of inductance that the calculated number of turns would yield in a typical situation.  To do this, I would have wound a known number of turns onto the bobbin and assembled the coil into a core and made inductance measurements so that the permeability - particularly that when an air gap was added (more on that later) - could be measured, but instead I simply bulldozed ahead and started winding turns!  What this means is that I probably would have wound a coil with fewer turns and, possibly, heavier-gauge wire.

Starting the wind:

With the necessary parts (bobbins and core material being "E150" size from Edcor, the wire and polyimide insulating tape from other sources) I began to wind a choke - the simplest of the devices and (hopefully) hardest to screw up!

Figure 5:
The start of the wind with the ending wire (orange) having been insulated and
secured with polyimide (a.k.a. "Kapton" (tm)) tape.  Note how the end wire
is secured to screws on the wooden bobbin holder to keep it out of the way.
Click on the image for a larger version.
The first step in the wind was to drill a hole in the bobbin through which one of the external connecting wires would be attached.  Carefully scraping - to avoid nicking and weakening the copper - tinning, twisting and then soldering the start of the coil's wire (29 AWG) to the heavier lead that emerged from the bobbin, I insulated it with several layers of polyimide tape, secured it in place on the bobbin, laid down another insulating layer of tape on the bobbin itself and began to wind.

The general advice on winding transformers seems to be that it is best to assure that all wires are laid side-by-side on nice, even layers.  By doing this one avoids one turn from crossing another and putting tremendous point-pressure on the insulation of the two wires as they cross.  This advice hales from the days when wire was insulated with simple, comparatively fragile varnish that could be easily penetrated from vibration due to hum and thermally-related movement and by its softening at higher temperatures.

According to the Turner Audio web pages (reference #1) modern wire, with much more durable insulation, it is permissible to wind chokes that allow wires to cross at shallow angles, saving the need for expending time and effort on assuring a very consistent parallel lay of wire on the bobbin.

Meanwhile, on the Homo Ludens web page (reference #2) he makes note that if the wire is of good quality and that one keeps to a very shallow angle of crossing - that is, slowly moving across the face of the bobbin as several layers "neatly" build up - and avoiding excess wire tension that even with transformers it is acceptable to forgo the painstaking "side by side" winding, provided that one insulate insulate each "layer" of 2-3 wire thicknesses before starting across the face of the bobbin in the other direction.  All of this assumes that one has enough room on the bobbin to accommodate the reduced "packing efficiency" of this method and will be satisfied with being able to fit fewer turns.

Both authors allude to having seen rather poor transformers that seem to haphazardly throw wire onto bobbins with the author of the Turner Audio pages being particularly critical of the methods that he'd observed on badly-built transformers.

No matter who you believe there are several things in common between these two sources of advice:
  • Use good quality wire:  NEVER re-use wire from another transformer as it will likely have nicks and scratches in its insulation.  Modern, high-temperature wire (e.g. that rated for 200C) is more likely to handle a little bit of abuse.
  • When wires are crossed, a very shallow angle is necessary.  This automatically rules out any "scramble wound" (a.k.a. "random wound") windings which can cross at sharper angles.
  • While one can apply fairly significant tension when laying wires side-by-side with each layer being individually insulated, more care should be taken to avoid excess tension when doing the "not as neat" method of winding where wires can lay atop each other:  They should still be tight enough to not easily move around and wear in each other with thermal cycling and the inevitable "buzzing" from magnetic fields, but not so tight that the insulation of one turn will eventually "bite through" to the turn underneath!
  • It is arguably more important that windings that are not carefully parallel-wound be immobilized with appropriate varnish - particularly on a transformer in which the windings are subject to constant vibration.
  • It would seem to be more "acceptable" to forgo the neat, side-by-side winding on very small tranformers - particularly when very fine wire is involved.  While I suspect that at least some of this is due to practicality (e.g. it is difficult to machine-wind very fine wire with a nice, neat side-by-side lay) but it may also be due to more carefully-controlled wire tension, that these are typically vacuum-impregnated with varnish and the fact that a smaller transformer is more likely to have a more consistent thermal profile through its volume, which is another way of saying that a small transformer has less opportunity to trap heat deep within the middle of some windings that it cannot dissipate.

Since this was my first large power choke I decided to take the "neat, even layer" approach for the most part, but what this meant was that during each and every turn I would have to watch exactly where the wire turn lay, often scrunching it close to its neighbor if it shifted away and "un-crossing" it if it happened to overlay another.  This also meant that after I finished winding every layer  of approximately 150-156 turns I had to stop, temporarily tape the source wire to the bobbin to keep in from unraveling, apply a layer of 2-mil (0.5mm) polyimide tape over the top of the layer and then resume winding.

As is the case with such things, it is a bit more difficult to do this than one might at first expect.  For the first several layers I had to contend with the "lump" and the "gap" at the "start" end of the bobbin where the external wire was attached and I did this by filling in the void with very thin strips of cardboard laid down to match the width and height of the heavier, connecting wire. After several layers, the layers equaled the height of this "lump" and with the matching thickness of the cardboard strips, it disappeared, allowing me to more easily wind across the entire width.

Figure 6: 
Pausing at the end of winding a layer, securing the end with a piece of
tape and small, plastic clamp to avoid wire damage.  Already one can see
ripples and uneven-ness starting to appear in the surface of the
winding - something that I had to continually correct as I continued on!
Click on the image for a larger version.


After a dozen or so layers the windings started to form "ripples" caused largely by the fact that the polyimide tape overlapped in approximately the same place each time - a problem exacerbated by the fact that I had, at the time, only one width of tape, limiting the degree to which I could "stagger" the overlap. The biggest problem with this was not necessarily asthetics, but the fact that the as the wire was wound it tended to slip into the trough of the ripple making it very difficult to maintain evenness and the nice, side-by-side wire lay for which I was striving - and with each layer, these irregularities grew!

What I had to do was to fold over some of the tape in half (sticky side facing outwards) to fill in some of the dips, and on the square outside "corners" between the faces of the bobbin I started to strategically add small bits of tape to level it out as it was there that the slippage was most likely to occur.  As I got into 10s of layers, some of the troughs seemed to resist the attempts at leveling so I carefully resorted to putting several turns of wire atop each other at shallow angles to help even the surface:  Only a tiny fraction of the turns were wound in this way.

The lesson here is to have on hand multiple widths of tape so that the overlaps may be staggered.  What would have also been handy would have been to have on-hand some thick (10 mil, 0.5mm) pieces of MNM ("Nomex" (tm)) insulating sheets to cut into strips to fill the voids.  It would have also been very help to have some tape that was exactly as wide as the bobbin, but such a specific width is not likely to be commercially available.

The results:

Figure 7: 
The winding of the bobbin is finally complete!
At this point the windings are covered with several layers of polyimide
tape with the soldered and insulated end of the coil captured
underneath.  The uneven-ness of the coil's surface can be seen, but
this degree was just manageable.
Click on the image for a larger version.
Finally, after 4905 turns and 33 layers, the bobbin had mostly filled up:  This number of turns and layers ended up being withioin the range that I'd calculated above.

Based on the DC resistance - around 277 ohms - this represents approximately 3384 feet (1031 meters) of wire - a bit more than a quarter of the 5 pound spool.  Carefully drilling another hole in the bobbin I attached the "finish" wire to the outside of the coil, insulated it and taped it securely into place.

By itself (no core) the inductance of the 4905 turns on the bobbin measured out at approximately 884 millihenries and when the core was installed - butt-stacked, but not carefully aligned - this increased to over 110 Henries:  If I had carefully interleaved all 109 E-I laminations and properly seated each piece this value would have likely been much higher!

Preventing core saturation:

Because this is intended to be used as part of a "choke input" high voltage power supply one must take into account the fact that DC current will flow through the choke, magnetizing the core material.  One property of practically any ferromagnetic material - including the steel used in the core of this choke - is that if the magnetic field exceeds a certain point, the core will saturate and the permeability (and the inductance) will drop.  While there are chokes that are designed to do this (e.g. "swinging" chokes - those that have inductance that, by design, drops with increased current) it was desired that this choke's inductance be more consistent over the current range.

The most common way to control this effect is to intentionally reduce the permeability of the core overall by the introduction of an air gap which breaks up the magnetic lines of force:  The larger the gap, the greater the reduction.  The trick here is to reduce the permeability - and thus the level of magnetization - to the level that the core does not saturate at the desired current, but not too much more.

Fortunately, there are some equations that help us calculate things like this.  Knowing that the core material that I am using ("M6" Grain-Oriented Silicon Steel) will operate at 1.6-1.7 Tesla (16000-17000 Gauss) and still be well below its 2+ Tesla saturation flux I could crunch some numbers based on what I already knew.

Taking the following equation from link #1 (the Turner audio web pages), above:

uE = (109 * ML * L) / (T2 * Afe)

Where:
  • uE = The permeability of the core
  • ML = Iron path length in mm (approx. the width plus length of a single assembled E-I section for a standard "economy" E-I core set.)
  • L = The measured inductance in Henries
  • T = Number of turns
  • Afe = The cross-sectional area of the core material inside the bobbin in mm2
Since I was using standard "economy" E150 cores with square bobbins, Afe = 382mm and ML = 209mm.

With the temporary butt-stacked arrangement (e.g. full of small gaps due to pieces not aligning perfectly) yielding approximately 110 Henries the calculated permeability was 525:  If I'd very carefully interleaved and stacked each lamination, I would have expected the permeability to be in the multi-thousand range!

Taking this into another equation, we can calculate the magnetic field strength using this equation, also from link #1:

Bdc = (12.6 * uE * T * Idc) / (ML * 10000)

Where:
  • Bdc = Magnetic field, in Tesla.
  • uE = The permeability of the core.
  • T = Number of turns.
  • Idc = DC current, in amps - the target being 0.2 amps for this design.
  • ML = Iron path length in mm, as above
Crunching the numbers, above, we find that Bdc is approximately 3.1 Tesla - a bit too high for our M6 material, so we need to add more gap than is present due to the haphazard stacking of the material.  All things being equal, since the magnetic field strength is proportional to permeability and since inductance is proportional to permeability, we now know that if we can add enough of a gap to reduce the inductance by approximately half we will be in the ballpark (e.g. a permeability around 225-260).

Figure 8:
The arrangement of the E-I laminations and the insertion of insulating
strips used to add an air gap to reduce the overall core permeability
and prevent core saturation.
In the middle and on the ends are single "E" sections that are interleaved
to help hold the other sections in place via compression when the screws
are installed and tightened.  As it is the most common type, the "E-I" core
segments used are of the "economy" type - that is, two "E" cores placed
facing each other will yield a pair if "I" cores from the material that is
punched out to make the "E"s, wasting the least amount of material.
Click on the image for a larger version.
Placing some 10 mil (.25mm) thick "fish" paper between the "E" and "I" pieces I observed that the inductance was now around 51 Henries which meant that the magnetic field was approximately 1.44 Tesla - within reasonable range of the M6 core material that I'm using.

After the original assembly of the core, I had to disassemble the choke's laminations again to mount the end bells as shown in Figure 1, above.  In the process I used a wooden block to more evenly seat the laminations:  Between this and cinching the screws tightly, the gap between the E and I sections was slightly reduced and the measured inductance went up to around 75 Henries - a bit too high to prevent saturation at 200 mA according to our previous calculations.  Adding a second piece of 10 mil insulating paper - for a total of 20 mils (0.5mm) of thickness (or 40 mils overall in the magnetic path) reduced the inductance to around 54 Henries as can be seen on the impedance bridge in Figure 9.

Final thoughts:

For the time being - and since this is a prototype - I'll leave the design alone, but it brings up some points for the next time that I might wind a similar choke:
  • Now that I have some actual, practical numbers for this particular core material and the effects of gapping, I should be able to predict ahead of time with reasonable accuracy the outcome of a particular winding configuration.  Using a different core (size, material) I would be certain to do a "test winding" to divine its aspects prior to finalization of the design.
  • 51-54 Henries is a bit higher than is typically used for a power supply choke, providing an inductive reactance of around 38-40k Ohms at 120 Hz, the AC ripple frequency for full-wave rectified 60 Hz mains.  (It would be about 32-34k for 100 Hz on 50 Hz mains.)  In general, the higher the inductance, the better - provided care is taken to avoid resonances related to the filter capacitance and the load.  The higher inductance will reduce the ripple - particularly important for single-ended triode amplifiers.
  • The self-capacitance of a choke of this inductance is likely to be significant.  While likely not much of a factor at the mains-related frequencies (100 and 120 Hz) it would likely be an issue for so-called "parafeed" tube-type amplifiers (e.g. those that use the inductance for decoupling the plate from the power supply and audio is extracted from a transformer effectively in parallel with this choke, typically via capacitive coupling) where this reactance could quash high frequency audio components unless the design were modified accordingly.
  • The design goal of the choke was to handle at least 200mA.  With a DC resistance of 277 ohms approximately 55 volts will be lost across the choke due to this resistance at the design current, implying a heat load of approximately 11 watts (resistive only and not including core losses) - an acceptable amount for a core this size.  The voltage drop - while higher than desired - can be simply accepted and/or taken into account when designing and building the high-voltage plate transformer and associated supply.
  • A more conventional inductance for a choke-input power supply is in the area of 3-10 Henries, so this design is likely an overkill - but then again, reducing the ripple on the power supply of a single-ended triode amplifier is not a bad thing! 
Were I to have more carefully measured the "typical" permeability of the core in its various configurations and gap sizes with a small number of turns I would have had a better "feel" as to its characteristics and cut the number of turns in half.  In so doing I would have (theoretically) ended up with about one quarter of the inductance - around 12-13 Henries - and half of the resistive loss.

Based on the equations, if I did that I could also have decreased the size of the gap to increase the overall permeability and, again, boost the inductance without fear of saturating the core which could permit a further reduction in the number of turns and winding loss.

Figure 9:
The completed choke (upper right) being measured on my old General Radio GR-1650A impedance bridge.
The measured inductance is approximately 54 Henries with a Q of approximately 4.1 at a frequency
of 1 kHz.  By the time I was able to take the picture, the inductance had drifted very slightly due to
change in temperature, moving the meter's needle away from a good null.
Click on the image for a larger version.

Doing this would allow the use of a slightly heavier gauge of wire to be used on the same-sized bobbin to further decrease ohmic losses and increase current-handling capacity.  In short, I suspect that something in the range of 1600-2000 turns of 27 AWG and a reduced air gap would yield something fairly close to a 10 Henry inductor with significantly reduced DC resistance (e.g. in the range of 55-75 ohms) with the current rating being restricted by the desired minimum inductance rather than the heat dissipated due to Ohmic losses.

At some point on the near-ish future, another such inductor will be wound but we have yet to determine the form it will take:  Will it be as neatly wound as this, or will it be done so that the wires are allowed to cross at shallow angles.  Will it have about as many turns as this choke or will it use a heavier conductor with fewer turns for less - but adequate - inductance?

Stay tuned!

Note:  There is a follow-up to this post linked here that discusses the design and building of a filament transformer.

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