Small Signal Transformers

[Earthscum]

A recent thread inquiring about diodes for a rectifier octave up circuit got me thinking... the only thing I understand about the impedance is, in the case of a 1k:8R transformer
a 1k load on the primary side translates to an 8 ohm  load on the secondary, and vice versa.

I can't really find a thread about small signal transformers, such as the ones Steve sells:

http://www.smallbearelec.com/Detail.bok?no=342
http://www.smallbearelec.com/Detail.bok?no=341
http://www.smallbearelec.com/Detail.bok?no=599
http://www.smallbearelec.com/Detail.bok?no=745

to list the more common ones.

Anyone wanna take the time and discuss these? Particularly in the instances they are used in stompboxes.

For example, does the impedance of different SST's affect the forward voltage of different diodes? (I'm sure load has some hand in it)

I've seen them used in signal splitters, DI's, octave ups, mini-amps, plus I've seen a couple used in some odd ways (filtering comes to mind, right along with pickup simulations).

Just getting idea starters. I've only seen a few discussions going in the middle of other threads about these, so why not just make an all-in-one resource thread?  

[R.G.]

OK, let's play transformers.

General understanding first. Transformers are voltage and current seesaws. They don't have impedances, they have ratios.

1. Transformers are passive devices. The power out is equal to the power in minus losses. Always. Mother Nature said.
2. They have ratios. The ratio can be 1:1 (for an isolation-only device), 10:1, 1:20, or anything else you want them to be (or buy them for). That ratio is expressed three different ways. For AC power transformers, it's expressed as a voltage ratio, as in 120Vac to 60Vac. They tell you the voltages, but what that really means is that the ratio is 120:60, or 2:1. This transformer will put out 1/2 the AC voltage you put in (neglecting the secondary effects mentioned later).

But Rule 1 says the power out is equal to the power in minus losses. Neglecting losses, that 120:60 transformer can put out twice the current that the input takes in, because 1*120 = 2*60. The current ratio is the inverse of the voltage ratio because the powers have to match.

You can express the identically same thing by quoting an impedance ratio. The primary of a 120:60Vac power transformer converts 120 vac to 60Vac - or 12Vac to 6Vac, same thing as far as the ratios go. What's the impedance ratio? It is the square of the voltage (or current) ratio. There is math that demonstrates it, but most people go to sleep when looking at algebra, so I won't do the math, just the result. The voltage ratio for our "mule" transformer is 2:1. It's impedance ratio is then 4:1.

What that means is that if you put a 1K load resistor on the secondary, and then try to measure the resistance between the primary wires [using AC means, inside the frequency passband, etc, etc.] you get the answer of 4K. The same 120Vac:60Vac transformer that has a 2:1 voltage ratio has a 1:2 current ratio and a 4:1 impedance ratio. Same, equivalent statements. All the same thing.

A 1K:8 impedance transformer is a 1000/8 = 125:1 impedance ratio transformer, and a SQRT(125) = 11.18:1 voltage ratio transformer.

All transformers can be run with either winding as primary or secondary, within the limits of the secondary effects to be discussed below.

[R.G.]

Secondary effects
Ideal transformers are imaginary perfect devices. Mother Nature does not allow ideal things to exist except in our minds. We can think of real transformers as ideal transformers with some carefully selected imperfections surrounding the ideal core. These imperfections let us model what real transformers do to any degree of accuracy that we need to work to.

Imperfection 1: Primary inductance
Transformers are magnetic field devices, so there's going to be inductance involved. If you hook up a transformer secondary to an open circuit  then the infinite resistance is reflected to the primary as an infinite resistance times the impedance ratio. Infinity times any ratio is infinity, so the primary impedance reflected from the secondary is infinite - or, in other words, the secondary is not playing in this game. All you have is a winding and a core - an inductor.  This inductance is always in parallel with what the secondary sends it in real transformers. It's called the primary inductance, and it's the fundamental limitation on low frequency response in real transformers.

An inductor has an impedance all on its own. It is linearly proportional to frequency, so at high frequencies it ... chokes... off any current flow. At low frequencies, it goes to zero. In fact at DC, an inductor does not impede current flow at all, and the current through an inductor at DC is limited only by the wire resistance, which is another imperfection we'll get to in a while.

So there's an inductor in parallel with the primary inside the transformer where we can't get at it very well. The primary current caused by this inductor is easy to calculate: it's Iac = Vac/Xl where Xl is the inductor impedance, and that is in turn Xl = 2*pi*f*L.

So a transformer with no load has a primary current in the primary inductance that increases as frequency goes down. With power transformers, at a single frequency, it's easy to calculate the magnetizing current - that being the current that flows because of the primary inductance. It's just the Iac shown above. Magnetizing current is the price that Mother Nature demands for Her letting tranformers work. It is what "charges up" the M-field in the core and makes power transfer across the isolated windings possible.

It is only in combination with a real secondary load that the low frequency response limitation of the primary inductance comes out. If there is primary inductance of L and a reflected secondary load of R, then when the frequency is high, the inductor impedance is high and almost all the current flows through the R. When it's low, almost all the current is "shorted" by the low impedance of the L. In the middle, when Xl = R, the current goes half to the reflected load impedance R and half to the inductor impedance Xl = 2*pi*f*L.

The low frequency response of the transformer is when these two are equal or Xl = R = 2*pi*f*L , or f = R/(2*pi*L). It is possible to compute the primary inductance if you know the low frequency rolloff for the transformer.

[R.G.]

Imperfection 2: Wire resistance
Since real transformers are wound with real wire that has a low, but measurable resistance, it only stands to reason that the windings have a resistance. Just picking a common example, wire gauge #35 has a resistance of 1079 ohms per 1000 feet, or roughly 1milliohm per foot. Wire cross section doubles or halves with each 3 wire sizes, so #38 wire has a resistance of 2milliohm/ft, and #32 is 0.5 milliohm/ft.

Small transformer primaries have a lot of turns to give the necessary primary inductance with such a small size, and small-diameter wire to fit in the small window. So it should come as no surprise that they have high winding resistances. A primary wound with 400 turns of #38 wire with an average turn length of 1.5" per turn gives 400*1.5" = 600 inches = 50 feet, and that is 50 times 2 milliohms or 100 milliohms, a tenth of an ohm. The secondary will also have a resistance. The finer the wire and the more turns, the higher the resistance of the wire.

For the small transformers under discussion, the makers generally specify the primary resistance and the secondary resistance. For instance, the Xicon 42TL013, with a 1K:8 ohm impedance ratio has stated resistances of 60 ohms primary and 1 ohm secondary. If you used your DC ohmmeter on the primary of this transformer, it should measure close to 60 ohms.

Resistance is always a power loser. It always eats electricity, turning it into heat and voltage loss. Wire resistance means that there is the equivalent of a resistor in series with the primary of a transformer and the secondary, and that it's equal to the measurable resistance of the copper wires inside. Whenever current flows through the windings, these resistance exact their losses no matter what we do. And they're inside the transformer where we can't get at them.

So we model them to let us predict what real transformers will do. Inside every real transformer there is an ideal transformer doing the actual voltage/current/impedance transformation. This is hidden behind the primary inductance, Mother Nature's fee for setting up the necessary magnetic field, and the winding resistances, Mother Nature's surcharge for actually flowing current through.

The wire resistances subtract off a voltage of Iprimary*Rprimary from the voltage from the outside world before voltage can get to the ideal primary inside. If there is no secondary load (Rload = infinity) then the current that flows is just the current to the primary inductance, which sets up the M-field. When a current flows in the secondary, the secondary wire eats a part of the secondary voltage equal to Isecondary * Rsecondary, and the primary resistance also eats a voltage on the primary side equal to I primary * Rprimary.

I have, in a sneaky way, been leading you to the standard model for an electronic transformer. It starts with the ideal transformer which has only a volt/current/impedance ratio and no losses; hence, infinite frequency response.  Then we add the inevitable, inescapable losses. Primary inductance is one of these; it lets current flow into the primary when there is no load on the secondary. Wire resistance is another. It eats up some of the input power going into the transformer, and also some of the voltage coming out of the secondary.

So the standard model looks like a "T". The leg of the T is an ideal Vpri to Vsec transformer, but paralleled on the primary side by the primary inductance. There is a resistor in series with the primary side going in of Rpri and on the secondary side of Rsec going to the load. The bottom of the T is connected to an ideal "ground" which lets return currents flow.

[Earthscum]

Very cool. I'm surprised, I actually knew more than I thought about transformers, but I just never put it all together. The Imperfection 1 is definitely full of new stuff. Thanks much. I'm still digesting  this at the moment.

So, to use an example for a question:
The 600R:600R, we'll say, is listed as a Telephone Line Isolation device. On the packaging, it lists a frequency range of 300Hz-3kHz. At 300Hz, the core begins to saturate, the signal at primary windings get closer to DC and loses energy to transfer to the secondary winding, and as the signal gets lower in frequency, less and less gets transferred. Correct? Then, at the other end, as the signal gets higher in frequency, the signal gets dampened again by what? Is this the rate of change of the magnetic field, how fast it can collapse and rebuild? Or is thes determined more by mother nature's limits?

Also, I've seen mention of it... how do the manufacturers come up with the figures? I'm sure there's a "testing condition", x amount of load, x amount of current. Is that figure kind of like relying on car manufacturer's listed HP ratings in the 70's?

[R.G.]

Very cool. I'm surprised, I actually knew more than I thought about transformers, but I just never put it all together. The Imperfection 1 is definitely full of new stuff. Thanks much. I'm still digesting  this at the moment.

Keep chewing.  Eventually it'll start tasting better.

So, to use an example for a question:
The 600R:600R, we'll say, is listed as a Telephone Line Isolation device. On the packaging, it lists a frequency range of 300Hz-3kHz. At 300Hz, the core begins to saturate, the signal at primary windings get closer to DC and loses energy to transfer to the secondary winding, and as the signal gets lower in frequency, less and less gets transferred. Correct?

Pretty close. Actually those are inequalities, not equations, and I'll explain those a bit lower down. Also, there are two competing effects, one linear and one nonlinear. The primary inductor has some impedance, so it sucks down a current equal to Vac/Xl. The only way this is different from a resistor is that Xl goes down with decreasing frequency.  If the transformer has a -6db response at 300Hz (it's better than that, but probably about all the maker will guarantee) then 300Hz is the frequency where Xl = 2*pi*F*L is equal to the resistive load from the secondary, which in this case is 600 ohms (nominally). So we can calculate this like an R-C filter, which is what it is. In this example, 2*pi*F*L = 600, so L must be 600/(2*pi*F) = 0.318H . Actually, the maker swears (in the datasheet) that it's at least that good, so L > 0.318H. They may have specified the loss at only 1db at 300Hz, or 0.1db; both of these are just a different power ratio, and can lead to other minimum values of minimum inductance to get down to the specified frequency of 300Hz.

The nonlinear one is saturation. For R-L filtering type of low frequency response, the R and L make a the frequency response fall off even if the inductor is nowhere near saturation. By stating response is linear (i.e. a maximum distortion specification) the maker has in a very backwards way said "the transformer is at least X volt-seconds away from saturation at 300Hz, 600 ohm, 600mW." The maker is pretty much stuck with it not being too close to saturation at the low frequency spec. Power transformers typically get closer to saturation than audio transformers do, because distortion rises rapidly near saturation. But as the voltage at 300Hz or whatever the lowest frequency is, rises, there comes a point where you start entering saturation.

Entering saturation means that so much force has been applied to the magnetic materials in the core that no more magnetic domains can be aligned, and so any further increase of the M-field in the volume of space inside the core material can only be done at a rate supported by the M-field change of free space. It is the change in M-field that transfers through the core to the secondary winding, and since the changes are now thousands of times less for each additional bit of primary voltage, to the secondary it looks like the primary is less coupled to it by several thousand times. Effectively, voltage stops being transferred across to the secondary. It's a clipping mechanism. (I know what you just thought and we'll get to it in a minute.  )

The secondary quits getting more voltage transferred, but the primary inductance can no longer help current from the signal source be opposed by inductive reactance. In power transformers, the AC power line current is limited by the inductance of the primary, and with this dramatically reduced, current gets hugely bigger, sometimes leading to the destruction of the transformer if not otherwise limited. In signal transformers, the signal source usually can't supply that much current, so the secondary just gets limited and distorted.

You were thinking "Oh, wow! A cool new clipper mechanism!" Yes, but it only happens at a specific volt*time. You can only clip the lowest frequencies. Bummer. Not useful in effects, at least not simply.

The transformer maker guarantees you that saturation will be far enough away that it won't have more than X% distortion at the lowest guaranteed frequency. But at some lower frequency, it will start saturating. This is why I could use an opamp to extend the low frequency response of these transformers. It's OK to use an amplifier to simply goose in more current as long as the tranformer doesn't over heat and as long as it doesn't saturate. There is a lower frequency limit that you usually don't hit. At least not too badly.

Then, at the other end, as the signal gets higher in frequency, the signal gets dampened again by what? Is this the rate of change of the magnetic field, how fast it can collapse and rebuild? Or is thes determined more by mother nature's limits?

Imperfections 3 and 4: leakage inductance and self capacitance. More on those later.

Also, I've seen mention of it... how do the manufacturers come up with the figures? I'm sure there's a "testing condition", x amount of load, x amount of current. Is that figure kind of like relying on car manufacturer's listed HP ratings in the 70's?

Yep. Lies, d@mned lies, and datasheets. Most of it is by design. The designer has to design a real part that will meet the specification limits set for him by his bosses and their evil-minion MBA pets. He/she is told that he has to design something that will have no worse loss than -6db (or -1, or whatever) at 300Hz at 500mW of power across, and do it so that > 97% of all production parts will pass that test, and do it so it can be sold for only $0.23. And be made by demented gorillas with simple hand tools in the Bolivian highlands.

The trafo designer uses the tricks of computing how much inductance, how much wire, how much iron, what kind of interleaving/layering, etc. give the frequency response, and is incredibly cheap and simple to build. If  he/she does too well, he gets a bad performance rating for not backing down on the materials so it could be made more cheaply. If he doesn't do well enough, he gets a bad performance rating for not meeting targets. If it's perfect, he gets to do two more designs by the end of next week. And gets laid off in a downsizing in a month.

There is a wealth of incredibly useful, pertinent information hidden by the datasheet specifications. Datasheets are *advertising* with a legal hook hidden inside. They are there to convince equipment designers to buy them. They are full of engineer-p0rn to catch the wandering eyes of EEs; E-GAD but dc to daylight is s3xy!
But the maker can be legally required to produce what they say in datasheets, so they are really, really motivated to not say too much, even if it happens to be true.

[arawn]

wow that is a lot to digest, but thanks R.G. I feel ever so smarter now 

[Tony Forestiere]

Yep. Lies, d@mned lies, and datasheets. Most of it is by design. The designer has to design a real part that will meet the specification limits set for him by his bosses and their evil-minion MBA pets. He/she is told that he has to design something that will have no worse loss than -6db (or -1, or whatever) at 300Hz at 500mW of power across, and do it so that > 97% of all production parts will pass that test, and do it so it can be sold for only $0.23. And be made by demented gorillas with simple hand tools in the Bolivian highlands.

The trafo designer uses the tricks of computing how much inductance, how much wire, how much iron, what kind of interleaving/layering, etc. give the frequency response, and is incredibly cheap and simple to build. If  he/she does too well, he gets a bad performance rating for not backing down on the materials so it could be made more cheaply. If he doesn't do well enough, he gets a bad performance rating for not meeting targets. If it's perfect, he gets to do two more designs by the end of next week. And gets laid off in a downsizing in a month.

The truth was never spoken so plainly. Great article(s).

Gentlemen: I submit to you that we have witnessed the birth of "The Technology of the Transformer". 

[brett]

Thanks RG. Really good stuff.
As you say, DC resistance and self inductance get in the way of using transformers as pure ratio devices. I've found that half to double the quoted ratio is a useful range for most applications. e.g. a 1k:8 ohm is good anywhere from 500:4 to 2k:16, without affecting the total impedance or frequency response too much. At low ratios DC resistance really starts to change the ratio and reduce efficiency.
Again, thanks.

[R.G.]

Imperfection 3: Leakage inductance
Magnetic fields *want* to be inside ferromagnetic materials if they can get there. Relative permeability is a measure of how many times more the field wants to be inside the ferromagnetic materials. For fairly ordinary iron and alloys, this multiple is about 10,000 or a bit more. It can get as high as many tens of thousands of times in special materials.

But magnetic fields also like to spread out. So no matter how good the core of a transformer is, how hard it sucks field into itself, some of the field that the primary establishes works its way outside the iron and outside the regions where it can link to the secondary. This leaked magnetic field depends almost totally on the physical layout and construction of the coils and core.

Leaked magnetic field best resembles a separate air-core inductor in series with the primary of a transformer.  The leakage inductance can be measured for any transformer shorting the/a secondary, then measuring the inductance on the primary leads. Shorting a secondary reflects a load to the primary by the impedance ratio. The value is the value of the secondary winding resistance and secondary leakage, and these appear in series with the primary wire resistance and primary leakage inductance. In general, the primary inductance is much larger than the leakages, so ignoring it causes no noticeable errors for quick calculations.

An inductor in series with the primary, which is how this looks and acts, has a profound effect on the high frequency response of a transformer. For most of them, it is the most important determiner of the high frequency response. An inductor (choke!) in series with the reflected secondary load literally chokes off the current flow to the load, because the impedance of the leakage inductor increases linearly with frequency. Again, when it reaches the point where its value is equal to the secondary load, the output from the secondary is 6db down. The inductor's impedance is large enough to keep half the voltage from reaching the load by voltage divider action.

The study of how to get good high frequency audio response in transformers is largely a study of how to reduce leakage inductance. Winding self capacitance does play in the response a bit, but it's a minor contributor compared to leakage inductance. Since leakage is largely controlled by the physical setup of the windings, it can be reduced by special winding tricks. the further apart the primary and secondary windings are, the more space there is for flux to leak out of. So reducing leakage is largely a matter of interspersing a bit of primary, a bit of secondary, more primary, more secondary. Sometimes every alternating layer is switched from primary to secondary.

The worst possible situation for leakage is to wind the primary and secondary side by side on the center tongue of the transformer. Second worst is to wind all of the secondary (or primary) on the bottom, then all of the primary (or vice versa, secondary) on top of it. Leakage is lowered by winding primary and secondary as nearly over one another in one long, skinny layer as possible.

That's a toroid. Toroids have the ultimate long, skinny layers. Another way that's good is to interleave primary and secondary layers.

The best possible way to wind a transformer for lowest leakage is to wind one primary and one secondary wire side by side, so they are as physically intermixed as it's possible to get and still have electrical isolation by the wire resistance. Of course, by doing this bifilar (side by side) winding, you are limiting the transformer ratio to 1:1. Multifilar winding lets you have simple whole-number ratios by winding three, five, six, or more wires at a time, then putting each wire together to make a series/parallel setup for more flexibility in ratio. However, as you could guess, it's very labor intensive to get this right, and very hard to get the 25:1 ratios typical of tube amp output transformers. It also maximizes capacitive leakage from primary to secondary, so there is a competing effect.

For the small transformers that were the subject of this thread, the high frequency response is typically much, much better than the data sheet says. I measured a half-power point on a 300-3Khz unit at one time at 28kHz, not 3 kHz. This is one place where smallness helps - leakage is made worse by large physical size. This is why it gets harder and harder to get good high frequency response in higher power tube amps.

As a practical matter, most small transformers have better high frequency response than they promise, but you can't count on that if you are manufacturing with them, not doing a one-off.

I haven't done as much calculation on this imperfection as the earlier ones. Leakage is the primary contributor, it's fixed by the winding techniques, and there is not much you can do about it unless you are rewinding the transformer.

[WhenBoredomPeaks]

Can i get some extra distortion/harmonics from these small transistors if i drive them with a clean booster and then attenuate the volume with a vol pot after them?

I have a TM018 and a TM022 and i thought about driving them with a SHO but i thought i might ask before soldering.

edit: i don't try to get loads of fuzz out of the transformer, i just want to try out new kinds of clipping instead of diode stuff.

[R.G.]

As a practical matter, no. Quoting myself,

You were thinking "Oh, wow! A cool new clipper mechanism!" Yes, but it only happens at a specific volt*time. You can only clip the lowest frequencies. Bummer. Not useful in effects, at least not simply.

The transformer itself does do a nice, smooth clipping that's primarily third harmonic. But it happens at a steadily increasing input voltage level as frequency goes up. Double the frequency (that is, one octave up) and the level needed to make it distort is two times as big.

One thing that might happen is that the imperfect loading might make the driving circuit distort, and the transformer would obediently transform that. But it would be the sound of the overloaded driver, and there are other and easier to use ways to get that.

[PRR]

> The worst possible situation for leakage is to wind the primary and secondary side by side on the center tongue of the transformer.

There is a worser case. Small _power_ transformers are often wound on a square-O core, two legs, with all primary on one leg and all secondary on other leg. Two bobbins not even touching.

That gives MUCH better hi-pot numbers in safety testing.

While an EI side-by-side non-audio PT will often pass audio well-enough to 5KHz (and sometimes higher), this two-bobbin winding will be falling by 500Hz. CJ once posted measurements on an unidentified "audio" transformer, and I spotted it as a Signal 2-4-1 filament transformer which it happens I had used a lot for utility (yet high-clarity) audio.

> Multifilar winding ... very labor intensive

Also not good insulation. With modern varnishes it can stand hundreds of volts, IF the varnish is done well, but nothing like a layer of tape between windings.

> made by demented gorillas with simple hand tools in the Bolivian highlands.

Foot tools too. Doubles production.

But Bolivia? That's a long ocean away from where gorillas hang.

[PRR]

> I measured a half-power point on a 300-3Khz unit

"300-3KHz telco" is a special case. The "entire signal" is defined to lay between 300 and 3KHz. They don't care what happens outside. They DO usually demand "very flat" within the 300-3KHz range, because a full analog telco system will have many-many 300-3KHz bandpasses from one end to the other. Inside the main system, much less than 1db flatness; but we never go in there. End-points such as consumer supplied modems and answering machines have relaxed specs (there's only one or two customer modems in the line) but still "flatter" than hi-fi makers traditionally defined audio response.

In a simple system, the -3db point lays an octave beyond the -1db point.

The phone system usually works "semi-matched". There is significant source impedance most points on a line. When you can re-specify to have a power amplifier right AT the transformer (within a few ohms), you get into the low-impedance drive condition. For iron-core audio this may be 5-10 times better bass than nominally matched drive. I believe you have reported 60Hz from a "300Hz" part? What happens here, typically, is the very-small-signal response runs low, but anything larger than very-small distorts.

That's "300-3KHz telco" stuff. Anything else, is either weasel-truth or darned lies.

> smallness helps - leakage is made worse by large physical size. This is why it gets harder and harder to get good high frequency response in higher power tube amps.

Size, not really. Yes, as you go into dozens of kilowatts it gets tough. OTOH as you get below 0.01W (and far over $10) you can use the better core materials (MuMetal), less turns to get your bass, less stray L and C.

The "tube amp" problem is impedance. Leakage inductance tends (for a given interleave) to be proportional to main inductance. Both rise with intended impedance. At low impedances the bandwith is constant for 1 ohm or 1K ohms. OTOH stray capacitance does not change much with inductance (yes, more about size). The stray L and the stray C will resonate. For impedances over 5K-10K, this tends to be in the audio band and tends to be poorly damped. Here's where the heavy-thinking is needed. However 1-1K windings can usually be slung together any old way and cover the audio band to reasonable flatness. (OTOOH there are W.E. 150:150 repeater transfos with 8-layer interleave for very-very-flat response 300-3KC so that 10 can couple a 300-mile line and still be 1db flat.)

[R.G.]

> The worst possible situation for leakage is to wind the primary and secondary side by side on the center tongue of the transformer.
There is a worser case. Small _power_ transformers are often wound on a square-O core, two legs, with all primary on one leg and all secondary on other leg. Two bobbins not even touching. 

My experience failed me. I've never run into one of those. The versions I've seen have a split bobbin on each side with a vertical divider in the bobbin; this is the PCB mount "flat pack" style. You're right - primary on one leg and secondary on another would be worse. I suppose rod core and air core would be even worse than that. 

For a *very* leaky power transformer, I understand that there was a case where a farmer was able to pick up usable (somehow - ) power from his fence which paralleled the overhead high power transmission lines. But I've never seen the particulars on that one.

> Multifilar winding ... very labor intensive
Also not good insulation. With modern varnishes it can stand hundreds of volts, IF the varnish is done well, but nothing like a layer of tape between windings.

Yep. Safety specifications consider wire varnish to not exist as far as safety insulation goes.

> made by demented gorillas with simple hand tools in the Bolivian highlands.
Foot tools too. Doubles production.
But Bolivia? That's a long ocean away from where gorillas hang.

Foot tools?  I like the way you think. But the gorillas aren't native, of course. They were brought in as guest workers by the native monkeys who were much smarter. The natives are getting rich contracting out the real labor and investing their excess bananas in more factory space.

Hmmm. Did you ever hear of a "banana equivalent" radiation dose?

[Earthscum]

You're right - primary on one leg and secondary on another would be worse. I suppose rod core and air core would be even worse than that. 

For a *very* leaky power transformer, I understand that there was a case where a farmer was able to pick up usable (somehow - ) power from his fence which paralleled the overhead high power transmission lines. But I've never seen the particulars on that one.

A side note of interest, in the mid 1800's there was a solar storm that made it possible to use telegraph without adding power to the system, in much the same way:

From: http://solar.physics.montana.edu/press/WashPost/Horizon/196l-031099-idx.html

Humanity began feeling the effects of the solar maximum as soon as technology became sophisticated enough to respond. During the late 1800s, vast networks of wires were strung to carry telegraph and telephone traffic, setting the stage for a giant-scale reenactment of one of history's most famous physics experiments.

English physicist Michael Faraday discovered in his lab that, if you take a magnet and move it near a loop of wire, electrical current flows in the wire. The moving field induced a corresponding motion of charge in the wire. Faraday's "magnetic induction" soon was put to use in the first electric generator.

Exactly the same thing happened when solar storms triggered changes in Earth's magnetism, affecting thousands of miles of telegraph wires. Electrical currents induced by the changing fields often were so powerful that telegraphers didn't need battery power to send their information. Some operators were even treated to near-electrocution!

Placing wires under the ocean made no difference. In the Atlantic cable between Scotland and Newfoundland, 2,600-volt surges were recorded during a magnetic storm in March 1940. Short-wave broadcasts often were blocked for hours, and "technical difficulties" were expected and even jokingly tolerated.

Some effects of solar storms were far beyond the nuisance level, especially at higher latitudes. In August 1972, a 230,000-volt transformer at the British Columbia Hydroelectric Authority blew up when shifting magnetic fields induced a current spike. On March 13, 1989, a storm plunged Quebec into a complete power blackout, affecting millions.

[PRR]

> a split bobbin on each side with a vertical divider in the bobbin; this is the PCB mount "flat pack" style.

You may be right about a single bobbin molding. And I have seen them wound halt-pri half-sec on each leg. But I got some with the entire primary on one leg, entire sec on the other. Worked great 50Hz-100Hz, and good-enough to 500Hz (perhaps fair power transfer at 400Hz?), then 6db/oct underload. (Hi-Z load was better, showing it was all stray inductance.)

Pulling sneak-power from large distribution lines is old stuff. Rarely useful.

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Spark-coils are different. They slam from one extreme to the other.

And in particular: for 6V or 500V coils a little paper will stop sparks. At 40,000V we need MUCH more insulation. In a closed core we'd have sparks from the coil to the outer legs. OK, make the core more open window area. But that increases magnetic path, the core does less good. We make the core fatter, and fatter yet to maintain insulating space. In days of impure tars and half-raw rubber, it was just simpler to use rod-core. It's better than air-core, and cheaper than a huge closed core.

Some modern spark-coils appear to be closed-core. Some work good. But beware the older Miata! (The coils work fine, but there's only two coils for four plugs, so one leaky wire gives 2-cyl power with 4-cyl drag.)