Characteristics of Guitar Amplifier Output Transformers, and criteria for design

[Malcolm Irving]

... Also, making practical sense of BH curves in the context of voltage/current/frequency conditions. …

In the B - H curve, H is proportional to magnetising current and 'rate of change of ' B is proportional to primary voltage.
For a sine wave, the 'rate of change' is just another sine wave (but advanced by 90 degrees, i.e. a quarter of the wave period).

In a PT, for example, the primary and secondary voltages are close to sine waves, but the B-H curve means the current into the primary is distorted. The primary inductance (also called the magnetizing inductance) is a non-linear inductance (due to B-H).

The B-H curve shows the non-linearity and hysteresis between primary voltage and magnetizing current.

The frequency of the signal is how many times 'we travel around' the B-H loop per second.

I hope some of this is helpful and I apologise if I am 'teaching my grandmother to suck eggs'.

[Helmholtz]

That means I require a primary inductance of around 81.5H rated for min 25W. (Ideally)

Lp values this high are quite realistic in guitar amplifier OTs. But only around rated output power and at low frequenies (max. ac flux). I measured Lp of around 40 different OTs at 650Vpp and 50Hz and found Lp to lie between 60H and over 300H. But when measuring with an LCR meter @ 1kHz, the values were lower by a factor of 5 to over 10. (The reason for the different values is that the LCR meter measures at very low flux amplitudes where the ac ĩ is close to the initial permeability. The ac ĩ rises strongly with flux amplitude up to the onset of saturation.)

The results seem to indicate that the major design concern was to avoid excessive power loss from high magnetizing current at max. output, while the bass response at low output power may suffer. Of course NFB can take care of this.

[R.G.]

In transformer design, everything depends on everything else, so getting an optimal transformer is an exercise in optimizing many things at once. Accordingly, with so many ways to make things better in some sense, there are many ways to look at the transformer and its drive and loading. I mention this not least because Malcolm has presented some views that are correct. Here are some other views that strike me from your questions.

For instance, primary inductance is an important factor in audio transformers, where it is of no real design consideration in power transformers?

That particular question is answered in my mind as a question of objectives. Primary inductance is still a big deal in power transformers, but it's hidden behind other factors that are quoted. For PTs, the "bass response" is more subtle. You know the frequency response needed going into the design, so that's not the issue. The issue is how much of the incoming AC current leaks through that primary inductance, and correspondingly primary inductance is manipulated to get a "goodness factor" measured in dollars.

A power transformer will be fed a single frequency at a relatively fixed size for 100% of its life. A better primary inductance "bass response" means that the amount of electricity that unavoidably leaks across the primary winding as a result of the primary inductance impeding it. The primary inductance spec is tied up in the "magnetizing current" or "efficiency" specifications. Big primary inductances make magnetizing current smaller, and to the PT customer, that makes the dollars spent on electricity over the lifetime of the trannie lower. It also makes the transformer run cooler (in concert with several other factors), so primary inductance still matters, it's just hidden as a specification.

It would still be good if the primary inductance was huge, but huge costs money in terms of iron, copper, and labor.

Interestingly (to me anyway) is that primary inductance being too small in power transformers is what got line frequency wall warts made illegal. The unavoidable primary current leakage got noticed by the protectors of the planet in California. Wall warts that stay plugged in all the time "spend" this electricity all the time, and the multiplication exercise of X zillions of wall warts at Y milliwatts each, times Z hours plugged in came up to "Oh my &deity. we have to stop that!" and they legislated that no wall wart could have a no load current bigger than "too small to be a line frequency transformer", and also got the EPA to issue the same regs for the country. This had the effect of making only switching power supplies be legal. And so the world was saved from primary inductance.

PTs are all about power transfer (duuuh...) so their specs get wrapped up in volts, amps, phase angle and power loss terms. Fidelity is of little concern, so the funniness of BH curve bending and minor BH loops gets ignored, where it can't be for output trannies. Primary inductance and even leakage inductance gets hidden in the power specs.

The inductance needs to increase with loading impedance on the driving signal. This seems to indicate a relationship between inductance and magnetizing current?

Absolutely correct. Primary inductance is always across the driving signal and must be energized before any signal gets to the secondary. It's a price that has to be paid. To minimize magnetizing current, you maximize inductance.

More subtly, you minimize the area of the BH loop in the core. Transformer designers work with a chart of flux density (B) versus magnetomotive force (H). The more closely the graph of B versus H approaches a straight (and vertical!) line, the better the material is. The slope of the BH graph at any point is proportional to the primary inductance at that flux density, so higher slope is better. Real materials do not retrace the same path on the BH curve going up and coming down, making each cycle of signal be an odd, squashed-S loop. The area inside the loop is representative of the energy wasted per cycle in iron losses.

And put another way, the inductance varies at different levels of flux density. Yes, that means that an OT has distortion all on its own, due to the nonlinearity of the iron's magnetization. The more the iron "eats" of your signal (i.e. the lower the magnetizing inductance), the more the iron distorts your carefully prepared audio.

Also, making practical sense of BH curves in the context of voltage/current/frequency conditions. For instance, is there risk of saturation at low signal levels in high permeability cores?

I already got into that a bit. A BH curve is just a plot of how much magnetic flux density (magnetic field intensity) exists per unit of MMF. Flux density used to be measured in (maginary) field lines per square foot/inch/yard/etc. Now it's measured in Teslas, after the guy who had the nerve to read a newspaper inside a lighting generation machine. Whatever the units, it's still magnetic field intensity. MMF is measured in Oersteds, after a guy I don't have a good anecdote for at the moment. It's units are abstract as well, but it's proportional to ampere-turns, and so designers universally think of H as ampere turns times some funny constant to make the units come out right.

There is no concept of frequency in the BH chart. Iron has no frequency, and BH charts are ways of making statements about the magnetic material. Frequency gets into the whole picture because you have to drive the iron to a certain amount of ampere-turns to get a certain flux density, and how fast you can get there depends on how hard you can drive the primary inductance (slope of the BH line). It's always V = L *di/dt, so how fast you can get to a certain I depends on how much voltage you can impress on the total number of turns around the iron. All this is external to the material itself, and BH curves are about the material.

And yes, there is some issue with saturation of high permeability materials with low signals, but as with all things magnetic, it happens a funny way. Ferromagnetism happens BECAUSE unpaired electon spin directions in the atoms of iron, nickel, and cobalt can be oriented by a magnetic field. This orientability is what lets an M field "flow" through ferromagnetic materials more easily than they flow through free space. When all the spins are in random directions inside the material as they are in virgin materials, making a few of them line up to follow a magnetic field is easy, so you get a lot of alignment for little energy input. That means, lots of field density for little MMF, so the BH slope is high and the inductance is high. As you get more and more of them aligned, it gets harder to get the NEXT atom's spin aligned because the easy ones to align are already in line. So you get incrementally less alignment and field strength per unit of MMF trying to align them., And the inductance is resultingly less. At some point, all of them are lined up, and with no more easy alignments to be made, the material is saturated, and any additional MMF can create B only at the rate it does it in free space. That's saturation.

Some special recipes for iron, nickel, cobalt, aluminum, copper, and other metals and elements can make it easier for alignment to happen than in a pure sample of the big three (iron, nickel and cobalt), and so there exist special alloys with higher incremental inductance as reflected by steeper slopes on their BH curves. This being the real universe, there is no free lunch and you have to pay for this with lower saturation flux density, higher losses in terms of bigger area inside the BH loop, or both. So yes, there are materials with insanely high per-unit inductability ( I just made that word up) but these often saturate at low flux densities, so you can have high inductance, but low saturation. Still depends on how many turns and how big a lump you're driving with signal, though.

2XEL84s with a p-p load impedance of 10k2 and a peak sine wave output of around 17.5W. But square wave output at full drive, i'm guessing +25W maybe? Let's account for alternate tuning and the rare bass player who may want to plug in and set the -3dB at 20Hz.
That means I require a primary inductance of around 81.5H rated for min 25W. (Ideally)
Now What? (lets make some big iron)

And this is where designing gets easier. You're designing for your own edification, so you can spend as much on iron and copper, and winding labor and insulating materials as you'd like. If your job is designing transformers, you get pay raises and promotions in return for making the next design return higher profit, not for making it pleasing.

[Jazz P Bass]

At a lecture, Oersted passed a compass over a current carrying wire.
The compass needle was deflected.
(What the heck was that!)

When the current in the wire was reversed, the compass needle also swung the other way.
(Holy, Moley!)

So the man is credited with the 'discovery' that a current carrying wire has a magnetic component,

In actual fact, to this day, no one knows exactly what he was trying to prove at that lecture.

[Malcolm Irving]

At a lecture, Oersted passed a compass over a current carrying wire.
The compass needle was deflected. …

Oersted having shown that electric current creates magnetism, Faraday had the idea 'well maybe magnetism should create electric current'. He put a large coil around a big permanent magnet, and measured current in the coil using a galvanometer. There was no current. But then he noticed that there was a current when he removed the coil from the magnet or replaced it on the magnet. Faradays law: induced voltage is proportional to 'rate of change of flux linkage'.

[Mick Bailey]

Design is one thing. Build is another - at least here in the UK. I was discussing transformer design with an amp builder who had done the design legwork and then went from factory to factory to get the things built. The best deal he got was to meet the minimum order of 10,000 stampings for each lamination type. The amps that used the transformers had a short run so he's left with lots of stock.

Even when I've approached companies to build short runs of replica transformers they've directed me to current standardized sizes using off-the peg components, as anything custom is way too expensive for the small numbers involved.

[SoulFetish]

Primary inductance is in parallel with the load reflected from the secondary, so for an audio transformer the tubes supplying the OT have to provide current into that parallel inductance as well as into the proper load. At low audio frequencies, the reactance (2.pi.f.L) of the primary inductance is low and the extra current causes the primary voltage to drop (due to voltage drop across the output impedance of the tubes - if you like).
.

See, I knew I came to the right place. This makes complete sense. Thank you, this is a great exclamation!

[Gregg]

Even when I've approached companies to build short runs of replica transformers they've directed me to current standardized sizes using off-the peg components, as anything custom is way too expensive for the small numbers involved.

If you need a small run of something at maybe half UK prices (without quality loss) you should check some central and/or eastern EU countries where you can find small businesses that will accept small orders without any problems. Knowing a local also helps a lot.

[SoulFetish]

Now it's measured in Teslas, after the guy who had the nerve to read a newspaper inside a lighting generation machine.

R.G. c’mon man, I obviously know who Tesla is! I don’t remember the lightning thing though, I wasn’t at that show.
https://youtube.com/watch?v=9vwHuCC6nP8

[ric]

R.G. c’mon man, I obviously know who Tesla is! I don’t remember the lightning thing though, I wasn’t at that show.
https://youtube.com/watch?v=9vwHuCC6nP8

Well yeah, he's the guy building those cars and flying rockets.

What I don't get is which is the right OT ...Hammond 1609 or 1608?

From simple recipes to building your own induction cooktop and genetically engineering the ingredients, it's all here.

[Mick Bailey]

If you need a small run of something at maybe half UK prices (without quality loss) you should check some central and/or eastern EU countries where you can find small businesses that will accept small orders without any problems. Knowing a local also helps a lot.

I needed some gearbox parts for an old Harley and sent the worn ones to a machine shop in Poland to get them replicated. Heard nothing back for over 6 months and then a greasy parcel arrived. I was knocked out by the quality, finish and fit. Proper materials, properly hardened.

[SoulFetish]

So.... What's my next move? Choosing a core lamination grade and begin the process of sizing it out?
From what I've been reading, it seems that there are more than a few designers/builders of transformers who prefer to use non grain oriented steels for guitar OTs. (I understand that you'll find M6-M50 type lamination, with a variety of winding styles historically).
For instance, I know that Heyboer uses M50 for many OTs, and a few designers prefered M19. Any thoughts either way on this?

[Gregg]

Since you're asking about iron grade here's your first idea for experiments: wind a bobbin and use the same one with several types of iron to see (hear) the difference. Use a miked cab to capture the sound otherwise it will be all subjective due to ear fatigue as well. Also make sure the amp has the same settings at all times.
Finding laminations retail in quantities for single transformers is not easy though. Most of the time the manufacturer will sell them as 20-22kg stack from specific grade.
Over the years I've used M330 (0.5mm) and M6 (M165-35S according to DIN, EN 10107 - this is how it's known in Europe) grade iron and the results were quite good however I wasn't trying to replicate any specific transformer sound.

[J M Fahey]

Donīt overthink it

As Enzo says, these are guitar amps, not NASA Mars Mission Landers.

You must *really* strethc design limits and carefully balance conflicting requirements in Hi Fi transformers, and thatīs fine, not audiophoolery by any means, but on *Guitar* amps?
Why try to:
* lower distortion from 0.5% to 0.2% when tubes by temselves have 5 to 7% distortion ... when *clean* , and are usually clipped anyway?
Reach 50kHz so 20kHz response is still flat when Guitar speakers drop at 24dB/oct above 3500Hz?
And a speaker reaching 4500Hz (Italian Jensen) is deemed "unbearably nails-on-blackboard harsh/icepicky?"
* guitar lowest frequency is >80Hz and in many respected amps (Marshall) itīs attenuated below 160Hz?
Mind numbing below 700Hz or so in VOX amps.
* transformer self resonant peaks which in Hi Fi amps must be tamed and when present held >>25 kHz become not that important when considering speaker bandwidth.
* hard to achieve low phase shift to allow higher NFB without breaking into oscillation is not important in amps which either have relatively low NFB factor to begin with (Fender) , attenuate/kill higher frequency NFB (which is where problems appear), think Tweed and Marshall Presence control, or plain have NO NFB at all (VOX and many others).

An OT must be very horrible to damage Guitar sound ... and in many cases restricted bandwidth may be a bonus.

I wind my own, interleave a little within reason, from 1/2 Pri - Sec - 1/2 Pri to **at most** 4 primary sections interleaved with 3 Secondary ones, and that for Hi Fi amps, consider Marshall does 1/2 Pri in one continuous wind, 0-4 ohm winding , 1/4 Pri , 4-8-16 ohm winding (which has exact same number of turns as 4-8) , 1/4 Pri so itīs 5 sections in total.

Champ transformers are a joke ... on paper .... are wound for 200Hz minimum frequency ... not that bad considering the tiny light speakers usually fitted to them also fall like a brick below 200Hz, so ...

[SoulFetish]

I appreciate this, Juan. I know you know your way around iron, and this is practical advice.
I'm actually not interested in achieving the kind of fidelity required by hifi designs. But, in this particular case, I do want to design for (relatively) wide bandwidth, avoid saturating the core, and operate at full drive output without breaking a sweat.
As far as some of the classic amps you mentioned go, IMO they often were able to overcome some of their deficiencies and sound good, I don't necessarily think they sounded good because of them. (Although, I'm really surprised at the 700Hz figure for voxes. I wouldn't have guessed that.)
At the other end of the spectrum, I currently have a transformer which was made using M6/-1dB@20Hz to -1dB@20kHz/probably heavily interleaved. I'm not sure if I like this type of OT for a guitar amp... I'm not sure if I don't either. I would like something to compare it to. Something in between this and not close to a champ.