OT inductance and other calculations

[GainFreak]

Hi,

These days I'm diving into some OT calculations and I have several questions.
Let's take a simplified formula for calculating the required OT inductance at certain low frequency at -3dB. It goes like L=Ra/2*pi*f where Ra is the primary reflected impedance and f the low cut off frequency. For example if we go for a 100 Watt OT with 2k primary impedance and cut at 50Hz below the required L will be 2000/6.28*50=6,4H.
Questions:
1/ At what signal level and what frequency can you measure that to make sure you hit the goal? I have a DMM with inductance measuring and all 100 Watt OTs I measured so far fall into the 3,5-4,5H range. The measuring signal of DMM is 1V at 100Hz. If we assume higher cutoff frequency the measurements will fall pretty much into that range.
However very often one can see inductance figures measured at 120 or 240V AC which are in the 20-70H range and higher.
2/ How do you get those figures and what can one make of them considering they vary for different 100W OTs. For example let's take 2 Hammond guitar OTs where those figures are provided:
Fender Twin/Showman replacement
http://www.hammondmfg.com/pdf/EDB1760W.pdf
Marshall JCM900 replacement
http://www.hammondmfg.com/pdf/EDB1750X.pdf

Both are specified at 70Hz-15kHz, however inductances are different. The first one is 21.22H the second 50.93H, both measured at 240V, 50Hz considering the second one has larger iron core. Also the primary DCRs are very low which either indicated lower number of turns or thick wire.
I did some calculation and simulations according to which the primary wire would be somewhere into the 0,35-0,45mm range (less the enamel), otherwise it's not possible to get the DCR so low.
It's well known that detailed data about well known guitar OTs like interleaving, wire size etc are very scarce. From what I could gather from the net it looks like there are 2 types of 100W OTs. Let's call them A/ Mesa type and B/ Marshall type.
A/ has around 1600 pri turns (0,25-0,3mm wire, less enamel) and 74 sec turns B/ has around 1200 pri (0,35-0,4mm, wire, less enamel) and 54-58 sec both for the 4 Ohm tap.
After some more calculations and simulations it turns out that no calculation ever would produce 1600 turns of primary at those low cutoff frequencies and iron sizes. Usually you get 1000-1200 turns. The only way you can get 1600 turns of primary is when you design a 50W HiFi specs transformer. Actually Mesa iron sizes and interleaving indicate just that. It's well known that both OT types will produce more than enough low frequency content so what's the deal here? The only advantage I see in using a 50W HiFi specs OT is Mesa likes "mismatched operation" by switching 2 tubes off for 50W where a higher inductance OT (which is in the 7-9H range for small signals) would provide adequate loading for two tubes.
Secondaries' wire thicknesses also vary between 0,6mm and 1,3mm (in parallel or single) so I'm somewhat confused about how manufacturers decide what type of OT to use or they're just using similar iron to what they had by hand when they first started building amps and it's well known that it wasn't always of good quality although (or because) it contributed to the tone they are known for.

[J M Fahey]

Congratulations on getting interested that deep

1) To begin with, [trust the Math] (tm)

2) to be fully understood, plain values by themselves may not tell the full picture, it's important to know under what conditions they were measured and are intended to be used.

Let's take a simplified formula for calculating the required OT inductance at certain low frequency at -3dB. It goes like L=Ra/2*pi*f where Ra is the primary reflected impedance and f the low cut off frequency. For example if we go for a 100 Watt OT with 2k primary impedance and cut at 50Hz below the required L will be 2000/6.28*50=6,4H.
Questions:
1/ At what signal level and what frequency can you measure that to make sure you hit the goal? I have a DMM with inductance measuring and all 100 Watt OTs I measured so far fall into the 3,5-4,5H range.

Trust your Math.
Clearly they are not flat down to 50 Hz.
Recalculate and post the actual cutoff frequency.
That said, if 80Hz or less, we don't have a problem.

The measuring signal of DMM is 1V at 100Hz. If we assume higher cutoff frequency the measurements will fall pretty much into that range.
However very often one can see inductance figures measured at 120 or 240V AC which are in the 20-70H range and higher.
2/ How do you get those figures and what can one make of them considering they vary for different 100W OTs.

What I did, long ago, considering I was a poor student with more enthusiasm than funds or Lab Equipment (besides a Central 200H needle multimeter, very popular in the late 60's), was to put the transformer primary in series with 220Vac, 50Hz (a.k.a. wall voltage) in series with a resistor so that it dropped 10 to 20Vac, easy to measure with my cheap voltmeter.

Current thus calculated was much lower than what transformer DC resistance would have allowed, so I could calculate inductance with reasonable precision (say, 20% ) which was more than enough.

For example let's take 2 Hammond guitar OTs where those figures are provided:
Fender Twin/Showman replacement
http://www.hammondmfg.com/pdf/EDB1760W.pdf
Marshall JCM900 replacement
http://www.hammondmfg.com/pdf/EDB1750X.pdf

Both are specified at 70Hz-15kHz, however inductances are different. The first one is 21.22H the second 50.93H, both measured at 240V, 50Hz considering the second one has larger iron core.

Probably a sophisticated version of what I did long ago, but basically the same principle.
Only problem is that it uses pure AC (wall voltage) while OTs can and do suffer DC because of power tube mismatch (remember Silverface Fenders, tweaked by Engineers, preferred to put a current balance pot instead of a simple bias setting one) .
A small DC component can be a great inductance killer.
Those Hammonds state huge inductance, and I believe them, I'd love toremeasure it with , say, 20 or 30mA imbalance.

Also the primary DCRs are very low which either indicated lower number of turns or thick wire.

Thick wire of course, those are good transformers.

I did some calculation and simulations according to which the primary wire would be somewhere into the 0,35-0,45mm range (less the enamel), otherwise it's not possible to get the DCR so low.

Pretty accurate, I thought you unwound and physically measured them with a caliper.

It's well known that detailed data about well known guitar OTs like interleaving, wire size etc are very scarce. From what I could gather from the net it looks like there are 2 types of 100W OTs. Let's call them A/ Mesa type and B/ Marshall type.
A/ has around 1600 pri turns (0,25-0,3mm wire, less enamel) and 74 sec turns B/ has around 1200 pri (0,35-0,4mm, wire, less enamel) and 54-58 sec both for the 4 Ohm tap.

Reasonable.
More turns means "mo' bass" but poor treble; less turns means sharper biting sound.
Exactly what both brands try to achieve.

After some more calculations and simulations it turns out that no calculation ever would produce 1600 turns of primary at those low cutoff frequencies and iron sizes. Usually you get 1000-1200 turns. The only way you can get 1600 turns of primary is when you design a 50W HiFi specs transformer.

Why not?
Both types search for different goals.
FWIW I MUCH prefer old Marshalls to any Mesa.

Actually Mesa iron sizes and interleaving indicate just that. It's well known that both OT types will produce more than enough low frequency content so what's the deal here? The only advantage I see in using a 50W HiFi specs OT is Mesa likes "mismatched operation" by switching 2 tubes off for 50W where a higher inductance OT (which is in the 7-9H range for small signals) would provide adequate loading for two tubes.

Maybe.
Since the very first model: Mark I , switching 2 tubes off without switching taps is not only tolerated but encouraged, both in the user manual and the schematic, go figure.

Secondaries' wire thicknesses also vary between 0,6mm and 1,3mm (in parallel or single) so I'm somewhat confused about how manufacturers decide what type of OT to use or they're just using similar iron to what they had by hand when they first started building amps and it's well known that it wasn't always of good quality although (or because) it contributed to the tone they are known for.

Regular manufacturers, specially in the old days, simply did not design transformers by themselves, but approach manufacturers with what the circuit demands, say "3800 ohms, 50W, 80/5000HYz range" and transformer manufacturers do the designing.
By the way, because of their experience and access to proper materials,not usually sold over the counter, having specialized Lab equipment, they are much more qualified than amp designers.

[Chuck H]

Like Juan said. Which is way more than I ever could on the matter. I've put myself in the hands of transformer winders, Heyboer specifically, with good results. I just told them what I wanted and they made it a reality to a successful end.

There is one other issue that Juan hinted to in a response. Once an OT is at it's limits, saturating, things will change. I can't say just how or whether this is a linear effect no matter the construction or specs. My experience has been that most any OT with the desired impedance and rating will be sufficient for a guitar amps limited frequency requirements and the real difference will be in how the OT behaves when pushed. I don't know that any finite study has ever been done in this area but it's likely the more important consideration WRT guitar amps.

[loudthud]

Quick question: Do you measure the inductance of a push pull transformer end to end of from the B+ wire to one end?

[Chuck H]

I'm going to guess from the CT to one end. But that's just a guess. I'm only posting it as a commitment so I have to or get to own it, right or wrong. More fun that way.

And what about the fact that there's two windings? Primary and secondary. Is the impedance at the secondary with load so low that meeting the required inductance requires less consideration.

[GainFreak]

Trust your Math.
Clearly they are not flat down to 50 Hz.
Recalculate and post the actual cutoff frequency.
That said, if 80Hz or less, we don't have a problem.

As I mentioned this was a simplified formula for the inductance at -3dB. For -1dB the inductance should be twice as big so If we take Hammond's specs for their OTs being 70Hz-15kHz at +/-1dB I guess 50Hz would be somewhere in the -3dB region.

...was to put the transformer primary in series with 220Vac, 50Hz (a.k.a. wall voltage) in series with a resistor so that it dropped 10 to 20Vac, easy to measure with my cheap voltmeter.

Can you please provide the formula you used to calculate that and resistor approx value?
Even after we measure the inductance that way I still don't understand what to make of this value. I've never seen any calculation method using it or it's just a curiosity number or something?

Pretty accurate, I thought you unwound and physically measured them with a caliper.

I did measure some but knowing some basic OT data and certain calculation methods it's possible to find out that as well.

More turns means "mo' bass" but poor treble;

Not necessarily. The way that Mesa OT is built it will certainly go above 20kHz. And the last thing you need in a Dual rectifier is more bass.

Why not?

It just wouldn't. If anyone calculation for a 100 watter assuming those iron sizes and low frequency cutoff would produce 1600 turns of primary please I must have somehow missed it and I tried quite a lot of them.

Once an OT is at it's limits, saturating, things will change.

Saturation is very unlikely to happen in real life at least most of the time unless we're talking some very poor designs and unusual operating conditions.

Quick question: Do you measure the inductance of a push pull transformer end to end of from the B+ wire to one end?

From end to end. Measuring from CT to both ends will produce 4 times lower numbers.

[Chuck H]

Saturation is very unlikely to happen in real life at least most of the time unless we're talking some very poor designs and unusual operating conditions.

Hmmm... I'll wait for others to chime in, but I was under the impression that "poor design" and OT saturation is part of the reason some vintage amps sound the way they do. The way we like them to. Obviously you wouldn't want this in something like a 100W high gain preamp design, but what about some of the old Silvertones and Gibsons.?.

From end to end. Measuring from CT to both ends will produce 4 times lower numbers.

I'm aware of the squaring of the figure but in a push/pull design (the only types that use a center tap) why should the inductance of the entire wind be the relevant figure when the tube is only conducting through half of it? I'm not throwing this up in your grill or anything, I'd like to learn why this should be.?.

[J M Fahey]

Quick question: Do you measure the inductance of a push pull transformer end to end of from the B+ wire to one end?

Don't know what Hammond and others do, but it's really the same.

Say a transformer is 4000 ohms plate to plate, then inductance is also measured end to end.

If now you measure plate to center tap, turns will be half, inductance will be 1/4 .... but impedance will also be 1/4 (1 kohm) so actual low frequency limit will be exactly the same.

I guess stated inductance is measured end to end, for the very good reason that impedance is also usually stated end to end (plate to plate) .

[jazbo8]

1/ At what signal level and what frequency can you measure that to make sure you hit the goal? I have a DMM with inductance measuring and all 100 Watt OTs I measured so far fall into the 3,5-4,5H range. The measuring signal of DMM is 1V at 100Hz. If we assume higher cutoff frequency the measurements will fall pretty much into that range.

The B-H curve of an iron core is non-linear, so the effective inductance would change for different excitation levels. Since your DMM only applies a small (1V) sine wave excitation voltage to the primary winding, your readings would be much lower than the specs. To get a more realistic reading, you can try connecting the primary winding to the AC mains (even better with a variac) with a 100R current limiting resistor, then use algebra and Ohm's Law to calculate the inductance.

[GainFreak]

...I was under the impression that "poor design" and OT saturation is part of the reason some vintage amps sound the way they do.

Core saturation is a nasty thing on the scope and to hear as well.

...your readings would be much lower than the specs

We should define "specs". The "spec" for the required primary inductance is given always by the formula above. Since inductance varies depending on the frequency and excitation level the Hammond "specs" are just the resulting inductance at that level and frequency. In the same time the low level measurement is pretty close if not the same considering that the real inductance of the OT is not exactly the same as the one given by the formula.