Hello all --
Searched around a bit on this subject and found several specific discussions but nothing more general in nature ... so ... I would like to pose this question to the gurus (engineers) ... I are not ah engineer
, but I am ready to try to understand the nuts and bolts of this thing .
What are the various scientific and 'shade tree' (if you will) methods for selecting an OT for a particular output section? I am interested in the various impedence, wattage, inductance, and frequency response considerations.
I ask because I have read various methods. For example, one can consult tube datasheets for the 'load resistance', but this is not the same thing as the OT impedence ... or is it? This 'load resistance' is also (obviously) not the same thing as the DCR of the OT ... right? What is the 'translation' method for these ''load resistance' specs?
What if I want to use some oddball tube that has no load resistance specified in the datasheet. I have heard various 'thumbnail' approaches like take 10% of the plate resistance. I am interested in all these "design for dummies' approaches people have successfully used.
I have also read of people finding 'optimal' impedences which must involve some math - I am interested in these methods too.
There also seems to be some tribal knowledge about improving high and low end response that involves the inductance or weight of the OT.
Please feel free to respond to all of any part of this subject. Thanks much for your time.
Searched around a bit on this subject and found several specific discussions but nothing more general in nature ... so ... I would like to pose this question to the gurus (engineers) ... I are not ah engineer
, but I am ready to try to understand the nuts and bolts of this thing .What are the various scientific and 'shade tree' (if you will) methods for selecting an OT for a particular output section? I am interested in the various impedence, wattage, inductance, and frequency response considerations.
I ask because I have read various methods
. For example, one can consult tube datasheets for the 'load resistance', but this is not the same thing as the OT impedence ... or is it? This 'load resistance' is also (obviously) not the same thing as the DCR of the OT ... right? What is the 'translation' method for these ''load resistance' specs?What if I want to use some oddball tube that has no load resistance specified in the datasheet. I have heard various 'thumbnail' approaches like take 10% of the plate resistance. I am interested in all these "design for dummies' approaches people have successfully used.
I have also read of people finding 'optimal' impedences which must involve some math - I am interested in these methods too.
There also seems to be some tribal knowledge about improving high and low end response that involves the inductance or weight of the OT.
Please feel free to respond to all of any part of this subject. Thanks much for your time.
I notice you have just posted. If I may kick off with a brief overview; others can quote the formulae or internet tutorial references.
1. The tube data recommendation for 'load resistance' is based on the optimum figure for the other conditions stated, which normally represent the popular use. Thus other conditions can exist where one or other parameter is optimised.
2. As for the transformer characteristics: One wants the transformer to 'transform', without its own characteristics being in the way. Now the impedance of an inductor decreases with frequency, thus there will be a low frequency where its own impedance will become small compared to the load. That is where it will start to attenuate those and lower frequencies. One wants the inductance high enough at the lowest frequency of interest not to start messing matters up. When one uses the ever-present -3dB concept, that is where the inductive impedance will be equal to the load resistance in parallel with the tube internal resistance (simply put).
Example (neglecting transformer wire resistance): One uses a 6,6K impedance (common for p.p. EL34s) and one desires a lowest frequency of 20 Hz. The tubes' internal resistance (say for UL) will be of the order of 8K.ohm. From the formula
Rl = 2.Pi.f.L
one finds the figure of 28,6 Hy. for primary inductance.
3. High frequency attenuation comes where the leakage inductance (i.e. the magnetism 'lost' because the primary and secondary do not couple perfectly), is sufficient to cause a 3dB drop in power output. This acts in series with the load and tube internal resistance (the latter being 14,6K.ohm = Re say). Now the highest frequency of interest is say 20kHz. With the same formula, one finds a value of 116 mHy.
Practical examples often extend these frequency limits because of other design factors. It is typical to find a p.p. EL34 output transformer of 70 Hy inductance and 16mHy leakage inductance.
4. High freuqency attenuation also occurs as a result of inter-winding capacitance - very often ignored! To calculate this accurately is difficult and depends on the winding tecnique, etc. Enough to say at this juncture that it does play a role; often the final result is best found by establishing these freuqencies in a practical hook-up and design from there.
5. These are the salient parameters. I did not include primary/secondary winding ratio; I am sure you know that. As important is naturally also to have a large enough transformer. Flux density for transformer cores for optimal use as power transformers are usually available from the core manufacturers. But for an output transformer of low distortion one might use only half of that figure, or whatever other guidance is apparent from the characteristics of the particular steel.
6. Types of core: The classic E-I type of core is well-known. But since its development grain-orientated steels are useful for giving lower distortion. In this case the transformer core is strip-wound to the particular dimensions and then sliced in two halves, later to be strapped together over the windings. Such cores are called C-cores, and provide superior transformers, also for power transformers, but at a cost penalty.
Lastly you would have seen toriod transformers. They are similar to C-cores, but not cut in half; the windings are put on by a special machine.
This very briefly and somewhat approximated. A complete guide to output transformers comes in "Radio Designer's Handbook" by F Langford-Smith (p. 206 - 233) (it is unfortunately out of print, but available on the internet). There are also PC design programmes. I am sure others will join in with more particulars and reading references.
1. The tube data recommendation for 'load resistance' is based on the optimum figure for the other conditions stated, which normally represent the popular use. Thus other conditions can exist where one or other parameter is optimised.
2. As for the transformer characteristics: One wants the transformer to 'transform', without its own characteristics being in the way. Now the impedance of an inductor decreases with frequency, thus there will be a low frequency where its own impedance will become small compared to the load. That is where it will start to attenuate those and lower frequencies. One wants the inductance high enough at the lowest frequency of interest not to start messing matters up. When one uses the ever-present -3dB concept, that is where the inductive impedance will be equal to the load resistance in parallel with the tube internal resistance (simply put).
Example (neglecting transformer wire resistance): One uses a 6,6K impedance (common for p.p. EL34s) and one desires a lowest frequency of 20 Hz. The tubes' internal resistance (say for UL) will be of the order of 8K.ohm. From the formula
Rl = 2.Pi.f.L
one finds the figure of 28,6 Hy. for primary inductance.
3. High frequency attenuation comes where the leakage inductance (i.e. the magnetism 'lost' because the primary and secondary do not couple perfectly), is sufficient to cause a 3dB drop in power output. This acts in series with the load and tube internal resistance (the latter being 14,6K.ohm = Re say). Now the highest frequency of interest is say 20kHz. With the same formula, one finds a value of 116 mHy.
Practical examples often extend these frequency limits because of other design factors. It is typical to find a p.p. EL34 output transformer of 70 Hy inductance and 16mHy leakage inductance.
4. High freuqency attenuation also occurs as a result of inter-winding capacitance - very often ignored! To calculate this accurately is difficult and depends on the winding tecnique, etc. Enough to say at this juncture that it does play a role; often the final result is best found by establishing these freuqencies in a practical hook-up and design from there.
5. These are the salient parameters. I did not include primary/secondary winding ratio; I am sure you know that. As important is naturally also to have a large enough transformer. Flux density for transformer cores for optimal use as power transformers are usually available from the core manufacturers. But for an output transformer of low distortion one might use only half of that figure, or whatever other guidance is apparent from the characteristics of the particular steel.
6. Types of core: The classic E-I type of core is well-known. But since its development grain-orientated steels are useful for giving lower distortion. In this case the transformer core is strip-wound to the particular dimensions and then sliced in two halves, later to be strapped together over the windings. Such cores are called C-cores, and provide superior transformers, also for power transformers, but at a cost penalty.
Lastly you would have seen toriod transformers. They are similar to C-cores, but not cut in half; the windings are put on by a special machine.
This very briefly and somewhat approximated. A complete guide to output transformers comes in "Radio Designer's Handbook" by F Langford-Smith (p. 206 - 233) (it is unfortunately out of print, but available on the internet). There are also PC design programmes. I am sure others will join in with more particulars and reading references.
Further:
I have not answered all of your questions. Many of those are involved with the specific circuit design, and requires background that you might best read up on the internet - any successful (tube) design is intimately involved with the output transformer inter alia.
One thing you asked about: No, the transformer 'impedances' have little to do with dc winding (wire) resistance. In fact one keeps the latter as low as possible because it constitutes a loss. To better understand what 'impedance' is is a story on its own - I am sure there internet references out there. Sorry not to quote; I do not have any titles at this time.
Hope all this helps.
I have not answered all of your questions. Many of those are involved with the specific circuit design, and requires background that you might best read up on the internet - any successful (tube) design is intimately involved with the output transformer inter alia.
One thing you asked about: No, the transformer 'impedances' have little to do with dc winding (wire) resistance. In fact one keeps the latter as low as possible because it constitutes a loss. To better understand what 'impedance' is is a story on its own - I am sure there internet references out there. Sorry not to quote; I do not have any titles at this time.
Hope all this helps.
To add to the transformer basic requirements information.
The inductance required is a complex number, combining both the "Load Line", or AC impedance with the DC Plate resistance. This parallel addition (1/load line + 1/ Rp) must then be added to the direct DC resistance of the transformer primary and the reflected DC resistance of the secondary. All of the tube information can be derived from the tube curves and application data. Just which application data to use is not always clear. Once a total tube and transformer impedance number has been developed, you should use 100 ohms as a primary DCR and 10% of the secondary impedance to derive a number for secondary DCR, as transformer modeling numbers, you derive the required inductance as shown above. This - 3dB down number is your lowest distortion point in the bass and does not reflect an inductance that you might find by using an LCR bridge measuring at 120 Hz and 1 volt as this condition is for a minimum excitation of the core. Instead this is a point on the attached PDF that corresponds to the total AC and DC flux load being applied to the primary of the transformer. To obtain a -0.5 dB frequency response you must multiply the -3 dB amount by 2.76, for -1 dB down multiply by 1.93. The formula for derived performance prediction of inductance can be found in the RDH vol. 4 at the top of page 245. You will find an M6 core perm chart on the preceding page, note that it is for maximum core performance and my curve is for nominal core performance, for all M grades.
In a general sense, if you have 450 volts DC and 30 ma DC across the primary, your maximum AC swing voltage will be 48% of that number X 0.707 for AC RMS voltage applied to the transformer primary, at maximum power. In an ideal situation this swing voltage would cause your peak point on the core permeability curve to be about 8 kilogauss for push pull (PP) and the same for single ended (SE). The problem with SE is that the DC flowing in the primary creates flux that is added to the AC flux for a total permeability and the DC flux provides the starting point. So, for SE you want the ampere turns to equal about 4 kilogauss and the AC signal flux to equal another 4 kilogauss. The reason for the 8 kilogauss peak point is the distortion caused within the window in each of the planar magnetic fields, created within the window for each core layer. Above 8 kilogauss (for all commercial M series iron core material) peak signal saturation, as opposed to RMS saturation, will begin to pinch the linear phase transform between windings and this will cause mid and high frequency distortion. Most commercial audio outputs do drive the peak point beyond this 8 kilogauss point, often out to 12 kilogauss or more based on the assumption that very few audio signals are going to cause a full power signal and that the speakers being driven are going to be distorting far more than the amp.
The entire design of an output transformer is a balancing act. If you use extreme perm core, like amorphous C core, you cannot make use of capacitive coupling or low dielectric constant insulating materials because the result is a Q peak in frequency. Hence you find primaries and secondaries wound side by side in these designs. This does limit the amount of internal gradient information that the transformer can maintain. These types of transformers measure very well, when built properly, are very clear with great dynamics and transients.
Using commercial core requires you to utilize capacitive coupling for all frequencies above 400 Hz in the M series, 3500 Hz for 48% nickle and 7000 Hz for 80% nickle. When properly built these types have superior performance in internal gradient information, are also very clear with very rich transient structures. They do not measure as well as the amorphous core units and have an overall "softer" presentation due to the slightly higher distortion they produce.
Both types will provide excellent musical reproduction, but you need to think about which will suit your particular taste.
Bud
The inductance required is a complex number, combining both the "Load Line", or AC impedance with the DC Plate resistance. This parallel addition (1/load line + 1/ Rp) must then be added to the direct DC resistance of the transformer primary and the reflected DC resistance of the secondary. All of the tube information can be derived from the tube curves and application data. Just which application data to use is not always clear. Once a total tube and transformer impedance number has been developed, you should use 100 ohms as a primary DCR and 10% of the secondary impedance to derive a number for secondary DCR, as transformer modeling numbers, you derive the required inductance as shown above. This - 3dB down number is your lowest distortion point in the bass and does not reflect an inductance that you might find by using an LCR bridge measuring at 120 Hz and 1 volt as this condition is for a minimum excitation of the core. Instead this is a point on the attached PDF that corresponds to the total AC and DC flux load being applied to the primary of the transformer. To obtain a -0.5 dB frequency response you must multiply the -3 dB amount by 2.76, for -1 dB down multiply by 1.93. The formula for derived performance prediction of inductance can be found in the RDH vol. 4 at the top of page 245. You will find an M6 core perm chart on the preceding page, note that it is for maximum core performance and my curve is for nominal core performance, for all M grades.
In a general sense, if you have 450 volts DC and 30 ma DC across the primary, your maximum AC swing voltage will be 48% of that number X 0.707 for AC RMS voltage applied to the transformer primary, at maximum power. In an ideal situation this swing voltage would cause your peak point on the core permeability curve to be about 8 kilogauss for push pull (PP) and the same for single ended (SE). The problem with SE is that the DC flowing in the primary creates flux that is added to the AC flux for a total permeability and the DC flux provides the starting point. So, for SE you want the ampere turns to equal about 4 kilogauss and the AC signal flux to equal another 4 kilogauss. The reason for the 8 kilogauss peak point is the distortion caused within the window in each of the planar magnetic fields, created within the window for each core layer. Above 8 kilogauss (for all commercial M series iron core material) peak signal saturation, as opposed to RMS saturation, will begin to pinch the linear phase transform between windings and this will cause mid and high frequency distortion. Most commercial audio outputs do drive the peak point beyond this 8 kilogauss point, often out to 12 kilogauss or more based on the assumption that very few audio signals are going to cause a full power signal and that the speakers being driven are going to be distorting far more than the amp.
The entire design of an output transformer is a balancing act. If you use extreme perm core, like amorphous C core, you cannot make use of capacitive coupling or low dielectric constant insulating materials because the result is a Q peak in frequency. Hence you find primaries and secondaries wound side by side in these designs. This does limit the amount of internal gradient information that the transformer can maintain. These types of transformers measure very well, when built properly, are very clear with great dynamics and transients.
Using commercial core requires you to utilize capacitive coupling for all frequencies above 400 Hz in the M series, 3500 Hz for 48% nickle and 7000 Hz for 80% nickle. When properly built these types have superior performance in internal gradient information, are also very clear with very rich transient structures. They do not measure as well as the amorphous core units and have an overall "softer" presentation due to the slightly higher distortion they produce.
Both types will provide excellent musical reproduction, but you need to think about which will suit your particular taste.
Bud
Bud,
You practically took the words out of my mouth!
Well, that is, if I understood anything about Transformers.
Transformers: Where the "Black Arts" and Science contend.
Best Regards,
TerryO
Well Terry, as you delve into this smokey space, keep in mind that the requirements for good power transformers are antithetical to those for good audio transformers. Not everyone who starts out to design, build and measure these beasts knows this at the beginning.
Other than that, jump in, not a very deep pool of black magic, at least until you get to the pointy hat grotto.....
Bud
Other than that, jump in, not a very deep pool of black magic, at least until you get to the pointy hat grotto.....
Bud
thx for the input --
For me Bud this info is very helpful -- had to read this about 10 times but it slowly is making more sense to me -- it will be a task to get on top of the math.
BTW - some kind soul posted the chapter of the RDH that you refer to here. For those following along, you can get it here (permeability chart and all):
http://www.gyraf.dk/schematics/RadioDesigners Handbook - Ch.5 - Transformers.pdf
Once again thanks.
For me Bud this info is very helpful -- had to read this about 10 times but it slowly is making more sense to me -- it will be a task to get on top of the math.
BTW - some kind soul posted the chapter of the RDH that you refer to here. For those following along, you can get it here (permeability chart and all):
http://www.gyraf.dk/schematics/RadioDesigners Handbook - Ch.5 - Transformers.pdf
Once again thanks.
perhaps 'art' is a better term than magic
the ancient greeks had a wonderful word for this 'techne" (teknay) ... there is the scientific theory and technology -- and then there is the artful application of it ... making xformers seems to be a great example of this idea.
but comon you other gurus -- don't be bashful here - there is this heavy stuff -- very interesting -- but many great amp makers do their thing without using any of this stuff -- lets hear how you do your black magic too!!!
the ancient greeks had a wonderful word for this 'techne" (teknay) ... there is the scientific theory and technology -- and then there is the artful application of it ... making xformers seems to be a great example of this idea.
but comon you other gurus -- don't be bashful here - there is this heavy stuff -- very interesting -- but many great amp makers do their thing without using any of this stuff -- lets hear how you do your black magic too!!!
Some background reading http://www.jensen-transformers.com/an/Audio Transformers Chapter.pdf
Boy and how true that is. I finally began letting the secondary turns / wire size for one layer, of 1/4 of the total required CMA (circular mils per Amp Moon) for the 4 ohm secondary wire, with CE 6500 rated narrower winding offsets from the primary (3mm), determine my basic construction layout. Doing this dropped the deviance to below 1% across a 100 pc run. Makes the OPT's a bit bigger than typical commercial size, but I am not out for large volumes, AT ALL. For DIY designs I relax even further from commercial standards and allow low DCR to drive the design layout.
Moon, I have only scratched the surface here. There are actually philosophical, musical concerns to take into account. And then there are production concerns, dielectric materials, matching coil and core permittivity, how much of a dielectric circuit to build into the coil and then we can talk about core...
Bud
the ancient greeks had a wonderful word for this 'techne" (teknay) ... there is the scientific theory and technology -- and then there is the artful application of it ... making xformers seems to be a great example of this idea.
but comon you other gurus -- don't be bashful here - there is this heavy stuff -- very interesting -- but many great amp makers do their thing without using any of this stuff -- lets hear how you do your black magic too!!!
While others are compiling their comments ...
Moonbird,
As a word of relief perhaps, I would caution against overly much dedication of this art business to something that is really quite normal science. In this business it is always wise to take a sober look at the science behind a product before giving a logical thing an aura of black magic or whatever. Yes, there is quite a wide field to cover before total control is achieved. One need to know quite a bit about power tubes and NFB stability theory (basics of which is found in the analyses of a mathematician called Nyquist), but the width of knowledge should not lead to confusion with complexity. In the end all will come together quite nicely, if one starts at the beginning and progresses step by step without skipping any.
You will realise that your initial questions (if not said so then) asked questions about both transformer design and tube technology. That is why I pleaded for some reading to be posted by those having such information (mine is mainly in books); it will save lengthy explanations here. Concerning the design of a p.p. output transformer not too much remains ... in the sense that one usually have certain parameters provided, and just have to fit them into the empty spaces.
See my next post somewhat later - I must unfortunately go off now.
Johan,
I have a friend that teaches electronics, that is about the sharpest guy I've ever met and he's a pure science guy. All electronics can be known through Applied Physics, etc., but he acknowledged that the exception is transformer design which seem to defy the normal rules and ends up depending on the experience and skill of the winder. It was like pulling teeth to get that out of him, but that was about two years ago, so maybe things have changed.
Do you have a spread sheet that will enable us to to plug in the values needed when the design has progressed to the point where one usually has "certain parameters provided, and just have to fit them into the empty spaces?"
The reason I ask is that it would be neat to show up the handful of transformer guys, like Bud, that have had us at their mercy all these years.
Best Regards,
TerryO
hello there Bud,
my new year's resolution for 2010 is to wind myself an OPT based on your guidelines, i have the z11 cores, i have bobbins, what i do not have at this time is time.....but will get there....as always i have the power transformers made....that one is eassy...
again many thanks for your tips...
my new year's resolution for 2010 is to wind myself an OPT based on your guidelines, i have the z11 cores, i have bobbins, what i do not have at this time is time.....but will get there....as always i have the power transformers made....that one is eassy...
again many thanks for your tips...
To continue
Again, with respect, I hope after this that would prove not to be quite the case. Skill of the winder: Yes, but only inasmuch as proper winding is concerned, not slapdash windings-pouring-over-the-side sort of thing.
Yes, www.dissident-audio.com/OPT_da/OPT_da-322.zip
A friend of mine has used this with success. I have not tried it, having used RDH (Radio Designer's Handbook) since before there were internet and pcs. That is then also what I will refer to below, finding it quite convenient. (To me the RDH procedure allows me a kind of 'overview', where if necessary I can more easily do back-engineering if required!)
Further I have been given by others:
www.turneraudio.com.au/output-trans-pp-calc being a complete calculated procedure.
... says the man with exemplary diplomacy, that I must put my typing finger where my mouth is!
But no - I am not here to 'show up' BudP or anybody else. Bud seems to know his stuff well, also being in the business professionally (see his profile). Only, Bud and I had two different approaches. I only noticed near the end of his first post that he was actually describing single-ended transformers (normally with air gap), which are quite specialised! With respect, I judged that it would be best to start with principles of the normal push-pull (p.p.) output transformer before advancing to specialities. It would show that reading wider about the principles of transformers would help the uninitiated to better understand, and that is included in the RDH chapter kindly supplied to the thread earlier. I would then kindly ask that those interested down-load the RDH reference first. It would save reams of narrative to be able to refer to the graphs there, etc. (One of my difficulties is that I do not know Moonbird's background, thus apologies if I seem to under-estimate.)
Just going back to calculating from the previously determined primary inductance, the common formula here is
Lp = 3,2*A*µ*N²/l*10(power 8)
with L in Henrys, A = core cross sectiona area (inch²); l = length of magnetic path (inches); N=number of primary turns (to be determined from this), etc. (RDH p.211)
In fact, everything else appear in RDH p.215 - 228. (Reading section 5 about power transformers gives good magnetic basics.)
Thus what remains after my initial contribution is the matter of leakage reactance (Lr) which determines the upper transformer limit, barring C-effects.
Most important and easy to use are the graphs on p. 218 - 219. (For myself I have made enlarged copies of these to use for each design, thus saving the book. These have thin lines; I hope the reference supplied here would print clearly. Otherwise someone with the original could enlarge the figures only and post here.)
It should appear logical that in order to have tight coupling between P and S, these should be sectionalised and interleaved. But that should occur in a certain way often ignored, even by reputable manufacturers. In fig 5.13E is a table showing that sectionalising in the right way offers substantial advantage over wrong ways. To summarise, if one 'cuts' primary and secondary windings into equal sections, and interleave in such a way that the beginning and end sections are ½Ps each, it gives a 4x improvement over the wrong way.
Example: One wants three secondaries (explained later). The above way appears under N² = 36 (top, right hand column). [And darn it, they would use the symbol 'N' here. It has nothing to do with the number of turns itself - rather it should have been F² or S² or whatever - this 'N²' is only valid for figs. 5.13E and 5.13H. Also note that we shall see that the higher N² the lower the leakage.] But to continue, it will also be noticed that for the same factor, immediately under the top 3 Ss, there is a sectionalising with all of 6 Ss - 12 P and S sections altogether, but giving the same factor because of unwise proportioning. Alternately, doing our 3 S-sectioning the wrong way, lands one under N² = 9 only.
One can now go determine Lr from the graph in fig. 5.13H. The keys are shown in figs. 5.13F and 5.13H, which should be clear. One starts with the previously determined N² at the bottom, and follows the route shown in fig. 5.13G.
And that is it!
OK, not quite; there is still the question of wire gauge and the dimension 'c' depending on the intersection isolation material, and a few practical things. But this is getting lengthy and the hour late; perhaps tomorrow.
Thanks for patience.
PS: I have often used these procedures over many years; how accurate are they? In my latest design of a 100W p.p. output transformer with 3 secondaries etc., the calculated Lr figure as above was 6,5 mHy. Two transformers measured 6,2 and 6,7 mHy respectively. I would submit that that is more than acceptably accurate.
Again, with respect, I hope after this that would prove not to be quite the case. Skill of the winder: Yes, but only inasmuch as proper winding is concerned, not slapdash windings-pouring-over-the-side sort of thing.
Yes, www.dissident-audio.com/OPT_da/OPT_da-322.zip
A friend of mine has used this with success. I have not tried it, having used RDH (Radio Designer's Handbook) since before there were internet and pcs. That is then also what I will refer to below, finding it quite convenient. (To me the RDH procedure allows me a kind of 'overview', where if necessary I can more easily do back-engineering if required!)
Further I have been given by others:
www.turneraudio.com.au/output-trans-pp-calc being a complete calculated procedure.
... says the man with exemplary diplomacy, that I must put my typing finger where my mouth is!
But no - I am not here to 'show up' BudP or anybody else. Bud seems to know his stuff well, also being in the business professionally (see his profile). Only, Bud and I had two different approaches. I only noticed near the end of his first post that he was actually describing single-ended transformers (normally with air gap), which are quite specialised! With respect, I judged that it would be best to start with principles of the normal push-pull (p.p.) output transformer before advancing to specialities. It would show that reading wider about the principles of transformers would help the uninitiated to better understand, and that is included in the RDH chapter kindly supplied to the thread earlier. I would then kindly ask that those interested down-load the RDH reference first. It would save reams of narrative to be able to refer to the graphs there, etc. (One of my difficulties is that I do not know Moonbird's background, thus apologies if I seem to under-estimate.)
Just going back to calculating from the previously determined primary inductance, the common formula here is
Lp = 3,2*A*µ*N²/l*10(power 8)
with L in Henrys, A = core cross sectiona area (inch²); l = length of magnetic path (inches); N=number of primary turns (to be determined from this), etc. (RDH p.211)
In fact, everything else appear in RDH p.215 - 228. (Reading section 5 about power transformers gives good magnetic basics.)
Thus what remains after my initial contribution is the matter of leakage reactance (Lr) which determines the upper transformer limit, barring C-effects.
Most important and easy to use are the graphs on p. 218 - 219. (For myself I have made enlarged copies of these to use for each design, thus saving the book. These have thin lines; I hope the reference supplied here would print clearly. Otherwise someone with the original could enlarge the figures only and post here.)
It should appear logical that in order to have tight coupling between P and S, these should be sectionalised and interleaved. But that should occur in a certain way often ignored, even by reputable manufacturers. In fig 5.13E is a table showing that sectionalising in the right way offers substantial advantage over wrong ways. To summarise, if one 'cuts' primary and secondary windings into equal sections, and interleave in such a way that the beginning and end sections are ½Ps each, it gives a 4x improvement over the wrong way.
Example: One wants three secondaries (explained later). The above way appears under N² = 36 (top, right hand column). [And darn it, they would use the symbol 'N' here. It has nothing to do with the number of turns itself - rather it should have been F² or S² or whatever - this 'N²' is only valid for figs. 5.13E and 5.13H. Also note that we shall see that the higher N² the lower the leakage.] But to continue, it will also be noticed that for the same factor, immediately under the top 3 Ss, there is a sectionalising with all of 6 Ss - 12 P and S sections altogether, but giving the same factor because of unwise proportioning. Alternately, doing our 3 S-sectioning the wrong way, lands one under N² = 9 only.
One can now go determine Lr from the graph in fig. 5.13H. The keys are shown in figs. 5.13F and 5.13H, which should be clear. One starts with the previously determined N² at the bottom, and follows the route shown in fig. 5.13G.
And that is it!
OK, not quite; there is still the question of wire gauge and the dimension 'c' depending on the intersection isolation material, and a few practical things. But this is getting lengthy and the hour late; perhaps tomorrow.
Thanks for patience.
PS: I have often used these procedures over many years; how accurate are they? In my latest design of a 100W p.p. output transformer with 3 secondaries etc., the calculated Lr figure as above was 6,5 mHy. Two transformers measured 6,2 and 6,7 mHy respectively. I would submit that that is more than acceptably accurate.
Thanks for all the time and effort kind sir - however this link seems busted?!?!
Just looking around on this site ... have not found the calculator yet but check this out ...
output-trans-theory
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