[Amps] Transformers

[Will Matney]

All,

I want to explain some of this so some don't get confused. When a transformer is first designed, the output power in volt amperes is used to determine the core size needed in square inches or square centimeters. There's a published formula for this which quickly determines it. Most of these formulas use a value of flux density with it at 75 kilolines per square inch which is 11,626 gauss when using the CGS system. They will also say it is approximately 12 kilogauss in some (which is really 400 gauss off!). In other words, by using the power formula for the core size, and the turns per volt formula, it comes out to that flux density. The core area (a) formula for 75 kilolines at 60 Hz is a = 0.16 x Sq Rt of Power in VA. Next, the turns per volt is simply TPV = 5 / a. Now, to use 12 kilogauss which makes an even number, one can use these following short formulas. For the area, A = 0.1725 x Sq Rt of P, and for the turns per volt, TPV = 4.85 / a. One can show these were derived from the long formulas mathematically. VA or volt amperes is calculated by multiplying the output power in watts by the power factor which is generally 0.9. The long formula for area is below;

a = V x 10^8 / 4.44 f N B

a = Core area in In^2 or CM^2
f = Frequency in Hz
N = Number of turns
B = Flux density

The flux density can be found by;

B = V x 10^8 / 4.44 f a N

>From this one can see that if any of the figures to be multiplied together below the divisor line are changed it will change the result. If the area is changed to a smaller figure in the flux density formula, the flux density will rise because the bottom number will be lower. If any transformer that is designed to first run at a certain flux densities core size is reduced, the flux density has to rise. Likewise, by adding more iron to the core, it will drop the flux density. As flux density rises, so does the Magnetizing force H in Oersteds. That in turn means higher heat from a transformer. This can be seen by looking at the BH curve for the type of steel chosen. The BH curve means what it looks like, B is flux density, and H is Oersteds. Permeability almost runs linear to the flux density as it rises until it gets to the knee. At the knee, as flux density increases, permeability starts to drop off, and the magnetizing force starts to increase more and more compared to flux density. Finally, Permeability takes a nose dive at some point, flux density hardly raises any more with more magnetizing force applied, inductance can go from low to no inductance, and this is saturation.

When weight and cost is a concern, designers try to run the core at the highest possible flux density. The problem is that the extra magnetizing force causes more heat and losses. The watts per pound loss goes up with flux density and is shown in the loss charts for each type steel. This also causes more voltage sag. Sag is controlled by this and the I^2 R losses of the wire.

To read about this, I would recommend two books on the subject. The first is Practical Transformer Design Handbook by Eric Lowden. The other is Reference Data For Radio Engineers by ITT. There's also 2-3 books by Col. William McLyman which goes into deeper research on the subject. However, all are based around the calculations above.

Best,

Will

*********** REPLY SEPARATOR  ***********

On 7/15/06 at 12:52 PM Will Matney wrote:

>*********** REPLY SEPARATOR  ***********
>
>On 7/15/06 at 6:45 AM Tom W8JI wrote:
>
>>> Why does Heathkit show in their manuals the open circuit 
>>> voltage, and the full load voltage that
>>> calculates to 15% sag (OCV / FLV )? They show this in 
>>> several of their models.
>>
>>Manuals are written from other manuals, and the goal was to 
>>always be conservative. Manual writers at Heath were a 
>>completely different group than engineers. I don't think I 
>>talked to a manual writer more than a dozen times.
>>
>>> I should have worded this different. No they don't 
>>> saturate under load.
>>
>>That's right, you should have worded it much differently.
>>
>>>However, the
>>> amount of iron is what controls the power output in watts. 
>>> Not enough iron and you have
>>> a high flux density, a higher magnetizing current, and 
>>> more sag.
>>
>>That's not correct. That still implies flux density controls 
>>maximum power.
>
>
>Well Tom, that's not what the 15-20 or so books I've read on the subject
>says, nor what the
>manufacturers of the iron lams say either. I can quote these if you want.
>Are all these authors
>wrong on the subject?
>
>The lesser the amount of iron in the core at a given power, the higher the
>magnetizing current is, 
>and surely a higher flux density. Also, the very first step in designing a
>transformer is calculating its 
>core size from the output power in watts it needs to deliver. That's a
>fact, and it's in every 
>book on the subject! The amount of iron in the core in square inchers (or
>square CM) is 
>exactly what determines the flux density and the amount or power in watts
>it's capable of.
>If there's not enough iron in the core when the current is applied to the
>primary, it can staurate.
>If there's not enough iron in the core under load, it will get hot, and
>the voltage regulation will
>be terrible. I can't change the laws of physics, that's just the way it
>works.
>
>
>>
>>>>Maximum flux density, which means closest operation to
>>>>saturation, occurs with NO load. As load is increased flux
>>>>levels do not increase. Increased current, because of
>>>>resistive losses in the primary circuit, actually causes 
>>>>the
>>>>transformer's flux level to decrease. When a transformer 
>>>>is
>>>>designed the highest primary voltage under no load is used
>>>>to set flux density at a safe level.
>>>
>>> correct
>>>
>>>
>>>>
>>>>The actual mechanism inside a transformer is the secondary
>>>>develops a counter-MMF. This opposing flux would reduce 
>>>>flux
>>>>density, but primary current increases in order to try and
>>>>maintain the **same**  flux density. When mains and 
>>>>primary
>>>>resistances carry more current from increased load, the
>>>>primary voltage drops slightly. This REDUCES flux density,
>>>>moving the transformer further from saturation. Not closer
>>>>to it.
>>>
>>>
>>> correct
>>
>>The idea flux density sets maximum available power is not 
>>correct.
>>
>>73 Tom 
>>
>>
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>Will
>
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