Magnetic Transistor Theory

By Dave Squires
Date: 11-03-2000

To make any transistor you need a material region where you can control a great amount of the flow of something with a small amount of something. This gives gain or amplification. For a magnetic amplifier the goal would be to use a small amount of input current to switch a large amount of magnetic flux into an output coil. A strong rare earth permanent magnet would be used to serve as a magnetic battery or permanent source of magnetic flux.

If any core material the amount of coil flux required to switch the magnet flux would be equal to the magnet flux. The H or magnetic potential required to reach this flux level is determined by the permeability, the shape of the BH curve, the number of coil turns, the coil length, and the coil current. The equation is stated as follows.

H = NI/L -- where N is the number of turns, I is the coil current and L is the coil length in meters.

The magnetic flux density, B, is written as:
B = aH;  where a is the permeability and H is the magnetomotive force or potential as shown above.

a here is the absolute permeability and not the relative permeability.
Relative permeability is expressed as,
r = a/0 where 0 is the permeability of vacuum

So the absolute permeability we need is:
a = r0

Substituting in the equation for B we get,
B = r0H

Then substituting for H we get,

B = r0NI/L

For the case where we will be switching a constant magnetic flux from a permanent magnet the magnetic flux density B will then be constant as long as the same core cross section is maintained.
Now let’s assume that we will use two different core materials in the magnetic circuit. We will use a core material of relative permeability r1for one core and r2 for the other core. Also, let’s assume that N and L could be different for the general case. So we have N1, N2, L1, and L2.

Now since the magnetic flux density B will be constant we can set two equation equal to each other as follows.

B1 = B2 and then substituting the expanded formulas for each we get,

r10N1I1/L1 =  r20I2/L2

If we then solve for I2 we get 

            r10N1I1/L1      r10N1I1L2 
I2 = ------------------ = ------------------- 
            r20N2/L2             r20N2L1 
As you can see 0 will cancel out and the result for the general case reduces to, 
                       r1N1L2 
I2 = I1 -------------- 
                       r2N2L1

So it can be seen that if the number of coil turns and the coil lengths were equal the output current would be the ratio of the control coil relative permeability r1 to the output coil core permeability r2times the input current. The equation for this special case would reduce to, 

                 r1 
I2 = I1 ---------- 
                  r2

Now we must keep in mind that we need a changing magnetic field to cause any induction in the output coil. So the control coils in a magnetic transistor device must be constantly switched with a periodic waveform of some kind. The rate of change of the flux or dB/dt must be as fast as possible to get the maximum output from the output coil. Also, the cores must never go much past the saturation point. The material can be made to traverse its BH curve just up to the knee of the curve for the material, but should remain on the steep slope portion so that extra H is not wasted with little change in B. Even going around the knee of the curve would waste energy with little benefit unless the knee is sharp.

It can also be seen from the above special case that if the material is uniform in permeability that there is no gain and you have a 1:1 transformer. Of course this is the ideal case where core losses are not taken into account. When core losses are subtracted the output current is less than the input current by some small amount of 1% to 5%.

The objective is to use as small as possible an input control current to control a large flux from a strong permanent magnet. It is obvious we need to match the magnet’s B field for the given core cross section to be able to switch the magnet flux completely. The control coil would operate in blocking mode with opposing flux to do this. It would then have its permeability approach 1 and look like an air gap. To get the smallest H to do this we need the highest permeability material we can find with a high enough saturation induction level capability. We also need a square loop BH curve with a small sharp knee to the curve. The more vertical the curve the better. Metglas 2605SA1 material from Honeywell Amorphous Metals fits this bill nicely. For the rest of the core we can use cheap M1 grain oriented silicon electrical steel. Metglas is expensive, but fortunately we only need a small amount for the coil core.

One other item is that we must make sure that there is no coil wound on the same high permeability material that is allowed to conduct when switching the magnet flux with the control coil. If this is allowed then the Lenz's Law back flux reaction (counter EMF) will oppose the control coil equally with lower current and destroy the gain we want. Any power extracting coil must be wound on the lower permeability material so that higher current and power can be extracted to generate the equivalent Lenz's Law back reaction to the changing flux from the magnet.

It should be easy to see that saturation of any of the cores must be avoided. Otherwise flux will be lost outside the core. If this happens the required H is lowered and the gain will be reduced. Therefore it is desirable to keep all the flux contained inside the core at all times. Flux leakage will be detrimental to maximum efficiency.

Summary and Conclusions
1.  A magnetic transistor can be made by using materials in the magnetic circuit that have widely differing relative permeabilities.
2.  The gate or control area should use the highest permeability material so that a lower magnetomotive force H is required to generate the same magnetic flux density B in the magnetic circuit core. Lowered H means lower coil current and lower input power.
3.  A constant cross section of core material for the control section and the lower permeability section should be maintained.
4.  Magnetic saturation should be avoided in all core sections. The control gate core can be taken right up to saturation, but should not be pushed beyond it because the H requirement goes up rapidly and energy will be wasted lowering the efficiency.
5.  The BH curves of the core materials should have square loop characteristics with low hysteresis. This means that a small H is required to get a large B field density.
6.  The control coil section operates to oppose the magnet flux. When not required it must be open circuited and no current allowed to flow. It does not need be used to generate attractive mode flux to favor the magnet flux flow. There is no need to do this. The off core simply completes the magnetic circuit for the magnet through the control core.
7.  The gain realized is the ratio of the control coil core relative permeability divided by the output coil core relative permeability.
8.  Since the control coil current is so much lower small power MOSFETs or medium power bipolar transistors can be used for the switching controller.

Why this Should Work in the MEG
Lenz's Law back reaction says this must work.
Consider that the magnet flux is constant through all portions of the magnetic circuit. We just need a lower H value to switch the magnet flux because of the very high permeability material in the control coil core. We assume we must create a B field in the control coil core equal in magnitude to the magnet's B field in order to block it completely.  Now we have switched the magnet flux into a different magnetic circuit by blocking the magnet flux and allowing it to flow into the opposite leg. The control coil there is off and no Lenz's Law back reaction is allowed from the "off" state control coil. One hundred percent of the magnet flux is switched to the opposite leg of the circuit. Now Lenz's Law says that while the flux in the output core is changing there will be a back reaction to oppose the change in flux that will be equal in magnitude. This assumes that maximum current is allowed to flow in the output coil. To get a B field of equal magnitude to the magnet flux you will need a much larger value of H due to the much lower permeability of the output coil core. A larger value of H means a larger current must be generated in the output coil to create this amount of back flux. So Lenz's Law is responsible for the OU gain we can achieve.  OU factors in the range of 30x to 50x should be easily attainable. These are efficiencies of 3000% to 5000% minus some small core and copper losses.  And the whole unit would be solid state increasing the reliability tremendously.

Dave Squires ( 11-03-00 ) djsquires@plix.com

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