# Response time of a magnetic circuit and its elements

This one is for people working with electromagnets (more specific, DC) etc. I have a few questions that I am struggling with:
1. I am quite comfortable with the concept of the response time (time constant) of a coil in free space, μ0 =4π x 10-7 . The thing I am struggling with is the response time of the whole magnetic circuit (coil, conducting magnetic material, core etc.). How can I calculate that?
2. I know that for a compact magnetic circuit a soft magnetic material with a high saturation point (like iron) is required. However, what type of magnetic conductor do you select if you require a fast response time in the magnetic circuit (assuming the coil is fast enough)?
3. There are a lot of material available to calculate the magnetic field in a circuit where the core is on the inside of the coil. How would you calculate the magnetic field in a circuit when the core is on the outer diameter of the coil.
Any help is appreciated. If any thing is unclear, please tell me.

Thanks

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meBigGuy
Gold Member
I'm not a magnetics expert, but:
I think the response time of the circuit is determined by the RLC circuit represented by the electromagnet. The magnetics are part of what determines the L (inductance). More core = more inductance = slower current slew = slower magnetic buildup. In other words, there is a 1 to 1 instantaneous relationship between the coil current and the magnetics.

So it is mostly a matter of determining the inductance, etc from the coil parameters and core characteristics, and then calculate the electrical circuit response to determine the magnetic circuit response.

I don't know exactly what happens when you try to encase a coil in a magnetic material.

I had the same idea, I am just not sure what is valid. For example, I can calculate the reluctance of the circuit (which has units 1/Henry), but is the total inductance of the circuit just as simple as inverting the total reluctance of the circuit? My strong point is mechanical systems, this is a whole new area for me.

This is more like and RL circuit I think, there is not a lot of damping present.

I left something out in my original question. There is a core on the outside of the coil, but there is a composite core on the inside as well. The inside core is made up of Aluminium, MR fluid and steel. I have simulated the magnetic in MSC Marc which is quite simple. The only reason I need an analytical method is to formulate an optimum design problem.

meBigGuy
Gold Member
Again, I am not a magnetics expert.

To the extent that the reluctance of the magnetic circuit is significant with respect to time, it will affect the inductance you see, and therefore the electrical response. I can't help you figure out the inductance with respect to time, nor the optimum materials. For example, in the extreme, if the core saturates, etc.
Hopefully someone else will pick up this thread. Sorry.

Hopefully more people will pick on this thread.

Thanks anyway. :)

Baluncore
2019 Award
Jet Boer said:
I know that for a compact magnetic circuit a soft magnetic material with a high saturation point (like iron) is required. However, what type of magnetic conductor do you select if you require a fast response time in the magnetic circuit (assuming the coil is fast enough)?
The skin effect applies to both conductive and to magnetic materials. http://en.wikipedia.org/wiki/Skin_effect
It takes a significant time for the magnetic field to diffuse into magnetic core material. A laminated transformer or solenoid core has a lamination thickness selected to make all the magnetic material quickly accessible to the magnetic field via the insulated surface of the laminations. Laminations can work up to 20 kHz. Small particles of iron powder in a non-magnetic insulating matrix give faster access to the magnetic material and can work up to about 1MHz. At higher frequencies ferrites are used. Above 100MHz air is really the only option.

Ok, the way I understand it is that the skin effect is most significant with an alternating current source. I am however using direct current (DC), so if my understanding of the concept is correct, then the skin effect does not really apply in my situation. I am merely applying a step voltage. Unless for that short period during the step, you have to regard the current as being AC.

Another limitation I have, and I should have probably mentioned it earlier, is that my material needs to be solid. I am using the electromagnet with applications in magneto-rheological (MR) fluids. Laminations would therefore not work that well.

I just wish to clarify my second question a bit given the current discussion. I am merely trying to find out what property to look for in a material that allows for a fast formation of the magnetic field. In other words, the quicker the magnetic field reaches its full potential, the better.

Baluncore
2019 Award
Jet Boer said:
I am merely trying to find out what property to look for in a material that allows for a fast formation of the magnetic field. In other words, the quicker the magnetic field reaches its full potential, the better.
The fourier transform of a step pulse contains all frequencies. The sharpness of the step is proportional to the bandwidth of the circuit. To get a fast step you will need a wide bandwidth and that requires all the available magnetic material can come into play quickly.

The magnetic particles in the fixed magnetic path must be small. A MR fluid is also composed of small magnetic particles in an insulating fluid. There is little advantage in having particles in the fixed magnetic path smaller than those in the MR fluid. I would expect that a ferrite material such as is used for RF transformers would be used to fabricate the magnetic path. Alternatively you could use a tube containing the MR fluid as the fixed path.

Magnetic field is proportional to current. Remember that for an inductance; v = L * di/dt and so di/dt = v / L. To maximise di/dt you need to maximise voltage, v, and minimise inductance, L.
Since the current ramps up when an instant step voltage is applied, to get a faster rise of magnetic field, you should apply a high voltage spike to the coil, not a simple flat topped voltage step.

The fourier transform of a step pulse contains all frequencies. The sharpness of the step is proportional to the bandwidth of the circuit. To get a fast step you will need a wide bandwidth and that requires all the available magnetic material can come into play quickly.
I do agree with that, but because I am working with fluids and need a leak free device I will first try to look at other possibilities. There will definitely some unavoidable latency due to a bandwidth limit.

The magnetic particles in the fixed magnetic path must be small. A MR fluid is also composed of small magnetic particles in an insulating fluid. There is little advantage in having particles in the fixed magnetic path smaller than those in the MR fluid. I would expect that a ferrite material such as is used for RF transformers would be used to fabricate the magnetic path. Alternatively you could use a tube containing the MR fluid as the fixed path.
Ok, I sort of get what you are saying, but Magneto-Rheological (MR) fluid is not a great conductor of magnetic fields. It has a relative permeability of only 5 - 10, so it is great for fast response, but to get the desired MR effect you require an enormous magnet. This is due to the high reluctance of MR fluid.

Magnetic field is proportional to current. Remember that for an inductance; v = L * di/dt and so di/dt = v / L. To maximise di/dt you need to maximise voltage, v, and minimise inductance, L.
I aware of the fact that in order to reduce the response time, the inductance L of the circuit needs to be reduced. Simply enough, the answer is in the formula for the inductance of a solenoid. I was very aware of the fact that in order to reduce the response time, the number of winding's and\or surface area should be reduce or the length should be increased. The one variable I constantly over looked is the permeability of the core. The most common assumption is that of an air core, but only a few sources shows an example with a different type of core. It turns out that to decrease the response time you need a material with a low permeability, that is why a magnetic field can develop so fast in air. So I will be looking for a material with low permeability. A good candidate is a low carbon steel.

Another thing that I have noticed is that the strength of the magnetic field also determines the material you choose. For example, in applications where the magnetic field strength is low (< 1 kA/m), you need a high permeability material to allow for a quick response (see Applications in <http://cartech.ides.com/datasheet.aspx?i=103&e=207&c=TechArt>). Though it would seem that with high strength magnetic field ( > 300 kA/m) you need a low permeability material to decrease the reluctance of the circuit.

Since the current ramps up when an instant step voltage is applied, to get a faster rise of magnetic field, you should apply a high voltage spike to the coil, not a simple flat topped voltage step.
I am well aware that the use of an current controlled power supply will decrease the response time, and I will definitely be using it once I am happy with the magnet itself.

Baluncore
2019 Award
There will definitely some unavoidable latency due to a bandwidth limit.
After all, that is what delay and limited bandwidth are. I was saying that you must not have large particles, they must be small and embedded in a non-conductive matrix.
So I will be looking for a material with low permeability. A good candidate is a low carbon steel.
It is actually the particle size and the presence of a non-conductive matrix that decides rise-time or fall-time of a magnetic field. That is demonstrated by the use of ferrites for HF and VHF inductors. Solid iron would be very bad, it would need to be powdered and baked in a ceramic matrix.
It turns out that to decrease the response time you need a material with a low permeability, that is why a magnetic field can develop so fast in air.
The energy stored in air is very low so it is quick to rise. A magnetic path needs permeability to work as a path. By lowering the permeability you are increasing the area and length of the path. That is not good.
I am well aware that the use of an current controlled power supply will decrease the response time, and I will definitely be using it once I am happy with the magnet itself.
You have misunderstood the primary requirement for a fast changing magnetic field. You want a magnetic step function, but that requires a current step function. Because v = L * di/dt, the maximisation of di/dt requires a very high voltage. It does not need a voltage step, but needs an infinite voltage spike that when integrated produces a current step. Obviously infinite voltage is impossible so you must find a compromise and settle for a finite rise-time.

After all, that is what delay and limited bandwidth are. I was saying that you must not have large particles, they must be small and embedded in a non-conductive matrix
It is actually the particle size and the presence of a non-conductive matrix that decides rise-time or fall-time of a magnetic field. That is demonstrated by the use of ferrites for HF and VHF inductors. Solid iron would be very bad, it would need to be powdered and baked in a ceramic matrix.
Ok, I sort of understand now what you are saying about particle size. Here is the dilemma though, I am only trying to build a prototype system and unfortunately I have some nasty geometry involved so using powdered iron that is baked in a ceramic matrix is not possible for me. I need a solid material that I can machine to within tolerance. Unless there is another way. Does it need to be small particles, how about using a material with small grains, or heat treating the material after machining to achieve small grain structure.

The energy stored in air is very low so it is quick to rise. A magnetic path needs permeability to work as a path. By lowering the permeability you are increasing the area and length of the path. That is not good.
I saw the mistake in my assumption when I looked at the formula for reluctance of a magnetic circuit element, there permeability is a denominator, so higher permeability means less reluctance.

I read a paper by Grundwald and Olabi (Design of magneto-rheological valve) where they suggested that in order to reduce the response time of the magnetic circuit, the volume of ferromagnetic steel in the magnetic circuit needs to be reduced.
They also have an answer to one of my other questions, about the inductance of the whole magnetic circuit. They give it as L = N^2/(Total Reluctance of the magnetic circuit). Using proper search terms I actually found it on other sources as well.

You have misunderstood the primary requirement for a fast changing magnetic field. You want a magnetic step function, but that requires a current step function. Because v = L * di/dt, the maximisation of di/dt requires a very high voltage. It does not need a voltage step, but needs an infinite voltage spike that when integrated produces a current step
Ok, I may have used poor wording. My understanding of a current controlled power supply is that given a predetermined current (i.e. the current step), the power supply regulates/adjusts/spikes the voltage to achieve the desired current as quickly as possible. Such systems, as I understand it, is usually under-damped which causes the voltage spike.

Baluncore
2019 Award
I need a solid material that I can machine to within tolerance.
To make your magnetic path, use RF ferrite components such as round rods and toroids. Cut them with a thin circular diamond saw as is used for gem stones. Grind or polish the faces to make them flat as is done for microscope study of rock samples. Glue the faces together with super-glue to make the magnetic path modules you require. Clamp the modules together to build your experimental arrangement.
HF Magnetic materials are available everywhere if you look. Used computer switch-mode power supplies, cheap AM transistor radios, etc. You need to specify the bandwidth or transition time to select the optimum material.

so higher permeability means less reluctance
Yes, you need to make a physically short magnetic path that has sufficient cross section along all it's length that it will not saturate with the field you require.

current controlled power supply
You need an active amplifier or pulse generator to produce the turn-on / turn-off voltage spikes. A current controlled power supply still sounds to me more like it will limit maximum current while it is supplying a fixed maximum voltage.

I would consider a DC supply of up to 600 volt, with an H-bridge made from four MOSFETS. The bridge output would be AC coupled to your electromagnet coil through a selected HV capacitor. The capacitor will provide the voltage spike that gets the magnet current flowing quickly.
E = ½ L*I2, and also E = ½ C*V2. So C selection sets the maximum coil current and the slew rate of the current for your L. The topology is very similar to a series resonant converter, but without the output stage. It has the switching H-bridge network, the series LC “tank” is your coil and coupling capacitor. See; http://ecee.colorado.edu/copec/book/slides/Ch19slide.pdf

To make your magnetic path, use RF ferrite components such as round rods and toroids.
In that article I mentioned (link: http://doras.dcu.ie/15062/1/Design_of_magneto-rheological__MR__valve-24-04-2008.pdf) look at page 4. That is the layout and geometry I am using for my experiment. I am also working with fluid pressures 5 times higher than that (approx 10 MPa). It needs to be machined with proper sealing surfaces and mechanical strength. The magnetic circuit and annular flow passage cannot be separated.

Yes, you need to make a physically short magnetic path that has sufficient cross section along all it's length that it will not saturate with the field you require.
I had the same idea. The whole problem for me is trying to find a suitable compromise for the material (reasons mentioned above). I have tried to determine the response time that I will be satisfied with, and anything from 20 ms to 40 ms would be great. The faster the better of coarse, but this is a reasonable speed for my application (which is MR suspension).

I will definitely have a look at your suggested method for a power supply.

jim hardy
Gold Member
2019 Award
Dearly Missed
You only need milliseconds ?

I'm no magnetics expert either, but have experimented a little. Here's some tangential experience that might help formulate your ideas....
Baluncore's point about iron not magnetizing instantly is significant. Magnetization of a solenoid core proceeds from the outside in, slowed by eddy currents. In my 1901 textbook it's called "Retardation of Magnetization" and could amount to minutes in large railway dynamo poles of the day.

To observe it one can place two coils around a core, energize one and use the other as a flux detector. Induced voltage in the flux detector coil should be di/dt of the exciting coil current. The flux detector coil can be connected to an integrator to produce a flux signal that's observed on an oscilloscope. Using a sinewave excitation current, one will see sinewave flux. Interestingly, one will see retardation as phase difference between current and flux. I started with a home-made integrator that wasn't very good, and looked at Lissajous patterns on the 'scope. Results were confusing so we moved to approach in next paragraph.

Lacking a practical integrator, one can excite the first coil with a current signal whose derivative is known, and observe the induced voltage in detector coil. Any deviation from expected is due to something going on in the core.
With sinewave excitation current you'll just see sinewaves not in phase and it's not intuitive what's happening.
But driving with let's say triangle wave current, which has for its derivative a square wave, things look more interesting.
Here's photos of a 12 foot tall core surrounded by two coils, one excited by triangle waves at three different frequencies- 3, 10, and 60 hz.

In each photo top trace is current (20milliamps peak to peak) and bottom is voltage induced into detector coil.
Triangle current through an inductor should produce square wave voltage.

Observe that this core is mighty slow. You can see in the first photo that the corners of the 3hz square wave are rounded off. At higher frequency retardation becomes the dominant effect.
But removing the core gave nearly ideal looking square waves , even at 60 hz..
So the inductor was "ideal" until we gave it a core.

So i'm suggesting you have some fun poking at sample core materials with known MMF's. Above is an easy method that's quite graphic.,
My core was a stainless steel rod about 2" diameter unlaminated. I don't know exactly what alloy but think it's similar to Carpenter 430 Solenoid grade stainless. Drawings said it was an obscure Allegheny alloy. My windings weren't quite bifilar , just multiple individual coils stacked in alternating layers.

I hope above helps cement the concept of eddy current effects . You can sure see them this way.

Here's some Carpenter information

http://www.cartech.com/techarticles.aspx?id=1562
http://cartech.ides.com/datasheet.aspx?i=103&e=64
http://www.cartech.com/techarticles.aspx?id=1476

Sounds like a fun project.

old jim

Last edited:
Thanks Jim, I will definitely try a similar experiment to try different core configurations and materials.

So far I have gathered to following from this thread and other research I have been doing. I am basing this summary on a DC magnetic field.

Magnetic circuit size
If I want to make the magnet small I need to use a material with a high point of saturation.

Efficiency
To make the magnet more efficient, a material with high permeability at the operating point is best as it is the better conductor. A more efficient circuit requires a smaller coil as well since there is less magneto-motive force needed, which in turn reduces the size of a magnetic element in my case. Together with a high permeability, the smaller the magnetic elements or rather the cross sectional area, the better.

Response time
Now this one I am not completely comfortable with, but I think I have enough info to move forward. From the paper of Olabi and Grundwald I referenced, they suggest that the smaller the device is the faster the response will be. This I can relate the formula for calculating reluctance, so I understand it.
Still looking at the formula for calculating the reluctance it would seem that a higher permeability is also beneficial to improve the response time. Since the magnetic field goes from zero to its steady state value, or rather 62.3% level, over a certain period of time (response time), the permeability changes as well. It would seem that a high permeability during this initial period would benefit the response time of the circuit, since there would be a lower reluctance. I have been looking at some B-H curves from magweb.us and not all materials have a high permeability at low magnetic fields.

The major factor that Baluncore explained was the effect of particle size and surface effects. I am a mechanical engineer, so it took a while for me to understand him. Since magnetization proceeds from the outside inwards, and the presence of eddy currents use is made of insulated lamination's.

The Compromise
It would seem that all I have to do not is find a compromised between all the requirements. I want a small device, so I need a magnetic material with a high saturation. I want reasonable efficiency, so I need a material with a high permeability at the operating point (steady state).
For a fast response, I need small magnetic particles embedded in a non-conductive matrix, or a laminated core. Both of which is a bit difficult to implement at the moment since I have no idea how to embed particles in a non-conductive matrix and laminated core would have leaking problems with the fluid. Also I have to take manufacturing into account as well, at the moment it is just a milling and turning operation which is quick and not too costly.

Am I missing something in my summary?

Baluncore
2019 Award
at the moment since I have no idea how to embed particles in a non-conductive matrix
A ceramic powder with magnetic particles is made into a paste that can be extruded or moulded. It is pressed into shape, then baked and fired. Investigate the manufacture and availability of powdered iron magnetic cores that have a geometry similar to that you require.

Ceramics are used for the hardest steel cutting tool tips. They are good in compression but are like glass, and so poor in tension. There are ways to give the ceramic a greater tensile strength. To withstand the high internal pressure you may need to encase the ceramic material in a metal outer pressure vessel.

Consider winding the coil with half as many turns of wire, each turn having twice the section and twice the current. That can speed up the magnetic transition by a factor of four by lowering the coil inductance, since L is proportional to n2.

jim hardy
Gold Member
2019 Award
Dearly Missed
For a fast response, I need small magnetic particles embedded in a non-conductive matrix, or a laminated core.
I have tried to determine the response time that I will be satisfied with, and anything from 20 ms to 40 ms would be great.
by ms do you mean milli or micro seconds?
That's why i linked to stainless - it has higher resistivity than ordinary magnetic iron so eddy current effects are less.
But its permeability is lower....
I guess you'll be after high resistivity for response time and high permeability for small size?

Here's some of their papers on selecting magnetic materials

http://www.cartech.com/techarticles.aspx?id=1562

from http://www.cartech.com/techarticles.aspx?id=1624

In that paper you linked i saw modest flux only around a half Tesla in the fluid, but i guess it'll be higher in your magnetic path ?

This nickel-iron has great permeability and should be available in bars....
but i don't know about its AC performance in thick cross sections , you'd have to test a piece similar to your product.
http://cartech.ides.com/datasheet.aspx?i=103&e=206&c=TechArt

Interesting project. i hope you keep us posted

old jim

old jim