# fastest B field rise time in an inductor/electromagnet

What is the fastest attainable pulse rise time for either

• a pulse or
• a square wave

using a iron core aka transformer steel laminated core, assuming the laminations are of the best possible quality for the task.

I know that this is largely dependent on the inductance of the inductor.

For me there are multiple smaller paralleled inductors all driven with the same signal, so the inductance will be very low.

Is it possible to get ns or maybe even pico second rise times for a pulse in a core that is not air core?

Do Ferrites have better parameters with regards to this.

My need is to get a B field in an airgap that increases from zero to its maximum value as fast as possible.

Does the B field rise curve follow the coil current rise?

• Hi! This feels like you're not familiar with the basic equation that describes voltage and current over/through an inductor. Commented May 22, 2020 at 7:59
• Well , tell me about it then ? Commented May 22, 2020 at 8:58
• wikipedia "Inductor", $v(t) = \frac{\mathrm d\,i(t)}{\mathrm dt}$, hence this is physically limited by winding inductance. As long as you use your transformer as transformer, you'll have an inductance counteracting any sudden current changes. What's the purpose of the transformer? Pulses aren't usually what you send through transformers to preserve their pulse shape... Commented May 22, 2020 at 11:16
• Well the idea is that I have a rotating conductor and I wan't to generate a current from the Lorentz force so if I want this current to be sharp with a steep rise I need my B field to also be like that and so the whole thing about the inductor as an electromagnet is just that an inductor, so it is not like a transformer but rather an inductor with just a few turn coil and ,many such inductors placed in parallel to cover a wider area with B field Commented May 22, 2020 at 17:45

For me there are multiple smaller paralleled inductors all driven with the same signal, so the inductance will be very low.

If all those inductors are wound on the same magnetic core and have the same number of turns then they will behave pretty much like one inductor made of thicker copper wire. In other words, due to magnetic coupling between them, the net parallel inductance will be hardly different to the inductance of one coil.

I know that this is largely dependent on the inductance of the inductor.

Correct, when applying a voltage pulse, the current will rise at V/L amps per second. Paralleling many inductors on the same core will not make "L" any smaller theoretically.

Do Ferrites have better parameters with regards to this.

They will have fewer losses at higher frequencies but, at the end of the day inductance is the limiter of speed so, to counter that you need to apply a higher voltage but, current will ramp all the same. Current does not "follow" voltage for an inductor.

Does the B field rise curve follow the coil current rise?

It does.

• current doesn't follow voltage rise time wise but larger voltage through a fixed inductance will get more current through at the same rise time right? Also no I don't have the coils on the same core, each coil is on a separate core just that the cores are adjacent to one another, so in theory they are multiple inductors in parallel. So by having paralel inductors the total inductance decreases which means the current rise time will get faster and more current will flow through at the same voltage correct? Commented May 22, 2020 at 9:13
• Part2 of your comment: If the coils are not magnetically connected then the total inductance is as you say. If you try and combine the magnetic fields in some way then this doesn't work quite so well. Commented May 22, 2020 at 9:53
• Part 1: No, current does not rise at the same rate as voltage. The rate of change of current rise is V/L so, if, for instance, you applied 1 volt instantly across a 1 henry inductor, current would reach 1 amp in one second, rising linearly. If you applied 10 volts across 10 uH inductance current would reach 1 amp after 1 microsecond. Commented May 22, 2020 at 9:55

For an air coil, the magnetic field is proportional to the current flowing through it. An iron core amplifies the field a lot, but only up to a certain value, where it starts to saturate.

With the (inner) resistance R of the wire and the inductance L, the current flowing through an inductor when connected to a voltage source, is given by

$$I(t)=\frac{U}{R}(1-e^{-t/\tau});\qquad \tau=L/R$$

After a time of $$\\tau\$$, the curren reaches 63,2% of its final value, after $$\5\tau\$$ it's about 99%.

By increasing the voltage, the current rises steeper, and will reach a higher value, but the time it takes stays constant.

To change the time until the current reaches its maximum, you have to change R or L, though often, changing one will change the other, too.

Also no I don't have the coils on the same core, each coil is on a separate core just that the cores are adjacent to one another, so in theory they are multiple inductors in parallel.

No. The inductance of a coil is influenced by any iron in its field. That is, placing several cores next to each other creates one big core. You can not simply apply the formula for parallel inductors, because they are not independent.

See it like this: Instead of one wire with 10000 turns a big core, you have 10 wires with 1000 turns each. To get the same field, you have to drive the same current through either the single or each of the 10 wires. Your power supply must source 10 times the current, but only 1/10 the voltage due to the lower resistance.