I was hoping that someone, somewhere had integrated the current curve for a DC square wave across an inductance and determined a simple formula.

We have shown those formulas.
Do you not understand them?

 

I'd just like to maximize the saturation of the coil at a given frequency without oversaturating and unnecessarily heating it up and wasting power. I need to select coils over the whole gamut from 60 Hz to over 5000 Hz that perform like this. Hopefully there will be enough overlap that I'll only need a few different coils to cover the range.

I was hoping that someone, somewhere had integrated the current curve for a DC square wave across an inductance and determined a simple formula.

I'm thinking the current wave would be an exponential decay curve upward, then another downward (looking like shark fins) with the rate determined by a time constant L/R. If this curve could be integrated, a formula for reactance could be determined.

...my head hurts.

Don

I think you are approaching the problem from the wrong angle.
You should change the duty cycle of a constant drive frequency instead of changing the frequency.

 

Well, maybe it's not that tough. The current would decay upward when voltage is suddenly applied, then decay downward when voltage is released. It would never reach its full DC value upward nor zero downward. But the waves would be mirror images of each other, so the current would average out exactly between Idc and 0, or 1/2 Idc, just like a pure resistance.

Don

 

Well, maybe it's not that tough. The current would decay upward when voltage is suddenly applied, then decay downward when voltage is released. It would never reach its full DC value upward nor zero downward. But the waves would be mirror images of each other, so the current would average out exactly between Idc and 0, or 1/2 Idc, just like a pure resistance.

Don

Just like I said.

 

. It would never reach its full DC value upward nor zero downward.

That depends upon the pulse frequency, duty-cycle and coil inductance.

 

Theoretically an exponential decay never reaches 100%.

Don

 

What's the point/engineering objective of driving these relay coils with pulsed DC waveforms at various (5000Hz?) frequencies?

 

I'm forcing the vibration of various ferrous objects.

Don

Thanks.

 

Well, now I'm losing a little confidence in this theory. I'm looking back in my notes at some trials I did with some coils a few years ago and current definitely drops off with frequency. For example, I tested a 27 mH coil at 5V and 55 Hz and it pulled 50 mA. At 3520 Hz the same coil pulled only 20 mA.

How can this be explained other than by reactance?

Don

 

Theoretically an exponential decay never reaches 100%.

Of course that's common knowledge by most of us on this site.
But by ten time-constants it reaches 99.995% of the final value.
Is that close enough?

How can this be explained other than by reactance?

Of course it is the reactance.
But you can't use reactance to calculate the current for a pulse waveform unless you use Laplace transforms to convert the pulse to it's constituent sine frequencies.
Don't know about you, but that's a bunch of math I would not want to tackle.

 

You said you had shown me the formulas and then snidely asked if I didn't understand them. What formulas?

Don

 

You said you had shown me the formulas and then snidely asked if I didn't understand them. What formulas?

Don

The equations I posted.
But If you think that's a snidely question, than I'll just bow out of the conversation, since you obviously haven't understand what I have said.

 

I still don't have an answer, kid. Yes, I could conduct scientific experiments like I'm Michael Faraday. Yes, I could painstakingly integrate the infinite Fourier series. I already knew that. But instead I thought I'd consult the Internet to see if someone experienced in these sorts of things might have already run across this situation and would know the solution, saving me a lot of time. I have to believe there is a simple equation for this. It's not like pulsing an electromagnet is an exotic application.

I'm not trying to be mean. I just get frustrated when I get treated like an imbecile child, yet still get bogus answers. I've been an engineer for 37 years.

Don

 

I still don't have an answer, kid. Yes, I could conduct scientific experiments like I'm Michael Faraday. Yes, I could painstakingly integrate the infinite Fourier series. I already knew that. But instead I thought I'd consult the Internet to see if someone experienced in these sorts of things might have already run across this situation and would know the solution, saving me a lot of time. I have to believe there is a simple equation for this. It's not like pulsing an electromagnet is an exotic application.

I'm not trying to be mean. I just get frustrated when I get treated like an imbecile child, yet still get bogus answers. I've been an engineer for 37 years.

Don

I think part of the problem is a lack of information on your part. You say you're pulsing relays but it seems that the relay function is secondary to the electromagnetic transfer of energy to some sort of ferrous object as a vibration power transducer. If you had selected a characterized transducer for this it would have been a lot easier IMO for you than trying to translate data-sheet RL circuit characteristics of coils designed to open and close contacts.

 

Semantics. When I said "relay coil" I meant "relay-type coil".

All I'm asking for is a formula for inductive reactance for a pulsed DC square wave on an inductor. It should begin with "X =", followed by an expression with an "f" and an "L" in it. If you don't know it, just scroll on and ignore this thread.

Don

 

Semantics. When I said "relay coil" I meant "relay-type coil".

All I'm asking for is a formula for inductive reactance for a pulsed DC square wave on an inductor. It should begin with "X =", followed by an expression with an "f" and an "L" in it. If you don't know it, just scroll on and ignore this thread.

Don

It's still X=2πfL, but you have to calculate it for each of the Fourier components of your squarewave, then calculate the current for each Fourier component of the squarewave, then add them up as vectors (magnitude and phase). That's why we don't do it that way.
Working out the first order differential equation based on dI/dt=V/L twice, once for the ON part of the squarewave and once for the OFF part is much easier.
Most engineers would approach this with an approximation by calculating the time constant τ=L/R and comparing it to the pulse repetition time.
If τ is much larger, then the peak is little different from the average.
If τ is much smaller then the peak current is calculated from dI/dt=V/L for the pulse width, as the current will return to zero before the next pulse.

 

I still don't have an answer, kid. Yes, I could conduct scientific experiments like I'm Michael Faraday. Yes, I could painstakingly integrate the infinite Fourier series. I already knew that. But instead I thought I'd consult the Internet to see if someone experienced in these sorts of things might have already run across this situation and would know the solution, saving me a lot of time. I have to believe there is a simple equation for this. It's not like pulsing an electromagnet is an exotic application.

I'm not trying to be mean. I just get frustrated when I get treated like an imbecile child, yet still get bogus answers. I've been an engineer for 37 years.

Don

What's with the attitude and exaggeration? You are here to learn so maybe humble yourself a bit and open your mind instead of being a baby. Besides, you'll catch more flies with honey than vinegar.

 

EDiT : - i guess i may have got your problem wrong
https://www.google.com/search?q=magnetic+circuit+design+electromagnet
-------------------------

All I'm asking for is a formula for inductive reactance for a pulsed DC

I'd just like to maximize the saturation of the coil at a given frequency without oversaturating ... I need to select coils over the whole gamut from 60 Hz to over 5000 Hz that perform like this.

no matter the waveform - the inductance that holds the magnetic flux up is inversely proportional to frequency for 60 Hz is about 1H and more
the relative permeability of the core
https://www.google.com/search?q=permalloy+core+relative+permeability
https://www.google.com/search?q=ferrite+core+relative+permeability
https://www.caracoltech.com/iron-power-core
each have their pros and cons - defines your coil size
the following may contain hints about the response to square wave stimulus
https://www.google.com/search?q=ferrite+core+square+wave+frequency+response
https://www.google.com/search?q="ferrite+inductor"+choosing+"PWM+frequency"
https://www.google.com/search?q="ferrite+inductor"+PWM+induced+flux

 

Since the terms of the Fourier series for a square wave decay asymptotically toward zero, I'll just bet the solution converges in the limit to something simple. I wouldn't be surprised to learn that the solution is 1/2 * wL, or 1/sqrt(2) * wL, or something like that.

I'll also bet that the solution is already given in more than one text on this subject. It's not exactly an esoteric situation. I was hoping someone might have run across it.

Don

 

you might just look the links - it is (for) all not that simple as you'd see

yes , you could find the \(X_L\) formula for the square wave - but the reactance depends on coil geometry (parasitic.-s) , core parameters (thus also your signal amplitude), frequency , etc. ...