- #1

- 864

- 17

Hi,

The origin of this question was contemplating how to express the impedance of an inductor as a function of frequency, for non sinusoidal voltage wave-forms such as triangle waves, but in particular rectangular pulse trains.

So going back to basics, I watched this video:

He derives the impedance of the inductor from v = L* di/dt

where i = e

so v = L * d(e

= jwL* e

and so v/i = jwL

which I don't like because it seems like it is putting the cart before the horse, because you can apply a voltage across an inductor, but it's the current which is the dependent variable.

So I'd prefer to set v = e

i = 1/L * ∫ v dt

= 1/L * ∫ e

= 1/L * 1/jw * e

∴ v / i = jwL - Constant

My first question is, is there a reason why both methods are justified? I can see that the former is more simple because you don't have the 'constant'.

Okay, back to the main question of this post, taking for example a triangle wave as the current:

So say I only went to n degree of 1 for simplicity. Then this would be:

V = L

V = L

so X_l = L

which would be very complicated...

Am I thinking about this right?

The origin of this question was contemplating how to express the impedance of an inductor as a function of frequency, for non sinusoidal voltage wave-forms such as triangle waves, but in particular rectangular pulse trains.

So going back to basics, I watched this video:

He derives the impedance of the inductor from v = L* di/dt

where i = e

^{jwt}so v = L * d(e

^{jwt})/dt= jwL* e

^{jwt}and so v/i = jwL

which I don't like because it seems like it is putting the cart before the horse, because you can apply a voltage across an inductor, but it's the current which is the dependent variable.

So I'd prefer to set v = e

^{jwt}soi = 1/L * ∫ v dt

= 1/L * ∫ e

^{jwt}dt= 1/L * 1/jw * e

^{jwt}+ Constant∴ v / i = jwL - Constant

My first question is, is there a reason why both methods are justified? I can see that the former is more simple because you don't have the 'constant'.

Okay, back to the main question of this post, taking for example a triangle wave as the current:

So say I only went to n degree of 1 for simplicity. Then this would be:

V = L

_{inductance}* (d f(x)/dt)V = L

_{inductance}* 8/Pi^2 * Pi/Fourier_L * cos (pi*x / Fourier_L)so X_l = L

_{inductance}* 8/Pi^2 * Pi/Fourier_L * cos (pi*x / Fourier_L) / f(x)which would be very complicated...

Am I thinking about this right?