# inductive reactance formula

Discussion in 'General Electronics Chat' started by lokeycmos, Mar 2, 2011.

1. ### lokeycmos Thread Starter Active Member

Apr 3, 2009
432
7
ok, so the formula for xl is xl=2*pi*f*l.
does this formula apply to ALL forms of AC, such as square wave, sawtooth, sinewave.

would this also apply to pulsed DC, such as a dc squarewave into a transformer?

2. ### Papabravo Expert

Feb 24, 2006
11,123
2,171
The thing about sinusoids is that they are not changed in shape by a reactance. The phase does change however. This is because:

1. The derivative of the sin(x) is the cos(x)
2. The derivative of the cos(x) is the -sin(x)
What is true for other types of AC voltage and current is the 1st order differential equation that relates current and voltage. For an inductor the relationship is:

V = L*(di/dt)

and for a capacitor it is

I = C*(dv/dt)

I've not seen reactance used with non-sinusodal vaveforms, but I don't know why the waveform would affect the behavior of the component.

3. ### russ_hensel Distinguished Member

Jan 11, 2009
821
49

simply stated no. it is a steady state solution to the underlying equations. you can ( in some cases ) break all waves down to sine ( cosine ) waves and use the equ. on each part.

4. ### Teri Member

Apr 3, 2009
12
0
Yes, BUT ...
Unfortunately, the question gets complicated with magnetic core inductors.
Air-core inductors do not change inductance with applied voltage. The formula holds true. But we are probably talking about a magnetic cored transformer -- it also does not change inductance with the applied voltage BUT only over a small portion of its operating voltage. If at some point in the AC voltage cycle the core's magnetic flux becomes saturated, the inductance (and therefore reactance) drops to near zero at that point in the cycle. This is true regardless of the voltage wave shape.
some transformers/inductors are designed to be used in circuits that saturate their cores in this way, but others are designed to be used only at levels well below the saturation point. For most efficient operation, mains power transformers are designed to be used just below the point of saturation.

5. ### JMac3108 Active Member

Aug 16, 2010
349
67
XL=2*pi*f*L applies only to a SINGLE frequency f. This means a sine wave of frequency f. A squuare wave for example has lots of other frequencies in it and you can not apply the formula to it.

6. ### Vahe Member

Mar 3, 2011
75
9
If you can decompose your waveform into its fundamental and harmonic components, you could perform sinusoidal analysis for each component separately using superposition. So the reactance for each frequency would still be of the form you mentioned. Square wave has odd harmonics, so at the nth harmonic the reactance would be 2*pi*n*f*L where n=1,3,5,... (n=1 corresponds to the fundamental frequency).

Cheers,
Vahe