# Inductor Current and Maximum Power Calculator

Inductors used in switch mode power supplies and buck or boost topologies are normally driven with pulses of voltage. An inductor increases in current linearly as a ramp as a function of time when the voltage across it is constant. Thus, as the longer the pulse time the higher the instantaneous current will reach.

Ipk= V*Ton/L

For example,assuming zero initial current, if a 1mH inductor has 10V applied for 1ms, then after 1 ms the current will be:

Ipk= 10V*1ms/1mH= 10A,

So we can see current can quickly climb in a typical inductor.

Since power inductors use some sort of core material to increase inductance over a mere air coil, most inductors and transistors will saturate if the current goes above the rated saturation current. Saturations is the point at which the core disappears and looks like "air". Since air coils have lower inductance, (after all that's why were are using the core) the inductance plummets and the current shoots up correspondingly as shown from the equation above. Current shooting up out of control has the tendency to burn up MOSFETs. In fact, if you are driving a coils with a MOSFET and it is burning up, then it is likely a saturation problem, which can be solved by using an inductor with a higher saturation specification.

So the questions arise if you are using a coil, and it is powered in discontinuous mode, i.e. the current is completely discharged on each cycle: What is the maximum pulse on time that you should use? How much power is being transferred to the coil?

#### Equations

These equations assume that the coils dissipates all current on each cycle.

F_{min}= 1/(2*Ton_{max})

Ipk= V*Ton/L

Ton_{max}=I_{sat}*L/V

Irms= Ipk/sqrt(3),

Vrms= Vpk*sqrt(Duty_Cycle)

P= I*V*sqrt(Duty_Cycle)/sqrt(3)

in the case of a 50% duty cycle

P= I*V/sqrt(6)

E= L*I^2/2