Freewheel Diode

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Series R-L circuit is the time circuit with resistor and inductor. Since current through inductor can’t be stopped instantly, freewheel diode must be added in parallel to inductor. Series R-L circuit with mosfet as the switch and freewheel diode is shown in figure bellow.

freewheel-diode

When mosfet switch is “ON” equivalent circuit looks like this

series-l-r-circuit01

According to KVL, differential equation that describes series R-L circuit is

l-r_eq01

Solution gives exponential function for inductor current.

l-r_eq02

So current rises up exponentially towards maximal value of

l-r_eq03

Since general form of exponential function with the time constant is

l-r_eq04

for series R-L circuit time constant is

l-r_eq05

When current in the inductor is higher then zero, according to above equations, current can’t drop to zero in no time at all. It will drop to zero exponentially, and additional path for discharging must be provided. For this reason, freewheel diode is added in parallel to inductor. When mosfet switch is “OFF” according to the Lenz’s law, negative voltage over inductor would be induced and forward bias freewheel diode.

series l-r circuit02

Differential equation for this circuit is

l-r_eq06

Solution is

l-r_eq07

In here, I0 is initial current, i.e. current that was in the inductor before switch was turned off. Time constant during freewheel diode conduction is

l-r_eq08

where RD is resistance of conducting diode. On the first glance, it might be confusing how is the time constant reversely proportional to resistance. Point is that voltage decrement is equal to current resistance product. If resistance is smaller, smaller is decrement and it takes longer time to reset inductor current, and vice versa.
It is important to notice that without freewheel diode in parallel with the inductor, sudden cutoff would damage the mosfet or other switch.

Note: real freewheel diode with 0.7V voltage drop will relax inductor current faster then it would do ideal diode with no voltage drop.

Go to R-L circuit simulation

 

External links:

series R-L circuit on electronics-tutorials
series R-L circuit on Electrical Engineering
series R-L circuit on Wikipedia

 

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