# Recirculation Current in an Inductor

• EigenFunctions
In summary, EigenFunctions is trying to find an equation for a simple inductive circuit with an initial current flow, using Kirchhoff's law. The basic equation is Vdiode=Vinductor+Vresistor, where the inductor is L*di/dt, the resistor is i*R, and the diode is represented by n*VT*ln(i/Is+1). This results in the differential equation di/dt + [i*R/L - (n*VT/L)*ln((i/Is)+1)] = 0. EigenFunctions is unsure how to solve for the expression in square brackets and is seeking suggestions. They also mention adding an additional term for a diode's ohmic resistance and solving
EigenFunctions
I am trying to derive an equation for a simple inductive circuit which is the serial connection of an inductor (L), a resistor (R) and a Diode (D). The initial condition is a current flowing (Izero). Using Kirchhoff's law, the basic equation is:

Vdiode=Vinductor+Vresistor

The inductor is L*di/dt, the resistor is i*R and a simple model for a diode is n*VT*ln(i/Is+1) where n, VT and Is are constants. So the differential equation becomes:

L*di/dt + i*R = n*VT*ln(i/Is+1)

Putting it in standard form:

di/dt + [i*R/L - (n*VT/L)*ln((i/Is)+1)] = 0

I don't know how to deal with the expression in the square brackets.

Any suggestions?

Thanks,
EigenFunctions

PS - the diode function comes from Idiode(v) = Is*(exp(v/(n*VT)-1) as used in spice. Later, I will sum in an additional term for a diodes ohmic resistance.

#### Attachments

• Recirculating diode (NL ODE).pdf
46.1 KB · Views: 311
Solve numerically the way Spice would. Also check your signs. Shouldn't all terms in your ODE be positive?

Inductor is energy source re: Recirculation Current in an Inductor

marcusl said:
Solve numerically the way Spice would. Also check your signs. Shouldn't all terms in your ODE be positive?

You are correct, since the energy is stored in the inductor, it should be (see the updated attachment):

Vinductor = Vdiode + Vresistor

It seems like there should be a way to solve it, maybe with a Taylor series or something like that.

Thanks,
EigenFunctions

#### Attachments

• Recirculating diode (NL ODE).pdf
52.9 KB · Views: 348

## 1. What is recirculation current in an inductor?

Recirculation current in an inductor refers to the flow of current that occurs when the power supply to the inductor is suddenly removed. This current is caused by the energy stored in the magnetic field of the inductor, which continues to flow through the circuit until it dissipates.

## 2. How does recirculation current affect the performance of an inductor?

Recirculation current can cause a sudden surge in voltage, known as a "flyback" voltage, which can damage the inductor and other components in the circuit. It can also cause unwanted noise and interference in the circuit.

## 3. How can recirculation current be controlled?

Recirculation current can be controlled by using a diode in parallel with the inductor, known as a "flyback diode". This diode allows the recirculation current to flow through it, preventing the voltage from rising to damaging levels.

## 4. What is the difference between recirculation current and reverse current in an inductor?

Recirculation current occurs when the power supply to the inductor is suddenly removed, while reverse current refers to the flow of current in the opposite direction through the inductor. Reverse current can be controlled by using a diode in series with the inductor, while recirculation current is controlled by a diode in parallel.

## 5. Are there any other methods for controlling recirculation current in an inductor?

Yes, aside from using a flyback diode, other methods for controlling recirculation current include using a snubber circuit or a clamp circuit. These circuits are designed to absorb the energy from the recirculation current and dissipate it safely.

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