# how to calculate kickback voltage for the inductor in a RLC circuit?

I am designing an RLC circuit and can anybody suggest the method to calculate theoretically the kickback voltage produced by the inductor to choose the flyback diode. I have tried simulating the circuit and measured the kickback voltage which was around 110 V in simulation.The following images consists of the circuit diagram IS there any theoretical method for calculating the kickback voltage without simulation. thank you in advance.

• that schematic looks wrong. and/or you're measuring the wrong place. Jul 17 '17 at 4:51

## 2 Answers

To a first approximation, assume that all the energy stored in the inductor $P = \frac{I^2L}{2}$ is transferred to the capacitor $P = \frac{V^2C}{2}$. If the circuit is highly damped it will be less as energy will be lost to the resistance during the first half-cycle.

Yes, you can solve for the positive-going peak of the first oscillation. Your circuit roughs out to the following equation, using Kirchhoff's current law:

$$\frac{\textrm{d}^2 V}{\textrm{d}t^2}+\frac{1}{R C}\frac{\textrm{d} V}{\textrm{d}t}+\frac{1}{L C}V=\frac{60\:\textrm{V}}{L C}$$

A solution I get to this using initial conditions at $t=0$ of $V=0$ and $\frac{\textrm{d}V}{\textrm{d}t}=0$, if I didn't screw up, is:

$$60\:\textrm{V}\cdot\left\{1-e^{\frac{-t}{2 R C}}\left[\operatorname{cos}\left(t\sqrt{\frac{1}{L C} - \frac{1}{\left(2R C\right)^2}}\right)+\frac{\operatorname{sin}\left(t\sqrt{\frac{1}{L C} - \frac{1}{\left(2R C\right)^2}}\right)}{\sqrt{\frac{\left(2R C\right)^2}{LC}-1}}\right]\right\}$$

If you take the derivative of the above and solve for 0 (peak or valley), you'll find that a solution is $t_1\approx 571\:\mu\textrm{s}$. Sticking that into the above equation gives $V_{t_1}\approx +114.554\:\textrm{V}$.

Looking carefully at your graph, I find that both the time as well as the magnitude and sign appear to be pretty darned close.

So, I'd argue that theory can calculate quantitative results which may match well with either empirical results or those from Spice. Aside from the basic physics of current, voltage, resistors, capacitors, and inductors, the method is called ... wait for it ... calculus.