# [HELP] Understanding the Mathematical Analysis of MOSFET and Inductor Circuit

#### Boplogz

Joined Oct 17, 2022
22
Hello everyone.

Thank you in advance to those who will help me.

First of all, this project Im doing right now is not student work; this is for my personal learning (though Im still a student).

Im still working on my Pizo transducer driver, and I followed a design from the internet. The circuit can drive the piezo transducer. But I want to understand how it works mathematically. Logically, I understand what's happening somehow, but when there is a change in signal input, I cannot explain why the shape of the signal output is this and that. Even I can't understand how to compute the possible max peak of the signal output. I would also like to know how I can determine their relationship, like how I can compute the proper value of the inductor with respect to the input signal frequency, etc.

Below is the circuit I implemented in the breadboard:

and here is the output:

Question by the way: I've read the the output that I have is not good because it can break the MOSFET. Is it true? would it be good if I add diode? or the sudden peak is needed to drive the Pizo?

I've tried changing the input signal frequency to around 1MHz, and the output signal (BLUE) was like a dumped sine wave:

Now Im confused whether the output I get from 1Mhz is okay or not. How can I make it just like the output from 110Khz?

Thank you so much.

#### Papabravo

Joined Feb 24, 2006
21,264
It is not so much the mathematics you need to understand but the physics.
1. Start with the MOSFET in the ON condition.
2. There is very little resistance from the 18V source through the inductor and the rds(on) of the MOSFET to Ground
3. Therefor a large current will flow through the inductor and the MOSFET to ground which forms a short circuit.
4. When the MOSFET switches from NO to OFF, there is a very sudden interruption in the current.
5. An interruption in the current through the inductor will lead to a VERY large change in voltage across the inductor.
Copying circuits from the internet without understanding them is more than likely to let the magic smoke out of the devices you are using. How about giving us a link to your internet source so we can evaluate the claims made by this particular source, show you where you may have gone wrong, and help you find a solution that you feel comfortable explaining.

#### LowQCab

Joined Nov 6, 2012
4,218
All of the parts in this Circuit are being used in an unusual way,
to create an end result that is questionable at best.

The very first thing to do is to state what You want the end result to be,
then we can possibly make some sense out of
why You would want to build this Circuit in the first place,
and come up with suggestions that might get You going in the right direction.

Piezo-Elements, ( as well as Transistors, Capacitors, etc ),
have a maximum Voltage that they will "usually"
withstand without the "Magic-Blue-Smoke" leaking out.
The Circuit You are attempting to use may be
quite unpredictable, and may Smoke-Parts without warning.

What do You want the Piezo-Element to do ?
.
.
.

#### crutschow

Joined Mar 14, 2008
34,700
L1 and C1 form a resonant circuit, so the applied frequency relative to that will have a large effect on the MOSFET drain waveform.

And that circuit will basically cause the MOSFET to act as a switch, even though you are applying a sine-wave to its gate.
If you want the transistor to act as a linear amp then you will need to make it into a linear circuit configuration.

Yes, the inductive spike can damage the MOSFET if it's higher than the MOSFET's drain-source voltage rating.
You could add a Zener diode from the drain to source with a rated voltage less than the MOSFET's rating to protect it.