Inductor Efficiency via LC Oscillator

[AspiringEEngineer]

TL;DR Summary

I am doing a calculus project and want to incorporate an engineering application. I have a question regarding measuring the efficiency of an inductor with the area under the sine wave for an LC Oscillator.

I want to create an LC circuit with varying inductors and compare those inductors for efficiency. Would it be accurate to suggest measuring the area under the curve of the first cycle of the resonant frequency would determine which of the inductors are most efficient? If the area is greater, then wouldn't that mean the inductor can induce more current into the circuit?

If not, how could I incorporate calculus to compare the efficiency of the inductors?

Thanks ahead of time!

 

[berkeman]

Welcome to PF.

Inefficiencies in LC resonators come from parasitic resistance, mainly in the inductor. You can look on the datasheets for various inductors to see what their series resistance is. In general, given the same value of inductance, the inductor with the larger body and higher current-carrying capability will have a lower series resistance.

At higher frequencies (100s of MHz and GHz), you also get losses in the ferrite material that are in addition to the resistive conductor losses.

What does your full LC resonator circuit look like, including the AC source and source impedance?

 

[AspiringEEngineer]

Welcome to PF.

Inefficiencies in LC resonators come from parasitic resistance, mainly in the inductor. You can look on the datasheets for various inductors to see what their series resistance is. In general, given the same value of inductance, the inductor with the larger body and higher current-carrying capability will have a lower series resistance.

At higher frequencies (100s of MHz and GHz), you also get losses in the ferrite material that are in addition to the resistive conductor losses.

What does your full LC resonator circuit look like, including the AC source and source impedance?

I plan to build the inductor myself, so I do not have a datasheet for it. I am going to create a 3D printed mold to wrap and compress the copper windings to form an inductor. Then I will make another mold with a different circumference to form another inductor. Both inductors would have the same number of turns and wire gauge.

I plan to connect these homemade inductors to a bench power supply that I recently bought and connect a capacitor to the circuit (a 10-microfarad capacitor). Basically, it is the simplest possible LC circuit with an inductor, power source, and capacitor.

I haven't concluded what AC voltage I will use yet. I also have to determine the source impedance as well.

This is really a learning curve for me as I am taking Calc I and hope to switch majors to EE soon. I figured why not do a project on something I am passionate about.

 

[berkeman]

I plan to build the inductor myself, so I do not have a datasheet for it. I am going to create a 3D printed mold to wrap and compress the copper windings to form an inductor. Then I will make another mold with a different circumference to form another inductor. Both inductors would have the same number of turns and wire gauge.

Good for you. That is very creative, and a good project to learn from.

and connect a capacitor to the circuit (a 10-microfarad capacitor).

A non-polar capacitor, right?

I plan to connect these homemade inductors to a bench power supply that I recently bought and connect a capacitor to the circuit (a 10-microfarad capacitor). Basically, it is the simplest possible LC circuit with an inductor, power source, and capacitor.

A DC source is not appropriate for testing an LC resonant ("tank") circuit.

I haven't concluded what AC voltage I will use yet. I also have to determine the source impedance as well.

An AC source is better for determining the efficiency/loss of your tank circuit.

What frequencies are you looking at for testing this? The efficiency will vay across frequency.

 

[hutchphd]

I do not disagree with anything so far. Is there any way for you to obtain an oscilloscope or USB dongle capable of modest frequency response and at least two channel input? This will change your world. Consider it an educational expense. You will learn very much faster.

 

[AspiringEEngineer]

A non-polar capacitor, right?

How do I check to see if the capacitor is non-polar? It is from a Freenove electronics kit I have and it looks like this:

A DC source is not appropriate for testing an LC resonant ("tank") circuit.

I will have to use 120v then because this is the only power supply I have: https://www.amazon.com/dp/B0852JZQZR/?tag=pfamazon01-20

What frequencies are you looking at for testing this? The efficiency will vay across frequency.

I will just have to test it at 60hz from the 120V A/C.

Here are other tools at my disposal:

-Oscilloscope
-Function Generator
-Calipers
-Multimeter
-3D printer
-Clamp meter
-Graphing calculator
-Basic electronic components (resistors, sensors, capacitors, etc.)

 

[hutchphd]

A function generator is just what you need. And the oscilloscope and some education as to what to do. So describe your experimental process. What ...How ...why?

 

[hutchphd]

That is a polarized Cap and not suitable for the application

 

[AspiringEEngineer]

I do not disagree with anything so far. Is there any way for you to obtain an oscilloscope or USB dongle capable of modest frequency response and at least two channel input? This will change your world. Consider it an educational expense. You will learn very much faster.

I bought this oscilloscope and I am hoping it was a good investment:

https://www.amazon.com/gp/product/B0771N1ZF9/?tag=pfamazon01-20

The only USB dongle (where a USB type-C branches to 3 connection ports: HDMI, another type-C, and a type-A) is the one I just pulled out of my laptop case:

The wire I'm going to use is from a subscription service called "Curiosity Box" where a company sends you science stuff to learn. They recently sent a box that was themed electromagnetism, so I can salvage the copper wire they gave me from there.

 

[AspiringEEngineer]

That is a polarized Cap and not suitable for the application

Can I create my own non-polar cap then?

 

[hutchphd]

You want as non-electrolytic cap. I will let the experts tell you which. There are good ceramic caps available.
The scope looks just fine. Have you played with it yet?

 

[AspiringEEngineer]

A function generator is just what you need. And the oscilloscope and some education as to what to do. So describe your experimental process. What ...How ...why?

Okay, so my project is to take Calculus I concepts and apply it to a real-world application (be it engineering, business, or any life experience that can include calculus). I have been researching and fascinated by wireless induction for quite some time, so I figured why not center the project around that.

The research question I came up with is: If two inductors have the same perimeter and the same number of turns (thus made up of the same length of wire) but different shapes, will the inductance be equal?

My hypothesis is that they will not be equal because the cross-area section is different between the two shapes.

My first hurdle was to determine how I can have two shapes equal in length and perimeter. My answer to this was to take a circular coil for one inductor. The other inductor will have concave angles (like the shape of a star) to shrink the circular coil while maintaining the same perimeter (length to travel around the shape).

My paper would describe the different shapes by calculating their different areas inside the shape (so the circle would be π(r)^2 and the other shape will be the sum of the area of triangles and a polygon).

My second hurdle was to eliminate any possible measurement errors. Because wrapping a wire around something by hand could cause kinks or inconsistent shapes, I decided to make a mold with my 3D printer. I will use the free website TinkerCad to do this.

I just made this just now very quickly for explanation purposes and will look 100% better once finished. Basically, that shaded area on the blue will be exactly the diameter of the wire so once I coil wire in that space it will not be able to form kinks. Also, that black piece will be used to compress the wire so that there are no spaces between the turns of the copper wire. I am going to use my calipers to find the diameter of the wire.

From here I will connect a capacitor to the circuit to create this:

Once I have the circuit together, I well induce a voltage and see the LC tank on the oscilloscope which would look something like this picture I drew:

I will calculate the area under each cycle (hence introducing calculus concept: integrals) and sum them up for a total area. I will do this for both inductors.

I will then figure out which inductor has the greater total area and deem it more efficient because it resonates greater current before zeroing out.

I think I could just take the area under the first cycle and can conclude the same thing now that I think about it.

Originally, I wanted to build and test the inductor using wireless inductance. It would have looked something like this:

The circle and wire common in both conductors would have been my receiving inductor. I was going to measure the efficiency of the inductors by measuring the current they produce on the receiving inductor. The reason I chose not to do this, is because I do not know how to incorporate calculus into the experiment. Unless I create a curve of the shape's area to show how the current output varies area. Then I could use calculus to measure the change in current at a given shape area.

 

[AspiringEEngineer]

You want as non-electrolytic cap. I will let the experts tell you which. There are good ceramic caps available.
The scope looks just fine. Have you played with it yet?

I read the entire manual it came with and really enjoyed seeing a signal appear on screen just to calibrate the probes. Other than this I haven't done much because I'm afraid of ruining the internal components. I wanted to finish this super long tutorial on YouTube before I begin making simple circuits with an Arduino and display them on the oscilloscope. The function generator I haven't even turned it on yet because I do not know how to use it.

 

[Averagesupernova]

@AspiringEEngineer I realize you have now decided to use the function generator but the thought of a homemade coil and that 25 Volt polarized electrolytic capacitor hooked to the 120 volt line which was your previous intent really makes me question if you should be doing any of this without some actual guidance from someone in addition to the people on this forum.

 

[AspiringEEngineer]

@AspiringEEngineer I realize you have now decided to use the function generator but the thought of a homemade coil and that 25 Volt polarized electrolytic capacitor hooked to the 120 volt line which was your previous intent really makes me question if you should be doing any of this without some actual guidance from someone in addition to the people on this forum.
-
What is your reason to be using a capacitor?

The reason to use a capacitor is that an LC circuit requires one. The current has to be able to oscillate back and forth from an inductor, and it can using a capacitor. I wasn't expected to use 120V at first, but I found out my DC power supply will not work.

There are no teachers or experts at my location, so I have to self-teach myself and get input online from others in order to do this. I am going to take the safety precautions necessary and ensure the circuit has a fuse (even if the fuse is part of my main circuit breaker).

 

[hutchphd]

I like your approach and enthusiasm very much. How is it that you have a pretty good lab set up and no particular guidance? For instance, only the signal generator should drive the RLC network

 

[AspiringEEngineer]

I like your approach and enthusiasm very much. How is it that you have a pretty good lab set up and no particular guidance? For instance, only the signal generator should drive the RLC network

It is because I am not around any engineers, and I am taking calculus online through UMGC. Once I get back to the states, I plan to transfer to a different university with an engineering department. (I am looking at UMD or possibly Texas Tech. But, my goal is to get accepted into Georgia Tech one day.) I really want to be an engineer and I bought so many books, equipment, and watch YouTube videos endlessly about electricity. I haven't had the chance or "know-how" to implement my ideas, so I figured why not start with this little project. My background knowledge is only from a trade school where I learned about residential wiring and a small bit of EMF and Ohm's law. I didn't mind the wiring but the theory is what really got me interested.

But to digress back to the topic, I didn't know I could use the signal generator as a source for current in my circuit. I thought it is only used to insert a waveform calculation and see what it would look like in real-time on an oscilloscope. Now that I think about it, if that was its only purpose, then it would just be a live graphing calculator for trig functions and that's it. It is a good thing I now know it can be used to induce an alternating current into a tangible circuit.

How do you determine what frequency is ideal to test the inductors I described? Earlier I said 60Hz just because it is a common frequency, but I would like to find a reason behind what frequency to choose.

 

[eq1]

AspiringEEngineer, you might want to take a look at this webpage. The experiment is very well written up and quite similar to what you're attempting. I think you could pick up a lot of good pointers from it.
https://www.giangrandi.ch/electronics/ringdownq/ringdownq.shtml