# Current in coupled loops (transformer design)

#### artis

I think I know the answer,but just to make sure.
I have two coupled inductors through a core that provides better flux permeability, aka a transformer, I provide say 5v and 1000 amps AC to the primary loop, in my secondary loop I have a capacitor in series with the loop (of sufficient capacitance for given frequency in order for the reactive resistance to be negligible) will there be just as much current and voltage in my secondary loop? Assume that both loops have the same turns count and wire thickness so from a practical viewpoint a 1:1 traffo.

I am asking this because I'm making a device but in my case I have two coupled toroidal loops each consisting of a single loop of very thick conductor, both loops have a capacitor in series with the loop, the primary loop is an oscillator but I also need current induced in my secondary loop which I assume there will be.
provided the frequency is high, how could I calculate the losses in my air core transformer to know what percentage of my primary current will show up in my secondary side? I assume that copper losses and capacitive reactance losses will be negligible as my copper is short and thick and my capacitor will have sufficient capacitance and low ESR in order to present a 0.0...something ohms in the chain (hopefully)

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#### essenmein

A capacitor in series is in of itself not an issue, like you say as long as its sized appropriately. This is a common practice in SMPS where volt*sec balance between two bridges cannot be guaranteed (eg pro delay differences, switching time differences etc), so a capacitor prevents what is essentially a small DC voltage being applied to the transformer, which would otherwise walk into saturation.

I will say though, making a capacitor with a sufficiently low ESR to not loose a good chunk of that 5V at 1kA is not trivial. 1mOhm ESR would result in 20% voltage loss!

Also note in air, coupling will be a lot lower than if you had a decent permeability core, you may think you have a transformer, but the leakage inductance will likely be quite large, esp with a single turn => not very well coupled.

• artis

#### essenmein

Note also you only need the DC blocking capacitor on the driven side of the transformer, the load side (unless you are doing something weird) should not need it.

#### artis

it's not an smps , and yes I am doing something weird.
well my problem is not ESR as for normal caps where the leads are only attached to certain places, in my case imagine the wire is attached to every part of the capacitor plate periphery, my problem is different , I need sufficient capacitance in order to get reactance low enough so that my loop total resistance at any particular frequency is not so high I lose voltage there.

right now I am focusing on a device intended for 1Mhz and above, the reason I can only have one loop is because each loop requires a capacitor in series and putting more capacitance in series will decrease the total capacitance so increase capacitive reactance. Also at higher frequencies I wouldn't want multiple loops as that would increase my inductance and limit current at some point.

Oh gosh , thanks for pointing out the simple ohms law thing, I completely forgot, in order not to drop a volt or two from an otherwise already low voltage supply I need my total loop resistance very low.

but even without a core material it is still a loop, well two loops actually and I wonder if for example the current in one loop would be 1kA then how much of that would get induced in the other loop given both loops have the same resistance and the same loop area and wire length?

#### essenmein

The SMPS reference was simply an anecdotal point to back up the assertion that series capacitors with transformers is not an issue, you can interpret it how you want, there was no implying you are building a SMPS.

Since you've demonstrated an awareness of ohms law, I assume then you've heard of Faradays law of induction?

Current in loop A, produces a changing magnetic field, some of which is shared with loop B, the amount of shared field results in a value called mutual inductance. Then in loop B, as per Faradays's law, a voltage is induced proportional to rate of change of flux, the amount of current that subsequently flows in this secondary is determined by ohms law and the secondary load. This current is then reflected back to the primary via the mutual inductance, and added to the magnetizing current.

In an air cored transformer, the amount of mutual and self inductance is somewhat difficult to determine empirically, especially from words that in no way describe the geometries involved, when the geometries are the single thing that determines these inductance's. IMO, either build and measure, or simulate (eg HFSS since well HF).

Then, when you are talking about keeping coil inductances low, you have to be aware of which inductances you are talking about, self (or magnetizing inductance), mutual inductance? Leakage inductance (dif between self and mutual) etc, you also have to consider the reflected impedance of the secondary load.

Why 5V and 1kA, why not 50V and 100A? MMF = N*I, so 10turns * 100A is the same magnetically as 1turn*1kA. Decent magnetic coupling will likely be easier to achieve with more turns (eq bifilar wingdings).

#### artis

Well I can't exactly know the voltage as I haven't built the device and tested it, the reason why I can't have multiple turns is because it's not a traditional transformer, one part of it is rotary so i'm limited by space and mechanics and physics from all sides.
I'm trying to keep low the coil self and leakage inductance of course, the mutual inductance should be good for more efficient energy transfer from primary to secondary as in all traffos.

By the way, in a transformer assume both primary and secondary windings are wound the same way in the same direction, say looking at the core from above both are wound clockwise, then if the primary current also looking from above is clockwise what would be the direction of the secondary current? My intuition tells me it should be in the opposite direction because if it would be in the same direction it (under large current/load) conditions would only strengthen the primary field and so a "free" energy situation would arise , I'm I right?

One more thing, imagine my primary winding is also a resonator with certain frequency , energy to which is supplied from an outside source, if my secondary draws heavy current, as long as my primary source can keep up the frequency shouldn't drop , is this assumption sound?
obviously I'm talking voltage, as for a resonator voltage/current determines the charge discharge time and so the frequency.

#### essenmein

If you are resonating with the primary, ie since you are talking about series capacitor, is it series resonant system?

Its really hard to figure out what exactly you want to achieve. But I'll take a stab at assuming.

I'm going to assume that the primary resonant circuit is intended to transfer HF energy to the secondary to a load of some impedance connected there.

So the "L" the primary LC resonant circuit is seeing is Lleak+(Lmag//Lload).

You can see now, minimizing Lleak is good, a high Lmag is not a problem since Lload is where you want to put the current, not the magnetizing inductance.

Yes current flows in opposite direction. Think of xfrm symbol, two winding, both dots at the top, current flows in one dot on one winding and comes out the other dot for the other winding.

• artis

#### Baluncore

You are hypothesising two air coupled single turn loops. The coupling coefficient can be calculated from equations that have been around for over 100 years. First of all, more data is needed.

1. Are the coils coaxial?

2. How far apart are the planes that contain the coil's wire centres?

3. Are the coils round? what are the coil diameters?

4. What is the wire diameter, or is it flat tape or tube?

5. What is the approximate frequency of operation?

#### artis

@Baluncore Well the design is specific and not that easy so I am planning on trying to simulate it in some simulation software like solidworks, but sketching a simple example would be like this, imagine a toroidal transformer, but without the iron core instead an air core, so essentially a toroidal loop.

1)no they are not
2)i'm not sure I fully understood this question (what is the radius of the toroid inner core?)
3)they are mostly round, so one can assume they are round, (the loop consists of multiple parallel connected smaller wires , some are tape like flat and some round for a number of reasons, so assume round for the most part)
4)the multiple smaller wires distributed equally around the toroid in parallel (for better current capacity at high frequency) probably will amount to a large overall diameter of the loop, so say it's something like 100mm
5) well since it's an oscillator (for which i'm still figuring out a a variable capacitor) the frequency might be anything from a couple of Mhz up to (as high as it will go physically) so one can choose a number within this scale like 10 Mhz for example.

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#### Baluncore

Sounds like you are building another mythical beast, this time along the lines of a Rogowski Coil. The coupling will be very poor. You can expect an open circuit secondary voltage but almost no secondary current.
https://en.wikipedia.org/wiki/Rogowski_coil

#### artis

not another , i'm building one device i'm just investigating many different areas of interest that are partly connected with what i'm doing. You are always very critical of me and my ideas and I thank you for that as everything someone tells me I turn into a lesson learned , well at least I try.

it is complicated to communicate complicated ideas through a bunch of sentences online and that is why probably i sound the way I do.

But it's not a Rogowski coil and definitely not a current transformer, it has two loops that are the shape of any ordinary toroidal traffo just without the core.
I guess the best thing I could do is to get myself a pc and some sophisticated simulation software like solidworks and simulate it and see what it does.

#### essenmein

For me at least, I can't even really visualize what "two loops that are the shape of any ordinary toroidal traffo just without the core " looks like, how do you make a single turn look like a toroid baring some fancy hydro formed metal?

Maybe the first step is just knock up a quick 3d model to show what this is intended to look like?

#### artis

well it's rather simple, (maybe i did not explain in enough detail) take a toroid and divide the single turn into multiple parallel turns then distribute them evenly around the 360 degrees. in such way not only i get more even B field but also increase the current capacity of the turn which in my case needs to be large and as low resistance as physically possible.

#### Baluncore

well it's rather simple, (maybe i did not explain in enough detail) take a toroid and divide the single turn into multiple parallel turns then distribute them evenly around the 360 degrees.
How much more confusing can you make it.

A toroid is one single turn of toroid, or you could wind a single turn of wire through the hole in a toroid. Indeed, what is meant by parallel on a toroidal surface? How can a single 360° turn be spread parallel over 360°?

I simply ask that you express yourself not with sentences, but clearly with a diagram that has some dimensions. If you cannot explain your magnetic circuit here, then how can you possibly simulate it with FEM modelling.

"Current in coupled loops (transformer design)"

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