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Two air coils next to each other - transformer or not?

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T3sl4co1l:
What dimensions do the coils have (by themselves, and in relation to each other)?  There are tables to calculate the coupling factor (see Radiotron Designer's Handbook 4th ed. (RDH4) for example).  We can plug the results into a simulator and show exactly what you're measuring. :)

Transformer, yes, absolutely.  A practical definition may be wanting, however.  In that case we might say that a transformer transforms voltages and currents, transmitting power rather than storing energy.  Which means a very high inductance and coupling factor.  Whereas inductors store energy rather than transmit it.  We would then call this a coupled inductor: the self-inductance is significant (low), so energy is stored.  Power is also transmitted (coupled), and energy is also stored in that coupling (indeed, you can convert a nonideal transformer to a tee or pi of inductors, of values that aren't necessarily realistic, but the math doesn't mind that :) ).

Tim

fourfathom:

--- Quote from: Cerebus on February 19, 2020, 12:50:51 am ---The impedance of free space (i.e. the 'medium' for radio waves) is 377 \$\Omega\$.

So your 90:25 turns ratio becomes a ~13:1 impedance ratio. Your 377 \$\Omega\$ free space impedance now 'looks like' ~4900 \$\Omega\$ to the rest of your circuit.

--- End quote ---

But don't get too attached to that 377 Ohms value.  The actual impedance of a random-wire antenna (especially an electrically short one) is likely to be *much* lower than this, and highly reactive as well.  Still, the coupled coils will step up the voltage, and probably reduce loading on the tuned circuit, making for sharper-tuning and higher voltage gain.

petert:

--- Quote from: T3sl4co1l on February 19, 2020, 03:04:20 am ---What dimensions do the coils have (by themselves, and in relation to each other)?  There are tables to calculate the coupling factor (see Radiotron Designer's Handbook 4th ed. (RDH4) for example).  We can plug the results into a simulator and show exactly what you're measuring. :)

--- End quote ---
The smaller coil has a length of 1.15cm, the larger coil has a length of 4.1cm. This is a ratio of 3.56 and is no too far from the turn ratio of 3.6 (makes sense within measuring precision, due to wires squishing together or moving a bit etc.).
The distance between the coils is 0.4cm to 0.5cm.
Inner paper roll diameter is about 3.9 cm, outer diameter with the copper wire winding on top of it between 4 and 4.1cm.
The copper wire itself has a diameter of 0.4 mm.

I had a look at the book online, but it's quite involved. Is there some kind of online calculator or simulator as you mentioned?
I would also be interested to know the expected gain of the transformer for the given parameters and at which frequencies it is would be highest.
Any direct/specific formulas or calculators would be helpful, since I am trying to gain practice before going very deep into math or theory.

Some related references:

https://en.wikipedia.org/wiki/Leakage_inductance
https://de.wikipedia.org/wiki/Streufluss#Streuinduktivit%C3%A4t
https://de.wikipedia.org/wiki/Kurzschlussinduktivit%C3%A4t#Kopplungsfaktor_und_Streuinduktivit%C3%A4t

https://electronics.stackexchange.com/questions/96648/what-is-the-difference-between-a-transformer-and-a-coupled-inductor
https://electronics.stackexchange.com/questions/6316/coupled-inductor-vs-an-actual-transformer
https://www.nde-ed.org/EducationResources/CommunityCollege/EddyCurrents/Physics/selfinductance.htm

petert:
I could find calculators for inductors, but not for transformers/coupled coils that respect the geometry.

This calculator gives results that match pretty closely with the inductance measurements:
http://www.66pacific.com/calculators/coil-inductance-calculator.aspx

The following however was quite a bit off: https://rimstar.org/science_electronics_projects/coil_design_inductance.htm

Anybody know the formula for transformers/coupled coils that respect the geometry, such as the gap between the coils?

T3sl4co1l:
The first is the old Wheeler formula, which is generally pretty good.  It'll be within, say, 10% or so, which is maybe about as accurate as you should be working anyway, and you should design in an adjustment of comparable range to account for that and other errors.  The other is the long solenoid approximation, only true when L >> D.

A better approximation for rod cores is this graph,
https://www.seventransistorlabs.com/Images/Rod_Core_Pressman_Billings_Morey.png

By far the best calculator I've seen is:
https://hamwaves.com/inductance/en/index.html#input
This uses a helical waveguide model, with many adjustments and approximations for wave and material properties, to give a very realistic RL (or RLC when available) equivalent.  It is likely more accurate than the dimensions of any coil you can reasonably construct. :)

I don't happen to know any references for coupling, beyond RDH4.  For concentric coils of similar length, the coupling is roughly the area ratio.  For off-center coils and mismatched diameters, you might take a more general approach, like figure out the magnetic field at a distance (I forget the formula for that offhand, but it can be found in physics solutions) and do a cross sectional ratio.

Tim

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