Two air coils next to each other - transformer or not? - Page 1
Forum section: electronics / beginners

author: petert
author_rank: Regular Contributor
timestamp: February 18, 2020, 08:49:29 pm
content: Hello,I wound two air coils next to each other (with little distance), on a paper towel roll. One with 25 turns, and the other with 90.The signal from the primary coil couples into the secondary coil as expected.I chose various sine waves from 10-100kHz to feed into the primary coil to test the coil coupling properties.Interestingly, it does not matter which of the two coils I pick as primary (the one with 25 or 90 turns). On the secondary coil the signal will always be significantly weaker (but still have the proper frequency). Is that to be expected?Shouldn't it make a difference which is the primary, and which the secondary, or does this only apply to transformers that have a magnetic core?

author: Cerebus
author_rank: Super Contributor
timestamp: February 18, 2020, 08:59:59 pm
content: They are going to be very weakly coupled in the magnetic domain. I *suspect* that what you're seeing is them being linked by an electric field rather than by a magnetic field. It's something that you can calculate, if you've got all the parameters but a quick test for whether it's e-field or magnetic coupling is to stick a chunk of something ferromagnetic into the core and see if it starts behaving more like you'd expect a transformer to behave.

author: petert
author_rank: Regular Contributor
timestamp: February 18, 2020, 09:21:47 pm
content: I see a minimal change if I put something metalic in the roll or on top of the roll, such as a wrench, or a ruler.I don't have a proper inductance meter, just a component tester (TC1). It says the 90 turn coil has an inductance of 0.23mH and the smaller of 0.04mH. The turn ratio is 90/25 = 3.6, but the inductance ratio is 0.23/0.04 = 5.75. I expected the turn and inductance ratio to match more closely.

author: Cerebus
author_rank: Super Contributor
timestamp: February 18, 2020, 10:10:46 pm
content: Inductance of a classic single layer solenoid scales with thesquareof the number of turns. However, their are assumptions about the geometry that this works on, end effects, proximity effects and the like, so one shouldn't expect to get an exact theoretical 'proportional to the square of the number of turns'. You figures seem plausible for the inductance ratio you've given.Seehttps://en.wikipedia.org/wiki/Inductance#Inductance_of_a_solenoidfor the formulae.The figure that you're looking for to see how well coupled the two coils should be is 'mutual inductance' but be warned, calculating it is a job for one more calculus capable than me (unless my life depends on it). Seehttps://en.wikipedia.org/wiki/Inductance#Mutual_inductanceif you're feeling brave.

author: TimFox
author_rank: Super Contributor
timestamp: February 18, 2020, 10:18:13 pm
content: Ordinarily, a coil pair of this geometry, with a relatively low magnetic coupling, is used in narrow band applications, with one coil (sometimes both) resonated with a parallel capacitor. Otherwise, the leakage flux (flux that does not link the two coils) reduces the efficiency of the transformer.

author: petert
author_rank: Regular Contributor
timestamp: February 19, 2020, 12:00:46 am
content: Indeed, the intended use of the coil pair is as part of a crystal radio, which I built, following the instructions from this page:https://rimstar.org/equip/crystal_radios.htmThe original build (mine is similar):The "circuit diagram" can be seen below:An explanation of how the radio works is given in this video (linked as code to avoid embedding and distracting from the main post).Code:https://www.youtube.com/watch?v=0-PParSmwtEBut I wanted to understand the workings a bit more precisely.In other words, could you give a bit more detail on this:Quote from: TimFox on February 18, 2020, 10:18:13 pmEspecially, is such a coil pair considered a transformer or not? The secondary coil is clearly meant to resonate together with the capacitor to create a tank circuit, to tune in to a frequency (up to a certain precision). And I assume the primary coil couples to the secondary magnetically to avoid loading the antenna too much?I thought the coil pair should also amplify the signal with a transformer-like operation, but the tests showed otherwise.Why not connect the antenna to the tunable coil directly?

author: Cerebus
author_rank: Super Contributor
timestamp: February 19, 2020, 12:50:51 am
content: Ah, all becomes clear. Yes, you're making a transformer, a transformer designed to do impedance transformation. The impedance of free space (i.e. the 'medium' for radio waves) is 377. The impedance ratio for a transformer isZ1/Z2= (N1/N2)2Where the Zs are the impedances seen by the windings and the Ns the number of turns.So your 90:25 turns ratio becomes a ~13:1 impedance ratio. Your 377free space impedance now 'looks like' ~4900to the rest of your circuit. Your signal voltage goes up, and your signal current comes down. A piezo earpiece is quite happy to be driven from a high source impedance so you're getting a voltage gain of ~13 for 'free' while losing drive current that the earpiece wouldn't have taken advantage of anyway. That's a simplistic explanation ignoring the fact that we're dealing with a tuned circuit and complex impedance, not scalar impedance, but it's enough to get a flavour of what's going on.Why your transformer will behave happily at radio frequencies while being nearly useless at audio frequencies requires a longer explanation than I'm in the mood for typing, especially as a proper explanation can't avoid typesetting (or trying to typeset) some maths, and it's also past my bedtime. Succinctly, and completely trivializing it, it's to do with the rate of change of magnetic flux which will naturally be faster for higher frequencies. One for the textbooks really - anyone got a good online resource that would explain this?

author: TimFox
author_rank: Super Contributor
timestamp: February 19, 2020, 12:51:22 am
content: The coupled coils form a resonant transformer. The lower-inductance primary gives an impedance transformation, matching a low impedance into the primary to a higher impedance at the resonated secondary, increasing the voltage into the detector. See radio textbooks for details.

author: petert
author_rank: Regular Contributor
timestamp: February 19, 2020, 01:51:32 am
content: Reminding me that the piezo speakers are high impedance made me recheck the setup of my scope.(Btw, the coil pair is still used alone when doing these tests, and not connected to the crystal radio circuit.)I had the secondary coil (90 turns) connected using a 50 ohm coax cable, and a 50 ohm input termination with a 1x setting for the scope input.The signal was very low, in the mV range.I assume the secondary coil just can't be loaded that much when probing, despite the strong input signal from the signal generator (setting the load to HiZ or 50Ohm at the sig gen side made no difference).Is it because of the low magnetic coupling or is there another reason?So I made another experiment and used the normal scope probes. For a 2 MHz input signal of 1Vpp I get a 3.52Vpp output signal (when using the scope probe with 10x setting (a)). So that is a first success: the signal was amplified.1x setting of the probe reduces the output signal to 552mVpp. (b)The direct coax with 50 Ohm termination (and 1x setting on the scope) results only in a 18.4 mVpp. (c)Doing a frequency sweep (with the same load/scope setups as above) I get the following results:For (c) I would never exceed 280mV (reached at 49 MHz), no matter what frequency.For (b) it would max out at 18.2V (at 1.26 MHz).For (a) it would max out at 15.8V (at 2.3 MHz).So, the transformer is working under certain conditions (certain range of ideal frequencies and with high impedance loads = scope probes). Frequency dependence is expected. But since transformers are also used in power supplies, and I have a strong input signal source, why does it need a high impedance load?

author: chris_leyson
author_rank: Super Contributor
timestamp: February 19, 2020, 02:47:09 am
content: Most of the time you want tuned air cored coils to be well coupled to transfer.maximum power but sometimes there are occasions where you want minimum coupling. Look up Louis Hazeltines TRF receiver design from the 1920s especially US patent 1577421A.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: February 19, 2020, 03:04:20 am
content: 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

author: fourfathom
author_rank: Super Contributor
timestamp: February 19, 2020, 07:23:51 am
content: Quote from: Cerebus on February 19, 2020, 12:50:51 amBut 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.

author: petert
author_rank: Regular Contributor
timestamp: February 20, 2020, 05:05:00 pm
content: Quote from: T3sl4co1l on February 19, 2020, 03:04:20 amThe 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_inductancehttps://de.wikipedia.org/wiki/Streufluss#Streuinduktivit%C3%A4thttps://de.wikipedia.org/wiki/Kurzschlussinduktivit%C3%A4t#Kopplungsfaktor_und_Streuinduktivit%C3%A4thttps://electronics.stackexchange.com/questions/96648/what-is-the-difference-between-a-transformer-and-a-coupled-inductorhttps://electronics.stackexchange.com/questions/6316/coupled-inductor-vs-an-actual-transformerhttps://www.nde-ed.org/EducationResources/CommunityCollege/EddyCurrents/Physics/selfinductance.htm

author: petert
author_rank: Regular Contributor
timestamp: February 21, 2020, 09:43:22 pm
content: 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.aspxThe following however was quite a bit off:https://rimstar.org/science_electronics_projects/coil_design_inductance.htmAnybody know the formula for transformers/coupled coils that respect the geometry, such as the gap between the coils?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: February 21, 2020, 11:38:52 pm
content: 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.pngBy far the best calculator I've seen is:https://hamwaves.com/inductance/en/index.html#inputThis 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

author: The Electrician
author_rank: Frequent Contributor
timestamp: February 22, 2020, 03:00:31 am
content: Quote from: petert on February 21, 2020, 09:43:22 pmThis book has all the answers:https://www.amazon.com/Inductance-Calculations-Dover-Electrical-Engineering/dp/0486474402/ref=sr_1_1?crid=3GSR25RZ5FH5B&keywords=inductance+calculations&qid=1582340311&s=books&sprefix=inductance%2Caps%2C194&sr=1-1