I did not know that...

[simonbaker]

Being impressed with how often my intuition is wrong in this business, especially with coils, I decided to tempt fate once again. I was not disappointed.

My latest experiment (inspired by a picture mikebg posted of a search head with three coils) involves testing the combined inductance of two identical circular coils, in various connection configurations and amounts of lateral separation.

My original intent was to measure how the combined inductance of "cancelling" coils (connected in series with current circulating in opposite directions) varies with lateral separation. Can you visualize that??? I can't.

My speculation was that if the coils were centered at the same point (100% overlap) and one resting on the other, the inductance would be near zero. When separated by a good distance, the inductance should be L + L (sum of the inductances of the identical coils).

It's all about flux, I figured. It seemed to me that the two coils should share at least 95% of the flux if stacked as close as possible (but maybe looks are deceiving). And if the current circulates in opposite directions, the fluxes should cancel and the inductance go to near zero.

But flux has me flummoxed, as usual.

Well, yes and no.

Here is my conundrum wrapped in an enigma and dropped in a quandry basket: the inductance was not near zero but slightly more than L/2 !!!!!

What, you're not amazed? Let's think about it. Take a different case altogether: If I had two identical coils in parallel not sharing any flux (no mutual inductance), the combined inductance should be L/2. But these coils, albeit in series, are smack-dab slapped up against each other and phased in opposite directions. I would have sworn on my mother's bobbin that they should cancel nicely and have at most L/10 combined inductance.

But I was wrong...shocking...

However, I tried one other gambit, now connecting my stacked coils in parallel, still phased in opposite directions (as before) to cancel each other.

The combined flux was now approx L/7. Better, I guess. Maybe.

So I decided to study this one physical configuration (coils 100% overlapped) and take some measurements while connecting the coils electrically in different ways. I hereby present you gentlemen (and ladies?) with the results and scant further analysis.

Pictures of the coils are below to assist in pointing out the flaws in my thinking.

Coil(s) description:

Diameter: 22 cm
Turns: 20
Wire: 24 AWG

1. L1 Inductance of coil1: .251 mH
2. L2 Inductance of coil2: .255 mH (virtually same as L1)

3. L3 Combined inductance coil1 || coil2 (parallel), phased opposite: .038 mH (15% L1)
4. L4 Combined inductance coil1 || coil2 (parallel), phased same: .214 mH (85% L1)

5. L5 Combined inductance coil1 -- coil2 (series), phased opposite: .156 mH (62% L1)
6. L6 Combined inductance coil1 -- coil2 (series), phased same: .858 mH (340% L1)


Scant analysis:

Case 3 seems somewhat predictable, very low inductance with coils in parallel but phased opposite. I would have expected less than 15%, but flux has a way of leaking more than you think.

Case 4 fairly predictable - two identical coils with 100% mutual inductance should have same inductance as one coil but half the resistance. 85% is ballpark.

Case 5 - this one fooled me, I thought it would be more like Case 3. Ideas welcome.

Case 6 - need Qiaohzi's calculator for this one, but basically conforms to the power law of windings and inductance -- double the windings gives much more than twice the inductance.

Using Q's calculator:

Inner Radius: 105 mm (using 21 cm inner diameter)
Wire thickness: .511 mm
Turns: 20
Inductance: .252 (spot on!)

Turns: 40 (two coils stacked 100% overlap)
Inductance: .939 (compare to .858, not bad, considering leaking flux)

So it is really Case 5 that beguiles me. I have a feeling that some calcs using mutual inductance might explain it.

Cheers,

-SB

[mikebg]

Simon, please don't use the term WINDINGS instead term TURNS.
For approximate analyzis, we assume that the inductance is proportional to square of tuns number.
Your experiment was made in last May by Qiaozhi:
http://www.geotech1.com/forums/showp...8&postcount=50
Here are fotmulas for calculating the equivalent inductance of two coils connected in series:
http://www.geotech1.com/forums/showp...9&postcount=52

[Skippy]

I did some related experiments earlier this year. I had two identical coils, and was using one as transmit, one as recieve. One experiment I did was:- I placed them concentrically, and varied the spacing, measuring the output voltage relative to the input. I was surprised that the best output I could get, with the coils butted up against each other, was 0.5 times the input. This goes some way to explain the lack of cancellation/summation you saw with your experiments.
When I plotted the curve of the signal drop-off with distance, it did appear that if I could have had a true 'zero-distance' overlap, ie. the coils bifilar-wound as one, then I would have obtained near-100% output.

[Qiaozhi]

Simon - your experiments will be heavily affected by the coil coupling. As Skippy just pointed out, try the same tests using bifilar coils; then the coupling will be much tighter. Remember that the strength of the electromagnetic field changes in inverse proportion to the cube of the distance from the coil.

[simonbaker]

Thanks for the replies - yes, I'll try to use "turns" from now on.

In the absence of absinthe last night, my mind could not help pondering this experiment further.

By morning, it dawned on me that the following conjecture may be true:

"The inductance of two coils in parallel is always 1/4 of the inductance in series, regardless of the mutual inductance".

This explains my data as a quick calculation shows that:

4 * .038 = 0.152 approx equal to .156 measured.

More to come.

-SB

[simonbaker]

I did some related experiments earlier this year. I had two identical coils, and was using one as transmit, one as recieve. One experiment I did was:- I placed them concentrically, and varied the spacing, measuring the output voltage relative to the input. I was surprised that the best output I could get, with the coils butted up against each other, was 0.5 times the input. This goes some way to explain the lack of cancellation/summation you saw with your experiments.
When I plotted the curve of the signal drop-off with distance, it did appear that if I could have had a true 'zero-distance' overlap, ie. the coils bifilar-wound as one, then I would have obtained near-100% output.

I agree with you and Qiaohzi -- my intuition about the degree of coupling of coils placed in such a stacked configuration is just way off. There must be some heavy-duty flux lines very close to the coil wires that add up to a sizable portion.

I appreciate your sharing your experiment results -- this is how we develop our intuition.

Thanks mikebg for the links to formulas.

As it turns out, this lack of coupling will make my design easier for my next experiment. The next test is to take the same (stacked, opposing) coils and separate them laterally, and measure the combined inductance.

At infinity (a couple of feet?) the combined inductance should be about 2L I imagine.

The purpose of this experiment is to be able to predict how to wind two coils to get the desired inductance for a particular configuration where the coils are separated laterally by a certain distance.

Finally, I'd like to see if there is an optimal separation to make a usable detector with a tri-coil head as shown below, where the RX coils are phased oppositely.

The purpose of opposite phased RX coils is to try to remove EMI noise that haunts certain areas, including my workshop.

I have no illusions that such a tri-coil head would make a good general-purpose search head. First, each coil shares half the overall inductance, making each one less sensitive than a single Rx coil would be. Second, the coils oppose each other, so that a target somewhere in between might be invisible. However, it may be possible that as the head is swept over the target at an appropriate speed, that first one coil bumps the signal up and the next coil bumps the signal down in sync with the natural frequency of the filter electronics in the detector, and some practical detecting in a high EMI environment is possible.

Note that this is not the only configuration for dual Rx coil designs. I'm aware some detectors exist with the Rx coils stacked cocentrically, separated by a healthy distance so that the bottom coil does the detecting and the top coil presumable provides a noise-cancelling signal.

Another approach would be to have the two Rx coils unconnected, and perform the combined signal processing electronically in the MD circuit. This would be the most flexible (although introduce a little circuit noise). However, I thought I'd start with a simple direct connection of the coils.

So my goal is to eyeball a chosen coil separation configuration, use my experimental data to calculate the inductance of each coil needed to get a combined inductance of my choosing (6.5 mH for use with TGSL), and wind a circular Tx coil with 6.0 mH inductance.

Then see if the search head shows less EMI noise in my workshop.

A relatively simple project for my minimal spare time.

-SB

[Skippy]

I've just found my experiment notes. My coils were approx 3.5mm diameter round bundles, 90mm diameter. I did manage to get the coupling good enough to obtain 62% output, in a properly constructed coil I would probably get 50%, as I would have added mylar tape and a lead-foil or graphited-paper shield.
I did toy with the idea of building a 'Sunray' style probe, and this issue of combined inductance affects their design, as they are stacked concentric coils. So your results have relevance to more than just your specific search-head.

[simonbaker]

I've just found my experiment notes. My coils were approx 3.5mm diameter round bundles, 90mm diameter. I did manage to get the coupling good enough to obtain 62% output, in a properly constructed coil I would probably get 50%, as I would have added mylar tape and a lead-foil or graphited-paper shield.
I did toy with the idea of building a 'Sunray' style probe, and this issue of combined inductance affects their design, as they are stacked concentric coils. So your results have relevance to more than just your specific search-head.

Yes, the stacked concentric coils is also of interest to me because of this large EMI problem.

Another idea to combat EMI I'm toying with is to have a smaller coil simply used to sample the EMI and try to electrically cancel it by summing in the pre-amp. It could be located in a number of places so long as it is roughly parallel to the RX coil. It's smaller signal would need to have a greater gain factor, and so would introduce some circuit noise, but that may be a fair tradeoff when EMI is so dominant.

-SB

[moodz]

Being impressed with how often my intuition is wrong in this business, especially with coils, I decided to tempt fate once again. I was not disappointed.

My latest experiment (inspired by a picture mikebg posted of a search head with three coils) involves testing the combined inductance of two identical circular coils, in various connection configurations and amounts of lateral separation.

My original intent was to measure how the combined inductance of "cancelling" coils (connected in series with current circulating in opposite directions) varies with lateral separation. Can you visualize that??? I can't.

My speculation was that if the coils were centered at the same point (100% overlap) and one resting on the other, the inductance would be near zero. When separated by a good distance, the inductance should be L + L (sum of the inductances of the identical coils).

It's all about flux, I figured. It seemed to me that the two coils should share at least 95% of the flux if stacked as close as possible (but maybe looks are deceiving). And if the current circulates in opposite directions, the fluxes should cancel and the inductance go to near zero.

But flux has me flummoxed, as usual.

Well, yes and no.

Here is my conundrum wrapped in an enigma and dropped in a quandry basket: the inductance was not near zero but slightly more than L/2 !!!!!

What, you're not amazed? Let's think about it. Take a different case altogether: If I had two identical coils in parallel not sharing any flux (no mutual inductance), the combined inductance should be L/2. But these coils, albeit in series, are smack-dab slapped up against each other and phased in opposite directions. I would have sworn on my mother's bobbin that they should cancel nicely and have at most L/10 combined inductance.

But I was wrong...shocking...

However, I tried one other gambit, now connecting my stacked coils in parallel, still phased in opposite directions (as before) to cancel each other.

The combined flux was now approx L/7. Better, I guess. Maybe.

So I decided to study this one physical configuration (coils 100% overlapped) and take some measurements while connecting the coils electrically in different ways. I hereby present you gentlemen (and ladies?) with the results and scant further analysis.

Pictures of the coils are below to assist in pointing out the flaws in my thinking.

Coil(s) description:

Diameter: 22 cm
Turns: 20
Wire: 24 AWG

1. L1 Inductance of coil1: .251 mH
2. L2 Inductance of coil2: .255 mH (virtually same as L1)

3. L3 Combined inductance coil1 || coil2 (parallel), phased opposite: .038 mH (15% L1)
4. L4 Combined inductance coil1 || coil2 (parallel), phased same: .214 mH (85% L1)

5. L5 Combined inductance coil1 -- coil2 (series), phased opposite: .156 mH (62% L1)
6. L6 Combined inductance coil1 -- coil2 (series), phased same: .858 mH (340% L1)


Scant analysis:

Case 3 seems somewhat predictable, very low inductance with coils in parallel but phased opposite. I would have expected less than 15%, but flux has a way of leaking more than you think.

Case 4 fairly predictable - two identical coils with 100% mutual inductance should have same inductance as one coil but half the resistance. 85% is ballpark.

Case 5 - this one fooled me, I thought it would be more like Case 3. Ideas welcome.

Case 6 - need Qiaohzi's calculator for this one, but basically conforms to the power law of windings and inductance -- double the windings gives much more than twice the inductance.

Using Q's calculator:

Inner Radius: 105 mm (using 21 cm inner diameter)
Wire thickness: .511 mm
Turns: 20
Inductance: .252 (spot on!)

Turns: 40 (two coils stacked 100% overlap)
Inductance: .939 (compare to .858, not bad, considering leaking flux)

So it is really Case 5 that beguiles me. I have a feeling that some calcs using mutual inductance might explain it.

Cheers,

-SB

case 5 with the reversed series phase should leave approx the Mutual Inductance value ....

M=(Lseries - L1 - L2)/2

so assuming M = 0.156 ... what you measured.

then rearranging .... Lseries in phase

Lseries = L1 + L2 + 2M

Lseries = 0.251 + 0.255 + 2 * 0.156

Lseries = 0.818 ( calculated from your individual coil results )
compared to
Lseries = 0.858 ( your measured series total )

...whats that ... about 95% accurate

coupling coefficient k is approx 0.617 ... a bifilar wound coil will behave much better

moodz.

[Skippy]

Your experimental data is good.
Going through the maths for all 4 coupled conditions gives M (mutual induction) values of: 175,176,177,175 microhenries. Since for identical coils, M=K.sqrt(l1.l2)=KL, I calculate K=176/253=0.696. Ie. 69.6%, which compares well with the 62% value I obtained - my coil was a larger bundle, relative to the total loop size.
Here's a link that explains all:http://www.electronics-tutorials.ws/...nductance.html

[simonbaker]

Great review of mutual inductance! (any topic that flushes moodz out of the bush is well worth it). I'm very satisfied with explanations, it all looks consistent. My intuition was far off in eyeballing the magnetic coupling of coils.. experienced coil winders know better.

Fortunately my objective at the moment is not to achieve tight coupling (in fact the opposite is more useful), so next stop is Q's coil calculator and bang out some circular coils suitable for a 3-coil head for the TGSL.

I think nulling with 3 coils will have an extra degree of freedom.

Regards,

-SB

[satdaveuk]

Great review of mutual inductance! (any topic that flushes moodz out of the bush is well worth it). I'm very satisfied with explanations, it all looks consistent. My intuition was far off in eyeballing the magnetic coupling of coils.. experienced coil winders know better.

Fortunately my objective at the moment is not to achieve tight coupling (in fact the opposite is more useful), so next stop is Q's coil calculator and bang out some circular coils suitable for a 3-coil head for the TGSL.

I think nulling with 3 coils will have an extra degree of freedom.

Regards,

-SB

Hi Simon
I cant wait for your results this thread is so interesting, im eager to build one of your 3 coil projects, keep us informed.
Many thanks

[simonbaker]

Hi Simon
I cant wait for your results this thread is so interesting, im eager to build one of your 3 coil projects, keep us informed.
Many thanks

I don't expect this particular configuration to be deeper or easier to use, but the main objective is to see if it reduces EMI noise which is a big problem in certain areas. And who knows, any design has surprises.

I think the next step I'd like to try is, instead of two identical RX coils, to have a main RX coil in normal double-D configuration, plus a small "EMI sniffer" coil mounted above whose purpose is to sample the EMI noise, and then try to electronically subtract it out in the preamp.

I encourage you to try building a prototype also because I'm not great at construction and may get poor results because of my lack of workmanship.

----------------------------------

I made some quick measurements of "combined series inductance vs separation" of two identical circular coils, connected in series but opposite polarity, separated by varying distances.

Zero distance means 100% overlap -- coils centered at same location.

I normalized the separation distance to be a fraction of the diameter of the coils, so the graph could be more easily used for other coils. I also normalized the inductance to be a fraction of the sum of the inductance of each coil. I also cheated and put a point at 0.0, 0.0 as if the coils perfectly canceled when 100% overlapped. In reality, my coils had a value of approx .32 . I used the idealized value because if you press the coils together
you can get lower inductance, and flat coils would probably have less than jumble-wound, etc. Anyway, we're not too interested in coils with large % overlap because they cancel each other too much.

I will probably choose a configuration with the coils separated by just over a coil diameter -- in other words, side-by-side and touching.

This corresponds to a separation of around 1.0 on the graph.The inductance peaks near this point --hopefully I can estimate the inductance well enough.

-SB

PS. I'd be interested in comparing this graph to Skippy's.

[Skippy]

One interesting point of note on your graph is the point at a spacing of approx. 0.8, where L =1.0. This is the null - point, where mutual inductances neither help nor hinder the performance. This is where IB search-coils would be fixed, if they were circular, eg.Nexus type.
Unfortunately, my tests were concerned with spacing the two coils with them still concentric.

[simonbaker]

One interesting point of note on your graph is the point at a spacing of approx. 0.8, where L =1.0. This is the null - point, where mutual inductances neither help nor hinder the performance. This is where IB search-coils would be fixed, if they were circular, eg.Nexus type.
Unfortunately, my tests were concerned with spacing the two coils with them still concentric.

Interesting point. I don't know if there is significance for dual RX coils (other than makes calculating desired coil inductance simpler). Picking the max inductance point means less wire to achieve a given combined inductance, but that may be irrelevant to the ultimate goal of sensitivity to target.

I'm more and more feeling that such a dual RX design with opposite polarity coils connected in series is just not a great idea, other than hopefully reducing EMI noise. Each coil has about half the inductance and therefore probably half the gain of a single coil with the combined inductance. And because you don't take advantage of the square law of inductance, you have more wire in two coils than a single coil, meaning heavier search head.

Still, I'll try it to see what happens, then go from there with other ideas to suppress EMI.

-SB