Differential Coils ... theory.

[moodz]

The differential front end is designed to work with a differential coil. I am proposing that the differential PI coil is "self shielding" and no electrostatic shielding is required except in the most demanding applications. Since there is basically no data to support this proposition we will turn to established theory.....

The differential PI coil is very similar / same as an autotransformer.

Basically target information will appear in the coil as a differential signal (magnetic coupling) and EMI will appear as common mode signals(capacitive coupling). Refer to the attached PDF how common mode signals are rejected by the autotransformer over differential signals. By rejecting common mode signals coil self shielding is achieved.

( note that common mode signals includes capacitive coupling to ground ).


Of course if subsequently discover that I am wrong you never read this OK.

moodz_diff_coil.pdf

[moodz]

Differential coil is transmission line transformer.

In the year 1959 C. L Ruthroff presented a paper titled "Some Broad-Band Transformers" at the Proceedings of the IRE. See Proc. IRE Vol. 47, August 1959, pp. 1337-1342.

In that paper you will see two different versions of the UNUN and BALUN which are in common usage in radio frequency applications for matching and impedance transformations.

The differential coil proposed is exactly the same configuration as the Ruthroff Voltage balun. Because the differential coil is constructed from twisted pair ( bifilar ) the coil corresponds to a air cored balun in Ruthroff configuration.

Normally BALUNs and UNUNs are constructed with cores that should be near lossless for high efficiency. In the case of the metal detector the ground and targets now become the core of the BALUN and the resulting loss / induction / change in permeability results in a change in the performance characteristic of the coil and so can be detected when a pulse or other signal is applied and compared to previous measurements.

What this means is that there is now a new type of detector coil ...

TRANSMISSION LINE COIL

Also it is not just applicable to PI detectors but also arbitrary waveform, sine wave etc etc.

However trying to analyse the coil in spice is somewhat more difficult as coiled transmission line elements must be synthesised.

Here is a reasonable understandable reference.

http://www.bytemark.com/products/tlttheory.htm

Of course there is no references for metal detectors as these coil configurations have not been used before as far as I know.

Moodz.

[Qiaozhi]

Here's some more light reading on the subject.
Plus a link to an equivalent circuit with a worked example -> http://vk1od.net/balun/Ruthroff/R1-4.htm

[AdrianM]

Having built a pretty close facimile of moodz differential coil, I'm trying to understand its behaviour. It's pretty easy to determine the resonant frequency of these things, using either a loosely coupled signal generator and scope or simply putting it close to another working PI and scoping the terminals to see the decayed ringing at the resonance frequency. Armed with this info and an inductance meter the intrinsic capacitance can easily be calculated from



So with f=240kHz, L=800uH: C=550pf for my coil. It's made from a total length of 35m (21 pair turns) of 1mm 19SWG magnet wire so started off life as a 17.5 twisted pair. If we were to simply distribute all this capacitance between the two twisted wires the 550pF would be 31.4pF/m or just under 10pf/foot.

Plugging 1mm wire spaced at just over 1mm centres into this twisted pair impedance calculator indicates that about 100pf/m should obtain. Why would the empirical value (the LC resonance) be a third of this? Not complaining - it's bad enough as it is for obtaining a fast decay but I'm trying to understand the physics in order to minimise the decay time.

[Tinkerer]

Hi Adrian,

We get a similar incongruence with the shielding. Some of the capacitance does not show up.

My guess is that some of the capacitance is in series and some is in parallel, so the end effect is a "guesstimate".

Below is a good calculator for inter wire capacitance and inductance that I have been using a lot. With magnet wire I use a polypropylene/air spacer in the form of a pp string, twisted around the wire. It keeps the air spacing even and dramatically reduces inter wire capacitance, at the cost of a small reduction of inductance.

Guessing again, there is probably somewhere a sweet spot between coupling effect and inter wire capacitance, like everything it is a compromise.

http://www.mogami-wire.co.jp/e/cad/electrical.html

I like to see you thinking "outside of the box"

All the best

Tinkerer

[taliesin]

The differential front end is designed to work with a differential coil. I am proposing that the differential PI coil is "self shielding" and no electrostatic shielding is required except in the most demanding applications. Since there is basically no data to support this proposition we will turn to established theory.....

The differential PI coil is very similar / same as an autotransformer.

Basically target information will appear in the coil as a differential signal (magnetic coupling) and EMI will appear as common mode signals(capacitive coupling). Refer to the attached PDF how common mode signals are rejected by the autotransformer over differential signals. By rejecting common mode signals coil self shielding is achieved.

( note that common mode signals includes capacitive coupling to ground ).


Of course if subsequently discover that I am wrong you never read this OK.

[ATTACH]14031[/ATTACH]

i did this on my electric guitar pick ups.humbucking i think they call it.it does buck the hum

[moodz]

Having built a pretty close facimile of moodz differential coil, I'm trying to understand its behaviour. It's pretty easy to determine the resonant frequency of these things, using either a loosely coupled signal generator and scope or simply putting it close to another working PI and scoping the terminals to see the decayed ringing at the resonance frequency. Armed with this info and an inductance meter the intrinsic capacitance can easily be calculated from



So with f=240kHz, L=800uH: C=550pf for my coil. It's made from a total length of 35m (21 pair turns) of 1mm 19SWG magnet wire so started off life as a 17.5 twisted pair. If we were to simply distribute all this capacitance between the two twisted wires the 550pF would be 31.4pF/m or just under 10pf/foot.

Plugging 1mm wire spaced at just over 1mm centres into this twisted pair impedance calculator indicates that about 100pf/m should obtain. Why would the empirical value (the LC resonance) be a third of this? Not complaining - it's bad enough as it is for obtaining a fast decay but I'm trying to understand the physics in order to minimise the decay time.

You may get some funny results if you dont calculate the inductance of the coil properly. M is the mutual inductance. L1 and L2 are the symmetrically wound coils. The core is air so no need to factor in. The "centre tap" is not shown as it no current flows through it after switch turn off.

moodz.




PS
whoops forgot to add M = k x SQRT( L1 x L2 )

[AdrianM]

Tinkerer, thanks for the link. I was interested to hear about your spacer technique as I'm now pretty sure that twisted pairs of magnet wire are not the way to go. I think Tesla was cashing in on the free LC tank he got with this topology. However we don't want that particular property at all.

taliesin, you're so right! And I should have remembered this too - me being a big Gibson fan and all!

moodz, thanks - that formula is indeed the way to calculate the resulting inductance of the two seriesed coils and because I have an inductance meter I use it to work out the coupling constant by comparing the measured inductance of a single coil to the measured value across the two in series. It usually comes out between 0.8 and 1.

The problem I'm seeing here is with the distributed capacitance creating a pretty substantial LC tank out of the bifilar wound coil. This ultimately determines the minimum damping time, which is getting on for twice that of a single coil having the same turns.

In order to get around this I made another, otherwise near identical, coil using 24/0.2 stranded in a thick PVC sheath (OK, there's better dielectic materials out there but this was already in the cupboard!). The capacitance of this comes in at 200pF - much better than 550pF.

And while I was busy getting rid of Farads, I checked the capacitance of various cabling using the same technique as above. 13A Mains flex was adding almost another 100pF so I prepared a coarsely spaced quad helix out of the same wire used for the coil and this adds just 24pF. Now, with the same pulse energy damping is all done at 12uS.

And with a small but useful drop in DC resistance using stranded I can't see any point in making these coils using magnet wire. I would, in fact, advise against it.

(I was curious as to the effect of joining the two coils "down on the ground" compared with bringing them together "up the top" - the latter shaved about 200ns off the damping time - I haven't thought about it enough yet to decide if 4 wires up is the way to go)

[AdrianM]

Is it immune to RFI?

Comparing the schematic of Fig. 1 below (a classic twin loop PI front end) with Fig. 2 (the equivalent proposed for transmission line transformer) it would appear that radio pickup is not going to be cancelled in the latter. In fact, seen like this, I can't really see any difference from a plain centre-tapped coil feeding a differential amplifier

I pretty sure it's valid to reduce the coiled twisted pair down to the essentials shown in Fig. 2 Admittedly the pair form a transmission line with a different arrangement of distributed RLC components, but I'm don't have any intuition as to how this affects the outcome. All I can see at the moment is how it reduces to two windings in series creating one long aerial for RF.

[Tinkerer]

Hi Adrian,

I see that you are really into it, to find new solutions outside the box. So here is a hint, or you could call it a rope to climb out of the box.

The capacitance is the big problem.
One of the Eastern philosophies is it ZEN? says that if your opponent is stronger than you, you must use his own strength to fight him.

So, how about USING the capacitance instead of trying to eliminate it?

Sounds crazy, but it works.

Tinkerer

[AdrianM]

I'm sure that there are ways of getting around the extra capacitance this kind of winding has However, the most important question to me now is "is it worth the effort - what benefits would there be?"

I've redrawn my diagram above comparing the classic anti-phase twin loop with the differential coil, to integrate moodz drawings showing the relevant principles of transformer action. This has made it clear to me (at least!) that there is excellent rejection of electrostatic effects (voltages referenced to ground).

Now what I'm not so hot on is RF theory; if a long-wave radio signal (relating to the electrical length of the coil) intercepts the coil - is this a common signal from ground appearing identically at each end of the coil, or a differential signal appearing across the coil?

[mickstv]

Hi AdrianM, I would be expecting any MW or LW to be cancelled with regards to a differential coil with common ground "Moodz coil" because the received signal will be 180' out of phase.




Mick

[AdrianM]

Hi AdrianM, I would be expecting any MW or LW to be cancelled with regards to a differential coil with common ground "Moodz coil" because the received signal will be 180' out of phase.

Hello Mick, great to see another new poster on the Geotech forums! When I first glanced at moodz writeup I simply accepted that this would be so - but it doesn't seem to be the case.

The first thing that aroused my suspicions was when I realised, night after night, that the signal to noise ratio dropped when the Sun went down - skip I think it's called. I then went about systematically testing each part of the setup. Shorting the coil where the connecting lead joins on the search head totally silences the preamp stage - so the connecting lead and "above" is ruled out. I also check the balance of the differential preamp with a signal generator just to make sure that common mode signals were being rejected properly and they were. At this point I know it's all coming out of the coil itself. So finally, I added a parallel tuning capacitor across the coil and a pair of headphones to the output of the preamp and made myself a long-wave radio set!

OK, so the bandwidth was wide open but classic radio tuning sounds abound - plus some 50Hz, WiFi, Bluetooth - and worst of all (embarrassingly) my Tektronix TDS3014 scope. Everything but the kitchen sink basically.

So, back to theory - I appreciate that radio antenna systems employ a "ground plane" - either literally as the ground (or electrically large - compared to the wavelength being received - conducting surface) with a monopole sticking out of it, or a dipole where one arm provides a similar function. So radio signals are not necessarily referenced to ground (otherwise how would radio work in outer space )

With the differential search coil, despite the notional ground reference point at the centre tap, there are still two projecting arms "curled up" as a coil either side. The electrical length of these arms will accommodate a wide range of radio frequencies where the peak-to-peak distance puts a positive voltage on one end and a negative on the other. A differential voltage I believe. That is how it works, sort of, I think! (I never could get how nature can "unwind" a coil to pull off this sort of trick though). However, if I'm mistaken and nature can't "unwind" the coilI, it would be expected that pretty much the same voltage would appear at both ends. But then again, all kind of antennas are coiled up - particularly long wave ones! I'm sure some more words will be added by a RF expert...

[mickstv]

Hi AdrianM, That definately wasn't what I expected. I'm going to setup a diff coil over the next day or two and have closer look at the common mode rejection or a certain lack of and see what I can come up with.

At this point all my metal detector designs have been build around either mono coil or DD.



Mick

[Tinkerer]

Hi Adrian,

Which signals are common mode and which signals are not, is kind of a mystery to me.
I use a center tapped RX coil and am very happy with it. Why does it work so well, I don't know, but I certainly would like to learn why.

I do use a shield on the coils. Experimenting showed that it does help reduce the noise.
For the leads I use a twisted pair. That seems to work fine too, but I am going to try a shielded twisted pair. Unfortunately, my shielded twisted pair is intended for audio frequency, so I already know that it attenuates the higher frequencies considerably.

I tried varying the bandwidth of the preamp. Reducing the bandwidth from 320kHz to 150kHz showed noticeable reduction in the amplitude of short TC targets. (5us and less)

Now, where I have not been able to find differences in detection depth and sensitivity, is by matching the resistors on the differential preamp. I know that in theory any mismatch reduces the common mode rejection considerably. But the real life RX signal does not show any noticeable difference.

So where and when does common mode rejection function and where and when does it not?

One last comment:

The center tapped RX coil is an antenna for RF. How do the damping resistors affect the antenna efficiency? I know the target signal is affected and have an idea why, but I have no idea what the damping resistor does to the RF.

I find that when one has 4 or 5 coils interacting, it gets difficult to analyse what exactly is happening, so I just consider the 5 coils a black box and happily accept the results that come out of it. ( But still I am curious about the why and how)

Tinkerer