Transcranial Magnetic Stimulation

[Enthalpy]

Hello everybody!

Neurology uses Transcranial Magnetic Stimulation (TMS) for research and sometimes diagnostic and treatment.
Introduction there: http://en.wikipedia.org/wiki/Transcranial_magnetic_stimulation
Some documentation there, but other manufacturers exist: http://www.magstim.com/

As I understand it (but beware I'm bad on biology and neurology), not the magnetic field, but the gradient of electric potential and current it induces, creates the desired effect on the brains. The action resembles partially an electro-shock, but:

• The skull is tranparent to the magnetic field, while it hampers the electro-shock's current;
• Hence the skin isn't as brutalized by TMS;
• The path of the current and the intensity are better controlled;
• This let's concentrate the effect to some cm².

Since the gradient of electric potential is the time derivative of the magnetic vector potential A, the average of the gradient over a cycle is zero; I understand a net electrochemical effect is obtained because electrochemical reactions are non-linear (they often show a threshold to voltage) and the pulse is made asymmetric, with a sharp current rise that induces a strong short gradient, and a long current tail that induces a weak long gradient.

A pulse can have 100µs rise time and 1ms fall time. Series of pulses are also used, sometimes of alternate polarity, but always with pulses of asymmetric transition times.

A good gradient of electric potential needs a strong magnetic induction, and in these non-permeable materials, this means kA in a coil, many kW pulse power, and as a result, the coil is very loud and gets warm, which limits the duration of a session or demands active cooling.

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I propose to split each pulse into N shorter ones, scaling like that for understanding:

• Individual pulses are N times shorter, both at rise and fall time;
• The reactive volts per coil turn are kept the same;
• Hence the rate: amps*turns per time unit is unchanged;
• And the amps*turns are divided by N.

The effect on the brains should keep unchanged when introducing N, because:

• The electric potential gradient, which results from the rate of change of the magnetic potential, is unchanged; (if you prefer, it varies as the volts per coil turn, which are unchanged)
• The cumulated duration of the electric potential gradient is unchanged;
• The proportion between rise and fall time, hence the ratio of electric potential gradient is unchanged.

Beware a few things can go wrong here... For instance if some electrochemical reaction needs a consolidation time before it withstands the inversion of polarity of the electric potential gradient. As usual, I didn't check if this was proposed, tried and possibly abandoned - sorry for that - so interested readers should.

Provided the desired effect is still present, splitting the pulse provides big advantages to the apparatus:

• The current is divided by N, but the duration remains;
• Consequently, forces in the coil are divided by N²;
• The coil's deformation speed after N shorter pulses is divided by N, and the noise power by N²;
• The energy dissipated in the coil is lowered. By less than N2 because losses increase with frequency;
• Electronics can deliver N times less current if the voltage is kept, and the energy is N times smaller.

Transition times divided by N may cool down the enthusiasm of electronics designers. As well, it requires probably to brake the coil current actively, for instance with an H bridge, or braking diodes reinjecting current in the power supply, possibly by a secondary winding somewhere. A transformer before the coil can bring advantages: match the cable's and coil's impedance to the power supply and switching components' possibilities; have a separate winding to brake the current; produce inverted pulses by an other primary winding and two switches instead of an H-bridge.

Coils should be made of so-called Litz wire (probably a wrong translation for "braided wire"). In fact, if this isn't already done with 100µs pulses, it should have been: this limits the heat in the coil but may demand a current braker. The current braker could even be a series resistor, easier to cool than the coil. Shorter pulses demand wire braided more finely, which reduce the wire's section filled by copper, so the energy lost in the coil is divided not quite as quickly as N².

Marc Schaefer, aka Enthalpy

 

[0xDEADBEEF]

I would guess that they just connect a fat capacitor to the coil. So the rise time and maximum current are an effect of the R,C and L of the system. If you try to disconnect in the first half of the charging cycle you would produce strong back emf and you would also throw away most of the energy in your capacitor. While if you let it swing, it may even work through a few cycles. Maybe you are right and they use rectangular pulses or something like that. But they are neurologists, I think they just want a massive oomph. Like in electroconvulsive therapy our understanding of the brain is so bad that we do the equivalent of smashing it with a hammer in different places to see if it has an effect or cure a disease.

 

[0xDEADBEEF]

From magstim.com

The D702 has at least 25% extra stimulating power compared with previous generations of Magstim coil*, while also offering an 85% increase in the number of stimulation pulses feasible at 50% power when energised at 1Hz. This has been validated by independent research in which testing was carried out double blind.

Maybe I am too sceptical of physicians, but this sounds a lot like 25% more oomph to me.

 

[trini]

The only thing I wonder about is whether higher voltages are unsuitable for neuro-related devices. The neurologists probably didn't design the devices, they would have told electrical engineers they wanted a field of XX strength. The engineers probably would have done as you suggested, unless the neurologists warned them otherwise. Its just a guess as to why they use higher currents instead though.

Oh and if this was your public disclosure you've got a year to patent, clock's ticking bro ;) Perhaps look at some of the patents on the matter already, see if they mention these issues. gogogogo.

 

[Enthalpy]

And here's a diagram intended to clarify the changes in the waveforms. Log in if needed, lick to magnify.

I've sketched N=5 for clarity, but real apparatus will probably use a bigger N.

Wave forms are idealized; real-life ones are smoother, and shall be so to protect the components.

I've written Ruhmkorff mode on the last waveforms, by analogy with an ignition coil, but terms like Forward and Flyback mode would sound more familiar to power electronics engineers.

 

[Enthalpy]

A well designed TMS coil can have 1ms time constant, real ones have a bit less, but forward operation at N=10 or N=100, with fall time shortened accordingly, needs to brake the current actively. The brake circuitry (a lossy freewheel if you wish) is less than obvious, because the brake voltage is (say 10 times) less than the supply voltage, and the brake circuitry shall not misfire during pulse rise, despite users want pulses of both polarities with few ms between inversions.

Referring to the circuit example sketched below (log in if needed, click to magnify):

An IGBT opened long before the pulse decides the polarity. The TMS coil could have been connected between these collectors, but the second transformer insulates the TMS coil and permits a direct gate control. A big E ferrite core suffices for such a transformer, so I feel this combination easier.

The left IGBT defines the rise time of the current pulse, and the supply voltage defines the rise rate.

On this sketch the resistor sets the current fall time in the coil. Operation at big N is meant to reduce losses in the TMS coil, but here most supply power is dissipated in the resistor. While this power is smaller than at N=1, and the resistor easier to cool than the TMS coil, one may prefer to reinject the energy in the supply. A third winding can help this, but since the voltage and current must already challenge the existing main switch technology, this winding shouldn't step up the voltage, so the power dump rail must have a lower voltage than the supply.

An adjustable power dump rail would control the fall time independently, and a braking voltage constant over the pulse may improve the TMS operation by limiting to a uniform plateau the induced electric potential gradient. The rail must accept and transform power but be pre-loaded before the first pulse. Several braking windings of different voltage ratios may help. I preferred to draw a resistor on the sketch

At high N operation, hence with shorter commutation of a smaller current, MOS must be better than IGBT. Soft commutation (resonance) would be nice, except for the clarity of the sketch

Marc Schaefer, aka Enthalpy

 

[Enthalpy]

Up to now, supplied power increases the current quickly in a TMS coil, which must be the neuro-active phase when the induced electric potential gradient is strong, and a passive circuit let's the current decrease more slowly, in which phase I postulate the electric potential gradient must be below a threshold so it doesn't cancel out the effect obtained in the active phase.

If this model holds, the Flyback operation mode must produce the same result, where the powered phase increases the current slowly in the TMS coil, inducing a limited electric potential gradient, and the neuro-active phase brakes the coil current quickly to induce a strong electric potential gradient. (This must apply as well when the pulse is not split.)

In this other operation mode, the circuitry first supplies a moderate voltage to the coil to accelerate the current, then interrupts the current brutally, which results in a strong electric potential in the coil as well. Very similar to an engine's spark ignition circuit.
This operation mode seems advantageous:

• The smaller electric potential gradient, which I suppose is the more delicate phase, is better controlled as it results from the supply voltage;
• The brutal phase, when both U and I are strong, can flow in the circuitry through a diode, which is more robust than a transistor;
• The circuit example here is simpler.

Referring to the circuit diagram sketched below (log in of needed, click to magnify):

The diodes and transistors must withstand the inductive overvoltage when cutting the current; the supply voltage is much lower, roughly in the same ratio as current fall and rise times in the TMS coil, for instance 10 times lower. The inductive overvoltage is defined through the brake voltage in this example.

The power supply provides less peak power now, but the brake circuit absorbs more, and the transistors must cut the full I at full U, uncomfortable. If the brake windings have as many turns as the accelerating windings, these windings can be coupled very closely to protect the transistors, and can even be the same winding - but with the same number of turns, the brake voltage is much bigger than the supply voltage.

A different choice uses fewer turns at the brake windings, and injects the brake current directly in the supply. This limits to a fixed ratio between the current rise and fall time, which can be switched if additional brake windings provide different numbers of turns. The transistors demand a separate protection then. Anyway, circuitry to protect the components (and preferably soften the transitions) is necessary, though not drawn on the sketch.

Marc Schaefer, aka Enthalpy

 

[Enthalpy]

I would guess that they just connect a fat capacitor to the coil...

O yes! Because their maximum pulse is nearly 3kV and 7kA, leaving no room for extra flourish. Their circuit must be very similar to the one I built to make SmCo magnets: fat capacitor, overloaded thyristor, coil, freewheel diode - except that my pulse was a 10ms half-sine and theirs has to rise in 100µs because they seek dA/dt and I wanted H.

So the waveforms in the first case are just a simplification of my drawing. Their rise is much a true quarter-sine, and the fall nearly an exponential.

On the improved operation I propose, I'd like the lower-voltage phase to have a true plateau, not an exponential, because this limits the peak voltage there for a given flux and duration, and I suppose the neurologic effect of the pulse comes from non-linear electrochemical response to a strong a short phase versus a weaker and longer one.

 

[Enthalpy]

...the equivalent of smashing it with a hammer in different places to see if it has an effect...

Sure. The induced electric potential gradient extends well over 5cm for its strongest portion, and 10cm away it's only divided by 3...

In one use, neurologists check whether some muscles can be activated by induction in the brain. It tells if the spine transmits properly. The apparatus is good enough for that, and shows usefulness.

Which does not mean that neurologists are happy with said hammer. While the pulse sequences I propose don't improve the field pattern, the weaker peak voltage during the weak phase may improve operation. And anyway, avoiding the noise and heat associated with 7kA is better.

 

[Enthalpy]

...whether higher voltages are unsuitable... they use higher currents instead...

Well, with 3kV and 7kA they are from both sides. I hadn't mentioned the voltage...

My guess is: power components (thyristors) exist for 3kV, several in series is a difficulty, but a <3kA thyristor can dump 7kA, so this choice wasn't bad. They had to keep the cable's weight under control as well.

The coil would begin at 200V more or less, it's the voltage per turn I estimate - but 100kA then, worse choice. More than 3kV would make the apparatus even more dangerous, for neurology just as for any use, and insulator thickness gets fat then.

So within their pulse shape, duration and number, 3kV and 7kA is one reasonable combination. What I hope is that dA/dt matters, not A or B, and a shorter t can be offset through repetition, so A and B and I can be smaller (and then U as well, since the coil's number of turns gives some freedom between I and U).

 

[trini]

https://www.google.com/?tbm=pts#q=t...24c3c451ed711c&bpcl=37643589&biw=1440&bih=799

Have a look there, I filtered it to include utility patents only. Only about 8 pages of results so you can check through them all to see what is applicable to you. I haven't read them but check these:

http://www.google.com/patents/US785...a=X&ei=89GZUKiRDIuc9QSUg4D4CQ&ved=0CDsQ6AEwAg

http://www.google.com/patents/US799...a=X&ei=89GZUKiRDIuc9QSUg4D4CQ&ved=0CD4Q6AEwAw

http://www.google.com/patents/US801...&sa=X&ei=htKZUM-yMozS9QTA7YFw&ved=0CDgQ6AEwAQ

You should look at the patents asap before you get into any more theory. Good luck

 

[Enthalpy]

Here are the losses I computed for eddy currents in wires, because these predominate if thick wire is used at moderate or high frequency.

Omega is 2*pi*F
B the RMS induction
rho the resistivity (18e-9 ohm*m for cold copper)
d the diameter of individual wires
D the diameter of the bundle
l the length and V the volume of the conductors
eta the filling factor
mu the total permeability (pi*4e-7 H/m for vacuum).

A wire, thin enough to let an external field pass through nearly unchanged, dissipates as on the first attached formula (provided I didn't botch it, of course).

A round bundle of thin wires that creates its own induction dissipatesas on the second formula. This holds approximately for an annular coil BUT beware it's for 1 turn... Multiply by the turns squared. Note losses don't depend on the bundle's diameter.

The limit where eddy currents lose as much power as the DC resistance does is on the third forula - still when the bundle creates its own induction. It can be worse with a magnetic core, especially near an air gap.

The parry to eddy currents in conductors is a braided wire ("Litz wire") composed of insulated thinner wires twisted together. Round wires can occupy this fraction of the cylindrical section at best:
7/9 ~78% for a 7-wire Litz
19/25 ~76% for a 19-wire Litz
49/81 ~60% for a 7*7-wire Litz, and so on
knowing that a cylindrical section occupies at best 79% of the winding area of a coil.

Marc Schaefer, aka Enthalpy

 

[Enthalpy]

A coil can be made for N=100, that is 1µs and 10µs rise and fall time (or 10µs and 1µs in flyback mode) with small losses. It takes tiny wire, like d=71µm. Then, braiding it ("Litz wire") in several steps, like 19* and 19* and 7*, achieves a good copper section.

The coil may then have for instance 4 turns, so 500V suffice to induce the desired electric potential gradient. Because of the shorter times, the coil takes only some 350A despite having fewer turns (existing coils must have about 15 turns).

This can simplify the electronics - but times are shorter! Above all, it reduces the heat in the coil by >100 and the noise by a similar factor.

The cable between the generator and the coil must be braided also. It can consist of 4+4 strands, themselves braided in several steps, slightly smaller than the coil´s one, assembled in an 8-braid that is flexible. Pairs of strands in the 8-braid carry opposite currents. This cable is lighter and loses little power thanks to the smaller current.

Aluminium wire would improve a lot the cable´s weight, but braided insulated thin aluminium wire must be tailor-made.

Marc Schaefer, aka Enthalpy

p.s. My Internet access is broken, hope to read you all soon.

 

[trini]

enthalpy, i know what you're working on is just the coil, but maybe what is most needed is a way to focus the field so that it is concentrated in select areas rather than something which hits the whole brain. perhaps look into some kind of wave guide or focusing device? It could also be beneficial in terms of what you're doing as it would require less power if you are focusing the field.

 

[Enthalpy]

My Internet access is broken right now, my apologies for bad reactivity.

As shorter pulse times reduce the induction far below the present 1-2T, a ferrite core gets possible. Only outside the skull, but it can cut by two the magnetic path length and the current needed.

Smaller current and induction also enable coil shapes not circular. Though, neither induction nor the vector potential can be focussed at distance; at best, a subtractive pattern of currents could make the vector potential sharper. As creating the desired fields gets easier, we may consider subtractive patterns...

In every case (also at 1ms and 10ms), the turns of the coils should be spread apart where a concentrated field is not desired. This reduces the self-inductance hence the necessary voltage - or current if increasing the number of turns.

Marc schaefer, aka enthalpy

 

[Enthalpy]

Even shorter pulse times seem possible.

With a single thick turn, an 8-shaped coil with both D=70mm loops in series shows about 240nH. It still needs about 200V per turn, but limiting this to 5ns reduces the peak current to 4A approximately, and this is accessible to some RF transmitter transistors.

Then, the transistor, capacitor (or a cable´s capacity) and flywheel can sit in the coil head, and the cable transmit DC power instead of the strong pulse. Much gets simpler.

Can we exaggerate the pulse duration further? Yes, but with an electromagnetic pulse then, not just magnetic. It must have unsymmetric durations if my explanation holds. This one would fully enable to concentrate the field. More later, maybe.

Marc Schaefer, aka Enhalpy

 

[Enthalpy]

Here under is a coil enabled by the smaller current and induction: neither round nor flat. The turns are packed close where the effect is sought, and spread apart elsewhere to reduce the inductance.

Usual 8-shaped coils induce undesired potential gradients nearly half as strong under their return paths as under the central zone; the coil sketched here shall minimize them by placing the return paths farther away from the cortex, but near enough to reduce the effect of the main current path outside the central zone.

The angles of the turns (possibly more than 4, possibly of different sizes and shapes) should hence be optimized. I won't do it; a small software needs only to sum over the current path the contributions to the vector potential A to various positions at the target. The Biot and Savart formula is expected in the next message, and in
http://de.wikipedia.org/wiki/Biot-Savart-Gesetz

The active zone being ~45 mm long and the return paths ~85 mm, I estimate the inductance to 560nH with for instance 4 turns, using 4*500 nH/m where the turns are grouped and 1*500 nH/m where they're spread. To achieve the same 2,9 GA*turn/s as the 2* D70mm coil from Magstim fed with 2800 V, the design example takes only 725 MA/s and 406 V, and if the pulse's active duration is just 1µs, the peak current is only 725 A. Power components may prefer more turns.

The coil's wire consists for instance of commercial Litz wire (visual impression here under) of 33*Awg41 or 71µm individual wires. 7 such threads are twisted to a strand (for 2m in a lab, fasten them to the ceiling, put weights, and turn) and 7 strands to a conductor of 6.4 mm2 in D~4.5 mm, filled to 40%. Over the coil, 1.5 mohm DC resistance lose 2.8 mJ over one pulse of 1+10 µs * 725 A, while eddy currents lose roughly 1.6 mJ. Copper weighs 30g, so if hundred 1+10 µs pulses are one 0.1+1 ms pulse worth, the coil can absorb 2000 equivalents in 80K heating.

The cable may use the same 7*7*33* D=71µm conductors; 4+4 of them, insulated and braided, plus shielding and mechanical protection, make a 2 m bipolar cable. Copper weighs 0.91 kg; 2.8 mohm DC resistance loses 5.4 mJ and eddy currents some 1.8 mJ. The coil plus the cable lose 15mJ from a 150mJ pulse. Aluminium Litz wire would be highly welcome.

A pair of Toshibas's MG300Q1US51 - and certainly others - look capable of switching the pulse: 1200 V, 300 A, tr=50ns tf=100ns. The forward mode would reduce conduction losses in the IGBT. Regenerative braking reduces the supply's capacitors to ~1 dm3.

Marc Schaefer, aka Enthalpy
(Log in and click on the pictures to magnify)

 

[Enthalpy]

And here's the fourth picture needing a second message: Biot and Savart's law for the vector potential. You know, A, from B = rot(A). And mu/4pi is 10^-7 in S.I.

 

[Enthalpy]

Greater numbers of shorter pulses need even less power. Here the current shall increase for 5ns and decrease for adjustable 50ns.

The coil can keep the same shape as for 1µs but now thick rod or tube is good enough. The turns are now in parallel to reduce the voltage to 100V; or several generators can feed each a part of the coil; or the coil can consist of one single very broad conductor, preferably broader at the return leg, and accept a slightly smaller voltage. Over 5ns, the total current increases to 3.6A only.

The outer turns will swallow more current than the inner ones, which isn't bad for the induction pattern; to avoid this, put the turns on a square pattern (or hexagonal, etc) near the target zone, instead of side-by-side.

The fast main switch is a dual MOS meant for RF transmitters, like the BLF884P. Their supply is at most 50V, brought to 100V by a 1:2 transformer which also produces bipolar pulses. Braking through the diodes reinjects power in two special lines; the one that shall not brake is just fed over twice the supply voltage - this better design works for longer pulses as well. Some diode-capacitor pump can preload the braking lines, while voltage regulation defines the braking time. A few Zener chosen by transistors could dissipate the small power.

The diodes could be SiC Schottky like the C3D08060A. These would contribute 4W of the 7W switching losses at 70ns period, and to nearly all 4W conduction losses. These diodes begin at 600V in a LF package; a better fit would be welcome.

The HF electronics is at the coil, and the power and control cable is now easy and lightweight.

Marc Schaefer, aka Enthalpy

 

[Enthalpy]

With pulses like 70 ps long we leave the simpler near-field operation and magnetic coils. This is electromagnetic wave with antennas.

A strong short pulse followed by a weaker and longer compensation needs a wide band antenna, nevertheless directive and powerful. I sketch one possibility below (click to enlarge), where the rectangles are conducting elements meant to radiate.

The antenna comprises many dipoles side by side and butt, together with driving electronics. The shape should better approximate a section of a sphere; the dipoles can be driven with a slight time difference only, for fine steering, to compensate small tolerances, or to compensate diffraction at the target. The antenna has no reflector but can be backed by an absorber at some distance.

The dipoles are charged before each pulse; here resides the emitted energy. Each dipole has locally its own fast transistors to discharge it, for instance two BFG425W. The switch could also be behind a line, and possibly shared among several dipoles, but bigger transistors are uncommon at that speed.

Take dipoles 2* 20 mm long, wide to have 80 ohm wave impedance, charged at +-4 V. The transistors can reach the 50 mA in 30 ps; this constant current widens to 2* 20 mm within 70 ps, which defines the duration of the strong short plateau of induced electric field at the target.

10*12 dipoles at 200 mm distance would create in air the same field as present TMS apparatus with 3 GA/s. Permittivity at the brains and the cranial liquid reduces the field, and so do reflections at the scalp and the skull, but R² times more dipoles, R times more distant, create a field R times stronger.

When the current pulse reaches the ends of a dipole, fast diodes (for instance three BAT62 per dipole) allow the current to continue flowing, due to the antenna's inductance, this time between butt dipoles. The current decreases more slowly, first due to losses in the transistors and diodes, say 1.2 V versus 8 V accelerating voltage, and second due to the finite length cumulated by butt dipoles. This defines the weaker longer plateau of induced electric field, maybe 6 times weaker here than the strong plateau. Less asymmetric than before, but still better than present TMS apparatus.

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The dipole width or diameter can adjust the wave impedance a bit to match the components' current capability. They can't be too close, or their interaction will limit the current. The examples given are not optimum, especially the old diode is capacitive and slow (which cancels out partially). Stronger voltages would be very useful but MOS seem unavailable at this speed. I haven't checked other FET.

Driving the bipolars is difficult. I expect no charge gain per stage at 30ps, so the gain of the driving tree shall result from impedance transformation, but on a wide band and with floating voltages... Striplines similar to a gamma match, with ferrite for the bandwidth, and tapered to match the impedance?

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70 ps make a pulse 20 mm long in air, which relates to the best field concentration at the target. This speed is difficult for components, and isotonic water has only 49 mm penetration depth at 5 GHz and 22 mm at 10 GHz.

Operation immersed in a water-like (or brain-like) material would improve a lot. It could use a liquid gel at the hair and a solid gel on the way from the antenna. 2 to 5 GHz limit the losses; the ~150 ps pulse is easier to produce even if stronger and is only 5.5 mm long in water, which improves the field concentration at the target and the size of the dipoles.

Immersed operation also reduces reflections, as only the skull has strong interfaces, and reduces imprecision due to refraction. Subtle beam synthesis by electronic steering can compensate the aberrations due to the skull, but this difficult option is more futuristic.

If the antenna doesn't touch the skull, the beam can follow the optically observed head's movements, by limited electronic steering, or by automatic control of the antenna's position.

Marc Schaefer, aka Enthalpy

 

[Enthalpy]

A V antenna is wideband, and it can produce naturally the asymmetric pulse. Please refer to the sketch below; log in and click to magnify.

The source injects a current whose longitudinal components in both arms of the V compensate another's effect, and transverse components add. As only a fraction of the current radiates, the V antenna is much a transmission line; its line impedance should better be kept uniform so the current is as well: the conductors on the sketch are thicker where wider apart - or they can be sheet of variable width, or several wires packed closely at near the source and spread at the far end.

Inject a current pulse that raises in 70 ps for instance - easier than the previous 30 ps. It propagates in the conductors essentially at the medium's transverse electromagnetic speed, say 350 ps for some 100mm length, so the A field (magnetic vector potential) emitted near the source arrives at the on-axis target retarded by that additional delay, while near the tips, the field is emitted later but without the additional delay. The radiation cumulates over the length, with the net effect on-axis to radiate a 70 ps pulse as would the same current do over the width of the antenna, but over a broad band. Off-axis, the delays compensate badly so radiation is weaker. This is very similar to an ultra-relativistic particle that radiates when deflected. If the V is 2*10 mm wide for instance over 100 mm, the discrepancy is less than 2 ps.

After some 350 ps for 100 mm length, the pulse arrived at the open conductor tips is reflected and the current stops, beginning at the tips and extending to the source over the 100 mm in 350 ps more. Because the reflected pulse travels away from the target, its effect created near the source arrives at the target 2*350 ps later than the effect created near the tips, or 700 ps, so the A field takes this time to decrease. The induced electric field, which is the variation speed or A, is made asymmetric here, again more easily than with the butt dipoles.

Other antennas have a wide band (log-periodic, cigar) or rather wide (helical, Uda-Yagi...) but the V has naturally the uniform propagation time that takes care of a pulse's shape.

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The electronics can preload the antenna and discharge it with the 70 ps current rise time in a switch transistor near the antenna, where the current lasts for 700 ps - or the pulse can be produced by other wideband means. A propagation line can also reach a more distant component, say one output of an integrated circuit, but not too far since this prolongs the conduction time and worsens the achievable repetition rate. A distributed amplifier is an option.

An array of such antennas and sources brings the needed signal strength to the target. Arranging them on a section of a sphere remains good, and as the V antennas are much more independent, electronic steering and beam forming fits better here, especially if the integrated circuits can make the variable delays. Now the focus can follow the patient's movements.

Or if one (or few) source has enough power, a single antenna can feed a concentrating reflector or lens. With individual or collective lens, the antenna V can be wider and still focus to a narrow target.

Immersing the array in a water-like or brains-like material brings the advantages described for the butt dipoles. Electronic steering eases the compensation of diffraction at the skull to achieve full resolution in the very permittive medium: very few mm, even deep in the brains.

Marc Schaefer, aka Enthalpy

 

[Enthalpy]

The V antenna is more directive than a dipole, hence the wave that leaves it is wider than a half wavelength. Consequently, synthetic beam formation alone can't achieve the narrowest focus; something like a lens, individual or collective, is necessary, possibly in addition to phasing the array.