Sam's Trans-Cranial Magnetic Stimulator

Flexomatic Magnetic Pulser 1

Version 1.00 (14-Nov-15)

Copyright © 1994-2018
Samuel M. Goldwasser
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Sci.Electronics.Repair FAQ Email Links Page.

Reproduction of this document in whole or in part is permitted if both of the following conditions are satisfied:
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Table of Contents

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    Author and Copyright

    Author: Samuel M. Goldwasser

    For contact info, please see the Sci.Electronics.Repair FAQ Email Links Page.

    Copyright © 1994-2016
    All Rights Reserved

    Reproduction of this document in whole or in part is permitted if both of the following conditions are satisfied:

    1. This notice is included in its entirety at the beginning.
    2. There is no charge except to cover the costs of copying.

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    This device uses voltages and energies that will be instantly lethal if live parts of the circuitry are contacted while in operation or after shutdown due to the charge on the energy storage capacitors. The energy stored in the capacitors of the upgraded version (Rev. 2) is enough to electrocute five (5) or more healthy adults dead dead simultaneously even after the line power has been removed! Respect it! Read and follow ALL of the safety guidelines found in Safety Guidelines for High Voltage and/or Line Powered Equipment and the section: SAFETY, below. If in any doubt about your abilities or experience DON'T attempt to replicate a machine like this!

    Should you succeed in constructing and testing it or something similar without killing yourself in the process, the short or long term effects of TMS on the human brain, peripheral nerves, or other parts of human anatomy are not known and could result in permanent changes that are not immediately apparent.

    No claims as to any theraputic or neurologic effects are made by the author for this device. Use at your own risk. It is presented for information purposes only. Thus the "Shock" graphics don't only relate to electrical shock, but to other effects on brain function due to the TMS pulses.

    We will not be responsible for damage to equipment, your ego, county wide power outages, spontaneously generated mini (or larger) black holes, planetary disruptions, or personal injury or worse that may result from the use of this material. This includes premature hair loss or the development of a pimple on your backside twenty years in the future!

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    For anyone considering the construction (or servicing!) of a device like this, there are at least two major considerations:

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    A Trans-Cranial Magnetic Stimulator (TMS) device with an air-core coil is described that may be built using parts readily available new or surplus. Motor threshold is reached at at less than 40 percent of maximum energy using an optimized coil design based on the Magventure/Medtronic B70 butterfly/figure-8. Relevant parameters are: Maximum voltage = 1,450 V, energy storage capacitance = 163 uF (over 173 Joules at maximum voltage, coil with dual 8+ turn windings overlapped, inductance = 10.8 uH, biphasic period of 269 µs with better than 50 percent energy recovery, and repetition rate at near full energy of 1 pps, up to 10 pps at reduced energy. Polyphasic and monophasic pulse modes are also supported in the basic design.

    Based on publically available information on the winding parameters typical coils, maximum dB/dt, and biphasic period, this device is operating at greater than 3/4th of the energy and dB/dt of commercial TMS systems using air-core figure-8 coils. Tests with one subject (me) show that the motor and sensory thresholds, and occipital sensory threshold are reached at at less than 40 percent of maximum energy.

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    Trans-Cranial Magnetic Stimulation (TMS) is technique for exciting neurons in the human brain through the use of short intense magnetic pulses delivered via a coil placed on various locations of the head. TMS has been used to treat or diagnose various neurologic problems including depression, migraines, neuropathic pain, negative symptoms of schizophrenia and loss of function caused by stroke, and others. What follows is in no way promoting its use for any purpose other than curiosity. I simply considered it a challenge to see if it was possible to build a functioning TMS devices using readily available parts. There was something fascinating about a pulsed magnetic field being able to cause effects inside the brain.

    Any home-built TMS devices I've found on the Web do NOT appear to have been based on serious science. Their output was either too weak or of an inappropriate pulse shape or duration to have any effect. And the electronics, if more than half-baked, appeared most likely to short out, blow up, or catch fire after one or two shots.

    This document describes the implementation of a Trans-Cranial Magnetic Stimulator (TMS) developed based on publicly available scientific literature and TMS manufacturers' technical specifications. Performance was simulated using models developed or modified by the author. The prototype was constructed mostly from parts found in the author's junk cabinets and available surplus (mostly eBay).

    And it does work. The pulse energy of the Rev. 2 version is estimated to be at least 3/4ths that of typical commercial TMS systems from companies like Magventure, though at a slower maximum repetition rate. (That would be remedied in Rev. 4.)

    If you're not a MAD SCIENTIST type, please just click your browser's "back" button now and save yourself a lot of potential risk.

    Note that Rev. 2 was required to evoke a consistent and dramatic TMS response, Rev. 1 produced no confirmed TMS effects, though there could have been something below a conscious level. This is believed to have been primarily due to its low maximum energy despite the other pulse parameters appearing to be adequate. But Rev. 1 was useful for initial construction and testing. Around 40 precent of the maximum energy of Rev. 2 was required to achieve detectable brain stimulation in multiple areas including the sensory-motor cortex and occipital lobes. However, in addition to faciliating the testing of the electronics at slightly less lethal energy, Rev. 1 did provide a decent massage when used to stimulate verious perpipheral nerves and could project aluminum rings across the room. :)

    Oh, and while some people in the industry have suggested the use of TMS devices for sexual stimulation, a $5 vibrator turns out to be far superior. ;-)

    The following is not intended to be a research paper but simply a general article for the casually interested or die-hard mad scientist hobbyist experimenter type. ;-)

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    TMS functions by inducing a minute current inside the brain as a result of a magnetic pulse applied outside the head. To achieve a detectable response, the rate-of-change of the magnetic field must exceed a threshold value. But that's not all. To do this optimally, the stimulating pulse must be of short duration (but not too short as it turns out since the neural response has a finite time constant), have sufficient energy, and be of a specific shape - the biphasic (essentially one cycle of a damped sinusoid). The optimal biphasic duration is supposedly somewhat under 200 µs though there isn't a strong variation within this range. Commercial TMS devices appear to use pulse durations of 180 to 300 µs with a stored energy of more than 100 J. The TMS coil must be designed to maximize coupling for peak dB/dt in a localized region two or more cm from its surface. The electrical parameters interact so that, for example, increasing C also increases the pulse duration while increasing the number of turns of the TMS coil (to boost the magnetic field) increases L at approximately the square of the number of turns thus increases the pulse duration. For example the following are roughly proportional:

    Without an underlying understanding of these requirements, one might be tempted to simply dump as large a charge as convenient into an arbitrarily constructed coil and expect a useful result. This will not work. The power supply voltage, energy storage capacitor uF value, coil inductance must be traded off in the design to optimize performance.

    When initial construction was one, these requirements were not understood except in generalities. :( :) The electronic design was based on the availability of a large SCR! Only when the circuit worked perfectly but did absolutely nothing beyond giving a decent massage via peripheral nerve stimulation and tossing aluminum rings across the room, was a serious investigation of the literature undertaken. What followed were multiple attempts with various coil designs finally homing in on one (Sam #13) that is similar to a commercial TMS coil. This still did not work even though the pulse duration was optimal and its peak value appeared to be sufficient. At that point the BIG capacitors were called in to boost energy, first by a factor of 3 to 4 (which finally produced an unequivocal response), and then for good measure, to the present value of around 160 µF (171 J).

    Thus there are two separate systems that need to be optimized to work together:

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    These specifications apply to the two versions constructed to date (2015). Rev. 1 proved out the basic principles but at lower (and somewhat safer) energy. Once it was fully functional and proved useless for TMS (due to its low energy), Rev. 2 boosted maximum energy first to around 85 J resulting in an immediate trans-cranial neural response, and then to over 170 J in its final (for now) form.

    Front View of Complete Unit

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    Front Panel Controls and Indicators

    This is a certifiably low tech device with no embedded computers, no touch-screen, and no internet connection, sorry. ;-) The "user interface" :) is very simple. There are no menus and while there's no guarantee it won't blow up, the OS will not crash and never requires firmware updates. ;-)

    On the top left is the main power switch and indicator and below that the high voltage keylock switch. The timing circuits are enabled with main power so that the repetition rate can be set. Running without high voltage enabled but with charged capacitors is possible.

    The Variac controls the high voltage from 0 to approximately 1450 V on the capacitors. The meter and red LED below it show the charge on the capacitors.

    The knob to the right of the analog meter (!!) sets the pulse rate from approximately 1 pulse every 2 seconds to 10 pulses per second. The meter monitors the high voltage and is optimize for transient respone. The switch below it selects free run (up), off (middle), single shot fire (down, momentary). When used in this mode, the pulse repeat rate is still limited by the setting of the pulse rate control. The green LED lashes with each pulse.

    The knob on the far right selects the pulse type: biphasic (CCW), polyphasic (middle), monophasic (CW).

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    Pulse Types

    The three types of pulses were chosen primarily based on implementation simplicity. :) Typical current waveforms are shown below, derived from a sense coil and integrator. The horizontal scale is approximate 150 µs/div.

    Waveform (Pulse) Types: Biphasic, Polyphasic, Monophasic

    1. Biphasic: This is close to the shape of a single cycle of current determined by the RLC parameters of the energy storage capacitor, coil inductance, and total effective circuit resistance. Because of the natural decay of the oscillations, the second half is slightly smaller than the first half and they are both distorted. The biphasic pulse is the only waverform that does not totally drain the capacitor(s) but retains up to 60 percent or more of the original energy depending on the coil inductance. Thus, the repetition rate for (nearly) full energy can be over twice as high for the biphasic pulse compared to the others.

    2. Polyphasic: Rather than being cut off after one cycle, the natural damped oscillation is allowed to continue essentially until it decays to nothing.

    3. Monophasic: The current is allowed to "free-wheel" around the coil inductance so that the current peaks based on the LCR parameters and then decays slowly until the capacitor is almost entirely discharged. Due (1) lack of utility for TMS and (2) implementation issues (excessive number of dead SCRs), the monophasic pulse has not yet been implemented in the Rev. 2.

    These waveforms in the photos used a coil with an inductance of approximately 34 µH with the original (Rev. 1) energy storage capacitors (25.4 µF total) resulting in a frequency of ~6.1 kHz or period of ~164 µs. With Rev. 2 having a capacitance totalling 163 µF and a 10.8 µH coil, the resulting frequency is ~3.7 kHz or a period of ~270 µs.

    The positive half-cycle is through the primary SCR. The negative half-cycle is through its associated parallel diode. The little blip at the end is believed to be due to the reverse recovery time of the primary SCR. (More below.) With another coil of only 10 µH, the damping factor ended up being slightly lower resulting in a more extended decay of its ~10 kHz oscillation.

    A spreadsheet for estimating the behavior of the RLC discharge circuit using coil parameters and calculating peak current, peak B-field, B-field a fixed distance from the coil, dB/dt, and more can be found at: Magnetic Pulser Modeler (Coming soon).

    The behavior of a simplified discharge circuit may be found at PartSim: Pulsar1-2.

    A Javascript program for estimating the magnetic field produced by 1 or 2 coils can be found at Calculator for Off-Axis Fields due to One or Two Coils.

    Matlab was also used to model the pulse discharge in more detail.

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    Coil Design and Fabrication

    TMS coil design has been described as a sort of art by some, and this is certainly not a bad way of putting it. Many tradeoffs have to be made in terms of dimensions, wire size, # turns, configuration (single or figure 8 or other), cooling, and others. For a given initial voltage, the total capacitance, inductance, and resistance, determine the discharge behavior for a damped RLC circuit. (This assumes that the thyristor and other losses are small and that the circuit behaves linearly, as is the case with an air-core coil. All bets are off if using an iron or other ferrous core that can saturate!)

    With the value of the energy storage capacitor(s) fixed and resistance mininized (which is generally assumed), this leaves the inductance of the coil as the principle variable used to determine discharge behavior. To maximum the peak field requires a larger number turns and to minimize pulse duration requires a small number of turns.

    Several programs were used to model discharge behavior for a large number of coil options, as well as at various energy storage capacities and voltages. An Excel spreadsheet computed (among other values) peak discharge current, peak on-axis magnetic field for a single circular coil, field at specified axial distance, dB/dt and induced electric field for this field. Inputs are coil winding parameters, energy storage capacitance, capacitor voltage, and estimates for parasitic inductance and resistance due to circuitry other than the capacitor and coil. A separate Javascript program was developed to compute the off-axis field of two coils with arbitrary sparation in 3 dimensions using the coil winding parameters and current as inputs. This is primarily used for the radial field calculation of single and figure-8 coils. Combining these into a single Excel spreadsheet would be possible but was deamed more involved than worthwhile given the need for elliptic integrals for the off-axis field calculation. In fact, simply using the values for the axial field at a specific distance ends up being fairly close for estimating the relevant values at the "sweet spot" of single or figure-8 coils.

    The final coil constructed to date (called "Sam #13") is a slightly smaller version of a design based on the Medtronics/Magventure B70, which uses a pair of overlapping pancake coils rather than thicker coils sitting side-by-side. Coil winding parameters and biphasic pulse duration were found from [x] and the Magventure Web site. From these, an estimate of the energy storage capacitor of their system could be estimated. The next coil planned called Sam #14 is very similar, but to be constructed from 1/8" copper tubing with an oil-to-air heat exchanger to perfmit continuous operation at maximum energy and repetition rate.

    Here is a summary of several commercial figure-8 coils as well as Sam #13 and #14:

        Mfr/Model      #Turns  ID     Mean      OD    Overlap  Wire Size   Angle
     Magstim 70 mm       9x2 5.2 cm  7.0 cm   8.8 cm  0.0 cm 1x7 mm          0 deg
     Medtronic MC-B70   10x2 2.4 cm  6.6 cm  10.8 cm  4.2 cm 3.5 mm (#8)  34.5 deg
     MagVenture CoolB70 11x2 2.3 cm  5.95 cm  9.6 cm ?3.6 cm 3x12 mm?     30.0 deg
     MagVenture MC-B70  10x2 2.7 cm  6.2 cm   9.7 cm ?3.5 cm 3x6 mm?      30.0 deg
     Sam #13             8+9 3.13 cm 5.72 cm  8.26 cm 2.5 cm 2.6 mm (#10) 30.0 deg
     Sam #14            10x2 2.9 cm  6.8 cm  10.5 cm  3.4 cm 3.18 mm Tube 30.0 deg

    Calculations show the overlapped configuration to have a slightly higher peak field and dB/dt for the same inductance. Testing with a Gauss probe at low currents results in slightly more than 1 G/A at 2 cm from the coil surface at the center position ("sweet spot") for Sam #13.

    See Commercial TMS Figure-8 Coils more detailed specifications for several models based on publicly available data, current as of mid-2016.

    Descriptions and photos of the author's coil attmpts to date may be found at Sam's TMS Coils.

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    Electronics Implementation:

    The pulsar implementation is what one might call dirt simple and brute force. ;-) It consists of the high voltage power supply and energy storage capacitor(s), voltage monitoring network, dual SCR discharge network, and low voltage power supply and logic controller. Here is the first version:

    Interior view with Plexiglas Safety Cover in Place (Rev. 1)

    The high voltage power supply uses the power transformer from a large 1950s black and white tube-type TV controlled by a Variac. :) The transformer has multiple line voltage taps and is set to produce the highest voltage. The otherwise not very useful 5 V and 6.3 V filament windings are also connected in series with the primary (reverse polarity) to further boost the output. The transformer hums a bit but doesn't get even detectably warm after a few minutes so it can't be too unhappy. With the Variac wired to go up to 110 percent of line voltage, its main output goes up to approximately 950 VRMS. A bridge rectifier consisting of 4 series pairs of 1N4007 diodes feeds the main energy storage capacitor via a 1.05K ohm 150 W series resistor bank resulting the voltage on the capacitors of around 1,450 VDC. The resistor bank both limits the current from the transformer as well as providing isolation during the discharge to maintain a low damping factor.

    A voltage divider feeds the meter with a peaking circuit to improve response time. The red HV LED is driven from an emitter follower with an identical LED serving as a voltage regulator to linearize the response. The voltage divider is mounted along with the high voltage bridge inside a plastic box for insulation. The monitor circuits are attached to the back of the meter.

    A separate 12 V transformer powers the logic and SCR drivers.

    The main energy storage capacitors (Rev. 1) consisted of a pair of 10 µF (labeled), 1,500 V pulse discharge capacitors in parallel. Their actual capacitance was measured to be 25.4 µF

    Two high current SCRs and a high current diode are used to create the three pulse types. The "hockey puck" style devices visible in the second photo from the left were way over the top for Rev. 1 in terms of what was required with the relatively small energy. :) These are for the main pulse discharge. The ratings of the SCR are not known. It was acquired on eBay for $22 delivered described as an 800 A at 1,800 V unit, but these ratings are suspect, not because it doesn't work based on them, but because the closest datasheet Google has been able to locate shows a dramatically lower voltage rating, and by all rights, it should have blown up at well below the 1,450 V used here. (Happily, I had not seen that datasheet when first building this, basing my decisions on the eBay listing! More below.) The diode is spec'd at 1,500 A and 1,800 V. An SCR in the smaller IXYS unit on top implements the free-wheeling discharge path for the monophasic pulse (Rev. 1 only, removed for Rev. 2.). It is only rated at around 100 A and 1,600 V but for low repetition rate pulses, it should be able to handle 30 times this or more. The same IXYS unit would work for the main discharge except that its turnoff time was found to be way too long to be able to select out only the single cycle for the bipulse. The eBay SCR turned out to be a high speed (inverter) type, so the pucks had to be retained.

    All three pulse shapes start with the same 1/4 sinewave as shown in the expanded biphasic pulse below. The peak current is thus similar for all. What happens after that changes for the polyphasic and monophaisc.

    Biphasic Pulse Expanded on Scope Display

    That free-wheeling SCR switch for the monophasic pulse turned out to be the most difficult to implement due to the requirement that its gate and cathode swing up to almost +/-1500 V with respect to the circuit common during the discharge. My first attempt using a home-built ferrite pulse transformer lasted about 3 shots due to insulation breakdown. Ferrite is supposed to be an insulator, correct? Nope, at least not this batch of cores at high voltage. A Westcode N490CH20 Hockey Puck SCR rated 2,000 V, 1,200 A average and over 18,000 A pulsed, that is almost 3 inches in diameter weighing in at around 1 pound was originally installed for the free wheeling circuit. It failed shorted when its gate circuit arced through the trigger transformer core. Remarkably, nothing on the low voltage side was damaged. And the primary hockey puck SCR and diode, which were then discharging into basically a dead short. also didn't seem to care. The first replacement switch was a combined SCR/diode block (IXYS MCD95-16IO1B). While its current rating is about 1/10th that of the unlucky hockey puck, the low repetition pulse rating should easily be enough, hopefully. The companion high current diode was in series with the SCR (mainly because it was available), with a low current diode (a pair of 1N4948s in series) across the SCR so that the full reverse voltage would be taken by the large diode, hopefully reducing the turn-on time of the SCR. The core of the replacement trigger transformer has 2-3 layers of Kapton tape covered with Epoxy for insulation. :)

    As noted, the IXYS devices was removed from Rev. 2 since (1) there is no evidence that a monophasic pulse has any utility for TMS, and (2) because there would almsot certainly be more difficulties asssociated with it at the much higher peak current.

    Various Coils have been used with this machine.

    Air-core coils having an inductance from below 8 µH to over 33 µH were found to work with all 3 pulse types. This is rather surprising at the low end given that the primary SCR needs to recover within 1/2 cycle, which at 8 µH is under 50 µs. Most thyristor specifications don't include a maximum recovery time, and the typical values given are usually 2 or 3 times longer than this. In fact, the IXYS-MCD95-16IO1B was too slow to replace the primary hockey puck SCR and diode, resulting in the biphasic and polyphasic waveforms both being polyphasic. (The mounting and reduced space would have been much more convenient!)

    (Coils with an iron core have so far proven to be a disaster either due to core saturation or eddy-current losses resulting in poor damping and/or excessive current. The best case is that the waveforms are terrible or don't change depending on type; worst is that parts blow up. :( :) More below.)

    For an air-core coil with an inductance of only 2.5 µH (Rev. 1, 4 or 5 µH total), the biphasic and polyphasic waveforms still worked correctly. This is rather remakrable since a full cycle (biphasic pulse) is under 65 µs and most thyristors cannot switch that fast. Detailed specifications of the primary SCR (a GE 387NX198 found on eBay) have not been located, but it must be unusually fast. :) The closest datasheet I can find is for the GE C387 series - which is a fast 500 A (5,500 A peak) SCR with a typical turnoff time under conditions more extreme than what it's experiencing here of 40 µs. So less than 32.5 µs (required for the 65 µs cycle) seems plausible. But the highest voltage rating listed was only 1,200 V and the "N" version was only 800 V (assuming that's what the "N" in "NX" designates). I find it hard to believe that this thing is working happily at nearly twice that voltage! It's not impossible though - sometimes better devices will be relabeled to satisfy an order for crappier ones. :) Or, perhaps the part numbers have changed since the 1977 (!!) datasheet where the C387 was found.

    However, although the primary SCR performed perfectly at the low inductance, the free-wheeling SCR self-triggered with a capacitor voltage above about 700 V. So, then all three waveforms then looked like the monophasic pulse. :( :) (The same thing happened above around 1,400 V with the 10 µH coil.) The cause is an EM transient picked up either in the wiring to the gate of SCR or the driver. Disconnecting the gate drive cable eliminated this spurious triggering, so it wasn't a problem with the SCR itself. Adding a 1 µF capacitor across the SCR gate delayed the onset of the self triggering to a somewhat higher capacitor voltage. Adding a 5 µF capacitor caused the free-wheeling SCR in the IXYS block to make a plit'ting sound and fail shorted, which I assumed at the time to be due to too slow a rise in gate drive current. :( However, one of the screws on the IXYS block was found to be loose when I removed it, so that could have been the cause as well. Lucky these are inexpensive on eBay. ;-) I bought a couple spare dual SCR units (IXYS MCC95-16) as spares. Since the diodes in the MCD95-16s were still good, there will be 4 spare SCRs and 3 spare diodes just in case. :) (One of the 3 MCDs I bought already had a blown SCR.) In the end, adding a 10 ohm resistor in series with the gate drive seems to have eliminated the false triggering for bare coils. However, it reappeared when driving a coil in a steel yoke, which resulted in a damping factor of almost unity due to induced current in the center piece. That configuration performed poorly in just about every way, as should have been expected, and it has been retired. The bare coil had an inductance of 8 µH and works fine. Perhaps, the peak current was much higher due to the losses, and pickup from that is what was triggering the free-wheeling SCR. When the SCR in a second IXYS MCD95-16 blew while attempting to drive an iron-core coil (either due to core saturation or excessive eddy current losses), I installed a IXYS MCC95-16 using only one of its SCRs without the extra diodes (leaving the other SCR as a spare!), and that works fine. The problem would arise if the SCR shorted resulting in a dead short across the the coil. But since this thing survived that in the past, so it shouldn't really matter.

    One mystery remains though: The measured time constant of the biphasic pulse and decaying sinusoid is consistent with a damping factor about double what the calculations predict based on the capacitance, coil/cable/wiring resistance, and coil inductance. While there are some losses in the primary SCR and its high current diode, as well as the ballast resistor bank, these shouldn't result in even 10 percent of the observed effect. And yet the decay time for the monophasic pulse is close to the theoretical value. The most likely candidate is the real part of the capacitor ESR. The required resistance of about 0.03 ohms seems high for capacitors of this type but isn't totally out of the question. This would make sense though since the characteristics of the capacitors do not impact the time constant of the monophasic pulse. The specs other than uF and working voltage for the capacitors are unknown. The skin effect of the coil and cable conductors might also contribute a tiny amount. At a frequency of 10 kHz, the skin depth is around 0.66 mm, which is less than one half the diameter of the #14 conductors typically used for the coil (1.63 mm). But this will only increase the effective resistance by a few percent at most.

    The controller and its power supply are housed in the shielded Minibox. Whether the shielding is really needed is not known, but there was no point in taking chances with ~1000 A pulses floating around. :) (Even so, there is often a spurious pulse generated when switching the HV off.) The power supply provides regulated 12 VDC using AC from the small transformer mounted on the chassis. The "logic" consists of a pair of 555 timers. :) The first generates the clock for continuous (approximately 0.5 to 10 Hz), or single shot. It's output drives the Pulse LED and the 555 for the SCR trigger with a pulse width determined by Pulse Type: around 50 µs for Bipulse; 2 ms for decaying sinusoid and monophasic pulse. These values should work over a wide range of coil inductances.

    Power Supplies, Energy Storage Capacitors, Thyristors and Pulse Forming Network, High Side SCR Trigger (Rev. 1, Click to enlarge)

    Complete Schematic - Click to View or Download PDF Version

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    Rev. 2 Modifications

    Converting Rev. 1 to Rev. 2 entailed two principle changes:

    1. The original energy storage capacitors were replaced with a pair of 81.5 µF capacitors, boosting energy to over 170 Joules at maximum voltage (1,450 V). Since the replacement caps are each more than twice the size of the previous ones, both didn't fit. So one had to be mounted outside on the rear of the case.

    2. The freewheeling SCR for the monophasic pulse was removed anticipating a change to a Westcode N075WN160 to handle the higher current (pending). Peak current is still under 5,000 A for a coil inductance of 10 µH, which should be well within the repetitive peak current spec for the primary 500 A SCR and 1,000 A diode. This change may be completed someday once an optimal coil design has been settled upon. However, since the monophasic pulse has to real use in TMS, this is becoming less likely.

    Interestingly, the damping factor with the larger capacitor is nearly as low as it was before the swap, so the original capacitors must have had a larger than expected ESR. The ESR of the 81.5 µF capacitors is almost unmeasurable using my meter - less than 0.01 ohm and much of that may be due to the capacitive reactance of 81.5 µF at the meter's test frequency, not resistance. The total effective system resistance now appears to be between 30 and 40 milliohms including the coil and cable (about 20 mohm total). And around 50 percent of the energy is recovered with the biphasic pulse.

    Of course charge time is longer but so be it - for now. It's still near full energy at 1 pps. Coil heating is becoming more of a problem though. The latest coil (Sam #13) uses #10 wire but at 10 mohms dissipates 20-30 W at 1 pps.

    The photo below show the modifications. One of the two energy storage capacitors is visible. The other one is under the genuine imitation wood grain plywood cover at the rear. ;-) The higher current SCR for the monophasic has not as yet been installed.

    Interior view (Rev. 2)

    The next coil (Sam #14) is planned to use 1/8" copper tubing in place of magnet wire with a recirculating oil-to-air heat exchanger. All the parts have been procured but the time to completion of this project is uncertain.

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    Rev. 3 (Under consideration)

    Rev. 2 has been running reliably at up to almost 5,000 A but going higher is something I'd rather not risk with the poor "little" 387NX198 primary SCR assumed to be rated at around 500 A. Repetitive pulsed current ratings of SCRs are rarely given. And while when they are, they tend to be around 30x of the average maximum current (Itavg), there is no data on the 387NX198. SO, I found couple of these at a bargain price on eBay:

    CKE T77P3000F28 Monster High Speed SCR: 2,800 V, 3,000 A, tq=75 µs

    The CKE T77P3000F28 is over 4 inches in diameter and weighs around 3-1/2 pounds! :) That's just a wee bit more massive than I had expected.

    The target current is around 9,000 A to achieve a full biphasic cycle of 150-160 µs at 1,450 V and ~170 J into an inductance of 3-4 µH.

    Perhaps the new SCR should handle anything even I can throw at it, space permitting! :) However, if I find something more reasonable - closer to 1,500 A and 1,500 V with a tq of 75 µs or less - I'll use that instead. :) If not, I may yet risk the 387NX198. Based on specifications of the assumed to be similar C387, it may just handle 9,000 A in a short pulse! At least the C387 datasheet does have some data for moderately short pulses, though not quite short enough.

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    Rev. 4 (Future fantasy)

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    Rev. 5 (Future future fantasy)

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    References and Technical Documents

    These are not necessarily in any particular order of significance, mostly alphabetical by topic or first author. :) Even if there is no link, papers and reports should be available for free download by entering the name and/or authors into a search engine. Manufacturer's literature is readily available on-line. TMS manufacturers Web sites often have specifications for system performance and sometimes even coil design parameters.

    Note: The links below open in a single new browser window or tab.

    TMS-Related Papers and Reports

    1. Anthony T. Barker and Ian Freeston, "Transcranial magnetic stimulation", (2007), Scholarpedia, 2(10):2936. doi:10.4249/scholarpedia.2936.

    2. Eric Basham, Zhi Yang, and Wentai Liu, "Circuit and Coil Design for In Vitro Magnetic Neural Stimulation Systems", TBCAS-2008-Jul-0054.

    3. Anne Beuter, Isabelle Lagroye, Bernard Veyret, "Design and Construction of a Portable Transcranial Magnetic Stimulation (TMS) Apparatus for Migraine Treatment", University of Bordeaux 1,IMS, Site ENSCPB,UMR CNRS 5218,16, Avenue Pey Berland, 33607, Pessac Cedex, France.

    4. Kent Davey and Charles M. Epstein, "Magnetic Stimulation Coil and Circuit Design", IEEE Trans on Biomedical Enginssering, vol. 47, no. 11, Nov 2000.

    5. Kent Davey and Mark Riehl, "Designing Transcranial Magnetic Stimulation Systems", IEEE Trans. on Magnetics, vol. 41, no. 3, March 2005

    6. Lukas Heinzle, "A Theoretical Model for Mutual Interaction between Coaxial Cylindrical Coils"., 2012, v0.11

    7. Risto J. llmonieni, Jarmo Ruohonen, and Jari Karhu, "Transcranial Magnetic Stimulation - A New Tool for Functional Imaging of the Brain", BioMag Laboratory, Helsinki University Central Hospital, P.O. Box 508, FIN-00029.

    8. Angel V Peterchev, David L Murphy, and Sarah H Lisanby, "Repetitive Transcranial Magnetic Stimulator with Controllable Pulse Parameters", J Neural Eng. Jun 2011; 8(3): 036016.

    9. Axel Thielschera and Thomas Kammerb, "Electric field properties of two commercial figure-8 coils in TMS: calculation of focality and efficiency", Clin Neurophysiol 2004 Jul;115(7):1697-708.

    TMS/Neural information

    1. Wikipedia: Transcranial magnetic stimulation.
    2. ScienceDirect: Transcranial Magnetic Stimulation: A Primer.

    3. Motor Pathways (
    4. Sensory and Motor Homunculus (
    5. Sensory and Motor Homunculus (
    6. Sensory and Motor Homunculus (

    Electronics Information

    1. Electronics Calculators (

    2. Calculator for AC Resistance of a Round Straight wire (
    3. Air Core Inductance Calculator (
    4. Coil Inductance Calculator (EE Web)
    5. Damped Harmonic Oscillator (
    6. Magnet Formulas (Eric Dennison)
    7. Field Calculator for Off-Axis Fields Due to a Current Loop (Eric Dennison)
    8. Flat Spiral Coil Calculator (
    9. Magnetic Field of a Current Loop (
    10. Magnetic Fields of Currents (
    11. Skin Depth Calculator (
    12. Skin Effect in AC Conduction (
    13. Solenoids Magnetic Field Calculator (
    14. Time Constant Equations (
    15. 555 Astable Circuit Calculator (ohms law

    16. Thyristor Switching Characteristics (
    17. Diode/Thyristor manuals and applications notes from GE, Westcode, IXYS, Powerex, Dynex, etc.

    Some TMS Manufacturers Web sites

    1. Magstim
    2. Magventure
    3. Nexstim
    4. Neronetics