**How do you design an MPG, and calculate Peak Gauss output in the pulsed DC Magnetic Coil? **

*Revised: August, 2001*

The term Gauss is defined as “The electromagnetic unit of magnetic induction, equal to 1 Maxwell per square centimeter. [After K.F. Gauss]”.

The coil used in our Magnetic Pulser (MPG) provides the magnetic charge that is ultimately responsible for inducing the micro-currents (50-100 uA) of electricity into the conducting medium. It is very important to generate the necessary Gauss output from the coil in order to effectively induce this level of current at distances of up to 9″ penetration.

There are specific electrical and magnetic parameters on MPG design to ensure the minimum Gauss output is achieved. It takes a great deal of electrical energy, and the use of specific (usually expensive) electronic components, and good design practices in order accomplish this reliably and consistently.

**Critical components are:**

- The Power Supply.
- The Main charging Capacitor.
- The Switch (“charge dumping mechanism”).
- The Output Coil.

**How it all goes together:**

The power supply is used to charge the main capacitor. The main capacitor has the ability to store an electrical charge (it can be said that the capacitor gets “filled up” with electrons). The *capacity* of the capacitor is expressed in **Farads**. Because Farads is such a big value, most capacitors are rated in *micro*-Farads (uF). The larger the capacitor, the more electrons it can “hold”. Our MPG has a capacitor rated at 600uF. **NOTE:** Capacitors connected in parallel add together their respective capacitance algebraically. Example, 2 x 300uF capacitors in parallel have an equivalent capacitance of 600uF. Capacitors connected in series add together their respective voltages algebraically. Example, 2 x 250 Volt rated capacitors in series have an equivalent voltage rating of 500 Volts. This means these two capacitors when connected in series can safely operate with a 500 Volt potential across them. It does NOT mean that they have increased their output, it means they are capable of handling a 500 Volt potential, should one arise!

The main capacitor has a working Voltage Rating. This is the working potential it is designed to operate in. The higher the working voltage, the more electrical energy the capacitor can store as *work* without being destroyed. Work is expressed in **Joules** or **Watt*Seconds**.

The formula for calculating the amount of energy a capacitor has is:

**E=1/2*C*V*V**

Where E is Joules or Watt*Seconds, C is the capacitance in Farads, and V is the Voltage as measured across the fully charged capacitor. Our MPG’s capacitor is rated at 350 Volts DC (highest voltage it is allowed to charge to) and has a working voltage (typical charging voltage) of 330 Volts DC.

Applying the Energy formula we get:

E=1/2*[600 x10 ^-6 Farads]*330 Volts *330 Volts = **32.67 Joules** or **Watt*Seconds**.

Note the **Voltage** term is a squared function? Energy goes up *as a square of the voltage*. It also goes DOWN as a square of the voltage. Let’s say our 600uF capacitor is only charged to 1/2 of the 330 Volts:

E = 1/2*[600 x10 ^-6 Farads]*165 Volts *165 Volts = **8.17 Joules**.

The voltage went down by 1/2, yet the Energy dropped by 4. This is one reason why it is so important to have a minimum charge voltage on the capacitor of at least 300 Volts DC. At 300 Volts, E = 27 Joules. Still quite respectable.

**Joules** or **Watt*Seconds** is only one piece of the puzzle. This gives us potential to do work. But the coil needs **Amps** to make **Gauss**. **Amps** (or current) is generated when a **Voltage** is applied across an **Impedance** (resistor in DC terms). With all else being equal, the higher the **Volts**, the higher the **Current** and the higher the **Gauss**.

The **duration** of the magnetic pulse (how long it lasts) is largely in direct proportion to the Capacitance in uF of the main capacitor. If the pulse duration is too short, it is not available long enough to do much work. SOTA’s MPG has a pulse duration of ~2.5 mS (milli-seconds).

To re-cap, we use a large capacitor to store adequate energy for the pulse, and we also need a high enough voltage potential across the capacitor to drive the right amount of current through the coil. The main capacitor must reach a minimum DC Voltage in order to have enough potential to generate the current (Amps) necessary through the coil, which in turn produces the intense magnetic field (Gauss).

After being fully charged, the main capacitor’s store of energy must be “dumped” through some sort of switching device to the coil. Immediately after discharge, the power supply must then re-fill the capacitor with electrical energy (Joules).

When the capacitor gets fully charged, we must dump this high energy into the coil somehow. Originally a Xenon photoflash tube was used as a *thyratron* switch (the Xenon gas is ignited to a plasma which provides a low impedance path for the electron flow) for the do-it-yourself’ers. The Xenon tube presents about 1-3 ohms of resistance when ionized. It makes a good switch, but it does restrict peak current flow. Ringing can and does occur with the capacitor-coil combination because the current can back-feed into the capacitor. (This ringing affect can allow reverse-biasing of the main capacitor; degrading it’s life-span very quickly or destroying the capacitor under extreme conditions.) When a capacitor is in series with an inductor in this manner, it is known as an L-C (Inductive from the coil and Capacitive from the capacitor) circuit.

Xenon tubes get hot, and they waste energy in the form of heat and (of course) light. A better switch is an SCR (Silicon Controlled Rectifier) of appropriate voltage and current rating (800-1000 Volts @ 25 Amps is a good start.). An SCR provides a **one-way path** of current flow from capacitor to coil, inherently preventing ringing and therefore saving the capacitor from reverse-biasing. This one-way path ensures the output magnetic field is DC based or uni-polar. This means North magnetic pole will always be on one side of the coil, and **will not change** to South pole at any time.

**NOTE:** Although a typical SCR is a fast operating device, there will always be a “dead-time” where the device is in a conductive state (known as t_{q} which is typically = 35uS). This can allow reverse voltages to appear across the main capacitor which may eventually lead to a much shortened lifetime or the complete destruction of the capacitor. So, in order to prevent such an event we need to suppress this high-power content reverse voltage spike across the main capacitor. The simplest, effective and most economical way is to place a high-current diode in reverse, across the leads of the main capacitor. The CATHODE (-) lead of the diode connects to the POSITIVE (+) terminal of the capacitor. Remember, this reverse-voltage spike can contain many joules so you must use an adequately rated diode. We use an MR756 silicon rectifier. It is rated at 600 Volts DC, 6 Amps continuous and 400 Amps peak surge. I measured over 80 Amps of current in the reverse-voltage spike. **WARNING:** If you do not use a similar rated diode, it may very well blow up in your face! I know, because I had this happen many times while taking measurements. Scares the *heck* out of you!

Once the charge is dumped to the coil, the current flowing through the coil generates a *moving magnetic flux* as governed by the following equation. We must look at the coil as a DC electromagnet, because in essence that is what we have created. Thus:

**Bpeak = Inductance (L in Henries) of the Coil*Peak Amps*10^8 / (N*A)**

Where Bpeak is Peak DC Flux Density in Gauss, L is the inductance of the coil in Henries, Peak Amps is the measured RMS Peak Amps flowing through the coil, N is the number of turns in the coil, and A is the cross-sectional area of the air-core section of the coil.

SOTA’s MPG coil is rated at 2.5 milli-Henries, has 270 turns, and has a cross-sectional area of 3.22 cm^2. We measure 150 Peak DC Amperes on each pulse through our coil. Substituting we get:

**Bpeak**=0.0025 Henries*150 Amps*10^8 / (270 Turns*3.22cm^2) =**43,133 Gauss***

[*This 43,133 Gauss measurement is at the intercoil winding flux. Magnetic flux intensity follows the inverse square rule – the further you are away from the magnetic core, the faster the Gauss intensity drops off. At face of Magnetic Coil, the Gauss drops to ~6,000 Gauss.]

As you can see, all the components come together to generate the required Gauss output.

In order to drive the necessary amps through the coil, the coil must have a low impedance or DC resistance. The use of 18 AWG or **thicker wire** ensures this.

Our coil has a DC Resistance (DCR) of about 0.5 ohms. Theoretically, at 330 Volts across the coil, we could drive:

Current = Volts/Resistance = 330 Volts/0.5 ohms = 600 Amps through the coil. So, the coil’s DCR is not a factor for most MPG designs.

The Xenon tube injects a 1-3 ohm DC resistance into the path. So, theoretically Current = Volts/Resistance = 330 Volts/1 ohm = 330 Amps best case, and 330 Volts/3 ohms = 110 Amps worst case. Therefore the Xenon tube’s DC resistance can significantly impact on peak current.

The SCR, being a PN junction, does not present a impedance per say just a voltage drop (1.5 Volts, which is insignificant). A typical 25 Amp rated SCR has a peak one-cycle surge current of 350 Amps. This is more than adequate to handle the peak currents we are likely to encounter.

This is why an SCR makes an ideal electronic switch for MPG’s. It’s also **FAST**. And the speed of the switch governs the Rise Time of the pulsed wavefront. The rise time is a result of the change in Current over a change in Time, or dI/dT. The higher the dI/dT, the more current you will induce into the conductive medium. SOTA’s MPG has a rise time of <1.8 uS (micro-seconds).

Remember, why we are making an MPG in the first place? To generate, through inductive coupling, the micro-currents (50-100 uA) of electricity in the conductive medium. In order to inductively couple 50-100uA of current, you need a fast moving magnetic field of high enough Gauss intensity. Patents on pulsed magnetic field therapy actually call for Gauss outputs of 2 Tesla (1 Tesla = 10,000 Gauss, so 2 Tesla = 20,000 Gauss) and even up to 20 Tesla (200,000 Gauss). So, I believe that unless your MPG outputs at least 2 Tesla (20,000 Gauss) it is not effective as a pulsed magnetic field therapy unit and should not be used as such.

**NOTE:** In order to test the actual induced currents I performed a simple experiment: I placed a single wire across the MPG coil and connected a 2,000 ohm resistor in series with the wire. This then would mimic the 2,000 ohm impedance found in the human tissue. I used my ‘scope to measure the maximum voltage impressed across the resistor from pulses delivered from the MPG coil. I got a result of about 0.5 Volts Peak, which mathematically calculates out to 250 uA of current. I can make a fairly conservative conclusion that the MPG coil is capable of inducing greater than the required 50-100 uA into a 2k ohm conductive medium.

The main capacitor has definite ESR (equivalent series resistance), and can be a main contributor to the resistance to current flow through the coil. SOTA’s custom professional strobe capacitor used in the MPG has an ESR of only 0.076 ohms. At 330 Volts, it has a short circuit current capacity of Current = Volts/Resistance = 330 Volts/0.076 ohms = **4,342 Amps!** (This amazing current capacity, due to the extremely low ESR, is un-matched by standard camera photoflash capacitors.) It is important to note that the lower the ESR the less HEAT will be produced, and the longer the capacitor will last.

This is the main reason why SOTA’s MPG has such high performance. Capacitors having a high ESR (not good) get HOT during operation – very HOT! Heat destroys the dielectric, and burns the capacitor out. In addition, the build-up of heat further INCREASES the ESR. A higher ESR lowers the current on each pulse, which of course lowers the Gauss output on each pulse.

As mentioned above, the lower the ESR the longer the capacitor will last, and generally the faster you can charge and discharge it. SOTA’s custom professional strobe capacitor is rated at over 30 million pulses! This compares to 5-10,000 pulses from your typical photoflash capacitor found in most cameras. Remember, cameras were NEVER intended to be magnetic pulsing units.

Charging a capacitor follows simple electrical rules. For example, our 600uF capacitor is to be charged to 330 Volts. We know that the energy required is:

E=1/2*[600 x10 ^-6 Farads]*330 Volts *330 Volts = **32.67 Joules** or **Watt*Seconds** (that’s Watts TIMES Seconds)

Now, power is Watts/Second (that’s Watts **PER** Second, not Watts **TIMES** Seconds!). So, if you want to charge this big capacitor in say 5 seconds, you will require 32.67 Watt*Seconds / 5 Seconds (the Seconds term cancels out, leaving you with Watts) = 6.534 Watts input to the capacitor.

Now, most power supplies have a great deal of trouble raising 12 Volts from your typical battery (or 6 Volts from 4 x AA cells) to the required 330 Volt charging potential. If you get 50% efficiency, you are doing extremely well! So, at 50% efficiency, the power supply requires: 6.534 Watts / 50% = 13.068 Watts. At 12 Volts input, this translates to 1.089 Amps (I=V/R). Your battery (or Wall Adapter) must be capable of supplying at least 1.089 Amps to get the job done without overheating (in this example, you would choose a Wall Adapter with a 1.2-1.5 Amp rating.)

Using 4 x AA cells, which equals 6 Volts (4 x 1.5 Volts each) would require 2.178 Amps draw from the batteries. Those 4 x AA cells won’t like you very much! They will get real HOT, and won’t last more than probably 2-5 pulses. So you see, a high powered MPG requires a substantial power supply and the correct selection of critical components. Period. (And this gets expensive.) You can’t fool Mother Nature nor attempt to by-pass her fundamental electrical rules.

Most photoflash units simply cannot, and do not, perform to the level of a professionally designed MPG like the units we at SOTA Instruments Inc. offer.

I hope you enjoyed reading this dissertation on MPG’s. Your feedback and comments are very much welcomed.

Sincerely and Best Regards,

Russell J. Torlage, CTech