12V-180kV: a Battery Powered Marx Generator (and Introduction to Electronics)

If you're reading this Instructable, one thing is probably true: you're interested in high voltage! If so, you've come to the right place; Marx Generators can satisfy your thirst for sparks, bangs, and thrill. I made this Marx Generator several years ago, but it went out of commission after some experimentation and remained so until I fixed it up about a month ago. I decided it would be cool to detail the construction of the device, so others may too experience the excitement of Marx Generators!

I'd like to use this Instructable as an opportunity to describe some of the theory underlining the physical phenomenon that the Marx Generator employs. Electronics attracts a mixed crowd of enthusiasts, including some who are more familiar with physics and some who haven't had as much exposure. There already exist several very good Marx Generator Instructables (a tutorial by Plasmana). I just hope that readers will take away from this Instructable something much more exciting than the sparks: an enthusiasm for the science of electricity.

But first, I must remind you that there is real danger associated with electricity. Energy creates and energy destroys. But even low energy can be dangerous. Think of the human body as a sensitive piece of electronic equipment; it doesn't take much to fry the circuitry. Be smart. Electricity hurts! When in doubt, don't touch that wire. Goggles are always a good idea.

Alright, let's get started.

First, what is a Marx Generator? Maybe you aren't familiar, or perhaps you've been wasting your time on Tesla coils. Marx Generator > Tesla Coil >:) only joking

Anyway...

A Marx Generator is an electrical circuit consisting of capacitors, resistors, and spark gaps arranged in a ladder structure capable of producing high voltage impulses (which result in sparks) by first charging the capacitors in parallel and then discharging them in series.

Time to check Wikipedia. Let's see how well I did with my description...

"A Marx generator is an electrical circuit first described by Erwin Otto Marx in 1924. Its purpose is to generate a high-voltage pulse from a low-voltage DC supply. Marx generators are used in high energy physics experiments, as well as to simulate the effects of lightning on power line gear and aviation equipment. A bank of 36 Marx generators is used by Sandia National Laboratories to generate X-rays in their Z Machine." - (Wikipedia)

I suppose I did alright, though I forgot to mention the "low-voltage DC supply". As you can gather from the Wikipedia article, Marx Generators don't have much practical use to you or me, but they certainly are cool! Also, notice "high voltage...high energy". This means danger; be careful.

But maybe we need to back up a little further. Maybe this Instructable is your first exposure to electronics (plausible; I know how enticing high voltage can be).

Let's start with the basics (the very basics).

When we refer to electricity, we are talking about the interactions of charge carriers. These charge carriers can be subatomic particles like protons and electrons or charged atoms, ions, in solution. Due to their very low mass to charge ratio, electrons are the primary charge carriers in solid conductors. Charge is measured in units of coulombs (C). Charges interact with one another via fields. Magnetic fields influence only moving charges while electric fields influence both moving and stationary charges. The electric field produced by a single point charge (a proton, for example) can be shown by Gauss's Law to be proportional to the magnitude of charge and inversely proportional to the square of the distance from the point charge. Particles in a field experience a force that increases with the amount of charge they carry. That is, F=qE, where F denotes force, q denotes charge, and E denotes electric field magnitude. Thus, the force experienced by one charged particle in the field of another is proportional to both the charge of the particle producing the field and the charge of particle experiencing the field and is inversely proportional to the square of the distance between the two particles. This is referred to as Coulomb's Law.

Within electricity, there exist two realms of analysis: electrostatics and electromagnetics. Electrostatics deals only with stationary charges and is not able to describe as many physical situations as electromagnetics, which accounts for the more complicated physics introduced by charges in motion. Unless you've been living in an enclosed box all your life (and even then...), you've witnessed both electrostatics and electromagnetics. Displacing charge on your hair by rubbing it with a balloon is an example of electrostatic interaction. Microwaves, magnets, and the vast majority of electronic devices operate on the principles of electromagnetics. For our purposes, we will neglect electromagnetics in our analysis because the Marx Generator is one example in which electrostatics plays a much more noticeable role. You should, however, be aware of some of the relationships between electricity and magnetism. You should know that a time-varying magnetic field induces an electric field (Faraday's Law) and that a time-varying electric field induces a magnetic field (Ampere-Maxwell Law). The elegant symmetry of electricity and magnetism is exposed in Maxwell's Equations, which prove the existence of self-sustaining electromagnetic waves traveling at the speed of light (c = approximately 300,000,000 m/s !!!).

Electricity, like everything else in natural world, involves the conversion of energy between potential and kinetic forms. In physics, energy has units of joules (J). Energy can neither be created nor destroyed. Rather, during any physical process, energy is conserved*. The measures of voltage and current quantify the energy possessed by stationary and moving charges. Voltage is electrical potential difference and has units of volts (V) or joules per coulomb (J/C). It is equal to the energy change that would result from moving a charged particle from one position to another divided by the charge possessed by that particle. The result of charged particles moving from a higher voltage (higher potential energy) to a lower voltage (lower potential energy) is electrical current. Current can be calculated as the amount of charge (C) passing through a cross-sectional area, such as a wire, per unit time (s). Therefore, current has units of coulombs per second (C/s) or amps (A). Two factors determine the magnitude of current: the average drift velocity of charged particles and the net charge of all the particles. Current can be increased by increasing either the speed or number of particles passing through a given cross-section of a wire. Voltage and current can be related to power, the rate of energy consumption, by the equation P=IV, where P is power, I is current, and V is voltage. Multiplying power and time yields energy. Voltage and current relate to the conservation laws of energy and charge respectively. Knowing that energy is always conserved and that voltage represents the energy change of an electron moving from one point to another, we can conclude that the sum of all voltages in a closed loop (the path an electron would take around a circuit to end up back at its starting position) must always* be zero. This is know as Kirchhoff's loop rule. There exists a second rule, Kirchoff's junction rule, which states that the sum of the currents flowing into any junction, i.e. an intersection of wires, must equal the sum of the currents flowing out of the junction in order for charge to be conserved. Kirchoff's rules are especially useful for the analysis of more complicated circuits.

Voltage and current can also be related to another quantity: resistance, the opposition to current. Ohm's Law states that voltage, V, is the product of current, I, and resistance, R; V=IR. However, a more intuitive, and often more useful, form of Ohm's Law is given by I=V/R. In direct current (DC) circuits, resistance dissipates energy in the form of heat and is dependent on the resistivity of the conducting material. In alternating current (AC) circuits, resistance is transformed into complex impedance, which takes into account the frequency response of reactive elements such as capacitors and inductors.

Now, onto my favorite part of electricity: circuits!

Circuits exploit the aforementioned physics concepts in order to harness and manipulate electricity. Circuits are composed of circuit elements, discrete components each designed to perform a specific function by manipulating electricity according to some physical law. An understanding of how circuit components work aids in the analysis of complicated circuits. The basic Marx Generator circuit by itself only requires three unique components: resistors, capacitors, and spark gaps. However, for the purpose of providing an adequate introduction to electronics, I shall introduce several other major components as well.

Resistors: Oppose current. Resistors add resistance, the electrical analog of friction, to a circuit. Electrical loads, such as lamps, add resistance, or impedance if reactive components are involved, to a circuit. Wires possess an innate, material specific quality called resistivity, and the resistance of a wire can be calculated as the product of the wire's resistivity and length divided by its cross-sectional area. The resistance of a resistor, the voltage across a resistor, and the current through a resistor are all related by Ohm's Law. Potentiometers, rheostats, and trimmers are types of variable resistors, which can be configured to form adjustable voltage divider circuits. Resistors are used to limit current and/or voltage in circuits. In this Instructable, we will be using resistors to slow the charge and discharge of capacitors.

Capacitors: Store energy in an electric field. Capacitors are often composed of two parallel conducting plates on which charge accumulates when a voltage is applied. Between the plates, these forms a uniform electric field having magnitude proportional to the surface charge density of the plates. As charge accumulates, the electric field, and thus voltage, between the plates increases in magnitude. Once the voltage across the capacitor equals the source voltage, current will cease to flow. Decreasing the surface area of the plates will increase the voltage per unit charge and decrease the maximum charge accumulation accordingly. In this way, the product of the voltage and charge of a capacitor remains constant and defines an innate quality of each capacitor called capacitance, C. The energy (in joules) stored in the electric field of a capacitor at any instant can be calculated as 1/2CV^2. As a capacitor is charged through a resistor (an RC circuit), the voltage difference between the capacitor and the supply decreases and charging slows. Using calculus, we can solve a first-order differential equation for the current through the RC circuit with a steady supply voltage as a function of time. The result indicates the current decreases exponentially towards zero, with steeper decrease resulting from smaller capacitance and resistance values. The product of resistance and capacitance in an RC circuit is known as the RC time constant. The capacitor's opposition to slow changing currents (i.e. low frequencies) is known as its reactance, X. In AC circuits, reactance compounds resistance to yield complex impedance Z, defined as the sum of orthogonal resistance and reactance vectors. In short, at very high frequencies (approaching infinity), capacitors offer no impedance and act as short circuits. At very low frequencies (approaching 0; DC), capacitors offer infinite impedance and act as open circuits. In this Instructable, we will be using capacitors as the primary energy storage element.

Inductors and Transformers: Store energy in a magnetic field. Inductors are the magnetic analog of capacitors and mirror their behavior. Inductors are simply coils of wire, and as such, wire itself can exhibit non-ideal parasitic inductance (likewise, two wires lying adjacent can exhibit parasitic capacitance). Inductors exploit the principles of electromagnetism described by Ampere's Law and Faraday's Law. From Ampere's Law, current running through a wire produces a magnetic field that encircles the wire. From Faraday's Law, a changing magnetic field (magnetic flux) through a circuit induces a current that counteracts the magnetic field. Combining the laws, we see that the magnetic fields resulting from individual loops in an inductor serve to sustain current flowing through the inductor. This characteristic behavior of inductors is measured as inductance, L. The energy stored in the magnetic field of an inductor at any time can be calculated as 1/2LI^2. As with the capacitor, we can solve a first-order differential equation for the current through the RL circuit (resistor-inductor circuit) as a function of time. We find that the current gradually approaches a value equal to V/R (supply voltage divided by resistance) according to an exponential with a steepness that increases with decreasing inductance and resistance values, the product of which is referred to as the RL time constant. When the current through an inductor changes, an emf (electromotive force; voltage) is induced across the inductor that directly opposes the current which caused produced it. The magnitude of the emf produced is proportional to both the rate of change of the current through the inductor and the inductance of the inductor. In this way, the inductor opposes fast changing currents (i.e. high frequencies), giving it a reactance, X, that mirrors that of the capacitor. In short, at very high frequencies (approaching infinity), capacitors offer no impedance and act as short circuits. At very low frequencies (approaching 0; DC), capacitors offer infinite impedance and act as open circuits. Thus, the inductor's frequency response is inverse of the capacitor's. The inductive reactance vector points in the opposite direction to the capacitive reactance vector. Thus, there exists some frequency at which inductive and capacitive reactances cancel. It is at this resonant frequency that voltage and current will oscillate in an inductive-capacitive (LC; tank) circuit as energy sloshes back and forth [indefinitely] between the inductor's magnetic field and the capacitor's electric field.

Two inductor coils can be wound on core to form a transformer. One coil becomes the primary winding of the transformer and the other becomes the secondary winding of the transformer. The two windings share mutual inductance, a magnetic linkage or coupling. When the current through the primary winding changes, the changing magnetic flux through the primary is transferred to the secondary via the ferrite core. This induces a current in the secondary that is proportional to the current in the primary. The ratio of turns in the primary winding to turns in the secondary winding determines the relative magnitudes of the voltages and currents in each winding. Secondary voltage is equal to primary voltage divided by the ratio. Secondary current is equal to primary current multiplied by the ratio. In this way, power is not created but rather transformed. If the ratio is greater than 1:1, secondary voltage will be greater and the transformer is considered a step-up transformer. The reciprocal is true for a step-down transformer. Keep in mind that the primary and secondary winding designations are arbitrary; a transformer may be reversed to obtain the inverse ratio. In this Instructable, we will be using a transformer to step-up the supply voltage.

Diodes: Permit current to flow in only one direction. Semiconductor diodes are composed of a single junction of two doped semiconducting materials. The forward bias voltage (typically ranging from 0.7-1.4V) is the potential difference required for current to flow through a diode in the forward direction. The reverse bias voltage (typically much higher than the forward bias voltage) is the potential difference at which the diode will break down and allow current to flow in the reverse direction (this is usually considered non-ideal behavior; however, in the case of Zener diodes, the breakdown resulting from reverse bias is exploited for its "avalanche" effect). The negative (cathode) terminal of a diode is indicated by a band (see image). Diodes are commonly used to rectify AC to DC using a four-diode configuration called a full-wave rectifier or diode bridge. In this Instructable, we will be using diodes to rectify AC in a Cockcroft–Walton voltage multiplier circuit.

Transistors: Switch and amplify current. During the second half of the 20th century, the proliferation of solid-state transistors in electronics made obsolete previous switching devices, such as relays and vacuum tubes, and sparked the digital electronics revolution. Although there are several different classes of transistors, most adhere to a common basic structure consisting of three pins: a base (or gate), collector (or drain), and emitter (or source). Bipolar junction transistors (BJTs) are composed of two adjacent semiconducting junctions in either an NPN or PNP configuration. For a BJT, a small signal at the base can modulate the flow of a larger current between the collector and emitter. The high-gain properties of some transistors can be exploited to form logic circuits with binary states. In this Instructable, we will be using a high-power NPN transistor to switch the transformer current.

Spark gaps: Conduct electricity only at high voltages. Spark gaps consist of two electrodes separated by air or other dielectric. Up to a certain voltage, the dielectric will act as an insulator and inhibit current. However, once the electric field magnitude between the electrodes has exceeded the specific dielectric strength, the dielectric will breakdown and conduct. For the ionization of air, the rough approximation of 1kV per mm of separation is commonly used. In this Instructable, we will be using spark gaps to trigger the firing of the Marx Generator.

Specialty Components - Actuators, Transducers, and Sensors: Convert electrical energy into energy of another form and vice versa. The term "transducer" is used to refer to anything that facilitates such conversion. Motors and solenoids are examples of actuators, which convert electrical energy into angular and linear motion. Microphones, speakers, and piezoelectric materials also fall under the definition of transducer. The term "sensor" may refer to a transducer that uses minimal or ambient energy to derive information, such as light intensity or chemical concentration, about the surrounding environment.

Integrated Circuits: Package entire circuits into tiny chips. The integration density of ICs has grown exponentially since the invention of the IC by Jack Kilby. This growth phenomenon, known as Moore's Law, has seen ICs become smaller, faster, and cheaper simultaneously. Current technology enables billions of individual transistors to be packaged into a single IC. In this Instructable, we will be using a TLC555 timer, a common hobbyist IC, to generate a square wave signal.

• heavy duty 6V lantern battery (x2):

These will provide the 12V power supply for the Marx Generator.

• 9V battery:

When I first designed this Marx Generator, I used a 9V battery to power the 555 timer signal generator. However, the circuit can easily be modified so that the timer draws from the lantern battery power supply, which would be preferable.

• 555 timer IC:

A TLC555 timer IC will generate a square wave to modulate the transformer current.

• high-power transistor:

A high power (NPN) transistor is used to switch the transformer current.

• transformer:

A transformer steps up the power supply voltage before it is fed into the CW multiplier. I used a tapped transformer with a 20:1 turns ratio.

• diodes*:

Power diodes are needed for the CW multiplier circuit. Each stage of the CW multiplier requires two diodes.

• resistors (assorted)*:

Two resistors are needed to set the frequency and duty cycle of the 555 astable oscillator circuit. I used one 2.2kOhm resistor and one 3.3kOhm resistor. In addition, high-power resistors (at least 1/4Watt) are needed for each stage of the Marx Generator. For a Marx Generator of 'n' stages, '2n' such resistors are needed. In my design, I used 1/4Watt 1MOhm resistors.

• capacitors (assorted)*:

A low-value (I used 0.047uF) ceramic capacitor is needed to set the oscillation frequency of the 555 timer. High-voltage capacitors are needed for the CW multiplier and Marx Generator circuits. Each stage of the CW multiplier requires two low-value capacitors rated for at least 1kV. I used a combination of ceramic and metal film 1kV capacitors (between 220 and 560pF) for the CW multiplier. Each stage of the Marx Generator circuit requires a capacitor rated for the input voltage (about 8kV). I used 4kV 68nF Lithuanian capacitors in pairs to achieve the required 8kV voltage rating for the Marx Generator circuit.

You will also need wire, lots of solder, and maybe some tape to hold everything together.

*Specific quantities depend on the number of stages used. For example, '2n' diodes are required for a CW multiplier circuit of 'n' stages.

Once you've gathered the required parts, you can begin the very tedious process of constructing this Marx generator!

The Marx generator can be divided into three sections.

The first section consists of the power supply and the 555 control circuitry. It takes the 12V battery power supply and produces an AC output of about 240V. The 555 timer, configured in astable oscillator mode, generates a square wave which is fed into the base of the high-power transistor. The transistor switches the current through the smaller winding of the transformer, inducing a stepped-up voltage across the larger winding.

The second section is a Cockcroft-Walton (CW) voltage multiplier. It takes the 240VAC from the first section and produces a DC output of about 8kV. The AC input is filtered through a series of cascading capacitors and diodes. Each "stage" of the CW multiplier requires two capacitors and two diodes. The output voltage of the CW multiplier can be calculated as Vo = Vi (2n), where Vo is the output voltage, Vi is the input voltage, and n is the number of stages. Due to the reactive properties of capacitors, there are practical limitations to the number of stages in a CW multiplier. I used 16 stages in my design and experienced no serious performance issues.

The final section is the actual Marx Generator circuit. It takes the 8kV DC output from the CW multiplier and produces high voltage impulses of about 180kV! The Marx generator circuit consists of resistors, capacitors, and spark gaps arranged in a ladder structure. The Marx Generator operates by having the bank of high voltage capacitors first charge in parallel through resistors and then discharge in series through spark gaps. When the first capacitor exceeds a critical breakdown voltage, the first spark gap will fire, effectively connecting the first and second capacitors in series. Their voltages will add and trigger the second and subsequent spark gaps to fire, resulting in an avalanche of connections. The voltage across the equivalent series capacitor ideally follows Vo = Vi (n), where Vi is the input voltage and n is the number of stages in the generator with n = 45 for my design. If the combined voltage of all the capacitors is enough to ionize the final spark gap, a large spark will form, indicating that your battery powered Marx Generator is working!

The spark gaps for the Marx Generator can be formed by simply bending the resistor and capacitor leads of adjacent stages together. However, you may have to play around with the precise separations. Often it is preferable to mechanically trigger the first spark gap with a screwdriver so that the latter stages may be allowed to charge more fully.

If the Marx Generator you are building is going to be particularly large (as mine was), I would recommend more permanent spark gaps than the makeshift ones pictured above. It's always cool to see a Marx Generator with a really solid construction. Wrapping tape around the capacitors worked for me, but I reckon there are better solutions.

You can estimate the actual spark voltage by measuring the maximum spark distance and applying the 1kV per mm approximation. In my case, I observed sparks up to 18cm, corresponding to discharges of 180kV! You may notice that the math here doesn't seem to work out; given a 12V input, it would follow from the calculations that the final spark voltage should be 12*(20)*(32)*(45) = 345600V or about twice the estimated 180kV. The discrepancy most likely results from unaccounted losses and [very] crude methods of approximation.

Be careful about keeping the non-ground electrode of the final spark gap away from other circuitry; the sparks will readily jump to the CW multiplier (I've blown a few capacitors this way).

Innovations?:

Marx generators require that the capacitors discharge in series via the spark gaps rather than in parallel. The resistors in the Marx Generator schematic are included for this reason. Unfortunately, resistors add the undesirable side effect of reduced charge rate and lower firing frequency. One possible workaround would be to replace the resistors with inductors which exhibit high impedance upon firing and minimal impedance while charging. The inductors would have to be sufficiently large to effectively block the parallel discharge.

Alternatively or additionally, transistors could be used in place of the spark gaps, and the Marx Generator could be made to be completely solid-state. An external circuit could monitor the stage voltages and trigger simultaneous discharge when all stages had reached the desired level. Such a design would require the use of high power transistors and enough stages to generate impulses from a reduced input voltage.

I really enjoyed building this Marx Generator, and if you've come this far, I hope you're getting similar results! I also hope that you've enjoyed reading this Instructable and maybe even learned something cool about electricity from it.

If you have any questions about construction or parts, feel free to ask in the comments section. Be safe and enjoy the following videos of the finished battery-powered Marx Generator!

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