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15-Stage Compact Marx Generator Using
2N5551 Avalanche Transistors
T. Huiskamp, T. Borrias and A. J. M. Pemen
Electrical Engineering Department
Eindhoven University of Technology
Eindhoven, The Netherlands
[email protected]
Abstract—In this contribution, we present a 15-stage,
avalanche transistor Marx generator using inexpensive 2N5551
transistors. It can be used in low-power biomedical,
environmental and food applications where compact circuits to
generate high-voltage pulses are required. We characterized the
avalanche transistors and built a test setup with 15 stages which
provides 1.3-kV pulses into a 50 Ohm load and over 3-kV into a
small capacitive load (such as a small plasma reactor).
Furthermore, by optimizing placement of starting capacitances,
the rise time of the circuit could be adjusted to just under 2 ns,
which can still be further optimized.
Keywords—avalanche
generator
transistor;
pulsed
power;
Marx
I. INTRODUCTION
In low-power biomedical, environmental and food
applications (e.g. plasma wound healing, plasma air
purification, pulsed electric field treatment of food, etc.),
compact high-voltage pulse sources are required. One method
of generating these pulses is with a Marx generator. They can
generate output pulses up to an amplitude of n times the supply
voltage, with n being the number of stages [1]. When fast
switching methods are used to connect the stages, the output
pulse can achieve a very short rise time. Traditionally, spark
gaps are used because of their fast switching capabilities and
adjustable breakdown voltage. The medium in the spark gap
(e.g. air, oil) needs sufficient time to recover before the next
cycle begins, which makes them less suitable for Marx
generators working at a high repetition rates. In addition, they
are bulky and not suitable for compact applications. To
overcome this, another type of switch can be employed:
Avalanche transistors. They come in small packages and thus
allow for the construction of compact solid-state Marx
generators.
II. MARX GENERATOR
In general, a Marx generator is a device which can charge
capacitances in parallel and discharge them in series. This
results in a voltage multiplication from input to output. An
interesting property of the Marx generator is that while the
input is DC, the output is pulse-shaped. The shape is typically
determined by the stage capacitances, the switches and the
load. The maximal repetition rate is set by the charging of the
Fig. 1. Marx generator, with either series charging (top) or parallel charging
(bottom).
stage capacitances via the charging resistors. The most
commonly employed circuit is shown in Fig. 1. For large Marx
generators with high output voltages, the charging resistances
are connected in series to reduce their required withstanding
voltage. Smaller Marx generators can employ a parallel
arrangement of the charging resistors. This leads to an equal
time constant for each stage, whereas the series configuration
has an increasing time constant for each stage.
The key parameters that determine the properties of a Marx
generator are:



n:
Vswitch:
Rswitch:
Number of stages
Switch trigger voltage
Switch on-resistance


Cstage:
Rcharge:
Stage capacitance
Charging resistance
III. AVALANCHE TRANSISTOR
A. PN-Junction Breakdown
The non-destructive breakdown of a PN-junction can occur
in several ways, like Zener-, avalanche- and secondary
breakdown. Since the Marx generator requires a rapid
switching action, Zener breakdown is of not suitable.
Avalanche breakdown occurs when the voltage across the PNjunction is high enough to accelerate charges in the PNjunction to energy levels that will create free electron-hole
pairs in the PN-junction upon impact. These newly formed
charges are again accelerated and continue to create more free
charges, resembling an avalanche. The resulting current
continues to flow independent of the voltage across the
junction and only stops when the current is no longer sufficient
to maintain the breakdown. Secondary breakdown can occur
after an avalanche or power pulse, which causes local hotspots
in the PN-junction. Due to their higher temperature, the
avalanche withstanding voltage is lowered on these spots
allowing for secondary (avalanche) breakdowns. A more indepth description of these breakdown phenomena can be found
in [2].
B. Breakdown Voltage
An avalanche transistor can be connected in several ways,
leading to different breakdown voltages. Two common
connections are Open-Base and Shorted-Base, with their
respective breakdown voltages denoted by V(BR)CEO and V(BR)CES
Note that although these values are usually given in a
datasheet, they do not provide much information about the
avalanche behavior. Instead, they give the Zener voltage at a
given collector current (e.g. 100 µA or 1 mA). Using a resistor
between base and emitter, the breakdown voltage V(BR)CER can
be varied between V(BR)CEO and V(BR)CES , which is shown in
Fig. 2.
C. Avalanche Voltage
The actual avalanche effect in the transistor occurs at a
higher voltage than the specified breakdown voltage. It is also
Fig. 3. Test setup to determine the avalanche voltage.
Fig. 4. Avalanche breakdown voltage vs. base-emitter resistance of the
2N5551.
dependent on the rest of the circuit [4]. Since it is known from
the Zener breakdown voltage that there is a dependence on the
base resistance, it has been investigated if the avalanche
voltage is dependent on the base resistance as well. The setup
depicted in Fig. 3 was used to operate the upper transistor in
avalanche mode while the base resistance was varied. The
supply voltage is chosen low enough such that the lower
transistor will not avalanche when switched. When the lower
transistor is switched, the voltage on its collector (and thus on
the emitter of the upper transistor) will drop. This causes an
increasing VCE across the upper transistor, up to the voltage
when VCE will lead to an avalanche and a resulting drop in VCE.
By measuring the maximal VCE across the upper transistor with
an oscilloscope, the avalanche voltage for the given base
resistor is determined.
When looking at the voltage at which the avalanche
breakdown occurred (Fig. 4), the influence of the base
resistance is clearly visible. The avalanche breakdown voltage
can be changed from 230 V to over 450 V when the baseemitter resistance is changed from 10 kΩ to 2.7 Ω.
Fig. 2. Breakdown voltage vs. base-emitter resistance of the 2N5551 [3].
D. Starting Capacitance
During the initial avalanche breakdown, a conductive
channel is formed through the PN-junction. In the previous
section (Figs. 2 and 4) we showed that the voltage required to
achieve this is significantly larger than the Zener voltage of the
PN-junction. This poses a problem, as can be explained using
the test setup in Fig. 3. If the capacitor would be omitted, the
voltage on the emitter of the upper transistor would still drop
after a pulse. As the voltage across the junction increases, the
corresponding Zener current will increase as well. Due to the
absence of the capacitor, this current has to flow through the
(internal) supply resistor and thus reducing the collector
voltage. This situation is equivalent of a Zener with a biasing
resistor and an avalanche will only occur if the voltage across
the Zener gets sufficiently high.
Fig. 5. Marx equivalent circuit after switching.
A so called 'Starting Capacitor' is added to ensure that an
avalanche will occur. This capacitance keeps the voltage on the
emitter steady during the start of the avalanche, thus increasing
the available voltage across the PN-junction. The sizing of this
capacitor is highly circuit (single/stacked setup), transistor
(Zener/avalanche characteristics) and construction (due to e.g.
parasitic inductances) dependent. More is not always better, as
in this case a large capacitor also means more stored energy to
be dissipated in the transistor.
IV. CHARACTERIZING PERFORMANCE
A. Output Voltage
A simple equivalent circuit can be used to determine the
output voltage of a Marx generator. It consists of the (charged)
stage capacitances, in series with the switch on-resistance and
the (resistive) load. It is shown in Fig. 5.
The resulting voltage across the load can be expressed as:
𝑉𝐿 = 𝑛 ∙ 𝑉𝑠𝑡𝑎𝑔𝑒 ∙
𝑅𝐿
𝑛∙𝑅𝑠𝑤𝑖𝑡𝑐ℎ +𝑅𝐿
(3)
This simplification neglects two important factors. First, it
does not incorporate capacitor discharge. Second, the switch
on-resistance is taken as a constant. Nevertheless, it can be
used as an approximation and is useful for load-matching
purposes.
B. Rise Time
When it comes to pulses, the rise time is often used as a
figure of merit. A short rise time is a desirable property of a
pulse generator, but the way this is achieved can vary. Proper
construction techniques (reducing parasitic inductance), using
suitable parts for the purpose and applying the correct load all
aid the rise time without degrading the other aspects of the
Marx generator (e.g. output voltage/power). There also exists
another way to achieve very short rise times with Marx
generators: reducing stage capacitances. By doing so, these
capacitors will be drained before the output pulse can reach its
maximal value. In effect, this lowers the output amplitude and
the rise time. Sub-nanosecond rise times can be achieved by
using this technique [5-6]. When the purpose of the Marx
generator is to supply energy to a load, this technique should
be avoided as the output energy decreases significantly.
C. Fall Time
Fig. 6. First stages of the prototype Marx generator with a negative supply.
The transistors are of the type 2N5551, the capacitors are 3.3 nF and the
resitors are 8.2 kΩ. Node capacitances CPx on respective nodes can be added.
Looking at the equivalent circuit of Fig. 5, the fall time
appears to be characterizable by an exponential RC decay. This
assumption is correct, but has one problem: the switch
resistance is not constant during the pulse. After the initial
avalanche, the current through the transistor drops and the
resistance starts to increase. This causes the voltage across the
junction to increase again and trigger a secondary breakdown.
During all these phases, the resistance varies significantly.
Another look at Fig. 5 reveals a complication. Since the switch
resistance is part of a voltage divider through which the
exponential decay is measured, an increasing switch resistance
leads to a faster fall time at the load. This makes it impossible
to retrieve any information from the fall time of a pulse.
V. PROTOTYPE
A 15-stage prototype was constructed to test the feasibility
and performance of a Marx generator using avalanche
transistors. The schematic of the first stages is depicted in
Fig. 6. The stage capacitances were chosen at 3.3 nF to obtain a
flat-top pulse, useful for rise- and fall time measurements.
Charging resistances of 8.2 kΩ were parallel-connected to
allow for equal biasing of all stages. Assuming a 5  t charge
time, this setup would allow for a 3.7 kHz repetition rate. The
avalanche transistors were operated in an open-base
configuration, based on the data from Fig. 2, Fig. 4, bias
current, stage voltage and avalanche voltage. The used setup
results in a bias current of 0.5 mA per transistor at a capacitor
voltage of 200 V and an avalanche voltage of 230 V. This
biasing leads to a dissipation in the transistor of 100 mW,
besides the additional dissipation during the pulse. Using a
shorted base setup with a 1 mA bias current resulted in a
capacitor voltage of 300 V and an avalanche voltage of 450 V.
Shorting the base has increased the capacitor voltage, as
Fig. 7. Initial output pulse produced by the prototype.
Fig. 8. Output pulse when starting capacitances are used.
Fig. 9. Output pulse when additional starting capacitance is used.
Fig. 10. Output amplitude vs. load resistance. The output voltage increases to
over 3 kV for no-load conditions and over a small capacitive load.
expected, which is beneficial for the output pulse voltage. The
disadvantage is that the dissipation has increased to 300 mW
and most importantly, the difference between the capacitor
voltage and the avalanche voltage has increased from 30 V to
150 V. The first leaves less room for dissipation during the
pulse, the latter means that this setup will be much harder to
avalanche.
47 pF has been determined empirically for this prototype.
Although a capacitance helps the avalanche breakdown, adding
them on the transistors further towards the output will
significantly degrade the performance of the Marx generator as
they reduce the dV/dT rate at that point.
VI. RESULTS
The initial output pulse of the prototype Marx generator is
shown in Fig. 7. The oscilloscope used was a Lecroy
Wavesurfer 104MSx-B (1 GHz, 10 Gs/s) in combination with
Lecroy PP007-WS (500 MHz, 9.5 pF) probes. The pulse
behaves as expected featuring a sharp rise, flat top and
somewhat exponential decay. The rise time of 5 ns is higher
than expected of an avalanche transistor Marx generator [7].
From the theory in Section III.D, it is known that a capacitor
can aid the avalanche breakdown of the transistor. Adding such
a capacitance on the 2nd and even 3rd transistor (Fig. 6)
proved to be aiding, as can be seen in Fig. 8. Their value of
During the measurements on the prototype, it was observed
that the addition of oscilloscope probes had a significant effect
on the pulse form. The suspicion was that this was due to their
capacitance, in this case a mere 10 pF. Whilst such parasitics
normally degrade the signals and pulses, it turned out to be
beneficial in this application. To investigate and isolate this
effect, the probe capacitance was replaced by a normal
capacitance and placed at various nodes. Several capacitors in
the range of 4.7-39 pF were used, with the best (and most
observable) effect was obtained using 4.7 pF on the 10th
transistor. The resulting pulse and its parameters can be seen in
Fig. 9. Most notable is the decrease in rise time (4.07 vs.
1.94 ns), near equal pulse duration (tr +tss = 14.12 vs. 14.10 ns)
and increased overshoot. The energy delivered to the load in
each pulse using this last setup is 581 µJ, the highest of any
setup tested. The explanation for this rise time improvement
and overshoot may lay in the transmission-line nature of the
Marx generator for these pulses. The transistors and
connections introduce parasitic inductances, which in
combination with a capacitance can form a lumped
transmission line. While the steady state level is subject to the
matching of the resistive load to the Marx generator resistance
(as described in Section IV.A), the pulse edge is determined by
the complex load and source parameters. Small elements, such
as a 4.7 pF capacitor may change these parameters
dramatically, as observed in Fig. 9.
We can also verify Equation 1 and determine the
parameters of the prototype by varying the load resistance.
Doing so over a range of 5-593 Ω resulted in Fig. 10. The
displayed fit of Equation 1 resulted in a n  Vstage of 2.69 kV
and a n  Rswitch of 58 Ω. This stage resistance is higher than the
expected value of ≈ 3 Ω per switch [7], but such a difference is
not uncommon [7]. Finally, on a small capacitive load such as
a small plasma reactor, the voltage reaches more than 3 kV.
VII. CONCLUSIONS AND RECOMMENDATIONS
In this paper, the application of avalanche transistors in
Marx generators has been investigated and demonstrated using
a 15-stage prototype, using inexpensive 2N5551 transistors.
This prototype is capable of generating high amplitude (up to
2.5 kV) and fast rising (tr < 2 ns) pulses. The effect and
benefits of parasitic capacitances have been shown, leading to
a significant increase in performance. The pulse energy of
581 µJ and a maximum repetition rate of 3.7 kHz allow for an
output power of over 2 W.
In order to achieve even higher output voltages and
energies, four possible strategies could be used. First, the openbase setup could be changed to shorted-base (or resistive-base)
to allow for higher stage voltages. The limiting factor will then
be the dissipation in the transistors. Second, the number of
stages could be increased at the cost of a higher output
impedance. 30-Stage generators have already been
demonstrated [6], though higher stage numbers will be harder
to avalanche properly. Third, the charging mechanism could be
changed to allow for a higher repetition rate. Smaller
resistances, a higher supply voltage and burst-charging could
be used to reduce the charging time and thus increase the
repetition rate. Again, transistor dissipation will be the limiting
factor. Lastly, the outputs of multiple stages can be combined,
either in a bipolar way [7] or in a unipolar way [8].
Concluding, Marx generators with avalanche transistors are
suitable for compact, high-speed and high-repetition pulse
generation for low power applications.
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