Resistive (R) Loads where Q is the change in thermal energy, and m is the mass of

26.3.1 Resistive (R) Loads where Q is the change in thermal energy, and m is the mass of

the water resistance tube.

Pure resistive-type loads are not common in pulsed power Nevertheless, the use of water resistances brings some lim- applications, being the processing of liquids one of the excep- itations. First, with the temperature increase, air bubbles are tions, in applications such as liquid food sterilization, waste formed that change the resistance value. Second, the CuSO 4 water decontamination, and biomedical materials. However, molecule breakdown linked with electrolyses phenomenon has resistive loads are used frequently as a load reference for test- undesirable results: (1) gas release that increase the pressure ing and comparison of the pulse voltage waveform between inside the tube, a gas release aperture is advisable in the tube different types of modulators.

edges to prevent the increase of the pressure inside the tube; (2) The problem is to find a resistor that can handle the gen- the metallic copper decomposition in the cathode (i.e., copper erated power, the voltage level, at the same time, without transport from the anode to the cathode), changes the test

26 Solid State Pulsed Power Electronics 683 conditions. With time, the performance of a water resistance

may change in consequence of these effects.

E XAMPLE 26.4 Consider a HV pulse modulator that produces a 20 kV/10 A pulse during 10 µs with 100 Hz

C 1 R 2 repetition rate. Calculate the temperature increment of l = 1 − m tube (made from insulating material) with an

C 2 internal diameter of d = 2.5 cm when used as a load to the modulator during 60 s.

S OLUTION .

FIGURE 26.24 The energy per pulse is Simplified electrical equivalent circuit of a PBII load.

E p =V p I p t on = 20 × 10 3 × 10 × 10 −5 = 2 J. in the order of the microseconds and small compared with the pulse width; (c) the pulse duty cycle must be a few percent; (d)

The energy in 60 s is the pulse width and frequency should allow some load varia- tion; (e) there must be a current limit in case of short circuit; (f) in order to be practical, the power supply cannot be too

E 60 = 60f E p = 60 × 100 × 2 = 12 kJ. complex and bulky while including all the necessary protection

systems for personnel and equipments. The volume of water inside of the tube is

In capacitive-type loads, it is extremely important, also, that the modulator topology has the capability to short circuit the

2 2 = πr 3 l = π0.0125 = 0.491 × 10 −3 m = 491 g. load after the HV pulse, quickly discharging all the load and parasitic capacitances to zero, otherwise the load stays charged

Then, considering that 1 calorie = 4.2 J, results in

to almost full pulse voltage.

26.3.3 Inductive (L) and LR Loads

Inductive-type loads are present when a pulse transformer is used to further increase the voltage level of a modulator or

Hence, for an initial water temperature at 25 ◦

C, after 60 s,

when voltage pulses are applied to inductive loads such as coils. the temperature will reach up to 30.8 C. An example of the last is electromagnetic metal forming appli-

cation (EMF), where HV resonant topologies apply kiloampere

26.3.2 Capacitive (C) and RC Loads

current pulses, during hundreds of microseconds, into very low-inductance systems [8].

Pulse power applications associated with plasma and gas pro- For inductive operation, the modulator must clamp the load cessing, and occasionally liquids, present typically capacitive with an opposite polarity voltage after each HV pulse, dur- behavior to the PP modulators. In fact, some of the most chal- ing enough time to guarantee a zero average load voltage. lenging operating conditions are related with the operation In general, this is not accomplished with turn-off capability with plasmas.

semiconductor switches but rather with freewheeling diodes.

A typical example is plasma-based ion implantation (PBII) Also, the topology can either be dissipative or it can send the where a target is immersed in a plasma, produced in a confined energy stored in the magnetic circuit back to the power supply, volume, and almost rectangular negative HV pulses are applied increasing the efficiency of the modulator. to it. This results into a high current peak at the beginning of the pulse, rapidly decreasing to a much smaller value. The ini- tial transient current that charges the main system capacitances

26.4 Solid-State Pulsed Power Topologies

can be several orders of magnitude greater than the stationary current at the pulse end, when the load imposes almost open- The use of innovative techniques, supported on dc–dc isolated circuit impedance, presenting an additional challenge to the converter topologies, brought from solid-state power electron- modulator. The above load dynamic characteristics can be rep- ics, taking advantage of all the capabilities of such devices, resented in an RC electrical equivalent circuit as in Fig. 26.24 circumventing their limitations, is playing an important role to [29, 30].

the expansion of pulse power technology to a wide range of new For plasma loads such as PBII, considering plasma character- applications, needing compact, small size, and efficient pulse istics and typical wanted results, the modulator requirements modulators, spreading to almost every industrial and commer- can be sought: (a) the voltage pulse waveform must be inde- cial fields, from food sterilization, biomedical applications, and pendent of the load impedance; (b) the pulse rise time must be pollution control to surface engineering [30–35].

684 L. Redondo and J. F. Silva

FIGURE 26.25 Practical shape voltage pulse waveform.

Nevertheless, each pulsed power application represents a dif- is also proposed for distributing the voltage in series stacks of ferent challenge for the pulsed power technology and the load semiconductors. requirements normally imposes limits to the use of each type of

It is important to define some of the pulse parameters men- power converter topology. One important characteristic associ- tioned in the following sections, as shown in Fig. 26.25 for the ated with many pulse power applications is the low duty ratio, practical shape of unipolar voltage pulses.

D, pulse operation (i.e., usually lower than 5%, [1, 2]), where Considering Fig. 26.25, the voltage pulse can be character- the pulse width is much shorter than the pulse period, which ized by several parameters: reduces significantly the modulator average power and also the

• rise time, t r : period of time from 0.1 to 0.9 V, where V is dissipated power into the load, as the plateau amplitude of the pulse;

s : voltage excursion, after the rise time,

P av =V p I p D,

above the pulse plateau V ;

where V • p and I p are, respectively, the pulse voltage and current

: voltage excursion, after the fall time, amplitude, supposing a rectangular pulse with D =t on /T duty

below minimum voltage, 0 volt;

ratio. In order to take the most of each topology and also to be able •

V =V−V f ;

to extend these concepts to other topologies that have potential • fall time, t f : period of time from 0.9 to 0.1 V f , where V f is for high-voltage pulsed generation, it is important to under-

stand the concepts and to know the advantages and limitations when using each topology.

• tail: voltage descend during pulse fall. In this section, several topologies capable of generating high-