Parallel Stacks

26.2.5.3 Parallel Stacks

C S value is C S ≈L S I RR 2 / [n(κV RRM ) 2 ]. Resistor R S should available semiconductors do not present the needed current define the damping factor ξ of the equivalent RLC circuit, √ ratings. being R S = 2ξ L S /(nC S ). For controlled turn-on and turn-

Parallel associations of power devices can be used when the

For positive temperature coefficient devices such as MOS- off devices, the R S C S parallel snubber can be improved using FETs, SITs, and most of their derived structures, the devices

an extra diode (R V C V D V in Fig. 26.11, with L V =L S ). To can be just connected in parallel, taking care of symmetry to obtain near-balanced turn-on t r and turn-off t f times for each minimize stray inductances and capacitances and to balance series semiconductor, with direct current I AK , hold-off voltage junction temperatures. Individual gate drivers and protection κ V DRM and pulse on minimum time T pmin ,L S should have circuits (except if stray effects are not a concern) should also be

the value L S ≈ κV DRM t r /I AK and C V ≈I AK t f /(κV DRM ), being

used. This is not valid for the MOSFET intrinsic diode, which R V ≈T pmin ξ /(πC V ).

must be disabled.

For negative temperature coefficient devices such as diodes,

26.2.5.2 Generalized Cascodes

thyristors, bipolar transistors, GTO, and other bipolar devices, several methods could be used as follows:

To use a series stack of controlled turn-off semiconductors such as MOSFETs, SITs, or even IGBTs, the generalized cascode asso-

a. To select devices with very small relative parame- ciation (Fig. 26.21) is a valuable alternative to the simple series

ter variations (matched devices) and to balance their

26 Solid State Pulsed Power Electronics 681

D 35 0Ω

C 1 0Ω

Z16 V Z800 V

1.5 kV 1 0Ω

Z16 V Z800 V C

Z16 V Z800 V

FIGURE 26.21 Generalized cascade associations: (a) using SIT devices; (b) using only MOSFETs; and (c) alternative connection of gate capacitor.

junction temperatures by using a single heat sink and

26.3 Load Types and Requirements

symmetrical disposition;

b. To use current sharing transformers or coupled induc- Pulsed power applications present some of the most demand- tors (Fig. 26.22);

ing loads to the modulators in terms of pulse requirements,

c. To use current feedback control techniques [22] if the as, normally, almost rectangular pulses are needed to many paralleled devices have turn-off capability;

applications in capacitive and inductive loads.

d. To use small resistors in series with each power semi- Nowadays when evaluating a PP modulator topology, it conductor device (Fig. 26.23), calculated upon the is important to consider, in addition to cost, size, simplicity

maximum, minimum, and typical device parameters. It of operation, and efficiency, the flexibility for different oper- is possible to show that a rough estimate for the series ating conditions into various load conditions (i.e., resistive,

resistor R E is R E ≈ (V 1max −V 1min )/(I 2 −I 1 ) [10], where capacitive, and inductive).

V 1max is the device family maximum on voltage at the In fact, the growing variety of environmental, biological, minimum allowed current I 1 , and V 2min is the device medical, and industrial applications using positive or negative

type minimum on voltage at the maximum allowed high-voltage repetitive pulses, for enhancing the characteristics

of a product or method, impose various load conditions to the One of the previous approaches has to be selected upon modulator circuits [23]. the pulsed power application to minimize costs and maximize

current I 2 (I 2 > I 1 ).

For example, applications with plasmas or gases present performance.

normally capacitive behavior, like plasma implantation or air

682 L. Redondo and J. F. Silva

FIGURE 26.22 Using transformers or coupled inductors for paralleling power devices: (a) two diodes; (b) modeling the parallel connection of two diodes; (c) and (d) two ways of connecting n-paralleled power semiconductors.

presenting inductive behavior. There are expensive commer-

cially available types for HV and kW operations, alternatively, i1 −ip/n i2 −ip/n

it is possible to fabricate, much cheaper, water resistors for any v AK1

in −ip/n

v AK

power and voltage needed.

A water resistor is essentially an insulator tube filed with an aqueous electrolytic solution and a metal electrode in each R e R e R e R e extremity, capable of dissipating the average power and holding

the high voltage from the modulator. Typically, it is made up of dilute solution of copper sulfate (CuSO 4 ) in deionized water

FIGURE 26.23 Parallel connections of power semiconductors using cur- (a good electric insulator), which does not degrade the copper rent sharing resistors.

electrodes, the higher the CuSO 4 concentration the lower the resistance, being the total resistance proportional to the length of the tube [28].

processing for pollution control [24, 25]. Applications that use The energy dissipated in the water produces a change in coils present an inductive behavior, like electromagnetic form-

ing, or whenever a high-voltage transformer is associated to the specific heat of water, C p , modulator to further increase the output voltage [26, 27]. In addition, food processing and water treatment present resistive