Cascade Circuits

26.4.3 Cascade Circuits

The assembling of a single modulator circuit with very HV can

be a very complex task and result in a number of problems as follows:

• Transformer assembled with very high turn ratio and voltage output; • Many semiconductors stacked in series;

FIGURE 26.39 Series-stacked modulator topology. • Presence of HV in small distributed volume and safety

distances; supply. One of the possible methods includes the use of float- • Coupling parasitic capacitances and inductances between ing transformer secondary windings connected to an ac–dc devices.

converter, as shown in Fig. 26.39.

In order to avoid these problems, it is possible to cascade single During the pulse period, the voltages of the individual cells modulators circuits where the output voltage is the sum of the are added up, hence the output voltage is individual outputs. However, care is needed in the connection of each circuit as voltage sharing between them is essential.

v 0 =v 1 +v 2 +···+v n , (26.29)

26.4.3.1 Circuit without Output Transformers

and the current through all the switches is almost the same. The freewheeling diode D i in the output of each cell enables

In the topology shown in Fig. 26.39, there is no transformer the switch of each cell on and off independently of other cells, between the energy storing capacitors and the load, the system which makes the system capable of adjusting the output volt- is composed of basic pulse generator cells, made by a capacitor age. This technique protects also the switches during the on–off

C i and a switch S i , stacked in series. The challenge in this type commutation transient for any mismatch in the voltage distri- of generator is the uniform distribution of the voltage between bution, where the R i resistors help on equalizing the voltage in each cell due to the floating nature of each cells and the high the S i switches during off -state (see Section 26.2.5, “Semicon- dv/dt with respect to the ground occurring during the rise and ductor Series, Parallel Stacks and Generalized Cascodes”). falling time of the pulse. For this reason, great care must be

taken in order to limit capacitance between each cell and the ground [17].

26.4.3.2 Circuit with Output Transformers

For proper operation, the capacitors in each cell of Fig. 26.39 The construction of a single, high-voltage pulse transformer, circuit need to be charged using a galvanically isolated power needing a high enough turns ratio (N ≫ 1) to increase the

694 L. Redondo and J. F. Silva output voltage, is complex due to the transformer’s nonideal

Alternatively, Fig. 26.40b presents three transformers with behavior leading to significant parasitic effects as the output the secondary windings in series, each one designed for one- voltage rises. To solve this problem, it is possible to stack series third of the output voltage v 0 . In the primary side, windings are several pulse transformers with lower turns ratio, in order to in parallel, supplied by v in , and referenced to ground. Hence, have only a fraction of the total voltage in each one [27, 51, 52]. the isolation voltage between windings of each transformer is With a careful design, the leakage inductance and distributed different. capacitances of the equivalent circuit are reduced as compared

Considering Fig. 26.40b, although the secondary winding with one single equivalent transformer, leading to a better rise- potential in transformer T p2 and T p3 is, respectively, increased time performance [53].

by v 0 /3 and 2v 0 /3 through the secondary winding of transformer

The most common ways to associate pulse transformers are T p1 and T p2 , in the primary windings the reference potential shown in Fig. 26.40 [54]. The auto-transformer type cascade stays constant. As a result, each transformer holds a different layout, is shown in Fig. 26.40a, with three transformers, each voltage between windings, depending on the series position

one holding one-third of the output voltage v 0 of each transformer, which increases toward higher potentials. Thus, transformer galvanic isolation between windings must

be designed to v 0 /3 for T p1 , 2v 0 /3 for T p2 , and v 0 for T p3 . The above-mentioned drawback sets serious difficulties for In this topology, power is supplied to T p2 and T p3 from the pulse applications of the Fig. 26.40b circuit. Since the pulse previous transformers. Transformer T p1 and T p2 have three transformers placed at higher potentials hold higher voltages, secondary terminals, two of them to feed the primary of the isolation distance should be increased. Consequently, the the next transformer, and the third to step up the voltage of the pulse waveform is distorted due to the increase of the parasitic next transformer. This configuration decreases significantly the leakage inductance with the isolation distance. distributed capacitive between windings.

v 0 =v 1 +v 2 +v 3 .

To overcome this problem, it is possible to feed the pri- The major advantage of the cascade association, of mary windings of the pulse transformers with galvanic isolated

Fig. 26.40a, is that the isolation voltage between windings of power supplies. This can be achieved with the introduction of

each transformer is the same, and equal to v 0 /3. However,

isolation transformers, in order to keep the secondary windings of the pulse transformers in series, but with the same isolation

• Considering transformers with equal turn ratio N and voltage between windings. This solution has the immediate primary voltage, v in , as each transformer is fed by the advantage that all the pulse transformers are similarly built, previous one, each transformer has a different power. with the same minimum isolation distance, which helps to Considering Fig. 26.40a, if the load power is P, neglect- reduce the output pulse rise-time. Two configurations can be ing the losses, in the first transformer, the input cascade considered, Fig. 26.41, as follows: power is P. The following transformer withstands 2P/3, and the third transformer withstands P/3, being the total

• Independent isolation transformers (Fig. 26.41a); installed transformer power 2P;

• Cascade connected isolation transformers (Fig. 26.41b). • Due to the inclusion of an extra terminal in the high- For both circuits in Fig. 26.41, the secondary windings of the

voltage side with different current ratings, the trans- pulsed transformer are series connected, delivering each one former assembling is complex.

(T p1 ,T p2 , and T p3 ), v 0 /3 of the total output voltage v 0 . In the circuit of Fig. 26.41a, the primary windings of T p1 ,T p2 , and T p3 are fed, respectively, by the secondary windings of the isolation

T p3

T p3

transformers T i1 ,T i2 , and T i3 , these ones being fed by the input

voltage v in . In this way, the pulse transformers T p1 ,T p2 , and T p3 ν in

ν 3 3 can be assembled with the same structure and characteristics,

T p2

for the same isolation voltage of v 0 /3. The voltage increase due +

T p2

to the secondary winding series connection of T p2 and T p3 is ν in

ν 2 ν 0 ν 2 ν 0 sustained by the isolation transformer T i2 and T i3 . Then, for −

the worst running condition (considering a high capacitance T p1

between primary and secondary of the pulse transformers), the +

T p1

galvanic isolation of T i2 and T i3 must be predicted to hold,

in

1 in

respectively, v 0 /3 and 2v 0 /3. The isolation transformer T i1 is

not necessary.

In the circuit of Fig. 26.41b, the primary windings of T p1 , (a) (b) T p2 , and T p3 are fed, respectively, by the secondary windings

FIGURE 26.40 Simplified transformers association: (a) cascade; and of T i1 ,T i2 , and T i3 , with primary windings fed successively by (b) secondary windings in series.

the secondary windings of the previous transformer (i.e., T i3

26 Solid State Pulsed Power Electronics 695 T i3

T p3

the isolation transformers and the features desired for the pulse

generator.

Regarding the last, it is considered a great advantage for the

T i2

T p2

high-voltage pulse generator to be of modular construction,

built upon several equal modules, where each one could occupy ν 2 ν 0 any position in the generator.

T i1

T p1

E XAMPLE 26.8 Consider the generation of −15-kV

pulse from a series stack of three −5 kV forward

ν in

ν 1 HV pulse generators based on the topology shown in

Fig. 26.30, with the operating conditions of Exam- ple 26.6. Select the stack method to implement and draw

(a)

the complete assembly, taking into consideration a mod- ular perspective. Specify, also, the energy supply to the

T i3

T p3

three stages, the selection of semiconductors and their

ν 3 triggering.

S OLUTION . The modular high-voltage generator con-

T i2

T p2

struction is based on three main principles as follows:

ν 2 ν 0 • distribute the total voltage of a high-voltage circuit by

holding the potential of several points in the circuit

T i1

T p1

relatively to ground;

ν in

ν 1 • distribute the total voltage for several transformers

connected in series; • use isolation transformers to feed the primary of the

series-connected transformers, as shown in 26.41a. FIGURE 26.41 Simplified layout of series-connected secondary wind-

(b)

The proposed circuit layout is shown in Fig. 26.42. If posi- ings transformers fed by (a) independent isolation transformers and tive pulses are desired, it is only necessary to invert the polarity (b) cascade isolation transformers.

of the secondary diodes D ri , where i ∈ {1, 2, . . . , n}. Power is supplied to the three modules via isolation transformers (1:1), T ii , which must hold-off a maximum voltage of 1 k kV between

fed by T i2 , which is fed by T i1 , which is fed by v in ). In this primary and secondary. These transformers are assembled way, the pulse transformers T p1 ,T p2 , and T p3 can be assembled with primary windings in parallel, connected to a dc–ac high- with the same structure and characteristics, for the same isola- frequency inverter to reduce the size and increase the efficiency

tion voltage of v 0 /3. The voltage increase due to the secondary of the system. In addition, each secondary winding is con- winding series connection of T p2 and T p3 is held by the isola- nected to an ac–dc rectifier that produces the necessary v dci tion transformer T i2 and T i3 . The isolation transformer T i1 is voltage to the forward converters. not needed.

Considering the −5-kV voltage at each individual forward Taking into account the two circuits of Fig. 26.41 as follows: pulse generator with the operating condition of Example 26.3,

then 800 V semiconductors can be used. Hence MOSFETs can • In Fig. 26.41a, considering a load power P, neglecting

be selected for switches S i .

the losses in the transformers, each one is assembled Considering the three modules, in Fig. 26.42, with switch S i for a power of P/3 (i.e., the power installed in all the on, diodes D ri are conducting, and the voltage applied to the

transformers is 2P). However, in Fig. 26.41b, the pulse load is transformers are assembled with a power of P/3, but the isolation transformers have successive powers of P, 2P/3,

v 0 = − (v 01 +v 02 +v 03 ) = − 3 × 5000 = − 15 kV. and P/3. The total power installed in all the transformers

considering three equal modules, v 01 =v 02 is 3P;

=v 03 =v 0i . During this time, the voltage reference at the secondary terminal with

• In Fig. 26.41b, all the transformers have the same isola-

a dot point of each pulse transformer is raised tion voltage, whereas in Fig. 26.41a, the isolation voltage

in isolation transformers is different.

v ref Tp1 = 0V,

= − 5 kV gies, in Fig. 26.41, are equivalent. Hence, the choice between

Considering only the pulse transformers, the two topolo-

v ref

Tp2 = (2 − 1)v 0i

the two should be based on the characteristics preferred for v ref Tp3 = (3 − 1)v 0i = 2 × 5000 = − 10 kV

696 L. Redondo and J. F. Silva

dc supply

Fiber-optic MOSFET

Fiber-optic MOSFET

Control unit

fiber-optic

Isolated

Fiber-optic MOSFET

transmiters

power supply

receiver

drive

FIGURE 26.42 Modular, pulsed generator simplified layout for −15 kV output pulses.

During the off time of switches S i , the voltage applied to The Marx generator concept is presented in the circuit of the load goes to zero, diodes D ri in each module hold-off only Fig. 26.43, which comprises a number of modular stages con- the reset voltage of their respective pulse transformer. Voltage- stituted by an energy storage capacitor C i , two impedances sharing resistors, R si , are used to equally distribute the reset Z i (resistive and/or inductive) for charging and limiting the voltages of each module through diodes D ri . In order to hold self-short-circuit capacitor paths and a switch S i , for i ∈ the high-voltage potential in each module relative to ground, {1, 2, . . . , n}. During the charging period, a relatively low- high-valued R di resistances can also used.

voltage dc power supply V dc charges the C i capacitors in parallel Regarding the triggering of the MOSFETs in each stage, dc trough impedances Z i . isolated power supplies are used in each stage to supply the

When switches S i are turned on, the C i capacitors are con- necessary energy to the trigger drives that receives the signals nected in series and a voltage is applied into the load, equal to by optic fiber from the ground control circuit.

v 0 = − nV dc , (26.31)