High voltage switch with cascaded transistor topology

Abstract

A switching apparatus includes three or more series-connected transistors, and it further includes a balancing network. The balancing network includes a resistor network configured to divide a voltage from a voltage source across the series-connected transistors. The resistor network includes at least two resistive legs connected in parallel. In each resistive leg, two or more resistors are connected in series. The balancing network may further comprise at least one capacitive leg of series-connected capacitors connected across the series-connected transistors, and it may further comprise at least one leg of series-connected avalanche diodes connected across the series-connected transistors for overvoltage protection. In example embodiments, the series-connected transistors are JFETs. In other example embodiments, the series-connected transistors may be HEMTs or GaN transistors.

Claims

1. A switching apparatus, comprising: at least a first plurality of n series-connected transistors, each of said transistors having a respective source terminal, a respective drain terminal, and a respective gate terminal, wherein for n a positive integer at least 3, the first plurality of n series-connected transistors includes a first transistor herein denominated J.sub.1, a last transistor herein denominated J.sub.n, and at least one transistor herein denominated J.sub.i, i having respective positive integer values between 1 and n; a terminal S connected to the J.sub.1 source terminal; a terminal D connected to the J.sub.n drain terminal; a control terminal G connected to the J.sub.1 gate terminal; and a voltage-balancing network connected between terminal S and terminal D; wherein the voltage-balancing network includes a number, at least two, of parallel-connected resistive legs; wherein each parallel-connected resistive leg includes two or more series-connected resistors; and wherein for each transistor after J.sub.1, the pertinent gate terminal connects to one of the parallel-connected resistive legs such that the parallel-connected resistive legs collectively constitute a voltage divider for dividing voltage across the series-connected transistors.

2. The switching apparatus of claim 1, wherein the transistors J.sub.1, . . . , J.sub.n are JFETs.

3. The switching apparatus of claim 1, wherein the transistors J.sub.1, . . . , J.sub.n are silicon carbide or other wide-bandgap material JFETs.

4. The switching apparatus of claim 1, wherein the transistors J.sub.1, . . . , J.sub.n are normally-on transistors.

5. The switching apparatus of claim 1, wherein the transistors J.sub.1, . . . , J.sub.n are normally-off transistors.

6. The switching apparatus of claim 1, wherein the transistors J.sub.1, . . . , J.sub.n are GaN transistors.

7. The switching apparatus of claim 1, comprising at least one further plurality of n series-connected transistors connected between the terminal S and the terminal D.

8. The switching apparatus of claim 1, wherein: the balancing network further comprises at least one capacitive leg connected between the terminal S and the terminal D; and the at least one capacitive leg comprises n series-connected capacitors C.sub.1, . . . , C.sub.n.

9. The switching apparatus of claim 8, wherein each of the n series-connected capacitors C.sub.1, . . . , C.sub.n is connected between the gates of two sequential transistors J.sub.i, J.sub.i+1, except that one of the capacitors is instead connected between the terminal S and the gate terminal of J.sub.2, and one other of the capacitors is instead connected between the gate terminal of J.sub.n and the terminal D.

10. The switching apparatus of claim 8, wherein: the balancing network further comprises at least one avalanche-diode leg; the at least one avalanche diode leg comprises n−1 series-connected avalanche diodes; and each of the n−1 series-connected avalanche diodes is connected between the respective gate terminals of two sequential transistors J.sub.i, J.sub.i+1, i=1, 2, . . . , n−1.

11. The switching apparatus of claim 1, wherein the number of parallel-connected resistive legs in the voltage-balancing network is two.

12. The switching apparatus of claim 11, wherein n is at least 4, and wherein, for at least one positive integer i at least 1 and not more than n−3: a resistor of one of the two parallel-connected resistive legs is connected between the respective gate terminal of J.sub.i and the respective gate terminal of J.sub.i+2; and a resistor of the other of the two parallel-connected resistive legs is connected between the respective gate terminal of J.sub.i+1 and the respective gate terminal of J.sub.i+3.

13. The switching apparatus of claim 11, wherein the respective gate terminals of transistors J.sub.2 up to and including J.sub.n are alternatingly connected to a respective one or the other of the two parallel-connected resistive legs.

14. The switching apparatus of claim 11, wherein n is at least 4, and wherein: in one of the two parallel-connected resistive legs, a bottom resistor is connected between the terminal S and the respective gate terminal of J.sub.2, a top resistor is connected between the respective gate terminal of J.sub.n and the terminal D, and all resistors between the top and bottom resistors are connected between respective gate terminals of transistors J.sub.i wherein i is an even integer; and in the other of the two parallel-connected resistive legs, a bottom resistor is connected between the terminal S and the respective gate terminal of J.sub.3, a top resistor is connected between the respective gate terminal of J.sub.n−1 and the terminal D, and all resistors between the top and bottom resistors are connected between respective gate terminals of transistors J.sub.i wherein i is an odd integer.

15. The switching apparatus of claim 1, wherein: the number n of series-connected transistors equals four; the number of parallel-connected resistive legs in the voltage-balancing network is two; one of the two parallel-connected resistive legs comprises three resistors; and the other of the two parallel-connected resistive legs comprises two resistors.

16. The switching apparatus of claim 1, further comprising an auxiliary circuit adapted to apply a controlling voltage to the control terminal G for controlling a conductive state of the series-connected transistors.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a simplified schematic diagram of a switch circuit in an example embodiment having an arbitrary number of JFETs.

(2) FIG. 2 is a simplified schematic diagram of a switch circuit in an example embodiment having four JFETs.

(3) FIG. 3 is a graph of the predicted waveforms of the respective gate-to-source and drain-to-source voltages of the respective JFETs during the turn-ON process of an illustrative switch circuit. The predicted waveform of the current i.sub.DC in the switch circuit is also shown.

(4) FIG. 4 is a graph of the predicted waveforms of the respective gate-to-source and drain-to-source voltages of the respective JFETs during the turn-OFF process of an illustrative switch circuit. The predicted waveform of the current i.sub.DC in the switch circuit is also shown.

(5) FIG. 5 is a block diagram illustrating an architecture for a breaker circuit incorporating the switch circuit described here, in an example embodiment.

(6) FIG. 6 is a graph of the experimentally measured voltage versus time across a prototype switch circuit (“V.sub.breaker”) and the experimentally measured current versus time through the prototype switch circuit during a turn-OFF transition.

(7) FIG. 7 is a composite graph of the experimentally measured drain-to-source voltages versus time of the respective JFETs J.sub.1 to J.sub.4 of a prototype switch circuit.

(8) FIG. 8 is a portion of the preceding figure, showing the drain-to-source voltages over an expanded timescale.

(9) FIG. 9 is a graph that illustrates the distribution of steady-state drain-to-source voltages of the respective JFETs in a prototype switch circuit at ten different applied voltages.

DETAILED DESCRIPTION

(10) FIG. 1 is a simplified schematic diagram of a switching apparatus in an example embodiment in which the transistor devices are JFETs. It should be noted, however, that although a switching apparatus based on JFETs is particularly desirable for certain applications, the choice of JFETs in the following description is not meant to be limiting. Rather, the principles described below can be implemented with any of various types of three-terminal devices, not least of which are HEMTs and other power transistors. It should also be understood that although JFETs, as in the example embodiment described here, are normally-on devices, the principles described below can be implemented using normally-off devices as well, and such implementations are within the scope of the present disclosure.

(11) As will be seen below, the material composition of example JFETs suitable for use in an illustrative embodiment is silicon carbide. However, transistor devices of any of various semiconductor compositions, especially those formed of wide-bandgap materials, may also be suitable for use in alternate embodiments. Not least of these compositions, by way of example, are gallium nitride (GaN) and aluminum gallium nitride (AlGaN). Embodiments having any material composition suitable for implementing the principles described below are within the scope of the present disclosure.

(12) The switching apparatus, as shown, has various applications including applications as a high-voltage circuit breaker. As shown, an integer number n of JFETs 10, exemplarily SiC JFETs, are connected in series. The minimum number for n is 3. The n JFETs 10 constitute a JFET leg 12 of the circuit. As will be explained below, the JFET leg 12 is controllable to provide blocking, between the terminals 14, 16, respectively labeled “Source” and “Drain”, of a dc voltage V.sub.DC from a voltage source, which is not shown in FIG. 1. In other embodiments, there may be two or more JFET legs 12, as explained in more detail below.

(13) As shown, the Source terminal 14 of the switching apparatus is connected to the source terminal of J.sub.1, and the Drain terminal 16 of the switching apparatus is connected to the drain terminal of J.sub.n.

(14) Also shown in FIG. 1 is a leg 18 constituted by series-connected avalanche diodes D.sub.1-D.sub.n−1, and a leg 20 constituted by series-connected capacitors C.sub.1-C.sub.n. Each avalanche diode is connected between the gates of two sequential JFETs. Likewise, each capacitor is connected between the gates of two sequential JFETs, except that C.sub.1 is connected between the Source terminal 14 and the gate terminal of J.sub.2, and C.sub.n is connected between the gate terminal of J.sub.n and the Drain terminal 16.

(15) The avalanche diodes are to protect the transistors (i.e., the JFETs 10, in the present example) in the event that an overvoltage greater than V.sub.DC/n is applied across any of them. The capacitors are designed to dynamically balance the voltage during the ON and OFF transitions, which will be described below.

(16) FIG. 1 also shows a balancing network of resistors R.sub.1-R.sub.n+1, which is connected between the Source terminal 14 and the Drain terminal 16 to balance the static voltage across the JFET leg 12. It is noteworthy that this static balancing network comprises more than one leg of series-connected resistors. The illustrated example has two legs 22, 24. One leg 22 comprises resistors R.sub.1 to R.sub.(n/2)+1, and the other leg 24 comprises resistors R.sub.(n/2)+2 to R.sub.n+1. In alternate embodiments, the passive balancing network may have three legs, or even more, up to a maximum of n−1.

(17) As those skilled in the art will recognize, individual circuit elements such as transistors, resistors, and capacitors may be replaced by networks of multiple elements having equivalent function, such as serial networks, parallel networks, or serial-parallel networks, without deviating from the principles described here. Hence, any reference to an individual circuit element is meant to encompass equivalent networks of such components.

(18) In the illustrated example, each resistor, with certain exceptions, is connected between the gates of two JFETs 10 that are separated in sequence by one intervening JFET 10, with staggering by one JFET position between the two legs 22 and 24. The exceptions are:

(19) R.sub.1 is connected between the Source terminal 14 and the J.sub.2 gate terminal;

(20) R.sub.(n/2)+1 is connected between the J.sub.n gate terminal and the Drain terminal 16;

(21) R.sub.(n/2)+2 is connected between the Source terminal 14 and the J.sub.3 gate terminal; and

(22) R.sub.n+1 is connected between the J.sub.n−1 gate terminal and the Drain terminal 16.

(23) The gate terminals of the JFETs 10 (more specifically, the points of connection between the respective gate terminals and the capacitor leg 20) are labeled g.sub.2, g.sub.3, . . . , g.sub.n in FIG. 1. Various voltages and currents are also labeled in FIG. 1. For convenient reference, they are defined in Table 1.

(24) Accordingly, it will be seen that in the left resistor leg 22 (in the view of FIG. 1), the bottom resistor is connected between the Source terminal 14 and the J.sub.2 gate, the top resistor is connected between the top JFET gate and the Drain terminal 16, and all other resistors are connected between gates of even-numbered JFETs. In the right leg 24 (in the view of FIG. 1), the bottom resistor is connected between the Source terminal 14 and the J3 gate, the top resistor is connected between the second-from-top JFET gate and the Drain terminal 16, and all other resistors are connected between gates of odd-numbered JFETs 10. This scheme can be implemented for n=4, and it can be extended to greater numbers of JFETs 10 and balancing resistors.

(25) As mentioned above, alternate embodiments may include two or more JFET legs 12. For example, the entire network constituted by the JFET leg 12, the avalanche diode leg 18, the capacitor leg 20, and the resistive balancing network as represented, e.g., by resistor legs 22 and 24 of FIG. 1 can be taken as a unit and duplicated one or more times, so that two or more such units are connected in parallel between the Source terminal 14 and the Drain terminal 16. Such a parallel arrangement may be advantageous, in at least some cases, for mitigating stresses caused by high electric current. In other approaches, it may be possible to duplicate the JFET leg 12 without duplicating legs 22 and 24 of the balancing network, although such an approach would complicate the task of voltage balancing.

(26) TABLE-US-00001 TABLE 1 V.sub.DC Supply Voltage V.sub.th JFET Threshold Voltage V.sub.G− JFET Turn-off Voltage V.sub.G+ JFET Turn-on Voltage V.sub.gs(I.sub.0) Gate-to-Source Voltage at Full Load Current v.sub.gs Gate-to-Source Voltage (“Gate Voltage”) v.sub.gsi Gate-to-Source Voltage, i'th JFET v.sub.ds Drain-to-Source Voltage (“Drain Voltage”) v.sub.dsi Drain-to-Source Voltage, i'th JFET i.sub.g Gate Current i.sub.gi Gate Current, i'th JFET t.sub.Ri Resistor Current, i'th Resistor i.sub.d Drain Current I.sub.0 Total Load Current i.sub.DC The Current Through the JFET Leg R.sub.gi Gate Resistance, i'th JFET C.sub.gs Gate-to-Source Capacitance C.sub.gsi Gate-to-Source Capacitance, i'th JFET C.sub.gd Gate-to-Drain Capacitance C.sub.gdi Gate-to-Drain Capacitance, i'th JFET

(27) We will now briefly describe the operation of the switching apparatus, which for conciseness, but not for limitation, we refer to below as the “switch circuit”. A more detailed discussion can be found in Luciano A. Garcia Rodriguez, et al., “A High-Voltage Cascaded Solid-State DC Circuit Breaker Using Normally-ON SiC JFETs”, 2021 IEEE 12th Energy Conversion Congress & Exposition—Asia (ECCE—Asia) (2021) 1554-1561, the entirety of which is hereby incorporated herein by reference.

(28) Turn-ON Process. We will first describe the turn-ON process. It is noteworthy in this regard that JFETs 10 are normally-on devices. In order to maintain the switching apparatus in an OFF state, it is therefore necessary to use an ancillary circuit to supply a controlling voltage suitable to maintain the JFETs 10 in their OFF state. Such an ancillary circuit can be powered by power sources of various kinds, including, without limitation, batteries and taps from the high-voltage source. One advantage of using a high-voltage tap is that it offers assurance of continual control, even in a short-circuit event. An example of an ancillary circuit powered from a high-voltage tap will be provided below.

(29) For purposes of discussion, we take the steady-state OFF condition of the switch circuit as the initial condition. In this OFF condition, the total dc voltage V.sub.DC is divided evenly among the n JFETs 10. The gate-to-source voltages (referred to below as “gate voltages”) of the JFETs 10 are at a level slightly below the threshold voltage V.sub.th, except for V.sub.gs1, which is at a subthreshold voltage V.sub.G−; i.e., V.sub.G−<V.sub.th. The voltage across each balancing capacitor is V.sub.DC/n, except that the voltages across C.sub.1 and C.sub.n are V.sub.DC/n+V.sub.th and V.sub.DC/n−V.sub.th, respectively. Due to their high values, the balancing resistors R.sub.1 to R.sub.n+1 have no significant effect on the turn-ON and turn-OFF processes. Hence, we treat them as open circuits in the following discussion.

(30) For simplicity of presentation, the following analysis is directed to an illustrative embodiment in which there are four JFETs 10, denominated J.sub.1, J.sub.2, J.sub.3, and J.sub.4, respectively. The corresponding circuit diagram is shown in FIG. 2. Figure elements that are common to FIGS. 1 and 2 are identified using like reference numerals.

(31) We performed a modeling study to predict the waveforms during the turn-ON process for the respective gate and drain voltages, as well as for the current i.sub.DC through the JFET leg 12. The model that we used assumes an inductive load, as is common practice for modeling the behavior of power converters, although in practical applications, the load can have any combination of inductive, capacitive, and resistive components. Our model includes a free-wheeling diode together with the inductive load, in accordance with the well-known double pulse test (DPT) circuit configuration. Results of our modeling study, indicative of switching behavior, are shown in FIG. 3, to which attention will be drawn in the following discussion.

(32) Interval 0, from t=0 to t=t.sub.0. The process is initiated by raising the voltage ν.sub.Gate applied to control terminal 15 (i.e., the terminal “Gate” connected to the J.sub.1 gate terminal) to the steady value V.sub.G+, which will typically be several volts, for example 3V. This causes the voltage ν.sub.gs1 to begin rising from its initial value V.sub.G−, while ν.sub.ds1 remains constant at V.sub.DC/4. The capacitances C.sub.ds, C.sub.gs, and C.sub.gd, which are not expressly indicated in FIGS. 1 and 2, are inherent properties of the JFET devices.

(33) The J.sub.1 gate current, i.sub.g1, conducts through C.sub.gs1 to the Source terminal 14, and it also conducts through C.sub.gd1. Because C.sub.gd1 is much smaller than C.sub.gs1, the effect of C.sub.gd1 is neglected in this analysis. Because the drain-to-source capacitances of the JFETs 10 are also very small, their effects are likewise neglected in this analysis.

(34) An analytical calculation yields the following expression for the evolution of the J.sub.1 gate voltage in this interval:
ν.sub.gs1=V.sub.G++(V.sub.G−−V.sub.G+).Math.exp(−t/(R.sub.g1C.sub.gs1)).  (I)
The time interval 0 ends at time t.sub.0, when ν.sub.gs1 reaches the threshold value V.sub.th. The time t.sub.0 is given by:
t.sub.0=R.sub.g1C.sub.gs1 ln [(V.sub.G−−V.sub.G+)/(V.sub.th−V.sub.G+)].  (II)

(35) Turning to FIG. 3, it will be seen (curve 26) that ν.sub.gs1 has begun to rise, starting at t=0, and that at t=t.sub.0, the curve representing ν.sub.gs1 crosses the level marked V.sub.th.

(36) Interval 1, from t=t.sub.0 to t=t.sub.1. When t>t.sub.0, all JFETs 10 have a gate voltage greater than V.sub.th, so they all begin to conduct, as indicated by the rise in curve 28, which is the curve for i.sub.DC in FIG. 3. The reason for this is that when J.sub.1 reaches threshold, its channel begins to conduct current, causing a small decrease in the J.sub.1 drain voltage. According to the series connection of the JFET leg 12, the J.sub.1 drain terminal is connected to the J.sub.2 source terminal. Hence, the voltage drop at the J.sub.1 drain terminal raises the J.sub.2 gate voltage relative to the voltage at the J.sub.2 source terminal. This change raises the J.sub.2 gate voltage above threshold and causes J.sub.2 to conduct. The same process continues to propagate very rapidly up the JFET leg 12 in a chain reaction until all JFETs 10 are conducting.

(37) For all of the JFETs 10, the drain voltage ν.sub.ds is now greater than ν.sub.gs−V.sub.th, which places all of the JFETs 10 in the saturation region. Hence, the drain current i.sub.d of each JFET 10 is given by:
i.sub.d=g.sub.m(ν.sub.gs−V.sub.th),  (III)
where g.sub.m is the JFET transconductance.

(38) Since all JFETs 10 have the same current i.sub.d=i.sub.DC, the gate voltages ν.sub.gs are also equal, assuming that the JFETs 10 are identical. Interval 1 ends at time t.sub.2, when i.sub.d=I.sub.0. Analytical calculations predict the duration of Interval 1 as:
t.sub.1−t.sub.0=R.sub.g1C.sub.gs1 ln [(V.sub.th−V.sub.G+)/((I.sub.0/g.sub.m)+V.sub.th−V.sub.G+)].  (IV)

(39) Turning to FIG. 3, it will be seen that i.sub.DC rises linearly in Interval 1. The drain voltages of all of the JFETs 10, respectively represented in figure by curves 30, 32, 34, and 36, remain steady at V.sub.DC/4.

(40) Interval 2, from t=t.sub.1 to t=t.sub.5. The switch circuit has begun to conduct the entire load current I.sub.0, while the gate voltages ν.sub.gs of all JFETs 10 remain constant at V.sub.gs(I.sub.0), as seen in FIG. 3. All JFETs are still in the saturation region. Analytical calculations predict V.sub.gs(I.sub.0) as:
V.sub.gs(I.sub.0)=I.sub.0/g.sub.m+V.sub.th.  (V)

(41) The gate currents flow entirely through the gate-to-drain capacitances of the JFETs 10, and there is no current through the gate-to-source capacitances. While the JFETs 10 are operating in saturation, the discharge of the gate-to-drain capacitances reduces the drain voltages ν.sub.ds linearly, as seen in FIG. 3 (curves 30, 32, 34, 36).

(42) The well-known condition for JFET operation in the triode region is that the gate voltage is greater than the sum of the drain voltage and the threshold voltage. The time t.sub.2 occurs when J.sub.4 enters the triode region, i.e., when ν.sub.ds4=ν.sub.gs4−V.sub.th. At that point, the J.sub.4 gate voltage starts to rise, as shown by curve 38 in FIG. 3. Similar behavior is seen in J.sub.3 (curve 40), J.sub.2 (curve 42), and J.sub.1 (curve 26) as they enter the triode region at times t.sub.3, t.sub.4, and t.sub.5, respectively.

(43) Interval 3, t>t.sub.5. All JFETs 10 are operating in the triode region. The gate currents decay to zero, and the gate voltages 26, 38, 40, 42 decay to V.sub.G+. At that point, the JFET leg 12 is fully ON.

(44) Turn-OFF Process. Our modeling study also predicted the waveforms during the turn-OFF process. The results are shown in FIG. 4, to which attention will be drawn in the following discussion.

(45) Interval 0, from t=0 to t=t.sub.0. As the initial state, we take a steady state in which the JFET leg 12 is fully ON and is conducting the load current I.sub.0, and in which ν.sub.ds≅0, and ν.sub.gs≅V.sub.G+ for all JFETs 10. The turn-OFF transition starts when a negative voltage V.sub.G− lower than the threshold voltage V.sub.th is applied between the Gate and Source 14 terminals of the switch circuit.

(46) The response of the J.sub.1 gate voltage, as predicted by analytical calculations, is:
ν.sub.gs1=V.sub.G−+(V.sub.G+−V.sub.G−).Math.exp(−t/R.sub.g1(C.sub.gs1+C.sub.gd1)).  (VI)

(47) As shown in FIG. 4, ν.sub.gs1 (curve 44) decays exponentially until, at time t.sub.0, a constant voltage level equal to V.sub.gs(I.sub.0) is reached and J.sub.1 enters the saturation region. Analytical calculations predict a value for t.sub.0 given by:
t.sub.0=R.sub.g1(C.sub.gs1+C.sub.gd1)ln [(V.sub.G+−V.sub.G−)/((I.sub.0/g.sub.m)+V.sub.th−V.sub.G−)].  (VII)

(48) Interval 1, from t=t.sub.0 to t=t.sub.1. J.sub.1 begins to operate in the saturation region while the other JFETs 10 are still operating in the triode region. As the J.sub.1 drain voltage ν.sub.ds1 (curve 46) starts to rise at t.sub.0, the gate voltages of J.sub.2, J.sub.3 and J.sub.4 (curves 48, 50, and 52, respectively) start to decrease, as shown in FIG. 4. By analytical calculation, we predict a linear rise in the J.sub.1 drain voltage, according to:
ν.sub.ds1=[(I.sub.0/g.sub.m+V.sub.th−V.sub.G−)/R.sub.g1C.sub.dg1](t−t.sub.0).  (VIII)

(49) Interval 1 ends at time t.sub.1, where ν.sub.gs2 has decayed to the value V.sub.gs(I.sub.0), and ν.sub.ds2 (curve 54) starts to rise.

(50) Interval 2, from t=t.sub.1 to t=t.sub.3. The operation during the time intervals [t.sub.1−t.sub.2] and [t.sub.2−t.sub.3] is analogous to the operation during the interval [t.sub.0−t.sub.1]. As shown in FIG. 4, t.sub.2 and t.sub.3 are the time instants when the gate voltage of J.sub.3 (curve 50) and the gate voltage of J.sub.4 (curve 52) respectively decay to V.sub.gs(I.sub.0).

(51) The J.sub.3 drain voltage (curve 56) rises to V.sub.DC/4 at time t.sub.2, and the J.sub.4 drain voltage (curve 58) rises to V.sub.DC/4 at time t.sub.3.

(52) Interval 3, from t=t.sub.3 to t=t.sub.4. In this interval, all JFETs 10 are operating in saturation with their gate voltages clamped to V.sub.gs(I.sub.0). This interval ends when the voltage across Drain 16 and Source 14 terminals equals V.sub.DC. Analytical calculation yields the following expression for t.sub.4:
t.sub.4=[(R.sub.g1C.sub.gd1V.sub.DC/n)/((I.sub.0/g.sub.m)+V.sub.th−V.sub.G−)]+t.sub.0.  (IX)

(53) Interval 4, for t>t.sub.4. As noted above, our model assumes there is a free-wheeling diode connected across the switch circuit. In Interval 4, the free-wheeling diode conducts, clamping the voltage across the switch circuit at V.sub.DC. When the gate voltages 44, 48, 50, 52 of the JFETs 10 reach the threshold voltage V.sub.th, the current i.sub.DC (curve 60) in the switch circuit falls to zero. The gate voltages 48, 50, 52 of all JFETs 10 remain close to V.sub.th, except for ν.sub.gs1 (curve 44), which continues to decay to V.sub.G−.

(54) Steady-State Operation. Resistors R.sub.1 to R.sub.n+1 form the resistive balancing network of the switch circuit of FIG. 1. The main objective for this network is to maintain a stable and evenly distributed voltage across each JFET 10, particularly during the OFF state. Voltage mismatches can occur in serial connections of devices, due to parasitic resistances and parasitic capacitances that cannot be completely controlled for during device manufacture. Additionally, the resistive balancing between gate terminals of the cascaded JFETs 10 is subject to further voltage imbalance due to gate leakage currents.

(55) For example, the leakage currents in the resistors of FIG. 1 contribute to a total current in resistor R.sub.1 given by:

(56) $\begin{array}{cc}{i}_{R1}=i_{R\left(\frac{n}{2}-1\right)}-\underset{k^{\prime }=2}{\overset{n}{.Math.}}{i}_{g{k}^{\prime }},& \left(X\right)\end{array}$
with the summation taken only over even values of k′.

(57) The sensitivity S.sub.i.sub.gk.sup.i.sup.R1 of i.sub.R1 with respect to the J.sub.k gate leakage current can be calculated according to the following formula:

(58) $\begin{array}{cc}\begin{array}{c}{S}_{i_{gk}}^{i_{R1}}=-\frac{i_{gk}}{i_{R\left(\frac{n}{2}-1\right)}-\underset{k^{\prime }=2}{\overset{n}{.Math.}}{i}_{g{k}^{\prime }}}\mathrm{if}k\mathrm{even},\\ S_{i_{gk}}^{i_{R1}}=0\mathrm{if}k\mathrm{odd},\end{array}& \left(\mathrm{XI}\right)\end{array}$
with the summation taken only over even values of k′.

(59) It will be understood from the above formula that the sensitivity of the bottom resistor is affected by the gate currents from the upper JFETs 10, and that increasing the total number of JFETs 10 tends to increase the sensitivity. However, the above formula also suggests that the sensitivity tends to be low when the leakage currents are low and when the currents through the balancing resistors are high.

(60) It should also be noted that here, the summation is taken only over the gate currents of the even-numbered JFETs 10. This leads to a relatively low value for the sensitivity. This limited summation is a consequence of the, e.g., dual-leg topology, in which the odd-numbered JFETs 10 do not contribute to the sensitivity. This is in contrast to conventional resistive balancing networks that use only a single resistor leg.

(61) Circuit Breaker Architecture

(62) For purposes of illustration, FIG. 5 provides a functional block diagram of an example architecture for a high-voltage breaker circuit that incorporates the switch circuit of the present disclosure. As shown in FIG. 5, switch circuit 100 is connected in series on high-voltage bus 105. Fast switch 110 and energy-absorbing capacitor 115 are connected in parallel with the switch circuit 100 to absorb and dissipate power spikes when the switch circuit 100 changes state. A snubber circuit 120 is connected in parallel with the switch circuit 100 for protection against overvoltages. The energy-dissipating element in the snubber circuit 120 is shown here as a varistor, but alternative components could be used instead, such as a free-wheeling diode as discussed above. The load, which is not shown in FIG. 5, would be connected between the high-voltage bus 105 and the ground bus 125.

(63) Control for the breaker circuit is provided by low-voltage subsystem 130. As shown, an isolated step-down converter 135 and a power-distribution circuit 140 tap power from the high-voltage bus 105, step it down to a low voltage, and distribute it within the low-voltage subsystem 130 to components including digital signal processor (DSP) 145. The inputs to the DSP 145 include signals from current monitor 150 and voltage monitor 155, and the outputs include digital control signals for the switch circuit 100 and for fast switch 110. As shown in FIG. 5, the input to the DSP 145 is conditioned by module 160, which performs analog-to-digital conversion and filtering. The output is conditioned by digital output module 165, which generates the signals that trigger driver circuit 170 for the fast switch 110 and forward leg gate-driver circuit 175 for the switch circuit 100. The forward leg gate-driver circuit 175, with its controls and power supply, is an example of the ancillary circuit mentioned above for maintaining the JFETs 10 of the switch circuit 100 in their OFF state when desired.

(64) The DSP 145 implements fault-detection algorithm 180 to determine, in response to the current and voltage signals, whether a fault has occurred. Adaptive triggering module 185 within the DSP 145 responds to a fault detection by activating the trigger signals.

(65) In an example scenario, detection of a fault condition is followed by generation of a trigger signal that turns the JFETs 10 of the switch circuit 100 off. This is followed by a trigger signal that closes the fast switch 110 so that excess power is diverted into the snubber circuit 120 and dissipated there.

Example

(66) We constructed a 1.2 kV/10 A prototype switch circuit with the topology of FIG. 2. The design parameters are listed in Table 2.

(67) The SiC JFETs 10 selected for our prototype are UJ3N120035K3S JFETs from United SiC. These devices can be driven with voltages within the range −20V<ν.sub.gs<3V. We selected driving voltages of V.sub.G+=1V for turning ON, and V.sub.G−=−18V for turning OFF. For a gate driver, IC, we selected the UCC5390ECQDWVRQ1 integrated circuit from Texas Instruments. This device provided 10 A of source and sink driving current capability.

(68) For testing, we used a Magnapower TSD2000-15 dc voltage source, which is rated at 2 kV, 15 A and 30 kW, and a Chroma 63224A-1200-960 high-power dc electronic load, which is rated at 1.2 kV, 960 A and 24 kW. An auxiliary Keithley 2280S-32-6 power supply provided power to the gate-driver circuit. A BK Precision 4080B function generator was used to provide a trigger gating signal. A Tektronix 5-Series 8-Channels, 350 MHz oscilloscope was used for experimental readout.

(69) The values of the balancing resistors R.sub.1 to R.sub.5 were selected to maintain a stable dc voltage across the resistor left and right legs 22, 24. The steady-state voltages across the resistors, as can be inferred from FIG. 2, are:
ν.sub.R1=ν.sub.g2,  (XII)
ν.sub.R2=ν.sub.g4−ν.sub.g2,  (XIII)
ν.sub.R3=V.sub.Drain−ν.sub.g4,  (XIV)
ν.sub.R4=ν.sub.g3,  (XV)
ν.sub.R5=V.sub.Drain−ν.sub.g3.  (XVI)

(70) The gate voltages are calculated, assuming that the resistor left and right legs 22, 24 is perfectly balanced, as:
ν.sub.gi=[(i−1)/n]+V.sub.th, 1≤i≤n.  (XVII)

(71) The JFET threshold voltage V.sub.th in this example is −11.5V.

(72) Based on the desired maximum power dissipation P.sub.dmax of the passive network, the currents through the bottom resistors R.sub.1 and R.sub.4 were arbitrarily selected as:
i.sub.R1=i.sub.R4=I.sub.R≅P.sub.dmax/Σ.sub.i=1.sup.nν.sub.R1.  (XVIII)

(73) Then, by considering the gate leakage currents i.sub.g2−i.sub.g4, the currents though resistors R.sub.2, R.sub.3 and R.sub.5 are obtained as:
i.sub.R2=I.sub.R−i.sub.g2,  (XIX)
i.sub.R3=I.sub.R−i.sub.g2−i.sub.g4, and  (XX)
i.sub.R5=I.sub.R−i.sub.g3.  (XXI)

(74) Then, the balancing resistors can be calculated as:
R.sub.i=ν.sub.Ri/i.sub.Ri, 1≤i≤n.  (XXII)

(75) The capacitors C.sub.1 to C.sub.4 improve the dynamic performance and prevent voltage spikes across the drain-to-source terminals of the JFETs 10. Published formulas can be used to estimate the capacitor values; the estimated values can then be adjusted using simulation tools.

(76) FIG. 6 is a graph of the voltage 200 across the switch circuit (“V.sub.breaker”) and the current 205 through the switch circuit (“I.sub.breaker”) versus time during a turn-OFF transition of our prototype when under test. It can be seen that the turn-OFF transition takes about 2 μs.

(77) FIG. 7 is a composite graph of the drain-to-source voltages of the respective JFETs J.sub.1 (curve 210), J.sub.2 (curve 215), J.sub.3 (curve 220), and J.sub.4 (curve 225) as functions of time over an 80-ms timescale. The graph indicates that the balancing network operated successfully. FIG. 8 is a portion of FIG. 7, showing the drain-to-source voltages over an expanded timescale spanning 20 μs. No transient voltage spikes are seen in FIG. 8. This indicates that the capacitance network was well balanced.

(78) FIG. 9 illustrates the distribution of steady-state drain-to-source voltages over the JFET leg 12 when the prototype was subjected to different applied voltages. At each of ten applied voltages ranging from 100V to 1000V, the respective steady-state drain-to-source voltage is plotted for each of the four JFETs 10 as a cluster of data points. Because the data points are difficult to distinguish on the scale of the plot, a magnified view of each cluster is also provided. It will be evident from FIG. 9 that there is only a small divergence in voltage among the four JFETs 10. This indicates that the dc bus voltage is divided evenly in all devices, even at relatively low voltages.

(79) TABLE-US-00002 TABLE 2 1.2 kV/10 kV SiC JFET Super Cascode Parameters Balancing Resistors R.sub.1 288.5 kΩ R.sub.2 628.81 kΩ R.sub.3 341 kΩ R.sub.4 288.5 kΩ R.sub.5 638.7 kΩ Balancing Capacitors C.sub.1 2.9 nF C.sub.2 2.35 nF C.sub.3 1.8 nF C.sub.4 1.25 nF Gate Resistors R.sub.g1, R.sub.g2, R.sub.g3, R.sub.g4 15 Ω SiC JFETs J.sub.1, J.sub.2, J.sub.3, J.sub.4 United SiC-UJ3N120035K3S 1200V/46A @ 100° C. Avalanche Diodes D.sub.1, D.sub.2, D.sub.3 Vishay-BYG20J-E3/TR 600V/1.5A

(80) The invention may be embodied in other specific forms without departing from its spirit or essential characteristics. The described embodiments are to be considered in all respects only as illustrative and not restrictive. The scope of the invention is, therefore, indicated by the appended claims rather than by the foregoing description. All changes which come within the meaning and range of equivalency of the claims are to be embraced within their scope.