A novel structure of transmission line pulse transformer with mutually coupled windings Binxiong Yu, Jiancang Su, Rui Li, Liang Zhao, Xibo Zhang, and Junjie Wang Citation: Review of Scientific Instruments 85, 035110 (2014); doi: 10.1063/1.4867250 View online: http://dx.doi.org/10.1063/1.4867250 View Table of Contents: http://scitation.aip.org/content/aip/journal/rsi/85/3?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Transmission line transformer for reliable and low-jitter triggering of a railgap switch Rev. Sci. Instrum. 85, 095117 (2014); 10.1063/1.4896117 A 70 kV solid-state high voltage pulse generator based on saturable pulse transformer Rev. Sci. Instrum. 85, 024708 (2014); 10.1063/1.4864194 Static voltage distribution between turns of secondary winding of air-core spiral strip transformer and its application Rev. Sci. Instrum. 82, 094704 (2011); 10.1063/1.3625280 Novel high-frequency, high-power, pulsed oscillator based on a transmission line transformer Rev. Sci. Instrum. 78, 074703 (2007); 10.1063/1.2753833 Analysis of a modular generator for high-voltage, high-frequency pulsed applications, using low voltage semiconductors ( 1 kV ) and series connected step-up (1:10) transformers Rev. Sci. Instrum. 78, 034702 (2007); 10.1063/1.2709743
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 035110 (2014)
A novel structure of transmission line pulse transformer with mutually coupled windings Binxiong Yu,a) Jiancang Su, Rui Li, Liang Zhao, Xibo Zhang, and Junjie Wang Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi’an 710024, People’s Republic of China
(Received 29 September 2013; accepted 18 February 2014; published online 18 March 2014) A novel structure of transmission line transformer (TLT) with mutually coupled windings is described in this paper. All transmission lines except the first stage of the transformer are wound on a common ferrite core for the TLT with this structure. A referral method was introduced to analyze the TLT with this structure, and an analytic expression of the step response was derived. It is shown that a TLT with this structure has a significantly slower droop rate than a TLT with other winding structures and the number of ferrite cores needed is largely reduced. A four-stage TLT with this structure was developed, whose input and output impedance were 4.2 and 67.7 , respectively. A frequency response test of the TLT was carried out. The test results showed that pulse response time of the TLT is several nanoseconds. The TLT described in this paper has the potential to be used as a rectangle pulse transformer with very fast response time. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4867250] I. INTRODUCTION
II. PRINCIPLE
Transmission line transformers (TLTs) with good frequency characteristics and compact structures are widely used in high power pulse technology field.1–8 Some high power pulse generators based on TLTs can output voltage pulses with amplitudes of 100 kV, repetition-rates of 1000 pulses per second (pps). Linear TLTs do not use ferrite cores and all their transmission lines are kept straight. They have very wide bandwidth, and can be used to construct short pulse generator in radio frequency (r.f.) and flash X ray applications.1, 2 As pulse widths of delivered pulses get wider, the influence of parasitic inductance becomes more and more serious, which can cause gain loss of the TLT.9 To avoid this problem, all transmission lines of the TLT except the first stage were wound inductively with ferrite cores. TLTs with ferrite cores are called wound TLTs. According to the coupling intensity between the windings, wound TLTs can be divided into two types, the TLT without coupled windings and TLT with mutually coupled windings. Graneau and Smith analyzed the two TLT winding models using a referral method,8 and the results showed that a slower droop rate could be achieved by using TLT with mutually coupled windings. Reference 8 introduced a 3-stage TLT model with mutually coupled windings. In this device the top stage had two windings, one of which was mutually coupled to the winding of the second stage. With this method, more than one ferrite core is required, and n-1 pieces of ferrites are needed for a TLT with n stages. In this paper, a novel model of transmission line transformer with mutually coupled windings is introduced. All transmission lines except the first stage are wound on a common ferrite core. With this structure, the TLT has a slower droop rates, and only one ferrite core is used.
Fig. 1 shows the structure of the TLT with a common ferrite core. The 2nd and 3rd stage transmission lines of the TLT are wound on a common ferrite core. V stands for the input voltage of the TLT, and Z0 represents the characteristic impedance of each transmission line. I1 and I2 stand for the unbalanced current of the first and the second stage secondary parasitic lines, respectively. Mij are the mutual inductance between the ith stage winding and the jth stage winding. As the unbalanced currents in parasitic lines magnetize the ferrite, the induced voltages are generated across the windings wound on the ferrite core according to Faraday’s law. Assuming the turn number of the ith stage winding is Ni , and induced voltage on the ith stage winding is Vi (i = 2, 3), then, V2 : V3 = N2 : N3 .
(1)
According to Fig. 1, it is found that there is a potential drop of 2V across the 3rd stage winding. Similarly, there is a potential drop of V across the 2nd stage winding, so N2 : N3 = 1 : 2.
(2)
For an n-stage TLT with a common ferrite, Turns of the windings on the ferrite core satisfy N2 : N3 : . . . . . . Nn = 1 : 2 : . . . . . . n − 1.
(3)
Now, the referral method is used to analyze a 3-stage TLT with this structure. The first stage is not wound on the ferrite, and has no mutual inductances with other stages. So it can be obtained that Mi1 = M1i = 0 (i = 1, 2, 3). According to Faraday’s law, it can be derived that 3 Mij − Mij −1 dIj −1 /dt = (i − 1)V
i = 2, 3. (4)
j =2
a) E-mail: [email protected]
0034-6748/2014/85(3)/035110/4/$30.00
Assuming that the self-inductance of the first winding M22 is L0 , and coupling coefficients between windings are k 85, 035110-1
© 2014 AIP Publishing LLC
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035110-2
Yu et al.
Rev. Sci. Instrum. 85, 035110 (2014)
FIG. 1. A three-stage transmission line transformer with single magnetic core.
(leakage inductance of all the windings is considered to be equal), namely, j Mij = (i − 1) (j − 1) kL0 i = . (5) 2 i=j Mij = (i − 1) L0 So, Eq. (4) can be simplified as (2 − k)dI2 /dt + kdI1 /dt = V /L0 (2k − 1)dI2 /dt + dI1 /dt = V /L0
.
(6)
The solution to Eq. (6) can be got by Cramer’s law, and is shown below di2 /dt = V /2(k + 1)L0 . (7) di1 /dt = 3V /2(k + 1)L0 When k goes to 1, it is found that di2 /dt = V /4L0 di1 /dt = 3V /4L0
.
(8)
Now, it can be derived the equivalent schematics of Fig. 1 which is shown in Figs. 2(a) and 2(b). Fig. 2(a) shows equivalent circuit of the transformer output, and Fig. 2(b) shows the equivalent circuit of the transformer referred to the primary. According to Ref. 8, the output voltage of this transformer on a matched load was found to be as follows when a voltage step source of amplitude V is fed 5Z0 t . (9) Vo = 3V exp − 24L0 This winding technique can be extended in an n-stage device by winding all but the bottom line on one core, and turns of the windings on the core satisfy Eq. (3). The general expression for an n-stage transformer of this type can be derived similarly by Cramer’s law, which is presented as Eq. (10), (n + 2)Z0 t . (10) Vo = nV exp − 8nL0
FIG. 2. Equivalent schematics of a three-stage TLT. (a) Equivalent circuit of the transformer output; (b) Equivalent circuit of the transformer referred to the primary.
droop rate than a TLT with the structure mentioned in Ref. 8 when L0 and Z0 are kept the same, respectively. Additionally, when L0 is the same, a TLT with structure mentioned in Ref. 8 requires n-1 pieces of ferrite cores, each one of which had the same size as the ferrite core used in a TLT with structure in this paper. So the number of cores is largely reduced when the winding structure in this paper is used to build a TLT with stages larger than 2. III. PERFORMANCE
In order to test the rectangular pulse response characteristics of the TLT with a common ferrite core, a four-stage TLT using cables was developed. Each stage of the TLT consisted of 3 cables in parallel with a length of 2 m. the outer diameters of the cables were 5 mm, and the characteristic impedances
However, the output voltage of a TLT with mutually coupled windings mentioned in Ref. 8 whose structure was introduced in Sec. I was found to be (n − 1)Z0 t . (11) Vo = nV exp − 2nL0 Comparing Eq. (10) with Eq. (11) together, it is found that a TLT with structure mentioned in this paper had a slower
FIG. 3. Schematic for measuring pulse response characteristic of TLT.
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035110-3
Yu et al.
Rev. Sci. Instrum. 85, 035110 (2014)
FIG. 4. Measured results of response characteristic of the TLT. (a) Measured waveform when a 100 ns pulse is injected. (b) Measured waveform when a 300 μs pulse is injected.
were 50 . The impedances of transmission lines of the TLT were 16.7 , and the input and the output impedances of the TLT were 4.2 and 67.7 , respectively. Relative permeability of the used ferrite core was 1000, and the response frequency ranged from 0 to 1 MHz. An arbitrary pulse generator, agilent 33220 A was used as a rectangular pulse source, which can generate pulses with a rise and a fall time of 10 ns. The testing circuit is shown in Fig. 3. In this figure, R1 (50 ) represents the internal resistance of the pulse generator. R2 , whose resistance was 16.7 , together with the 50 sampling resistance of the oscilloscope, composed a 66.7 load which was matched with the TLT. The input and the observed output pulse waveforms are shown in Fig. 4. From the figure, amplitude of the input voltage pulse was 0.14 V, and amplitude of the observed pulse was 0.41 V, Considering voltage dividing function of R2 , the observed voltage was only three quarters of the voltage amplitude on the matched load. So the output voltage of the TLT on the matched load was 0.55 V. it was found that output voltage of the TLT was 3.93 times of the input. So transmission efficiency of the TLT was 98%. Besides, from the figure, it was found that output waveform of the TLT had almost the same temporal shape as the input, and its rise time was 10 ns, which demonstrated that the developed TLT has a very good frequency response characteristic. A rectangular pulse with a pulse width of 300 μs was also injected into the transformer to test its ability to maintain “flat top” over a relatively long time scale. The output waveform
is shown in Fig. 4(b). From this figure, a droop of 90%–10% can be obtained to response a pulse with width of 65.5 μs. The theoretic droop of the TLT was derived the same as,8 which was τ = 2.19
nL0 (50 + Z0 /n) , 50 (n + 2) Z0
(12)
where L0 was measured by a RLC meter, whose value was 109 μH. So, the calculated value of the droop was 40.1 μs. It was found the observed droop was even slower than the theoretic value. The theoretic value was not confirmed to be the observed results because we assumed that leakage inductances of windings of the TLT were the same during analysis. Factually, the leakage inductances of windings were different. So, the result of the theoretic value was not accurate enough. A small rectangular pulse generator was developed based on the TLT technology. The structure of the generator is shown in Fig. 5. The pulse forming network (PFN) whose impedance was 5 was charged to 5.5 kV by a DC voltage source in order to inject a voltage pulse of 2.5 kV into the transformer. R3 is the charging resistance, whose value was 1 k. The load resistance, R4 , is 66.7 , which is matched to the output impedance of the TLT. A HV probe, Tektronix 6015A, was used to measure the voltage waveform of the load, and the measured waveform is shown in Fig. 6. From the figure, it was found that the amplitude of the output pulse was close to 10 kV, and its rise time was only 8 ns.
FIG. 5. Structure of pulsed power source based on TLT.
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035110-4
Yu et al.
Rev. Sci. Instrum. 85, 035110 (2014)
several advantages. First, it has a significantly slower droop rate than the TLTs mentioned in literatures. Second, the number of ferrite core needed to build the TLT is largely reduced. Finally, it is easy to realize compactness. A TLT with a low impedance was developed, whose input and out impedance were 4.2 and 66.7 , respectively. The pulse response time of the TLT was only several nanoseconds, and the transmission efficiency of the TLT was 98%. 1 J.
FIG. 6. Output voltage waveform of pulse generator.
IV. CONCLUSIONS
A novel structure of transmission line transformer was presented in this paper. The TLTs with this structure have
J. Coogan, F. Davanloo, and C. B. Collins, Rev. Sci. Instrum. 61, 1448 (1990). 2 D. B. Pawelek, P. A. A. F. Wouters, and A. J. M. Pemen, IEEE Trans. Dielect. Elect. Insul. 14, 900 (2007). 3 C. R. Wilson, G. A. Erickson, and P. W. Smith, in Proceedings of the 7th IEEE International Pulsed Power Conference (IEEE, 1989), p. 108. 4 P. N. Graneau, J. O. Rossi, P. Brown, and P. W. Smith, Rev. Sci. Instrum. 67, 2630 (1996). 5 P. W. Smith and C. R. Wilson, in Proceedings of the 17th IEEE Power Modulator Symposium (IEEE, 1986), p. 281. 6 L. Pecastaing, T. Reess, J. Paillol, A. Gibert,P. Domens, and J. P. Brasile, in Proceedings of the 11th International Symposium on High Voltage Engineering (Institution of Electrical Engineers, 1999), p. 386. 7 K. K. Jain and P. W. Smith, IEEE Trans. Plasma Sci. 34, 1853 (2006). 8 P. N. Graneau, Rev. Sci. Instrum. 70, 3180 (1999). 9 P. W. Smith and J. O. Rossi, in Proceedings of the IEEE Pulsed Power Conference (IEEE, 1997), p. 610.
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REVIEW OF SCIENTIFIC INSTRUMENTS 85, 035110 (2014)
A novel structure of transmission line pulse transformer with mutually coupled windings Binxiong Yu,a) Jiancang Su, Rui Li, Liang Zhao, Xibo Zhang, and Junjie Wang Science and Technology on High Power Microwave Laboratory, Northwest Institute of Nuclear Technology, Xi’an 710024, People’s Republic of China
(Received 29 September 2013; accepted 18 February 2014; published online 18 March 2014) A novel structure of transmission line transformer (TLT) with mutually coupled windings is described in this paper. All transmission lines except the first stage of the transformer are wound on a common ferrite core for the TLT with this structure. A referral method was introduced to analyze the TLT with this structure, and an analytic expression of the step response was derived. It is shown that a TLT with this structure has a significantly slower droop rate than a TLT with other winding structures and the number of ferrite cores needed is largely reduced. A four-stage TLT with this structure was developed, whose input and output impedance were 4.2 and 67.7 , respectively. A frequency response test of the TLT was carried out. The test results showed that pulse response time of the TLT is several nanoseconds. The TLT described in this paper has the potential to be used as a rectangle pulse transformer with very fast response time. © 2014 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4867250] I. INTRODUCTION
II. PRINCIPLE
Transmission line transformers (TLTs) with good frequency characteristics and compact structures are widely used in high power pulse technology field.1–8 Some high power pulse generators based on TLTs can output voltage pulses with amplitudes of 100 kV, repetition-rates of 1000 pulses per second (pps). Linear TLTs do not use ferrite cores and all their transmission lines are kept straight. They have very wide bandwidth, and can be used to construct short pulse generator in radio frequency (r.f.) and flash X ray applications.1, 2 As pulse widths of delivered pulses get wider, the influence of parasitic inductance becomes more and more serious, which can cause gain loss of the TLT.9 To avoid this problem, all transmission lines of the TLT except the first stage were wound inductively with ferrite cores. TLTs with ferrite cores are called wound TLTs. According to the coupling intensity between the windings, wound TLTs can be divided into two types, the TLT without coupled windings and TLT with mutually coupled windings. Graneau and Smith analyzed the two TLT winding models using a referral method,8 and the results showed that a slower droop rate could be achieved by using TLT with mutually coupled windings. Reference 8 introduced a 3-stage TLT model with mutually coupled windings. In this device the top stage had two windings, one of which was mutually coupled to the winding of the second stage. With this method, more than one ferrite core is required, and n-1 pieces of ferrites are needed for a TLT with n stages. In this paper, a novel model of transmission line transformer with mutually coupled windings is introduced. All transmission lines except the first stage are wound on a common ferrite core. With this structure, the TLT has a slower droop rates, and only one ferrite core is used.
Fig. 1 shows the structure of the TLT with a common ferrite core. The 2nd and 3rd stage transmission lines of the TLT are wound on a common ferrite core. V stands for the input voltage of the TLT, and Z0 represents the characteristic impedance of each transmission line. I1 and I2 stand for the unbalanced current of the first and the second stage secondary parasitic lines, respectively. Mij are the mutual inductance between the ith stage winding and the jth stage winding. As the unbalanced currents in parasitic lines magnetize the ferrite, the induced voltages are generated across the windings wound on the ferrite core according to Faraday’s law. Assuming the turn number of the ith stage winding is Ni , and induced voltage on the ith stage winding is Vi (i = 2, 3), then, V2 : V3 = N2 : N3 .
(1)
According to Fig. 1, it is found that there is a potential drop of 2V across the 3rd stage winding. Similarly, there is a potential drop of V across the 2nd stage winding, so N2 : N3 = 1 : 2.
(2)
For an n-stage TLT with a common ferrite, Turns of the windings on the ferrite core satisfy N2 : N3 : . . . . . . Nn = 1 : 2 : . . . . . . n − 1.
(3)
Now, the referral method is used to analyze a 3-stage TLT with this structure. The first stage is not wound on the ferrite, and has no mutual inductances with other stages. So it can be obtained that Mi1 = M1i = 0 (i = 1, 2, 3). According to Faraday’s law, it can be derived that 3 Mij − Mij −1 dIj −1 /dt = (i − 1)V
i = 2, 3. (4)
j =2
a) E-mail: [email protected]
0034-6748/2014/85(3)/035110/4/$30.00
Assuming that the self-inductance of the first winding M22 is L0 , and coupling coefficients between windings are k 85, 035110-1
© 2014 AIP Publishing LLC
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035110-2
Yu et al.
Rev. Sci. Instrum. 85, 035110 (2014)
FIG. 1. A three-stage transmission line transformer with single magnetic core.
(leakage inductance of all the windings is considered to be equal), namely, j Mij = (i − 1) (j − 1) kL0 i = . (5) 2 i=j Mij = (i − 1) L0 So, Eq. (4) can be simplified as (2 − k)dI2 /dt + kdI1 /dt = V /L0 (2k − 1)dI2 /dt + dI1 /dt = V /L0
.
(6)
The solution to Eq. (6) can be got by Cramer’s law, and is shown below di2 /dt = V /2(k + 1)L0 . (7) di1 /dt = 3V /2(k + 1)L0 When k goes to 1, it is found that di2 /dt = V /4L0 di1 /dt = 3V /4L0
.
(8)
Now, it can be derived the equivalent schematics of Fig. 1 which is shown in Figs. 2(a) and 2(b). Fig. 2(a) shows equivalent circuit of the transformer output, and Fig. 2(b) shows the equivalent circuit of the transformer referred to the primary. According to Ref. 8, the output voltage of this transformer on a matched load was found to be as follows when a voltage step source of amplitude V is fed 5Z0 t . (9) Vo = 3V exp − 24L0 This winding technique can be extended in an n-stage device by winding all but the bottom line on one core, and turns of the windings on the core satisfy Eq. (3). The general expression for an n-stage transformer of this type can be derived similarly by Cramer’s law, which is presented as Eq. (10), (n + 2)Z0 t . (10) Vo = nV exp − 8nL0
FIG. 2. Equivalent schematics of a three-stage TLT. (a) Equivalent circuit of the transformer output; (b) Equivalent circuit of the transformer referred to the primary.
droop rate than a TLT with the structure mentioned in Ref. 8 when L0 and Z0 are kept the same, respectively. Additionally, when L0 is the same, a TLT with structure mentioned in Ref. 8 requires n-1 pieces of ferrite cores, each one of which had the same size as the ferrite core used in a TLT with structure in this paper. So the number of cores is largely reduced when the winding structure in this paper is used to build a TLT with stages larger than 2. III. PERFORMANCE
In order to test the rectangular pulse response characteristics of the TLT with a common ferrite core, a four-stage TLT using cables was developed. Each stage of the TLT consisted of 3 cables in parallel with a length of 2 m. the outer diameters of the cables were 5 mm, and the characteristic impedances
However, the output voltage of a TLT with mutually coupled windings mentioned in Ref. 8 whose structure was introduced in Sec. I was found to be (n − 1)Z0 t . (11) Vo = nV exp − 2nL0 Comparing Eq. (10) with Eq. (11) together, it is found that a TLT with structure mentioned in this paper had a slower
FIG. 3. Schematic for measuring pulse response characteristic of TLT.
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035110-3
Yu et al.
Rev. Sci. Instrum. 85, 035110 (2014)
FIG. 4. Measured results of response characteristic of the TLT. (a) Measured waveform when a 100 ns pulse is injected. (b) Measured waveform when a 300 μs pulse is injected.
were 50 . The impedances of transmission lines of the TLT were 16.7 , and the input and the output impedances of the TLT were 4.2 and 67.7 , respectively. Relative permeability of the used ferrite core was 1000, and the response frequency ranged from 0 to 1 MHz. An arbitrary pulse generator, agilent 33220 A was used as a rectangular pulse source, which can generate pulses with a rise and a fall time of 10 ns. The testing circuit is shown in Fig. 3. In this figure, R1 (50 ) represents the internal resistance of the pulse generator. R2 , whose resistance was 16.7 , together with the 50 sampling resistance of the oscilloscope, composed a 66.7 load which was matched with the TLT. The input and the observed output pulse waveforms are shown in Fig. 4. From the figure, amplitude of the input voltage pulse was 0.14 V, and amplitude of the observed pulse was 0.41 V, Considering voltage dividing function of R2 , the observed voltage was only three quarters of the voltage amplitude on the matched load. So the output voltage of the TLT on the matched load was 0.55 V. it was found that output voltage of the TLT was 3.93 times of the input. So transmission efficiency of the TLT was 98%. Besides, from the figure, it was found that output waveform of the TLT had almost the same temporal shape as the input, and its rise time was 10 ns, which demonstrated that the developed TLT has a very good frequency response characteristic. A rectangular pulse with a pulse width of 300 μs was also injected into the transformer to test its ability to maintain “flat top” over a relatively long time scale. The output waveform
is shown in Fig. 4(b). From this figure, a droop of 90%–10% can be obtained to response a pulse with width of 65.5 μs. The theoretic droop of the TLT was derived the same as,8 which was τ = 2.19
nL0 (50 + Z0 /n) , 50 (n + 2) Z0
(12)
where L0 was measured by a RLC meter, whose value was 109 μH. So, the calculated value of the droop was 40.1 μs. It was found the observed droop was even slower than the theoretic value. The theoretic value was not confirmed to be the observed results because we assumed that leakage inductances of windings of the TLT were the same during analysis. Factually, the leakage inductances of windings were different. So, the result of the theoretic value was not accurate enough. A small rectangular pulse generator was developed based on the TLT technology. The structure of the generator is shown in Fig. 5. The pulse forming network (PFN) whose impedance was 5 was charged to 5.5 kV by a DC voltage source in order to inject a voltage pulse of 2.5 kV into the transformer. R3 is the charging resistance, whose value was 1 k. The load resistance, R4 , is 66.7 , which is matched to the output impedance of the TLT. A HV probe, Tektronix 6015A, was used to measure the voltage waveform of the load, and the measured waveform is shown in Fig. 6. From the figure, it was found that the amplitude of the output pulse was close to 10 kV, and its rise time was only 8 ns.
FIG. 5. Structure of pulsed power source based on TLT.
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035110-4
Yu et al.
Rev. Sci. Instrum. 85, 035110 (2014)
several advantages. First, it has a significantly slower droop rate than the TLTs mentioned in literatures. Second, the number of ferrite core needed to build the TLT is largely reduced. Finally, it is easy to realize compactness. A TLT with a low impedance was developed, whose input and out impedance were 4.2 and 66.7 , respectively. The pulse response time of the TLT was only several nanoseconds, and the transmission efficiency of the TLT was 98%. 1 J.
FIG. 6. Output voltage waveform of pulse generator.
IV. CONCLUSIONS
A novel structure of transmission line transformer was presented in this paper. The TLTs with this structure have
J. Coogan, F. Davanloo, and C. B. Collins, Rev. Sci. Instrum. 61, 1448 (1990). 2 D. B. Pawelek, P. A. A. F. Wouters, and A. J. M. Pemen, IEEE Trans. Dielect. Elect. Insul. 14, 900 (2007). 3 C. R. Wilson, G. A. Erickson, and P. W. Smith, in Proceedings of the 7th IEEE International Pulsed Power Conference (IEEE, 1989), p. 108. 4 P. N. Graneau, J. O. Rossi, P. Brown, and P. W. Smith, Rev. Sci. Instrum. 67, 2630 (1996). 5 P. W. Smith and C. R. Wilson, in Proceedings of the 17th IEEE Power Modulator Symposium (IEEE, 1986), p. 281. 6 L. Pecastaing, T. Reess, J. Paillol, A. Gibert,P. Domens, and J. P. Brasile, in Proceedings of the 11th International Symposium on High Voltage Engineering (Institution of Electrical Engineers, 1999), p. 386. 7 K. K. Jain and P. W. Smith, IEEE Trans. Plasma Sci. 34, 1853 (2006). 8 P. N. Graneau, Rev. Sci. Instrum. 70, 3180 (1999). 9 P. W. Smith and J. O. Rossi, in Proceedings of the IEEE Pulsed Power Conference (IEEE, 1997), p. 610.
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