Fabrication and Operation Testing of a Dual Resonance Pulse Transformer …hvpe.cau.ac.kr/wp-content/uploads/2017/02/Fabrication... · 2019-09-03 · (b) Helical wire/strip transformer.

Journal of the Korean Physical Society, Vol. 59, No. 6, December 2011, pp. 3679∼3682

Fabrication and Operation Testing of a Dual Resonance Pulse Transformerfor PFL Pulse Charging

SooWon Lim∗

University of Science and Technology, Daejeon 305-333, Korea

ChuHyun Cho, Hong-Je Ryoo, Jong-Soo Kim, Geun-Hie Rim and Yun-Sik Jin

Korea Electrotechnology Research Institute, Changwon 641-120, Korea

(Received 15 December 2010, in final form 18 August 2011)

A high-voltage oil-submerged helical strip/wire type pulse transformer has been fabricated forcharging of a Blumlein pulse-forming line (PFL). As a primary coil, a copper strip of 25 mm widthwas wound helically around a mono cast (MC) nylon cylinder. For a secondary coil, a copperenameled wire of 1 mm in diameter was wound around a half-conical cylinder in order to provideinsulation between the two windings. The device has a coupling coefficient of 0.76, and a tuninginductor of 2.5 µH was inserted in the primary circuit to operate in the dual resonance condition.The maximum energy transfer efficiency and gain were measured to be 50% and 18.3, respectively.The transformer could charge a Blumlein PFL to 370 kV.

PACS numbers: 84.30.Ng, 52.80.Mg, 52.25.JmKeywords: High voltage, Pulse transformer, Pulse forming, Dual resonanceDOI: 10.3938/jkps.59.3679

I. INTRODUCTION

Air core pulse transformers are attractive alternativesto Marx generators as a simple and inexpensive high-voltage pulse source to accelerate intense electron beamsto relativistic energies in a compact assembly. They donot have a magnetic core, so they can avoid core satura-tion and operate with no limited frequency. The couplingcoefficients of air core transformers tend to be lower thanthat of magnetic core transformers [1–3].

There are two basic types of high-voltage air core pulsetransformers that can be operated in the megavolt range.The first is the helical wire/strip transformer built for thepresent experiments (see Fig. 1). The second is a spiral-strip-type transformer. These transformers differ fromeach other in the configuration of the insulation method.

Pulse transformer circuits are used for charging pulse-forming transmission lines (PFLs) by means of a voltagestep-up transformer. For operation at maximum energytransfer efficiency, the matched frequency mode (L1C1

= L2C2, where L1, C1 are the inductance and the ca-pacitance of primary circuit, and L2, C2 are the induc-tance and the capacitance of secondary circuit) is rec-ommended. There are two modes of charging the loadcapacitor or pulse forming line. The first is swing charg-ing, where the maximum secondary voltage is reached on

∗E-mail: [email protected]; Fax: +82-55-280-1491

Fig. 1. (a) Rohwein spiral-strip transformer. (b) Helicalwire/strip transformer.

the first excursion. The second is dual-resonance charg-ing, where the maximum voltage occurs on the secondvoltage excursion of the secondary (see Fig. 2) [4].

In this research, a helical wire/strip transformer isbuilt for charging a Blumlein PFL system to higher than300 kV. This transformer adopts a dual resonance modeto operate at high energy transfer efficiency. The design,fabrication and operation characteristics of a compacthigh-voltage air-cored pulse transformer are described.

II. THEORY

The equivalent circuit of an air-cored pulse trans-former is shown in Fig. 3. C1 is the primary capacitor, C2

is the secondary distributed capacitance, and L1 and L2

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Fig. 2. (Color online) (a) First-swing charge cycle. (b)Dual resonance charge cycle.

Fig. 3. Equivalent circ it of an air-cored pulse transformer.

are the primary and the secondary coil inductances, re-spectively. The primary capacitor C1 is initially supplieda charge q0. When the switch S is closed, the secondaryvoltage (Vo) as a function of time can be described forthe ideal case of no damping (R1 = R2 = 0) as [5–7]

V0(t) =V k

C2

√L1L2

cos(ωbt)− cos(ωat)ω2

a − ω2b

, (1)

where

ω2a − ω2

b =[

ω21 − ω2

2

2(1− k2)

± 12(1−K2)

√(ω2

1 − ω22)2 − 4(1− k2)ω2

1ω22

], (2)

ω22 =

√L2C2, ω2

1 =√

L1C1, (3)

k =M√L1L2

. (4)

The condition ω1 = ω2 and the quality factors Q1,Q2 (=ωL/R) 1 give maximum energy transfer fromthe primary to the secondary circuit. The system canoscillate on two normal modes of frequencies

ω± =ω0√

1∓ k2, (5)

where

ω0 =ω1 + ω2

2. (6)

The secondary voltage Vo(t) will be a superposition oftwo weakly damped sinusoidal oscillations of frequenciesω+ and ω−.

The maximum possible values of Vo can be achievedonly for certain values k, which are 1, 0.6, 0.385, 0.28,etc., corresponding to ω+/ω− equal to the ratio of twosmall integers. However, with air-core transformers,k = 1 is generally unrealistic and k = 0.385 and 0.28,

Fig. 4. Transformer circuit with tuning inductors.

which reach maximum voltage on the third or fourthvoltage excursions respectively, are of little practical in-terest. In a dual-resonance transformer circuit operatingwith k = 0.6, where can be adapted to a dual-resonancecircuit, the transfer efficiency at the second peak in-creases to a theoretical maximum of 100 percent [8].

Since eddy currents flowing in the vessel walls producea small decrease in the quality factors and the couplingconstant, exact resonant matching is difficult. This canbe done by adding small tuning inductors (Lt−1, Lt−2)to sections of the circuit (see Fig. 4). The values for theprimary and the secondary tuning inductances can easilybe found if the primary and the secondary capacitancesand the inductances of the transformer are known. Fromthe relation for the coupling coefficient, set k = 0.6:

M√LpLs

= 0.6. (7)

The values of total the primary and the secondary circuitinductance, Lp and Ls, become

Lp =1Ls

(M

0.6

)2

, (8)

Ls =1Lp

(M

0.6

)2

. (9)

Because LpC1 = LsC2, substitution gives

Lp =M

0.6

√C2

C1, (10)

Ls =M

0.6

√C1

C2. (11)

Thus, the tuning inductances are calculated by using thefollowing equations.

Lt−1 = Lp − L1, (12)Lt−2 = Ls − L2. (13)

III. DESIGN AND FABRICATION OF THEPULSE TRANSFORMER

For charging of a Blumlein PFL with a capacitance of180 pF to more than 300 kV, a helical strip/wire-typepulse transformer has been designed and fabricated. Byuse of the inductance calculation formula from Ref. 9, theinductance was obtained on the basis of the geometrical

Fabrication and Operation Testing of a Dual Resonance Pulse Transformer · · · – SooWon Lim et al. -3681-

Table 1. Inductance parameters.

Measured frequency 10 kHz

Primary inductance (L1) 9.8 µH

Secondary inductance (L2) 5.92 mH

Ratio of inductance (L2/L1)0.5 24.6

Mutual inductance 182 µH

Coupling coefficient 0.76

Resistance of primary coil 0.1 Ω

Resistance of secondary coil 6.2 Ω

Fig. 5. Layout of the designed pulse transformer inside aninsulation-oil filled vessel.

Fig. 6. (Color online) Photos of the fabricated pulse trans-former: (a) Primary winding, (b) secondary winding withglass tape wrapped after wire winding, and (c) combinationof two coils.

structure shown in Fig. 5. The primary winding con-sists of 9 turns of a 25-mm-wide copper strip wound ona mono cast nylon cylinder of 24 cm in outer diameter.The secondary winding of 260 turns of enameled cop-per wire is mounted on a half-conical mono cast (MC)nylon cylinder with a minor diameter of 14 cm and amajor diameter of 21 cm in order to provide insulationbetween two windings concentric with the primary wind-ing. The calculated self-inductance values of the primaryand the secondary windings were 11.3 µH and 7.2 mH,respectively. Figure 6 shows photos of the fabricated

Fig. 7. Circuit diagram for testing the pulse transformer.

Fig. 8. (Color online) Voltage gain and energy transferefficiency of the pulse transformer.

transformer. The transformer is oil-submerged in an alu-minium vessel with a 40 cm inner diameter. The induc-tance parameters of the transformer were measured byusing a LCR meter (FLUKE PM 6304) with two coilsbeing combined in the vessel. The measured parametersare summarized in Table 1.

The circuit diagram for testing the pulse transformer isshown in Fig. 7. The primary capacitance of 120 nF wasselected from the result of a previous work [10]. The loadcapacitor was a Blumlein PFL whose capacitance was180 pF. The output (charging) voltage of the BlumleinPFL was measured by using a capacitive voltage divider.The main switch was a Thyratron (E2V, CX1622) witha maximum repetition rate of 200 Hz.

IV. PERFORMANCE

As noted in Section II, when the coupling coefficientconstant k of the pulse transformer is larger than 0.6,use of a tuning inductor is desirable for maximum en-ergy transfer. Since the fabricated transformer had acoupling coefficient constant k = 0.76, a tuning inductorwas needed for dual-resonance condition. Due to the lim-itation of the transformer structure, the tuning inductorwas added only on the primary circuit. Figure 8 showsthe voltage gain and the energy transfer efficiency whenthe tuning inductance was varied from 0.4 µH to 4.3 µH.We used the peak voltage of the Blumlein PFL to calcu-late the energy transfer efficiency. Both the voltage gainand the energy transfer efficiency show maximum valuesat a tuning inductance of 2.5 µH. The maximum gain

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Fig. 9. (Color online) Typical waveforms of the pulsetransformer (upper: primary current, middle: secondary volt-age, and lower: primary voltage).

Fig. 10. (Color online) Breakdown waveform of the Blum-lein PFL charged to 370 kV (upper: secondary voltage andlower: primary voltage).

and energy transfer efficiency were measured to be 50%and 18.3, respectively.

Figure 9 presents typical voltage-current waveforms atthe primary and the secondary side for a tuning induc-tance of 2.5 µH. From the voltage waveform of the sec-ondary capacitor (Blumlein PFL), we can see that themaximum appears on the second half-wave. Therefore,the effective coupling coefficient is 0.6 in agreement withthe design. Figure 10 shows the breakdown waveform ofthe Blumlein PFL charged to 370 kV with the primarycharged at 20 kV.

V. CONCLUSION

A compact helical strip/wire type dual resonancepulse transformer for a charging Blumlein PFL is nowin operation. Dual resonance operation conditions wereachieved by optimizing the transformer parameters.The maximum energy transfer efficiency and gainwere measured to be 50% and 18.3, respectively. Thetransformer could charge a Blumlein PFL to 370 kV.

ACKNOWLEDGMENTS

This work was supported by Power Generation & Elec-tricity Delivery of a Korea Institute of Energy Technol-ogy Evaluation and Planning (KETEP) grant funded bythe Korea government Ministry of Knowledge Economy(No. 2009T100100542).

REFERENCES

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[2] J. C. Martin, P. D. Champney and D. A. Hammer, Cor-nel University Report, CU-NRL-2, 1967.

[3] J. C. Martin and I. D. Smith, US Patent No. 3456221,1969.

[4] W. J. Sarjeant and R. R. Dollinger, High-Power Elec-tronics (Tab Books, USA, 1989), Chap. 9.

[5] D. Finkelstein, P. Goldberg and J. Shuchatowitz, Rev.Sci. Instrum. 37, 159 (1962).

[6] P. W. Smith, Transient Electronics (John Willey & Sons,West Sussex, England, 2002), Chap. 5.

[7] I. Boscolo, G. Brautti, R. Coisson, M. Leo and A. Luches,Rev. Sci. Instrum. 46, 1535 (1975).

[8] C. R. J. Hoffman, Rev. Sci. Instrum. 46, 1 (1975).[9] R. Lundin, Proc. IEEE 73, 1428 (1985).

[10] Y. S. Jin, Y. B. Kim, J. S. Kim, H. J. Ryoo, C. H. Cho,G. H. Rim and S. W. Lim, Trans. KIEE 59, 939 (2010).