ANALYSIS AND SIMULATION OF PULSE TRANSFORMER CONSIDERING LEAKAGE INDUCTANCE AND CAPACITANCE

Transcription

1 ANALYSIS AND SIMULATION OF PULSE TRANSFORMER CONSIDERING LEAKAGE INDUCTANCE AND CAPACITANCE ABOLFAZL VAHEDI, HOSSEIN HEYDARI, and FARAMARZ FAGHIHI Electrical Engineering Departent, High Voltage & Magnetic Materials Research Center Iran University of Science and Technology Narak, Tehran, IRAN INTRODUCTION Pulse transforers capable of transitting substantially rectangular voltage pulses, with durations of less than one illisecond, were developed for radar application, NLC klystron pulse odulator, driving a icrowave aplifier, x- rays for edical and industrial use, gas lasers for plasa technology and plasa iersion ion iplantation [1-7]. Several application of the, need ediu or high voltage pulses (1 up to 700kV that ediu or high voltage pulse transforer increases the output pulse voltage to the value required for the load. The usually large nuber of turns in the secondary winding (the transforer ratio is frequently 1:10, together with the insulation gap between windings and between winding layers increase the value of the equivalent parasitic eleents (leakage inductance and inter-winding capacitance. These eleents extend the pulse rise tie and cause overshoot and oscillations. Hence, the design of the pulse transforer is critical, not only because all aterials ust sustain the ediu or high voltage across the, but also because the output pulse shape depends heavily on several transforer parasitic paraeters that are difficult to aster [8]. Pulse transforer odeling is done by two ethods: firstly, the well-known luped paraeter theory of transforer is used [3, 8]. Most pulse transforer odels treat each winding as a single circuit eleent. This liits analysis of these types of odels to the bulk properties of the odel. Details of winding interaction with stray capacitances can only be luped into a single circuit odel eleent and these values are usually deterined by easureent. This can liit a designer to a trial and error approach to the subtleties of pulse transforer design. Secondly, transforer considers as a distributed paraeter circuit [9, 10]. However, nonlinear core are not included [11]. The windings are separated into ultiple sections and all cobinations of utual inductances are calculated. The distributed capacitance between the core and priary, the priary and secondary, and the secondary to case are included. The individual inductance and coupling coefficients are calculated based on the agnetized inductances and the air utual. These values are used in a circuit odel developed in PSPICE. Especially, this ethod is used for siulation of air core pulse transforer [1-14]. On the other hand, because of the transforer parasitic eleents involved, the transforer is the critical device in shaping the rising characteristics of the output pulse [3, 15-19]. Other related works on pulse transforer are haronics, theral and echanical force using finite eleent ethod (FEM, reducing size, and electroagnetic interference (EMI and so on [4, 7, 0-]. To contribute to a better understanding of pulse transforer operation considering leakage inductance and inter-winding capacitance, this paper proposes a atheatical odel based on the flux linkage as state variable. Our ain ai is to identify a critical values causing unsuitable rise tie of the output, especially daaged output pulse copletely. It is interesting to deonstrate conditions for leakage inductance of windings, pulse frequency, and leakage capacitance that are destroying output pulse that hasn t been discussed clearly in the literature up to now. Finally results of siulation are able to show rated value of pulse transforer paraeters. If paraeters of pulse transforer are not allowable value obtaining easureent and calculation, we ust choose ethods for reduction of the, such as using auxiliary windings or active shielding and so on [8, 3]. Therefore, this odel is then used to suggest approachable parasitic eleents to optiize the design of a ediu or high voltage pulse transforer. Besides, using two auxiliary winding for iproveent of technical characteristics of output pulse is explained and new prove based on characteristic roots ethod is done. PULSE TRANSFORMER MODELING BASED ON FLUX LINKAGE AS STATE VARIABLE In this section, we will describe an arrangeent by which the voltage and flux linkage equations of a two-winding transforer can be ipleented in a coputer siulation. There is of course, ore than one way to ipleent a siulation of the transforer even when we are using the CIRED005

2 sae atheatical odel. For exaple, we can ipleent a siulation using fluxes or current as state variable. In our case, we will pick the total flux linkages of the two windings as the state variables. In ters of these two state variables, the voltage equations can be written as 1 dψ1 v1 = i1r 1 +., ωb (1 1 dψ v = i r +., ωb ( whereψ1 = ωbλ1 ψ = ωbλ ω b is the base frequency at which the reactances are coputed. The flux linkage per second of the windings can be expressed as ψ 1 = ωbλ1 = xl1i1 + ψ, (3 ψ = ωbλ = i + ψ, (4 and ψ = ω L i + i = x ( i + (5 b 1( 1 1 i The current i 1 can be expressed in ters of ψ 1 and ψ using Equation (3 siilarly, i can be expressed in ters of ψ and ψ using Equation (4. ψ1 i1 =, (6 x l1 ψ i =. (7 Substituting the above expressions of i 1 and i into Equation (5, we obtain ψ ψ1 ψ = + (8 x 1 xl1 Collecting the ψ ters to the right, we obtain the desired expression of ψ in ters of the two desired states, that is CIRED ψ1 ψ ψ ( + + = + x 1 xl1 xl1 (9 Letting = + + x M x1 xl1 (10 Equation (9 can be written ore copactly as ψ1 ψ ψ = xm ( + xl1 (11 Using Equations (6 and (7 to replace the currents, Equations (1 and ( can be expressed as integral equations of the two total flux linkages, that is ψ1 ψ 1 = ω bv1 ωbr1 ( xl 1 (1 ψ bv br ψ ψ = ω ω ( (13 Collectively, Equations (6, (7, (11, (1, and (13 fro a basic dynaic odel of a two winding transforer to which agnetic nonlinearity and iron losses ay be added if necessary. In this odel, the flux linkages are the internal variables, the terinal voltages are the required inputs, and the winding currents are the ain outputs. In the next section, pulse transforer odeling based on this odeling has been described. SIMULATION OF PULSE TRANSFORMER In any applications of pulse transforer, we need a flattop portion of the high voltage output pulse and fast rise tie. In order to achieve a rise tie that is less than 400nS we ust be iproved the design of a pulse transforer by trade off aong the droop, the core size, and the rise tie [4, 8, 9, 15, 16, and 4]. For investigation on effects of leakage paraeters in output pulse, siulation is done. Figure 1 shows the SIMULINK siulation that is in accordance with the flow diagra based on flux linkage as state variable. In addition to, leakage capacitance and load odel is defined in accordance with bellow equations: 1 v v = ic bb ( i. C = ω (14 R eq FIGURE 1- Siulation of pulse transforer based on flux linkage as state variable Table 1- Transforer paraeters (f=1 khz, Transforer ratio: 1:10 Paraeter Calculated value R R 0.14 x l1 = xl 0.6 R o 50 ω b 683 x c x 1 50 O

3 Initial siulation has been done in f=1 khz (paraeters of pulse generator: aplitude: 500V, periods: 0.001, pulse wih 0% of period with calculated paraeters (Table 1. Result of siulation is illustrated in Figure. This siulation is repeated in f=10 khz (Table and Figure 3. Effects of leakage inductance and inter-winding capacitance in ediu frequency (1 khz are shown in Figures 4 and 5. Therefore we can predict output wavefor of pulse transforer based on changing in period of input pulse, leakage inductance and inter-winding capacitance. FIGURE 3- Wave for of v (periods of pulse transforer: FIGURE - Wave for of v (periods of pulse transforer: Table - Transforer paraeters (f=10 khz, Transforer ratio: 1:10 Paraeter Calculated value R R 0.14 x l1 = xl 6.8 R o 50 ω b 6831 x c 300 x FIGURE 4- Wave for of v (periods of pulse transforer: 0.001, x l1 = xl = 1. 4Ω others according to Table 1 that is unwanted output. FIGURE 5- Wave for of v (periods of pulse transforer: 0.001, C = nf others according to Table 1 that is unwanted output. SIMULATION RESULT COMPARING WITH MODELS BASED ON DISTRIBUTED PARAMETERS CIRED005

4 For very high speed pulse, transforers were considered as a distributed paraeter circuit [9]. In this ethod, for a non-inverting type transforer (n: 1, the pulse rise tie response can be expressed as follow [9]: E OG v o ( t = [ u( t + u( t ntb An ] (15 n( k + 1 n= 1 ωb R where G =, k1 = n, R1 R1 R + R + n n n 1 1 k1 An = (1 ρ ( ρ, ρ = 1+ k1 Equation (15 coply with the corresponding siulations results. The discrepancies are alost 3% up to 3% in different conditions of our study. Thus our investigation is useful for analysis of pulse transforer and has good points for selecting and setting leakage paraeters of pulse transforer. RISETIME REDUCTION AND NEW MATHEMATICAL PROVE One of the techniques usually adopted to decrease the leakage inductance of the transforer adds two auxiliary windings to the transforer. If properly used, these auxiliary windings reduce the leakage flux and, therefore, the leakage inductance. As a result the pulse rise tie is reduced. Firstly, analysis of transforer with subtractive connection of the auxiliary windings based on previous studies is explained. We consider the transforer supplying power to a load and the auxiliary windings connected as in Figure 6. Now i = i0 where i0 is the load current. The third and fourth windings are connected in subtractive ode (terinals five and six are connected to terinals seven and eight, respectively. This circuit exeplifies the noral operating condition of the transforer. Considering that i 4 = i 3 = iaux, in Figure 6, applying to basic equation of four winding transforer and taking into consideration that N 3 = N 4 = Naux, yields, respectively v1 = R1i 1 + N1 + l11 l1 + ( l14 l13 v = Ri0 + N + l1 l + ( l4 l3 (16 v3 = R3iaux + Naux + l31 l3 + ( l34 l33 v4 = R4iaux + Naux + l41 l4 + ( l44 l43 CIRED005 Given that the third and fourth windings are connected as in Figure 6, then v 3 = v4, which yields ( l l + ( l l = Rauxiaux + laux M ( aux FIGURE 6- Scheatic representation of the transforer with loaded secondary, N, and the two auxiliary windings connected in subtractive ode, N 3 and N 4 [8]. where Raux = R3 + R4, laux = l33 + l44 and M aux = l 34 + l43. The current across the auxiliary windings is ruled by (17. It is interesting to observe that i aux is independent of the tie derivative of the resultant flux, φ. If the auxiliary windings have the sae nuber of turns, i aux exists only as the consequence of the leakage coupling between the priary and secondary leakage flux linking the auxiliary windings. Moreover, the current across the auxiliary windings results fro the difference between the leakage utual inductance coefficients of the priary and the secondary with respect to the third and fourth windings, ties the tie derivative of the priary and secondary currents, as shown in (17. The auxiliary current produces a flux that opposes the priary and secondary leakage flux. We can say that the auxiliary current, i aux, function of the leakage flux coupling between the priary and secondary with the third and fourth windings, generates a agnetic flux [3] that reduces the leakage flux of the priary and secondary windings. Consequently, the leakage inductance in the transforer is reduced. Secondly, New Proof Based on Characteristic Roots Method is presented as below: By considering resistance R a between third and fourth windings and ( x 1 = i 1, x = io, x = x 3, i aux = x 4 as state variables, state equations can be written. Coputing poles of transfer function with different aount of R a shows rise tie reduction for sall aount of R a (it is proof for connecting two auxiliary winding due to relation aong distance of poles fro origin point and rise tie. We calculated poles of the case study pulse transforer for values shown in table that is changed by adding auxiliary windings (N 3 =N 4 =5. For R a = 50Ω, s= 1.0e+006* (-.9905, i, i, -0.0.

5 For R a = 100Ω, s = 1.0e+006 *( , i, i, For R a = 0Ω, s= 1.0e+004 *( i, i, , Theses values prove our approach about connection of auxiliary winding for rise tie reduction in pulse transforer. CONCLUSION High voltage pulse transforers are often used in association with high voltage pulse generating circuits to further increase the pulse output voltage level. However because of the transforer parasitic eleents involved, the transforer is the critical device in shaping the rising characteristics of the output pulse. In this paper, we siulated a two winding pulse transforer based on linkage flux as state variable ethod. It has been considered leakage inductance and capacitance in siulation. We have obtained conditions for these paraeters causing unexpected output pulse. Finally subitted odel of pulse transforer was copared by distributed paraeters odel. Our investigation is useful for analysis of pulse transforer and has good points for selecting and setting leakage paraeters of pulse transforer. Especially, it helps us in stages of pulse transforer designing. Furtherore, using two auxiliary winding for iproveent of technical characteristics of output pulse is discussed and new proof based on characteristic roots ethod is done. REFERENCES [1] M. Akeoto, Y. H. Chin, and Y. Sakaoto, 001, Solid State Klystron Modulator for JLC, Proceedings Particle Accelerator IEEE Conference, [] R. Koontz, M. Akeoto, S. Gold, A. Kransnykh, Z. Wilson, 1998, NLC Klystron Pulse Modulator R&D AT SLAC, Proceedings IEEE Conference, [3] M. Akeoto, S. Gold, A. Krasnykh, and R. Koontz, 1998, Developent of the Pulse Transforer for NLC Klystron Pulse Modulator, Proceedings IEEE Conference, [4] R. Leet, 196, Reducing Size of Radar Pulse Transforer, IRE Transactions on Coponent Parts, [5] H. W. Lord, 1971, Pulse Transforer, IEEE Transactions on Magnetics, Vol. MAG-7, No. 1, [6] M. Gollor and W. Schaper, 1998, Design of a 130kV Pulsed Power Supply for a Space based CO Laser, Proceedings IEEE Conference, [7] S.C. Ki, S. H. Na, S. H. Ki, D. T. Ki, and H. Jeong, High Power Density, High Frequency, and High Voltage Pulse Transforer, Proceedings IEEE Conference, 00. [8] L. M. Redondo, E. Margato, and J. F. Silva, 00, Rise Tie Reduction in High Voltage Pulse Transforers Using Auxiliary Windings, IEEE Transactions on Power Electronics, Vol. 17, No., [9] N. Nishizuka, M. Nakatsuyaa, and H. Nagahashi, 1989, Analysis of Pulse Transforer on Distributed Paraeter Theory, IEEE Transactions on Magnetics, Vol. 5, No. 5, [10] R. Hitchcock, 1997, The Developent of a Distributed Linear Pulse Transforer Model, Proceedings IEEE Conference, [11] P. C. Hooke, D. R. Driver, and R. V. Major, 1974, Thin Gauge Nickel-Iron Cores Specification for Use in High Power Pulse Transforers and Saturable Reactors with Reset, IEEE Transactions on Magnetics, Vol. MAG- 10, No., [1] J. P. O Loughlin, and G. J. Rohwein, 1988, Air Core Pulse Transforer Design, Proceedings IEEE Conference, 3-7. [13] K. A. Khan and R. G. Colclaser, 1998, Air Core Foil Wound Pulse Transforer Design Concept, proceedings IEEE conferences, [14] J. L. Suthar and J. R. Laghari, 1995, Siulaton of Air Core Pulse Transforer, Proceedings IEEE Conference, [15] P. M. Ranon, D. J. Hall, J. P. O Loughlin, R. L. Schlicher, W. L. Baker, D. Dietz, 1988, Synthesis of Droop Copensated Pulse Foring Network for Generting Flat Top, High Energy Pulses into Variable Loads Fro Pulsed Transforers, Proceedings IEEE Conference, [16] P. M. Ranon, and et. al., 1989, Copact Pulsed Transforer Power Conditioning Syste for Generating High Voltage, High Energy, Rapid Rise Tie Pulses, IEEE Transactions on Magnetics, Vol. 5, No. 1, [17] R. L. Cassel, 199, A 00kV, 100nS, 4/1 Pulse Transforer, Proceedings IEEE Conference, [18] J. D. Ivers, G. S. Kerslick, J. A. Nation and L. Schachter, 1996, Design and Operation of a 700kV, 700A Modulator, Proceedings IEEE Conference, CIRED005

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