MODAL FILTER SIMULATION WITH LOSSES

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Introduction. As long-term practice of start and maintenance of the spacecrafts (SC) showed, reliability of the elements, devices of airborne computers and control modules functioning is one of the key factors defining success of the mission in general. Reliability assurance in special conditions of harmful space factors impact is con- nected with specific difficulties. One of such factors is interfering super short impulse (ISI). Its dangers are 8. Extension of all boundaries of cross-section of the reference conductor on Δn. 9. Calculation of inductance matrix L2 for the changed structure. 10. Calculation of ΔLj,k = L2j,k- L1j,k. 11. Calculation of non-diagonal matrix elements Rjj using formula: R = Rs æ -DL j,k ö , Оm/m. (2) extensively researched [1-5]. However, the increase j,k j ¹k m ç Dn ÷ in SC effective performance period (up to 15 years) leads to considerable degradation of the used materials’ proper- ties and also makes it problematic to predict the new ma- terials’ properties mutation in the future SCs. This will inevitably create conditions for harmful effects of ISI, causing improvements of protection against it. The use of the known protection devices is complicated by a number of contradictory requirements, for example, protection of 0 è ø 12. Extension of all boundaries of the cross-section of the 1st from N conductors. 13. Calculation of L2jj. 14. Calculation of ΔLjj = L1jj - L2jj. 15. Calculation of diagonal components of the matrix Rjj using formula: R = Rs æ -DL jj ö , Оm/m. (3) a bigger number of circuits, law mass of the safety device, jj m ç Dn ÷ ability to function effectively for 15 years in space. There- fore creation of new elements and protection devices of airborne computers and control modules from SIS proves to be relevant. Protection against short impulses based on modal filtering [6-11] is suggested. The physical princi- ple of such protection is based on the effect of splitting of interfering impulse in the segment of line into modes, each of which extends with the time delay. In case of un- homogeneous dielectric filling in the cross-section of the connected line segment, the difference of these time delays can exceed duration of interfering impulse, so that one impulse given between the active and reference con- ductors at the beginning of the segment will split into two impulses at the end of the segment. Often for the analysis of strip structures quasi static simulation is used. For exact simulation of such structures it is necessary to consider losses both in conductors, and in dielectrics. Meanwhile, accurate loss record is espe- cially important in certain cases. Thus, in modal filters (MF) output amplitude depends on losses. The purpose of this paper is to compare results of quasi static and electro-dynamic simulations of MF taking 0 è ø 16. Serial repetition of points 12-15 for each of the remained conductors, successively expanding boundaries of this conductor. The calculation algorithm of matrix R has been implemented. In cases where it is required to calculate L matrix, functions of the TALGAT system are used. In the algorithm extension of conductor boundaries by value Δn is applied. It is realized programmatically. The user value Δn is set for this purpose, or default value Δn equal to 0.1 from the lowest parameter of structure is used. For calcu- lation of default value of boundary with the lowest length whose value is equated to value of the lowest parameter is found. In order to expend the conductor i, where i = 1, 2, …, N, N - number of conductors multi-wire transmission line, applying scaling against the centre of the conductor, which transforms conductor coordinates p1,i; p2,i; …; pM,i, where M - the number of conductor angles i, into coordi- nates p1,i'; p2,i'; …; pN,i' so to obtain the conductor, in- creased by Δn from all sides. For this purpose scaling coefficients are calculated: into account loss record. Calculation of resistance per-unit-length matrix. fix l x + 2Dn = i ; l x fi y l y + 2Dn = i , l y (4) The algorithm of Calculation of resistance per unit length matrix of N-wire transmission line in which (N + 1) referwhere i l x , i i l i y - the width and thickness of conductor i. ence conductor, in quasi static simulation environment TALGAT [12] looks as follows [13]: 1. Input of conductor parameters: ρ - conductor spe- Further conductor center coordinates are calculated pс,i and transformation matrix is built: fix 0 0 cific resistance, µ - magnetic conductivity. 2. Input of frequency. 0 fi y 0 , (5) 3. Input of the initial geometrical parameters. px (1- f x ) py (1- f y ) 1 c,i i c,i i 4. Calculation of value of conductor boundaries exten- sion ∂n (value 0.1 from the lowest parameter is used by where x p c,i and y p c,i - components x and y coordinate p с,i. default). Transformation matrix can be applied in the following way: 5. Calculation of the conductor’s surface resistance uspx ¢ = f x px + px (1- f x ); ing formula j,i i j,i c,i i (6) py ¢ = f y py + py (1- f y ), Rs = pf mr. (1) j,i i j,i c,i i 6. Geometrical modeling of cross-section structure under initial parameters. 7. Calculation of per-unit-length initial matrix coeffi- cients of electromagnetic induction L1. where j = 1, 2, …, M. For the conductor boundaries extension transformation matrix should be applied (2) to every conductor angle. Extension of the infinite earth is done via displacement of all structure boundaries towards the line of the infinite earth on Δn. Simulation. The approaches described above are software realised and built-in in the TALGAT system. However, the use of this program for quasi-static simula- tion of real strip structures and comparing the received results with the results of electro-dynamic simulation was not shown earlier. For simulation MF structure, researched in [14], will be used. Quasi-static simulation is executed in TALGAT system, electro-dynamic - in CST MWS [15]. The cross-section and the diagram of MF switch are provided in fig. 1, where width and thickness of conductors w = 500 micron and t = 85 micron; conductor spacing - s = 200, distance between edge of the conductor and dielectric edge d = 1000 micron, substrate thickness h = 400 micron, FR-4 substrate material, line length l = 2.5. MF contains three copper conductors: A - the active, O - reference and p - passive. The impulse oscillator is connected to the active conductor with the following parameters: ampli- tude - 10 V and duration of peak td = 100 picoseconds, duration of the front and recession of tr = tf = 100 pico- seconds. Resistance values are R1 = R2 = R3 = R4 = = 100 Ohms. Results of simulation taking into account losses and dispersion are provided in fig. 2. а b Fig. 1. MF cross-section (a) and connection scheme (b) Рис. 1. Поперечное сечение (а) и схема включения (b) МФ а b Fig. 2. Voltage waveforms obtained in CST MWS (a) and TALGAT (b) Рис. 2. Формы напряжения, полученные в CST MWS (а) и TALGAT (б) Table Comparative results of amplitudes and impulses time delays Parameter CST TALGAT (CST - TALGAT)/(CST + TALGAT), % Amplitude of 1st impulse V3, В 1.1 0.88 11 Amplitude of 2nd impulse V3, В 0.73 0.71 1.4 Amplitude of 1st impulse V4, В -1.1 -0.88 11 Amplitude of 2nd impulse V3, В 0.73 0.71 1.4 Time delay of 1st impulse in nodes V3 and V4, ps 11.6 12.2 2.5 Time delay of 2nd impulse in nodes V3 и V4, ps 14.9 15 0.3 The results proved that with reference to losses in conductors and dielectrics, wavefront time and impulse drop on the MF output increase. Thus the voltage ampli- tude of output impulses (V3) is much less than a half of amplitude of an input impulse (V1). Impulse amplitude of the even mode appeared to be less than impulse amplitude of the odd mode. This results from the fact that currents of the even mode extend mostly in dielectric, while currents of the odd mode - in the air. Fig. 2 shows that voltage waveforms, calculated in TALGAT and CST MWS, coin- cide. Values of amplitudes and time delays of impulses are given in the table. Conclusion. Simulation results showed that the maximum deviation under impulses delays makes 2.5 % under amplitudes - 11 %. It proves consistency of results received by means of the approaches described in the present paper. Besides. calculation time in TALGAT was about 1 h, in CST MWS - about 50 h. Therefore. the soft- ware realized approaches can be used for MF simulation.

About the authors

R. R. Khazhibekov

Tomsk State University of Control Systems and Radioelectronics

Email: r300994@mail.ru
40, Lenina Av., Tomsk, 634050, Russian Federation

A. M. Zabolotsky

Tomsk State University of Control Systems and Radioelectronics

40, Lenina Av., Tomsk, 634050, Russian Federation

T. R. Gazizov

Tomsk State University of Control Systems and Radioelectronics

40, Lenina Av., Tomsk, 634050, Russian Federation

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