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Ministry of Higher Education and Scientific Research University of Technology Laser and Optoelectronics Engineering Department Republic of Iraq Ministry of Higher Education and Scientific Research University of Technology Laser and Optoelectronics Engineering Department DESIGN AND IMPLEMENTATION OF MARX GENERATOR FOR LASER APPLICATIONS A Thesis Submitted to The Laser and Optoelectronics Engineering Department, University of Technology in Partial Fulfillment of the Requirements for the Degree of Master of Science in Laser Engineering By Eng. Sarmad Fawzi Hamza B. Sc. Electrical and Electronic Eng. / Laser Eng. 2003 Supervised by Dr. Naseer Mahdi Hadi Dr. Kadhim Abid Hubeatir February 2008 A. D. Safer 1429 A. H. جمھورية العراق وزارة التعليم العالي والبحث العلمي الجامعة التكنولوجية قسم ھندسة الليزر والبصريات اﻻلكترونية ﺘﺼﻤﻴﻡ ﻭﺒﻨﺎﺀ ﻤﺠﻬﺯﻤﺎﺭﻜﺱ ﻟﺘﻁﺒﻴﻘﺎﺕ ﺍﻟﻠﻴﺯﺭ رسالة مقدمة إلى قسـم ھندسـة الليـزر والبصـريات اﻻلكترونيـة الجامعة التكنـولوجيـة كجزء من متطلبات نيل درجة الماجستير علوم في ھندسة الليزر تقدم بھا المھندس سرمد فوزي حمزة الھندسة الكھربائية واﻷلكترونية / ھندسة الليزر2003 بإشراف د. نصير مھدي ھادي د. كاظم عبد حبيتر شباط 2008م صفر 1429ھ الخﻻصة إن منظومات الليزر الغازية ذات عرض نبضة خرج قصير. وقمة طاقة عالية تحتاج إلى نبضات تفريغ كھربائي بمواصفات خاصة مثل محاثة واطئة, معدل تكرارية للنبضة وزمن نھوض سريع . وان مجھز قدرة نوع ماركس واطئ المحاثة ممكن أن يوفر ھذا النوع من نبضات التفريغ لتشغيل الليزرات الغازية بكامل مواصفاتھا . تم تصميم وبناء وتشغيل نوعين من مجھز قدرة ماركس . اﻷول مجھز قدرة ماركس ذو ثمانية مراحل تضخيم يمكن أن يوفر فولتية خرج لغاية 64 كيلو فولت كحد أقصى . تم شحن فولتية أولية 2 كيلو فولت وحصلنا على فولتية خرج فعلية 12 كيلو فولت بنبضة ذات زمن نھوض 666 نانوثانية ومحاثة 11 مايكرو ھنري وكفاءته 75% , أما المجھز الثاني فكان مجھز قدرة ماركس ذو عشرة مراحل تضخيم ممكن أن يوفر400 كيلو فولت كحد أقصى , تم شحنه بفولتية أولية 4 كيلو فولت وحصلنا على فولتية خرج فعلية بحدود 38 كيلو فولت بنبضة ذات زمن نھوض 50 نانوثانية ومحاثة 4.2 مايكرو ھنري وكفاءته %95 . تم تصميم نوعين من دوائر القدح لنوعي مجھز ماركس , اﻷولى دائرة قدح باستخدام مصباح وميضي مع محولة قدح لمجھز ماركس ذو ثمانية مراحل والثانية باستخدام محولة قدح (ملف إشعال) مع دائرة ترانزستور نوع (MOSFET) لمجھز ماركس ذو عشرة مراحل . تم الحصول على نبضة فولتية من دائرة المصباح الوميضي حوالي 4.5 كيلو فولت وعرض نبضة حوالي 2 مايكروثانية , بينما دائرة القدح الثانية حوالي 7.5 كيلو فولت وعرض نبضة حوالي 40 مايكرو ثانية . II Abstract Gas laser systems with high peak power and short pulse duration requires special properties of high voltage discharge pulses; i.e. low inductance, high pulse repetition rate and fast rise time. Low inductance Marx generator power supply can offer this kind of discharge pulses for the gas lasers optimum operation. Two types of Marx generators have been designed, built and tested. The first Marx generator with eight stages, can deliver 64 kV maximum output, is charged up to 2 kV and the high voltage output was 12 kV with pulse rise time of 666 ns and inductance 11 µH and efficiency of 75% . The second Marx generator with ten stages, can deliver 400 kV maximum output, is charged up to 4kV and the high voltage output is 38 kV with pulse rise time 50 ns, inductance 4.2 µH and efficiency of 95%. Many types of trigger circuits have been designed and implemented for triggering of two Marx generator systems. The first trigger is built circuit using Xenon flash lamp with a trigger transformer. The second trigger has been built using automobile ignition coil as a trigger transformer with a MOSFET driver .The Xenon flash trigger circuit of high voltage output pulse (4.5 kV) and pulse width of 2µs while the automobile ignition coil high voltage output pulse is 7.5 kV and pulse width of 40 µs. Appendices APPENDIX (A) no+ n+ = total electrons from cathode . αd Electron Multiplication equation. na = n0 e αd ………… ……………………………………….(1) na=() n o + n+ e n …………………………………………… . ..(2) n−() n + n = + a o + γ where γ : cathode yield in electrons per incident ion. αd na−()()() n o + n+ = no + n+ e − no + n + n n + = a (eαd − 1) γ eαd n e α d n = a ……………………………..………………….(3) a γ (e α d − 1 ) from eq.(2): n + ()na− n o = n + + γ ⎡ 1 + γ ⎤ ( na − no ) = n + ⎢ ⎥ ⎣ γ ⎦ γ n− n (a o ) ………………………………………...……..….(4) ∴n+ = 1+ γ substitute eq.(4)to eq.(3): αd ()na− n o e na = ()1+γ ()eαd −1 n e αd n e αd o = a − n ()1 +γ ()e αd − 1() 1 +γ ()e αd − 1 a αd αd αd no e= na e − na ()1 +γ ( e −1) αd αd αd αd no e= na e − na e + na − n a γ ( e − 1) Appendices e αd n= n a o 1 −γ ()e αd − 1 e αd II= a o 1 −γ ()e αd − 1 Appendices APPENDIX (B) L1 G R1 C1 R2 C2 Circuit arrangement 1/C1s L1s R V(s) 1 R2 V/s 1/C2s Transform circuit V z V(). s = 2 s z+ z 1 2 Where; 1 Z1 = +L1 s + R 1 C1 s 1 R * 2 C s Z = 2 2 1 R2 + C2 s Appendices R2 V R. C s + 1 V(). s = 2 2 s R2 1 + +L1 s + R 1 R2. C 2 s+ 1 C1 s R2 V R2. C 2 s + 1 V(). s = 2 s RCs2 1 + RCs2 2 +1 + LCsRCs1 1 . (2 2 + 1) + RCsRCs1 1 ( 2 2 + 1) (R2 C 2 s+ 1) C1 s V = C2 1 3 2 L1 2 R1 s+ s + +s L1 C 2 + s +s R1 C 2 + s CRC1 2 1 R2 R2 1 = V. 3 2 ⎡ 1 R1 ⎤ ⎡⎡ 1 R1 1 ⎤⎤ 1 DD+ ⎢ + ⎥ + D⎢⎢ + + ⎥⎥ + ⎣CR2 2 L1 ⎦ ⎣⎣ LC1 1 LCRLCCCRL1 2 2 1 2 ⎦⎦ 1 2 2 1 Appendices APPENDEX (C) e− α 1t − e − α 2 t VE= T 2()α 2− α 1 Differential equation for found maximum time: −α t E −α 2t 1 0 = []α2 e_ α 1 e T2()α 2− α 1 − α 2 t − α 1 t α 2 e = α 1 e − α 2 t − α 1 t ln( α 2 e )= ln( α 1 e ) ln α 2− α 2 t = ln α 1− α 1t α ln(2 ) α 1 t max . = ( α2 − α 1 ) Appendices APPENDIX (D) 1 = V. 3 2 ⎡ 1 R1 ⎤ ⎡ 1 R1 1 ⎤ 1 DD+ ⎢ + ⎥ +D⎢ + + ⎥ + ⎣CR2 2 L1 ⎦ ⎣ LC1 1 LCRLCRCCL1 2 2 1 2 ⎦ 2 2 1 1 1 V(s) = V. 3 2 ⎡ L1 ⎤ ⎡⎡ 1 R1 1⎤⎤ 1 DLD1 + ⎢ + RD1 ⎥ +⎢⎢ + + ⎥⎥ + ⎣CR2 2 ⎦ ⎣⎣C1 CRCCCR2 2 2 ⎦⎦ 1 2 2 Where inductance L1=zero, D =s 1 = V. 2 1 R1 1 1 s R1 + s( + +) + C1 CRCCCR2 2 1 1 2 2 1 R 1 RCRCRC+ + R ( +1 + )( 2 2 1 1 2 1 )2 − 4 1 C CRC m CCR CCR s = − 1 2 2 1 2 1 2 2 1 2 2R1 Therefore CR2 1 RCRCRC+ + CR ( 2 2 1 1 2 1 ){ 1± 1 − 4[ 1 2 ]} CCR C R 2 1 2 ( 2 +1 + 1) 2 C R s = − 1 2 2 R 1 CR2 1 C R CR −( 2 +1 +1){1 ± 1 − 4 1 2 } C R C R 1 2 ( 2 +1 +1) 2 C1 R2 S 1,2 = 2RC1 2 Where s is α Appendices APPENDIX (E) 1/C1s Ls R V(s) =Vo Vi/s 1/C2s 1 V C s , V = i 2 ° 1 1 1 1 1 4L s R+ Ls + + where: = + , R = C2 s C 1 s CCC1 2 C 1 VC = i Cs C 2 1 2 Rs+ Ls + C s VC 1 sR+ Ls 2 =i [ − ] C s 2 1 2 s( Rs+ Ls + ) C R R 2 s + s 2 = C 4 Rs R 2 1 s( +s 2 + ) C 4 C 2 4 s + = RC 2 (s + ) 2 CR A B ⇒ + 2 ⎛ 2 ⎞ ⎛ 2 ⎞ ⎜ s + ⎟ ⎜ s + ⎟ ⎝ RC ⎠ ⎝ RC ⎠ Appendices A = 1 4 2 s + =s + + B RC RC 2 B = RC VCi 1 A B V° =[ − ( + )] C s 2 2 2 2 s + (s + ) RC RC 2 2 t − t − VCi RC 2 t RC = [1− ( e + e )] C 2 RC 2 − t VCi 2 RC = [1− (1 + t)] e C 2 RC Appendices Appendix (F) When L =zero 1/C1s R 1/C2s Vi/s 1 Vi C2 s Vo = × s R +1 + 1 C1 s C2 s 1 V C s = i × 2 s R + 1 Cs 1 RC2 s =Vi × s + 1 CR 1 V C = i × CRs C s + 1 2 CR ⎡⎛ 1 ⎞ ⎤ ⎜ ⎟ +1 VC ⎢ CRs 1 ⎥ i ⎢⎝ ⎠ − ⎥ = C 1 1 2 ⎢ s + s + ⎥ ⎢ CR ⎥ ⎣ CR ⎦ VC ⎡1 1 ⎤ = i ⎢ − ⎥ C⎢ s s + 1 ⎥ 2 ⎣ CR ⎦ ⎡ −t ⎤ VCi CR = ⎢1− e ⎥ C2 ⎣ ⎦ Appendices Appendix (G) VVVG 2 = B − G VVG = − VVVG =B + ⎡ ⎤ ⎢ CC1+ 3 ⎥ V = V ⎢ ⎥ BH ⎣ CCC1+ 2 + 3 ⎦ ⎡ CC1+ 3 ⎤ VVG 2 = ⎢ ⎥ + V ⎣ CCC1 +2 + 3 ⎦ ⎡ ⎤ CC1 + 3 VV=⎢1 + ⎥ CCC+ + 3 ⎣⎢ 1 2 ⎦⎥ Chapter One General Introduction 1 Chapter One General Introduction 1.1 Marx Generator Power Supply: A Marx Generator is a clever way of charging a number of capacitors in parallel, then discharging them in series. Originally it was described by Erwin Marx in 1924. Marx generators offer a common way of generating high voltage impulses that are higher than the available supply charging voltage. Discharge capacitors can also be kept at relatively lower voltages, usually less then 200 kV, to avoid bulky and very expensive capacitors as well as engineering problems associated with extremely high DC voltages. A charging circuit diagram of simple 3-stage Marx generator during charging state is shown in figure (1-1).
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