A Hydrib Pulse Forming Technique

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A HYBRID PULSE FORMING TECHNIQUE

by

William R. Cravey, B.S. IN E.E.

A THESIS

IN

ELECTRICAL ENGINERRING

Submitted to the Graduate Faculty

of Texas Tech University inPartial Fu lfillment of theRequirements for

the Degree of

MASTER OF SCIENCE

Appro\7etd

Accep ted

December, 1988



A C K N O W L E D G M E N T S

I wo uld l ike to exp ress my app recia tion to a n u m b er ind ividu als: Dr. T. R. Bu rke s for providing m e with the oppo rtuto do th is rese arch . Dr. WiUiam M. Portno y for his ass ist an ce

developing the work, and Dr. G. McDuff who provided me wva luable feedback in the completion of th is re sea rch. I would like to extend my appreciation to Susan Ball for her helpsug ges tion s an d com m en ts. Finally, I would l ike to th an k beautiful wife for the love, patience, and support she has shduring the writing of this thesis.

11



T A B L E O F C O N T E N T S

ACKNOWLEDGMENTS iiUSTOFTABLES v

LIST OF FIGUR ES vi

I. INTRODUCnON 1II. TRANSMISSION LINE TRANSIENTS 4

Wave Propagation in Tr ans m ission Lines 5

Analytic Solutionof Charged Tr ansm ission Line Eq uation s 14

III. PULSE FORMING NETWORKS 2 7

Th e Type 'C' Pu lse Form ing Network 2 7The Type 'A Pu lse Form ing Network 2 9

The Type 'E' Pulse Forming Network 3 2

O the rT ype s Of Pulse Forming Networks 3 3

IV. SE RIE S CONNECTION OF A TRAN SMISSIONLINE WITH A PULSE FORMING NETWORK 3 6

Ju nc tion Filtering 3 7LaboratoiyResults 4 3

Line Length Variations 4 7

V. THE PIYBRID NETWORK 5 0

Parameters Aífecting Pulse Shape 5 1

111



Im peda nce Co nside rations For The HybridNetwork 57Line Length Co nside rations 5 9

VI. DESIGN , CONSTRUCTION, AND EVALUATION OFTHE HYBRID NETWORK 6 4The Pulse Forming Network 6 4

The Tr ans m ission Line 7 3

Ev alua tion of the Hybrid Network 7 5

VII. CONCLUSION 7 8

REFERENCES 80

APPENDICES

A FOURIERCOEFFICIENrS 8 1

B TEST SYSTEM DESIGN 8 9

C VARIOUS SPICE CIRCUTT MODELS 9 4

IV



L I S T O F T A B L E S

Table 3.1.

Tab le4 .1 .

Table 6.1.

Table 6.2.

Table 6.3.

Table 6.4.

Table A.I.

Table A.2.

Table A.3 .

Table A.4.

Table A .5.

Table A.6.

Table A .7.

Values of bn's, Ln's, and Cn's for the t)T)e 'C'netw ork of Figure 3.1 (Glasoe an d Lebacqz, 192) 2

Su m m ary of series connection resu lts 4 9

Values of capacitance measured at each stage ofth e PFN us ing a vector im ped anc e bridge 6 8Values of inductance measured at each stage ofthe PFN usin g a vector imp edan ce bridge 6 8Calculated values of mutual inductance for eachstage 69

Table showing parameter changes for each testcase 76

Fo urie r coeffîcients for a trapezoid al pu lse sh ap e 8

Fo urie r coefficients for a parabo lic pu lse sh ap e 8 2

Fo urier coefficients for a sq ua re pu lse sh ap e 8 3

Normalized capaci tor values for a t rapezoidalpu lse sh ap e. Multiply Cn's by t/Z o 8 4

Normalized inductor values for a trapezoidal pulsesh ap e. Multiply Ln's by t Zo 8 5Normalized capacitor values for a parabolic pulsesh ap e. Multiply Cn 's by t/Z o 8 6

Normalized inductor values for a parabolic pulsesh ap e. Multiply Ln's by t Zo 8 7



L I S T O F F I G U R E S

Figure 1.1. Block diag ram of the hybrid netw ork 3

Figu re2 .1 . Voltage pu lses formed by (a) un de rm atc he d,RL < Zo, an d (b) overm atch ed, RL > Zo, loa ds 5

Figure 2 .2. Lu m pe d eq uiv a le n t c i rc u i t of lo ss les stransmission line used to describe the processof vol tage and cu rre nt wave pro pag ation intransmission lines 6

Figure 2.3 . Histog ram of wave pro pag ation for a charg edtransmission line with a matched load at oneen d an d a open circu it at the oth er end. Light-Initial voltage, Medium—Resultant wave, andDark—Propagating wave 8

Figure 2.4. H istogram of wave pro pag ation for a charg edtransmission line with a matched load at oneend and an ideal voltage source at the otheren d. Light—Initial voltage, M edium — Resu ltantwave, an d Dark—Propagating wave 10

Figure 2.5 . Histog ram of wave prop agation of two charg edtra ns m issi on lines an d a m atch ed load. Light—Initial voltage, Medium—Resultant wave, andDark-Propagating wave 13

Figure 2.6. Sm all sect ion of t ra ns m iss io n l ine u se d toderive the general solut ion of a chargedtransmission line 14

Figure 2.7. Non -ideal voltage sou rce at sen din g end of acharg ed tran sm issio n line 18

Figure 2.8. O utp ut resp ons e of charged tran sm issio n linewith a non-ideal voltage source at the sendingend an d a m atc he d load at th e receiving end 2 0

VI



Figure 2.9. Circuit use d in calculating the ou tp ut resp on seof a charged transmission line 2 1

Fi gu re 2. 10 . Plot generated usin g equation (2.4). Chargedsend ing end capacitor. C = IF, T = 0.62 5 s e c ,R = 50a 2 3

F i g u r e 2 . 11 . Circui t used in determining the output waveform of a charged tran sm ission line 2 4

Fig ur e2 .12 . Plot ge ne ra te d us in g eq ua t ion (31). LCnetwork at sending end of transmission line.L=50 ^H, R = 10 fí, T=10 îse c, C=2 |iF an dEo=200 V 2 6

Figu re3 .1 . Type 'C' netw ork of n sectio ns. Th e seco ndFo ster form 2 8

Figure 3.2. N um be r of sta ge s ve rs u s rise tim e of a PFNwith a Square (a), Parabolic (b), and atrapez oidal pu lse sh ap e (c) 3 0

Figure 3.3. Eq uiv alen t Type 'A' netw ork derived us in gFoster 's Reactance Theorem 3 1

Figure 3.4. Eq uiv alent ne tw ork s derived by co ntin ue dfraction ex pan sion of the im pe da nc e an dadmittance functions of the network in Figure3.2. The First Cauer Form or Type 'B' PFN (a).The Second Ca uer Form or ly p e 'F ' PFN 3 4

Figure 3.5. Useful ran ge s of va rio us t j^ e s of PFN anddistr ibuted netwo rks 3 5

F i g u r e 4 . 1 . PFN an d t r a n sm is s io n l ine in s e r i e s

combination 37Figure 4.2. SPICE generated ou tpu t of series com bination 3

Figure 4.3 . SPICE o ut pu t gen erated by varying the e ndind uc tan ce of the PFN, jun c t io n indu c tor.Plots for values of 4, 6, 8, 10, and 16microhenrys 40

v i i



Figure 4.4. SPICE ge ne rate d o u tp u t at load. Cu rve sge ne rate d for .5 , 5, an d 15 nf va riatio ns insh un t capacitor 4 1

Figure 4 .5 . SPICE gen era ted o ut p ut of Tee n etw ork .Variations of 0.01, 1, and 10 microhenrys endind ucta nce with a 1 nanofarad sh un t , and 10nan ohe nrys with a 5 nanofarad sh un t 4 2

Figure 4.6. Ph oto gra ph of the load voltage w ith a one-nanofarad sh un t capacitor 4 4

Figure 4.7 . Ph oto gr ap h of th e load voltage with a 56 -nanofarad sh un t capacitor 4 5

Figure 4.8 . Ph oto gra ph of th e load voltage with a one-n a n o f a r a d s h u n t c a p a c i t o r a n d a 4 . 5 -microh enry series inducto r 4 6

Figure 4 .9 . Ph oto grap h of the load voltage with 192 feet ofline, T=288 nanosec onds 4 7

Figure 4.10 . Ph oto gra ph of the load voltage with 40 0 feet ofline, T=600 nano second s 4 8

Figure 4.11. Photograph of the load voltage with 791 feet ofline, T=1.1875 microseconds 4 8Fig ure 5 .1 . The hybrid pulse forming network 5 2

Figure 5 .2 . SPICE ge ne ra ted o u tp u t of th e hy br idnetwork. 52

Figure 5.3. Typical ou tp ut res po ns es for a PFN disch argeinto a matched load, (a), and a transmissionline disch arge d into an ove rm atche d load, (b) 5 4

Figure 5.4. SPICE gen erate d ou tp u t of tra ns m iss io n linedischarged into overmatched load where Zo isthe impedance of the t ransmission l ine, andRo is th e res istan ce of the load 5 5

Figure 5.5. Resistive netw ork used to desc ribe the n eedfor a low imp edan ce tran sm ission line 5 5

Figu re 5.6. Sim ple resistive voltage divider 5 7

Vl l l



Figure 5.7. Percen t overshoot ve rsu s the im ped ance of theline. Where Zo is the line impedance, Ro is theload resistan ce 5 8

Figure 5.8. Percen t un de rsh oo t ve rsu s the imp eda nce ofthe line. Where Zo is the line impedance, Ro isthe load resistance, To is the delay time of theline, an d Tr is th e rise time of th e PFN 6 0

Figure 5.9. SPICE generated ou tpu t of a tran sm issio n linedisc har ge for var ious leng ths of hn e 6 2

Figure 5.10. Perce nt un de rsh oo t versu s the length of theline. Where Zo is the line impedance, Ro is theload resistance, To is the delay time of theline. an d Tr is the rise time of the PFN 6 3

Figu re6 .1 . P i c tu re of ex pe r im en ta l pu l se fo rmingne tw ork , (a) . Sk etc h of PFN i l lu stra t in gspecial featu res, (b) 6 5

Figu re 6.2. Sc hem atic of exp erim ental type 'E' PFN 6 6

Fig ure 6 .3 . Pho tograph of ou t-pu t pulse of the PFN 6 7

Figure 6.4. Ph otog raph of charg ing cu rre nt th ro ug h a 3Qviewing resis tor 6 7Figure 6.5. Ch arg ing circuit (a). Ph oto gra ph of cha rgin g

voltage across charging indu ctor 7 1Figure 6.6. Ch arg ing in du cto r wave form before (a) an d

after (b) the use of a RC- snu bb er 7 2Figu re 6.7. Photog raphs of transm ission line ou tpu t 7 4

Figure 6 .8 . Ph ot og ra ph s of Hybr id ne tw or k ou tp u tvoltage for a line delay of d=30 ns and a lineimpedanceofZo=10fí 77

IX



C H A P T E R I

INTRODUCTION

Lasers , h igh power rad io f requency genera tors , andelectromagnetic pulse (EMP) simulators are but a few of t

sys tem s th at require high-power rectang ular pu lses. Over the p45 years, the need for repetitive pulsers has expanded and chanto the point where, today, there are hundreds of different useThe design of a network which can produce a rise time of less ttens of nanoseconds is usual ly done by construct ing a PFN n u m er o us s tages, depen ding on pulse width. Ano ther app roau se d for pr od uc in g a pu lse of th is type util izes th e ch arg et ran sm iss io n l ine . Al though the t ran sm iss ion line pro du ces desirable pulse shape, when the pulse width is greater than a fmicroseconds, an excessive length of line is needed.

The work described here presents a pulse forming techniq

which has an advantage over the transmission line and the PFNth at , it can pro du ce pu lses of long du ratio n an d fast rise times .

pulse is produced by taking advantage of the desired characteris

of bo th the d is t r ibuted pa ram eter network, or the t ran sm iss i

line, and the lum ped para m eter network, or PFN. By this m ea

the network is able to produce a pulse of extended width and f

1



rise t ime without an excessive length of l ine or numerous PFsta ge s. Th e com bin ed circu it is referred to as the hybridnetwork since i t is a combinat ion of two dissimilar network(Figure 1.1).

C ha pt er II beg ins with an introdu ction to tra ns m issi on linean d the effects of va riou s loads up on their disc harg e. Th is ch ap tinvestigates transmission line transient behavior by looking at tw

m eth od s of an aly sis. First , the wave prop agation of tra ns m issi olines is dis cu sse d with the us e of histo gra m s; secon d, the loainteract ions are presented wi th the use of the mathemat icaeq ua tio ns describ ing the line behavior. FoIIowing the discu ssio n transmission lines, the pulse forming network (PFN) is introduceChapter I I I , as an a l ternat ive to the d is t r ibuted parameter

tra n sm is sio n l ine. A series coup ling of the two ne tw ork s idis cu sse d in Ch ap ter IV. The hybrid netwo rk is introd uce d iC ha pte r V with specific em ph asis placed on the ch arac teristic s im ped anc e and pulse sha pe . Cha pter VI describes the laboratotest system used to evaluate the hybrid networks performance anto compare the laboratory measurement with the SPICE generatda ta . Final ly, con clus io ns and rec om m en da t ion s for fur theresearch are discussed in Chapter VII.



uO

C

•c

(U

t-l



C H A P T E R I I

TRANSMISSION LINE TRANSIENTS

In gen eral, the tran sm issio n line is com posed of distrib utpa ra m ete rs or co ns tan ts (Ku, 282) . The dis t r ibuted par am e

network, or transmission line, has many useful characteristics pu lse sh ap ing . An init ially charged lossless tran sm ission line pr od uc e perfect rec tan gu lar pu lses into a m atch ed load (Wils13). Th e w idth of th e pu lse formed by the tra ns m iss io n line isfunction of the transmission line's length, geometry, and the wvelocity in the dielectric m ateria l from whic h it is m ad e. Tim p ed an ce , Z^ , of the line is ind ep en de nt of th e leng th of l(Javid, 33 5). A dr aw ba ck to the tra ns m issi on line is th e excesslength of line needed to produce a pulse of only short duration.§

An init ially charged transmission line can produce perfect

re cta ng ul ar pu lse s into a m atch ed load, Rj^. Fu rth erm ore , t

amplitude of such a pulse is equal to one half the init ial charvoltage of the transmission line. Variations to the rectangular pucan resul t i f the load is undermatched or overmatched, a

§The length of 50 ohm coaxial cable needed to produce a pu

of SLX

m icro -sec on ds is 20 00 feet.



i l lu str ate d in Figu re 2 .1 . Th ese wave forms are the re su lt o

reflected waves which are generated at the interface between thload and th e l ine. The grea ter the load m ism atc h, th e longer

takes for the reflected wave to dissipate.

v(t)^ v(t),

2T(a)

2T

(b)

Figu re 2 .1 . Vol tage pu lse sformed by (a) undermatched, R^

< Z Q and (b) overmatched, R^ >Z Q loads.

Wave Propagation in Transmission LinesWave propagation in t ransmission l ines is generated by the

dis trib ute d pa ra m ete r ch arac teristics of the netw ork. In orde r

explain th e proc ess of voltage wave prop agation in a tra ns m issil ine, the distr ibuted inductance and capaci tance of the l ine arelumped together in small finite amounts as illustrated in Figure 2

If the resistance of the l ine is neglected, the l ine is considerelossless, an d only this case will be con sidere d. Altho ugh th

lumped equivalent circui t is a useful way of describing wav



propagation, the description below neglects certain characteristi

related to lumped elements (i.e., infînitesimal element values).

L1 L2 L3 L4 L5

aîlh-«lí5h-fllílÛ-r-^^C2; C3: C4; 05;

Figure 2.2. Lum ped equivalentcircuit of lossless transmissionl ine used to descr ibe thepro ce ss of voltage and cu rre ntwave p ropaga t ion in t r ans -mission lines.

Ln

mhQ i

Th e voltage sou rce , E, of Figure 2.2 is switch ed into the line

t=0. Imm ediately, curr en t will begin to flow thr ou gh ind uc tor Lan d into cap acitor C l . Elem ent C l begin s to charg e cau sing

cu rre nt to flow thr ou gh ind ucto r L2 and into capa citor C2. In similar manner, C2 charges causing the current to flow through Lan d th e seq ue nc e co ntin ue s down the line. Th is effect re su lts in

voltage wave traveling down the line at a velocity determined by tm ate rial pro per ties of the line. Acco m panying the voltage wave is

current wave which is related to the voltage wave by the

ch ara cte ris tics of th e line. In fact, the cu rre nt and th e voltage anot separate waves; they are merely different aspects of the samwave of energy (SkiIIing, 263).

Three circuits are examined to illustrate the effects of wavpro pag ation in a tran sm issio n line. First , an open ended , charge

line w ith a m atc he d resistive load at one end is analy zed. Next,

source is added to the open end of the charged transmission lin



7an d th e res ul ting effects are observ ed. Finally, the c ha ra cte ris ti

of a wave traveling from one transmission line to another line ofdifferent impedance are examined.

Charged Transmission LineA cha rge d tra ns m issio n line with a m atch ed load at one en

and an open circuit at the other end is the simplest case of charg

tra ns m iss io n l ine t ra ns ien ts . Provided the t ra nsm issio n l ine idisc ha rge d into a m atch ed load, i t will pro duc e an ou tp ut p ulsacross the load of pulse width 2T where T is the one-way travtime on the line and an amplitude of EQ/2 .

In order to understand how this pulse is formed by thet ra ns m iss io n l ine , p rop er t i es of wave prop aga t ion m u s t be

con side red . Figure 2.3(a) i l lustrate s the circuit in thi s exam plThe open circuit end of the transmission line is labeled as x=

wh ile th e load side of th e line is at x=d. Th e va riab le x m u s t bintroduced because the voltage and current waves on the l ine a

fun ction s of time an d dist an ce x. The leng th of the hn e is dan d it h a s a one-w ay trave l time of T. Initially, the line is ch arg e

to vo ltage E Q . Th e im pe da nc e of th e line is Z^ fí. Th e line terminated into a purely resistive load of R=ZQ.

At t=0 the switch is closed and the initial voltage is divide

evenly betw een t he load, R, an d the line at x=d. Pro pag ation of tfirst wave begins at this t ime, and it propagates towards the op

circu it end of the line. The wave h a s an am ph tu de of - E Q / 2 and is



x.O

Zo

Eo

(a)

^ .

x . d

R = Zo

8

0 < t < T

E

n

^ ' i k

;

(b)

X

v(u)

T < t < 2 T

2T < t < oo

v(t.d)

Figu re 2 .3 . H istogram of wavepropagation for a charged trans-mission line with a matched load atone end and an open circuit at theothe r en d. Light—Initial voltage,Medium--Resu l tan t wave , andDark--Propagating wave.



illu stra ted in Figu re 2.3(b) by the dark est sha de d area . Th e lighsh ad ed a re a in Figure 2.3(b) rep res en ts the initial charg e on thline, and the me diu m sha din g is the su m of the prop agated w aveAs the wave propagates down the l ine the net voltage seen acrothe l ine becomes E Q / 2 . At t ime t=T the wave en co un ters the opencirc uit end of th e line an d is reflected with the sam e po larity. A

the reflected wave propagates back down the l ine, the resultawav e be co m es zero, Figu re 2.3(c). Finally, at tim e t=2T the w aencounters the matched load, and the voltage on the l ine is nozero. Th e wav e is no t reflected at the load, an d the syst em relaxeFig ure 2.3(d). Th e voltage see n acro ss the load res isto r, v(t,d), ispulse of magni tude E Q / 2 an d pu lse wid th 2T. This ou tp u t wave

form was determined by observing the change in voltage at x=(i.e., v[t,d]) du rin g wave pro pag ation . The o ut p ut voltage is sho win Figure 2.3(e).

Ideal Voltage Source at Sending End ofTransmission Line

In the following example, the open circuit end of the charge

line is rep lace d w ith an ideal voltage so ur ce . The voltage so ur c

appears as a shorted line to the propagating wave and will result

a reflected wave of opposite polarity to that of the incoming wave.

Th e circ uit (Figure 2.4[a]) is a ch arg ed tra n sm is si o n line o

len gth , d, im pe da nc e, Z^, an d one-way travel time, T. At one en

of th e line, a m atc he d resistive load is con nected th ro ug h a switc



Es.

x = 0

Zo

Eo

(a)

^ .

x = d

R = Zo

10

T < t < 2 T

2 T < t < oo

v(t.x)

Eo -

0 < t < T 0 .m nmmm

(b)

v(tP()

Eo -

^j.l.WJJ.ÛAiA'.i.HJJ.Ij.SMA^'Ai.'jAîM'.W^^

(c)

v(U)

(d)v(t.d)

E o -

I I I I I / / I tT 2T

(e)

Figure 2.4. Histogram of wavep r o p a g a t i o n for a c h a rg e dt r a n s m i s s i o n l in e w i t h amatched load at one end and anideal voltage source at the otherend . L ig h t - In i t i a l vo l t age ,Medium—Resul tan t wave , and

Dark—Propagating wave.



11The switch is closed at t=0, and on the sending end of the lin

x=0, there is an ideal source of voltage Eg = E Q .

A wave of m agni tud e E Q / 2 begins to propagate towa rds thse n di n g en d of th e line w he n the sw itch is closed. Figu re 2.4il lustrates the propagation wave with a dark shading. The initvoltage and resulting wave are represented with the l ighter am ed ium sha din g, respectively. W hen the propa gating wave rea c

the voltage source at time t=T, the wave reverses polarity and reflected. As the wave mo ves ba ck down the l ine, the res ultivoltage across the l ine becomes that of the voltage source, E(Figure 2.4[c]). The stea dy -sta te cond ition is ob taine d w he n twave reaches the receiving end of the line (the load end), thvo ltage ac ro ss the line is onc e again E^ volts (Figure 2.4[d]). T

output voltage wave form observed across the load is shown Figure 2.4(e).

Two-Section Transmission LineThe final case illustrates that the waves are not only reflecte

b u t are tran sm itted in some insta nc es. Two relations are neede d

des cribe the tran sm iss ion a nd the reflection of wave s pro pag ati

down the l ine. The two needed equatio ns are:

(2.1)^ o ^L ^ 'ô

andVi Z , - Z ^

(2.2)

Tt

Tr

=

=

VVo

V l

Vo

=

=

2 Z L

Z L + ZO

Z L - Z Q

Z L + Z Q '



12

w here Z ^ an d Z^ are the line imp edan ce. From equ ation s (2.1) (2.2) it is n ot ed t h a t at a Ju n ct io n of two line s of differeimpedance there will be a reflected wave and a transmitted wave

Th e circuit use d for thi s analysis is show n in Figure 2.5(a). Tcircui t consists of two series connected transmission l ines

impedances Z^ an d Z^. Ea ch line is of length d / 2 w ith line 2 beingco nn ec ted to the m atc he d resistive load R (i.e., R^Z ^). Bo th li

have a one-way transit time, T, and are charged to a voltage E^.At tim e t=0, line 2 is switched into the load an d a wave, W^,

magn i tude E Q / 2 begins to propagate towards line 1, Figure 2.5(b).

When the wave reaches the right end of line 2, part of the wavetransmitted down line 1, W^, and part of the wave is reflected bto w ard s th e load, W ^, as sho wn in Figure 2.5(c). This reflection

d ue to th e different imp ed an ces of the lines. After the switch hbeen closed for t=2T seconds, wave three, W^, reaches the end

line 1 an d is reflected bac k; while at th e sam e time, wave two, Wre ac he s th e load an d is dissip ated. The reflected wave from t

en d of line 1, W ^, is reflected w ith the sa m e m ag ni tu de a nd signth e forward going wave as see n in Figure 2.5(d). W hen wa

four,Wj^, reaches line 1 at time t=3T seconds, part of the wave itransmitted down the l ine where i t will be dissipated by the loaan d p ar t of th e wave is reflected ba ck tow ard s the open end of l

1. Th is pr oc ess co nti nu es indefinitely unti l a ll the energ y diss ipa ted in the load. Finally, the ou tp ut seen acr oss the loa

v(t,d) is fllustrated in Figure 2.5(e). This output is characteristic



2T < t < 3T

Z1 Z2

Eo

x = 0

v(t.x) ^

Eo.

(a)x>d

0 < t < T 0wi • . • . ^ . . . . • . ^ . . • . < ^ —

(b)

v(t.x) ^

Eo.

T < t < 2 T 0

w3SSSÍ'-.îv. x i f- •• .. .• •í, N •. ••^ ••X\V /v. ( •.V•^•Ã-Í :sS$ -. : u-.i.0.i.i.0.n.ti I n i 11 m i i 11 n i i f i ii fi ri a

w2

(c)

v(t.d)

E o -

^m^^^Mgí"v::;.''::'':<;;::;;::;;2T 3T

(e)

Figure 2.5 . Histog ram of wavepro pa ga t ion of two cha rgedt r a n s m i s s i o n l i n e s a n d am at ch ed load. Light- - In i tia lv o l t a g e , M e d i u m - - R e s u l t a n twave , and Da rk- -P ropa ga t ing

wave.

13

R = Z2



14the output response of two l ines of unequal impedance connecin series.

Analytic Solution of Charged Transmission LineEquations

The general solution of the charged transmission line equati

w as solved analytically. The equ ation w as solved us ing L aplatransform analysis (Ku 286). The first step in solving for the out

pulse solutions of a charged transmission line began by determinth e ge ne ral so lutio n of th e l ine eq ua tio ns . A sm all sectio n tra ns m iss io n line is illustrated in Figure 2.6. Let

R = resistance per unit length of line,L = inductance per unit length of line,

G = conductance per unit length of line,C = capacitance per unit length of line (Ku 283).

i — •; i

1 v Ax

i +

i

' v +

3i/3xAx

i ;

3v/3xAx ;

^ ;

Fig ure 2. 6. Sm all sec tion oftransmission line used to derivethe genera l solut ion of acharged transmission l ine.





16= V L C S = (38. Differentiating eq ua tion (2.6) w ith re sp ec t to x ansu b sti tu tin g into equ ation (2.3) yields

3Î(S,x) r^ • ^^âV(S ,x) or re ^ ío ft^- —^^r~ = l ^ + ^ ~d^ — = YÎ(S,x) (2 .8)

w he re Y=a+jP is the propag ation co nsta nt of the line. The g enesolutions of equations (2.7) and (2.8) are of the form

V(S,x) = AjeTx + Bê-TX (2.9)

I(S,x) = AêTX + Bê-Yx . (2 .10)

For a charged transmission line the initial voltage is equal to

ever^rwhere on the line for time t = 0, that is,

V(0.X) = EQ. (2.11)

Furthermore, the initial current flow at time t = 0 is zero, that is.

i(o,x) = 0. (2 .12)

Modifying equations (2.4a) and (2.4b) and taking the Lapla

transforms gives

^ ^ T l = SV(S,x) - v(0,x) = SV(S,x) - E Q (2 .13)

Í : [ ^ ^ ] = S I ( S , X ) . (2.14)

Equations (2.7) and (2.8) become

^^J^f' '^ = 72v(S,x) - (R + LS)Cv(0,x) (2 .1 5)



a | : X ) = , 2 i ( s . x ) . C ^ . ( 2 . 1 6 ) ' '

Since v(0,x) is a co nsta nt, C ^ ^ ^ ^ = 0.

For a lossless tra ns m issi on line, the line eq ua tion s red uc e to

^ ^ g l = p2 s2v (S,x ) - p2SE o (2.17)

^ ^ g ^ = p 2 s 2 l ( S , x ) . (2 .18)

Equations (2.17) and (2.18) have the general solutions

V(S,x) = A ê ^S x + Bê-J^Sx + ^ (2.1 9)

I(S,x) = - y ^ ^ - A i e ^ S x + Bê-J5SxJ . (2.20)

Equations (2.19) and (2.20) are the general solutions of thlossless, charg ed tran sm issio n line. The solutions to the circu

in the following examples were obtained by using equations (2.

and (2 .20) and the boundary condi t ions associa ted wi th eac

circuit .

Non-Ideal Voltage Source at Sending End ofTransmission LineIdeally, a voltage source has no intemal resistance and, often

not considered in circui t analysis ; however, ideal s i tuat ions

ge ne ral do no t tell th e com plete story. For thi s rea so n the so luti

of the charged transmission line with a non-ideal voltage source

ad dr es se d. The solution of the netw ork of Figure 2.7 sho uld g



18th e rea de r som e ins igh t in to th e effec ts of the no n- i de a

considera t ions .

Rs Zo

r-AAA^ ;Eo R

x=0 x=d

Figu re 2. 7. Non -ideal voltagesource at sending end of acharged transmission line.

The line in Figure 2.7 is a charged transmission line with resistive load at the receiving end and a non-ideal source at tse n d in g en d. Th e switch at th e receiving end is closed at t=

Letting the length of the transmission line be d, the followiboundary conditions exist:

V(0,x) = E Q (initially charged hne)

I(S,d) = p , an d (Oh m's law at th e receiving end)

1(0,x) = 0. (no initia l cu rr en t flow)In order to solve the general transmission line equations (2.1

and (3 .20) , the boundary condi t ions a t the sending end ar

req uir ed . Nodal ana lysis at the sen din g end yields:

5 M ^ - ^ = I ( S , 0 ) . (2.21)



19

By set tin g x= 0 in equ atio ns (2.19) and (2.20) and su bs titu tin g int

eq ua tion (2 .21), the following relation is obtained.

n:5,uj - 2 Q ^ i + Z O ^ l - SR S R S • RS SRS • (2.22)

From equation (2.20), the relationship for A and B^ is given by

Ai =

E -E o /J_ J_^SRs "^l Zo"^Rs

í ^ - —\^Rs Z o

(2.23)

Th e ot he r e qu at io n re latin g A^ to the netw ork is foun d from the

se co nd boun da ry cond it ion I(S,d)R = V(S,d). From this B^ wa s

found to be

Bi =^ + A i e S T ^ ^ + l

e-STfA. il^Zo

(2.24)

Th e co effic ients A^ an d B^ we re simplified by con sid er ing th e ca s

of a matched load (i.e. , R = Z Q ) . For a m atc he d load, A^ and B^

become:

^ l - " 2

Bi =

Eo e-sTS

Rx ZoJ

Rx "^ZÔ

/ E - E oSRx \Eo e-ST

(2 .25)

(2.26)

yR x Z o

Substi tuting equations (2.25) and (2.26) into equation (2.19) an

taking the inverse Laplace transform results in the t ime domain

equation for the voltage seen across the load (i.e., v[t,d]).



v(t,d) =E o E - Eo ,, ^ , / Zo - Rx \Eo , ^^ ,2 0

(2.27)

where u(t) is the unit step function.

Figure 2.8 shows a plot of the receiving end voltage versus timfor the case when E = E Q . A S the source resistance approaches zero,the output is that of an ideal voltage source at the sending endSimilarly, as the source resistance approaches infinity the outp

se en at th e receiving end is th at of a single charg ed tra ns m iss ioline. As a re su lt of eq ua tio n (2.27) an d Figure 2. 8, th e effect oconsidering the source resistance is seen to have a significant effeon the output of the system.

v(t.d)

Eo -

Rs = 0

l^Rs = Zo

^

I I I I ^TJ^T 2T Rs = «» 3T

Figure 2.8 . O ut pu t resp on se ofcharged transmission l ine witha non-ideal voltage source at thesending end and a matched loadat the receiving end.



2 1Charêd Capacitor at Sending End ofTransmission Line

Inform ation on the syste m res po ns e w as acq uired from th

so lu tio n of eq ua tio n s (2.19) an d (2.20). Th e eq ua tio ns are solv

for a charged transmission line connected to a charged capacitor

the sending end and a matched load at the receiving end (Figu

2.9).

Ro = Zo

x=0 x=d

Figu re 2.9 . Circu i t us ed incalculat ing the output responseof a charged transmission line.

The c i rcui t i s composed of a charged t ransmiss ion l in

connected between a matched res is t ive load and a chargecap acito r, Figure 2.9 . At t=0, the charged tran sm issi on line a

cap acito r co m bin ation is switched into the load. Letting the l ileng th be d, the bo un da ry conditions describing the circuit are

V(0,x) = Eo ; (initially ch arge d hne)

I(S,d) = p ; an d (Ohm's law at the receiving end)

l(0,x) = 0 . (no initia l cu rr en t flow)

Another important boundary condit ion is the current at the send

end for all time t, (i.e., I[S,0]). The sending end current is found





Taking the inverse Laplace transform of equation (2.34) obtains tt ime domain response of the output.

E o E o í -(t-2T) ^v(t.d) = -j-u ^t) + -2 l2 e cz . i) u(t-2T) . (2.3 5)

Figure 2.10 shows the results of equation (2.35) plotted againt ime. E qu at io n (2.34) w as plotted for Z = 50Q , C = IF an d T = .62sec on ds. The ou tp ut rep rese nts a t jîcal RC decay delayed by th

one-w ay tra ns m iss io n time of the line.

LC Section at Sending End of LineThe capacitor in the previous example was replaced with a

series inductor-capacitor combination (Figure 2.11) and the outpu

23

i i i i i i i i i i i i i i i i i i i i i i i i n m i M i i i i i i i m i i i i i i i i i i i i i m n i i m i i i i i i i i i i i i i i0 .0 0 0 .63 1 .25 1 .88 2 .50 3 .13 3 .75 4 .3 8 5 .00

Time in microseconds

Figu re 2.1 0. Plot ge ne rate dus in g equ ation (2.4). Ch argedsen din g end capacitor. C = IF,T = 0.625 sec, R = 50fí .



24

» Zo

VC: Eo Ro = Zo

x=0 x=d

Figure 2 .1 1 . Circui t us ed in

de te rmin ing the ou tpu t waveform of a charged transmissionline.

w as obse rved . AII th e bo un da ry con ditions for the circuit of Figu

2.9 hold for the circuit of Figure 2.11 except for the relation at t

receiving end current, I(S,0).

Applying Kirchoff s Voltage Law ar ou nd the send ing end loop

circuit (2.11) results in the foUowing expression:

- í ^ j i( t)d t + L - ^ - Vc(0 )j = V(t,0) .

The Laplace transform of equation (2.28) producesd(S,0) . rr^^rr^ r. . VC(0)A

(2.36)

V S,0) = - ^. LSI S, 0) - ^) (2.37)

As before, sett ing equation (2.30) equal to equation (2.37) and

reducing yields

n \A i + B i = - ^ ( - A i + B i ) ( ^ + L SV

(2.38)



2 5

Solving for A^ and B^ in equation (2.37) by substituting in thb o u n d ar y relatio ns given previously, yields

/

Eo EoV(S,d) = 2S • 2S

S 2 - ^ LCS2 + Sf+T7.

V L LCy

e-2ST , (2.39)

for th e voltage at th e receiving end. For the critically da m pe d cas

taking the inverse Laplace transform ^nelds the solution in the timdomain,

. z(t-2T)x

l - ^ ( t - 2 T ) e ' ' ^, ,. E o Eov(t,d) = 2 - ^ u(t-2T) (2.40)

Equation (2.40) is plotted against time and is shown in Figur2. 12. Th e va lues for Z, L, C, an d T where ch os en as 10 Q, 50 n2 îF, an d 10 |is, respectively.

It has been shown for the case of a charged transmission linwith a matched load at one end that the output pulse is clearlde pe nd en t on the netwo rk at the send ing end of the l ine. Iaddit ion, when the l ine is terminated into an overmatched o

u nd er m at ch ed load, the ou tp ut is also affected. The solu tions the boundaiy value equations were used to verify that the chargetransmission line acts as a delay between the sending end netwo

and the load.



26

10 20 30 40 50 6 0Time in microseconds

100

Fig ure 2.1 2. Plot ge ne rate du s i n g eq ua t io n (31). LCnetwork a t sending end oftr an sm is sion line. L=50 îH, R= 10 Q, T=10 (is ec , C=2 ^Fand Eo=200 v.



C H A P T E R I I I

PULSE FORMING NETWORKS

The pulse forming network, PFN, is a lumped parameteequ ivalen t of the tra ns m issi on line. Pulse forming netw ork s

com posed of nu m er ou s s tages of indu ctors and capaci tors . Aadvantage of the PFN is the duration of the pulse which can achiev ed. However, the PFN h as one major disadva ntag e, the p ush ap e . Specifically, th e rise time of th e PFN h a s a finite limw h i c h i s g o v e r n e d b y t h e c o m p o n e n t s c h a r a c t e r i s t i c sF ur th er m or e, the ge neral sh ap e of the pu lse (i.e., overshoo t ) is desired (Cook, 4).

The Tvpe 'C' Pulse Forming NetworkA transmission line can be modeled using a lumped parame

ne tw ork w ith the disa dv an tag e of its sh ap e (Wilson, 13). A typePFN is i l lu stra ted in Figure 3. 1 . The type 'C' netw ork is th

bu ildin g block from which all the othe r netw ork s are derived. Ttype 'C' ne tw or k is com prised of several sec tion s, eac h of w hrepresents a single term in the Fourier series of the pulse i t desig ned to sim ula te. For all pu lse forming netw ork s, the rise tof th e o u tp ut pu lse is determ ined by the n um be r of section s of

27



28PFN. Th e va lu es for th e indu cta nc es , L^^'s, an d ca pa cita nc es, Cj^for the type 'C' PFN are determined from the Fourier coefficientbj^'s, of th e desired pul se sha pe . Table 3.1 gives the F ourie rcoefficients, b^^'s and th e L's an d C's for a sq ua re , trapezo idal anflat top pe d pu lse with parabolic rise and fall. In addition , Figu re 3sho ws how m an y sectio ns are needed for a PFN to have a given ritime to pulse width ratio depending on its designed pulse shape.

Ll

C i

L3

C3

L5

C5

Ln

Cn

Figure 3.1. Type 'C' network ofn sec tion s. The second Fosterform.

Th ree var iable s m u st be defined for us e in Table 3 .1 . Thethree variables are the characteristic impedance of the network

Z , th e w idth of th e pu lse pro du ced by the network , t. an d th

ra tio s of th e rise time of the pu lse to the total pu lse width , aFrom this information each element of the type 'C' network can bdetermined for any one of the three pulse shapes given in Tabl3.1 . Ap pen dix A co nta ins the com puted valu es of the se coefficientIt is noted here that the type 'C' network is equivalent to th

Second Foster Form.



Ta ble 3 .1 . V alu es of b^^'s L^^'s an d Cj^'s for the typ e 'C'network of Figure 3.1 (Glasoe and Lebacqz, 192).

29

Wavform bn 's L's C s

Rec tangu la r _4_n

Znt4

4 Tn ^ Z n

Trapazoida l 4 ^ sl n (nTta) ^nn \ nm. )

Z n t

Ísin InTtaJ \nTia )

4 T sln(n7ta)rAî Zn nîca

Flat top andparabol icrise and fall

4.n7c)

/ ,n j ia . s2' 'sln (-5-)^njia

Zn t4 T

/ n7ta,s2

sinnjca^

The Tvpe 'A' Pulse Forming NetworkThe Type 'A' network (Figure 3.3) is derived using Foster'

R ea cta nc e Th eo rem (Glasoe an d Lebacqz, 200 ). By writing thadmittance function for the network of Figure 3.1 and invertinthe equivalent impedance function, Z(s), is obtained,

f l (LnCnS' +Z(S) = n=l

n n (3.1)I CnLn n (LmCniS^ + 1)n=l m = l 5 * n

where n = 1,3,5.... an d m = 1,3,5 Only the odd ha rm on ics are

nee ded be ca us e the pu lse wa s defined as an odd function. Parti

fraction expansion of Z(s) results in the impedance function for t

network shown in Figure 3.3. The partial fraction expansion of Z

can be written as



I

Square Pulse Shape

6 7 1Numbar o( StagM

12

(a)

Parabolic Pulse Shape

Nunbar ol StagM

(b)

30

Trapazoldal Pulse Shape

I

Numb*r ol Stag**

(c)

Figure 3.2. Number of stagesversus rise time of a PFN with aSquare (a), Parabolic (b), and a

trapezoidal pulse shape (c).



Cn

4L2 L4 L2n-1

«1 «1 «1 Ln

-mC2 C4 C2n-1

Figu re 3. 3. Eq uiv alen t Type 'A'network derived using Foster 'sReactance Theorem.

3 1

2n-2

Zp(S) = 'oBjjS + 1

n=2

+ A2nS . (3.2)

where Zp(S) is the partial fraction expansion of Z(S). The Aj^'s aBj^'s are the zeros an d poles of eq uatio n (3.1). Th e va lue s of Cjsj,

L2n» ^ d th e fîltering elem ents are given by

C]vj =A o '

^ n - -^^n •

L = Aj and,

B,^ n - An

n

(3.3a)

(3.3b)

(3.3c)

(3 .3d)

The values of C^ and L^^ make up the fundamental component of

th e o ut pu t pu lse. The resultin g ou tpu t from this configuration is

pulse of finite rise and fall times.

As before, the network of Figure 3.1 is determined by th

F ou rie r coefficients of the des ired wave sh ap e. In fact, ea c

element can be determined by the following two formulas:



32

Ln = r i t ^^ ^^

Cn = H ^ (3.5)

where ,

n = n um b er of sectionsZn = PFN impedance

t = pulse widthb n = Fo ur ier coefficients.

Once the values of the network of Figure 3.1 are determined, thequivalent Type 'A' representation can be found.

The Tvpe 'E' Pulse Forming Net^vorkBy using a combinat ion of network synthesis techniques, th

type 'E' PFN can be obtained from the type 'C'; however, in mocases the t^ê 'E' PFN is designed from an approximation metho(Glasoe and Lebacqz, 204). Th e type 'E' PFN is desirab le bec au se its sim plicity an d ease of co ns tru ctio n. AII th e ca pa cito rs of th

type 'E' are of equal value and the inductance of the PFN is obtainfrom a single soleno id. Since the type 'E' PFN w as us ed a s thlaboratory test system for this experiment, a detailed discussion its design is given in Appendix B.



3 3Other Types Of Pulse Forming Networks

It was seen in the previous section that the type 'A' PFN wa

der ived us ing Foster ' s Reactance Theorem on the impedancfunction of the network of Figure 3.1. Two more networks can b

derived from this impedance function using Cauer 's extension Fo ster 's rea ctan ce theore m . Both Ca uer forms are characterized

lad de r ne tw or ks . The First C au er Form , den oted as a type 'Bnetwork, is obtained from a continued fraction expansion of th

im pe da nc e funct ion of the network of Figure 3 .1 . The Seco nCauer Form, denoted as a type 'F' network, is formed by a continufraction expansion of the admittance function of the same networ

Bo th ne two rks are conical, th at is , they have the sam e nu m be r ele m en ts (Figure 3.4). Figure 3.5 gives som e useful ra ng es o

impedance and pulse width for f ive types of pulse formingne tworks .



L l-mC2

L3

C4

34L5 Ln-1

C6

(a)

C n

Cl C3

\{ r-\^L2XX

L4

i

C5

T6

Cn-1

X.--1

Lnr(b)

Figure 3.4. Equivalent networksderived by continued fract ionexpansion of the impedance andad m it tan ce funct ions of thenetwork in Figure 3.2. The FirstCauer Form or Type 'B' PFN (a).The Second Cauer Form or Type'F ' PFN.



35

5T5

C L

o

T3C L )

6S

coX5CoocooS-i

o

5

03

Uo

'O<u

- 0

c

cu( 4 - 1Oco(Ucn

o

co(D

ã

ocopl OCOoU4

srnno uî aouBpaduii



C H A P T E R I VSERIES CONNECTION OF A TRANSMISSION

LINE WITH A PULSE FORMING NETWORK

A charged transmission line was connected between the pu

forming network and the load, and the output voltage responsethe series PFN-transmission l ine combinat ion was s tudied usSPICE. Va riations include ch ang es in series ind uc tan ce and sh

cap aci tan ce. Th e re su lts gen erated by SPICE were com pared wthe laboratory m eas ure m en ts . Al though the ser ies comb inat i

was inferior to the hybrid network, the series work was useful understanding the output behavior of a distributed network wheis connected to a circuit composed of lumped elements.

Th e PFN w as a ni ne -st ag e type 'E ' GuiIIemin ne tw or(Appendix B), which produced a 6-microsecond pulse into

m atc he d load of 50 oh m s. The tran sm issio n line w as conn ected

th e p u ls e forming netw ork via a BNC coaxial co nn ecto r. Top er ati ng voltage of th e sy ste m w as 100 vo lts. The PFN atra ns m iss io n line were reso nan tly charged at the sam e t ime.

m erc ury wetted relay w as use d as the switch. Figure 4.1 i l lustrathe circui t arrangement.

36



37The system prod uce d a poorly sha pe d pulse at the load. Th

o u tp u t puls e h ad th e fast rise t ime of the tran sm issi on line, bu

there was a discontinuity in the output pulse produced by the serco m bin atio n of the PFN an d trans m issio n line. A SPICE plot of t

M M M M M M M MMercury

Relay

- rCI-T-C - rC - rC- i -C - r-C - i -CN+

-i=C9

TransmissionLine rtL

0

JFigure 4 .1 . PFN and t ra ns -m i s s i o n l i n e i n s e r i e s

combination.

ou tp u t pu lse pro du ced by the system is show n in Figure 4.2 . Th

o u tp u t pu lse ha d two dist in ct pa rts : f irst , the sq ua re pulse

produced by the transmission line; and second, the pulse formed

th e PFN. Th e disc on tinu ity in the ou tp ut wave form app eare d

the instant the t ransmission l ine pulse had subsided and the PFbegan to discharge.

Junction Filtering

Junction filtering involves a change in a signal resulting from

change in a series system introduced at the interface between th

syste m elem ents. Co m pon ent cha ng es here were m ade only at th



38

120

1 0 0 -

o>

O>"Oao

Tlme (microseconds)

Figu re 4.2 SPICE ge ner atedoutput of the ser ies combi-nation.

interface between the PFN and transmission line so that the init i

rise time of th e tra ns m iss io n line w as no t affected. N um ero us Lfiltering procedures were investigated including parallel LC filte

an d LC Tee netw ork s. In the u se of LC fîlters, it w as hop ed th at tgli tch or discontinuity of the output pulse would be reduced o

filtered to a desirable level, less than five percent of the designatou tp ut. The var iou s fil tering sch em es were evaluated first th roua SPICE sim ulation , the n tun ed with additional mo deling. W hen

scheme appeared suitable, i t was completed in the laboratory.



3 9Th e LC filters were developed sequ entially . Th e re su lts o

inserting a series inductor between the PFN and transmission liwere exam ined. Th en a sh u n t capa citance wa s adde d to the seri

ind uc tan ce and the outp ut pulse was examined. A T-network wde sig ne d for ad di ng a seco nd series ind uc tor . The effect on th

output of a single series capacitor, and for an uncharged shuncapacitor were then considered.

Series Inductance

In order to observe the varying effects of the output responsof the system, the value of the series inductance between the PF

and transmission line, that is, the fînal inductance stage in the PFw as varied in the SPICE mo del. The ou tpu t respon se w as observ

for in du ct an ce va lue s of 4, 6, 8, 10, an d 16 m icro he nry s. Theffects (Figure 4.3) of reducing the inductance were:

1. An ini t ial overshoot fol lowing the t ransmission l ined i scha rge became more p ronounced a s t he induc tance wareduced;

2. an d as the ind uc tan ce wa s red uce d, the rise t ime of the

pulse foUowing the transmission line discharge became shorter.The discontinuity in Figure 4.3 between the two discharged

pulses appears to be less prominent as the inductance is decrease

however, this effect is a result of the number of points plotted bSPICE. In actuality, the point of discon tinuity betw een the p uls

go es identic ally to zero . Sim ilarly, if the rise tim e of a PFN pu lwas observed, without the added transmission l ine, the viewe



40would also see an increase in rise time of the output pulse as tend inductance was decreased.

160 —

140

120 _

100

80 .

80 .

*0 .

2 0 . ,

0 .51 0 .88 0.98 1.11

Tlm* In MieroMcond*

Figu re 4 .3 . SPICE o ut p u t

generated by varying the endinductance of the PFN, junctionin du cto r. Th e plo ts are forinductance values of 4, 6, 8, 10,and 16 microhenrys.

Shunt Capaci tance

A shunt capaci tor was added to the last s tage of the pulse

forming netw ork on th e o u tp ut side of the final ind uc tor. Thcap acitor was varied in valu es of .5, 5, and 15 na no fara ds. Figu

4.4 sh ow s th e ou tp u t pu lse predicted by SPICE. Th ree effects w e

observed (Figure 4.4).

1. At time t=2T, th e voltage oversho ot dec reas ed as th e valu

of the shunt capacitor was reduced.



4 12. The un de rsh oo t w as increased as the value of capa citanc

was reduced.

3. Th e t ime co n st an t of the deca y from the ov ersho ot

increased as the capacitance was decreased.

Load

V0Itage

200 j

180 -•

160 ••

140 -•

1 2 0 • •

100 -r

80 -

60 •

40 •

20 -

0 i i in i i i i i i t iMii i i i i i t i i i i i i i in i i i i i i i i i i i i i i i i i i i immii i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i0 0.135 0.285 0.435 0.585 0.735 0.885 1.035 1.185 1.335 1.485

Tlme In Mlcroseconds

Figure 4.4 . SPICE gen eratedou tp ut pu lses at the load. Thecurves are for .5, 5, and 15 nfvariations in shunt capacitor.

These can be partially explained by considering the magnitu

of th e cap ac itan ce . Th e overshoot in the c ur ren t will be sm all if

capacitance is small; and for a given resistive load, the overshowas decreased with a decrease in capacitance, that is, a smaller R

discharge t ime.

Single T-NetworkBy add ing an add itional ind ucto r to the s h u n t capa citor, o

single T-network, i t was hoped the gl i tch would become le





4 3In effect, the added T-network accomplished the goal of

ad di ng an o th er stag e to the PFN. As expec ted, the pu lse wid th the PFN was slightly increased along with a faster rise t imeF u rth er m or e, as the rise t ime of the PFN w as incr ease d thdiscontinuity became less pronounced.

Laboratory ResultsAII th e me as u re m en ts p rese nted in this section of the repo r

were m ad e on the test system. The ph otog raph s were generatewith a Tektronix oscilloscope and one-megohm input amplifie

Voltages were measured with the Tektronix P-6006 probe.

Shunt Capaci torThe first effects to be tested in the lab were the change in

sh u n t cap acita nc e. As show n earlier with SPICE, the res ult s ha d ini t ial vol tage overshoot af ter the t ransmission l ine dischargfoUowed by an exp on en tial decay in voltage . In the labo ratory , tw

ca ses were exa m ined . Firs t , with a sh u n t cap aci tan ce of onnanofarad, then, with a 56-nanofarad capacitor.

Case IWith a one-nanofarad shunt capacitor, the output pulse (Figur

4.6) dissipated an initial overshoot with a fast decay following t

t ra ns m issi on l ine discha rge. At the end of the t ran sm issio n l in

disch arge , the ou tp ut voltage ju m p s to 120 volts. One hu nd re d a

twen ty na no sec on ds later, the outp ut voltage drop s to 45 volts. D



44to the fast decay after the voltage overshoot, the PFN was unable tdischarge completely.

Horizontal:Vertical:

200-nanoseconds20 volts

Figure 4.6 . Photograph of theload voltage pulse with a one-nanofarad shunt capacitor.

Case IIThe shunt capacitor was replaced with a larger capacitor of

valu e 56 nanofarad s. By increasing the sh un t capacitance, it wasseen that the decay time following the peak overshoot alsoinc reased . The inc rea se in the deca y time allowed the PFN torea ch its desig ned outp ut, Figure 4.7 . The deca y time w asm ea sur ed to be 70 0 na no sec on ds, or approxima tely 5 50nanoseconds slower than the rise t ime of the pulse forming

network . Sinc e the PFN was given enough time to discharge , the



45undershoot following the voltage overshoot did not occur.Furthermore, the increase in voltage following the transmission

line discharge occurred as predicted.

Horizontal:

Vertical:

200-nanoseconds

50 voltsFigure 4.7 . Photograph of theload voltage pulse with a 56-nanofarad shunt capacitor.

Single Tee

Measurements for the Tee configuration were made for onlyone case, a shunt capacitance of one nanofarad and a seriesindu ctan ce of 4.5 microhenrys. Figure 4.8 shows the outpu t voltagm easure d ac ross the load. The observed characteristics were:

1. A fînite rise time reachin g the peak overshoot followingtra nsm issio n hne discharge. The rise time wa s m easure d at 40

nanoseconds.



4 62. A sm aller am ou nt of voltage overshoot th an th e case of

single sh u n t. Th e overshoot wa s 20 volts as com pared to 30 vo

for the shunt case.3. Th e sa m e am o u n t of voltage dro p following the ove rshoot.

4 . Th e w idth of the d isc on t inu i ty dec reas ed from 34 0nanoseconds, Figure 4.6. to 250 nano-seconds, Figure 4.8.

The resul ts were s imilar to those obtained in the SPICEsimuIaU on except for the small am ou nt of un de rsh oo t imm ediatefollowing th e dis ch arg e of the t ra ns m iss io n l ine. Th e ini t iaundershoot was probably caused by the induc tance of thetransmission line switch connection.

Horizonta l : 200-nanosecondsVe rtical: 20 volts

Figure 4.8 . Ph otog raph of theload vo l tage wi th a one-nanofarad shunt capaci tor and a4.5-microhenry series inductor.



4 7Line Length Variations

The length of the transmission line between the PFN and theload had a strong effect on the m agnitud e of the d iscontinuity.Three different lengths of line were tested: 192 feet with a one-watravel t ime. T, of 28 8 nano seco nd s; 40 0 feet with T = 60 0nanoseconds; and 791 feet with T = 1.1875 m icroseconds. As thelength of transmission line was increased, the undershoot of thediscontinu ity diminished . This wa s the result of los ses in the line

Measurements, in this case, differed from the predictions of theSPICE sim ulation. Figures 4.9 , 4.10 , and 4.11 sho w the effects olengthening the transmission line, and Table 4.1 summarizes the

results of all the measurements.

Horizontal: 200-nanosecondsVertical: 50 voltsFigure 4.9 . Photograph of theload voltage v^âth 192 feet ofline, T=288 nanoseconds.



48



Figure 4.1 0. Pho tograp h of theload voltage with 400 feet ofline, T=600 nanoseconds .



Figure 4.11. Photograph of theload voltage with 791 feet of

line, T= 1.1875 microseconds .



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C H A P T E R V

THE HYBRID NETWORK

In C ha pt e r II the d i s t r ib u ted p ara m ete r ne tw ork w aintroduced and i t was shown that networks of this type c

produce perfectly rectangular pulses into matched resistive loaOne d i sad va ntag e of the d i s t r ibu te d pa ram eter ne twork ,

tr an sm is si o n line, w as th e excessive len gth s of l ine nee ded produce pulses of only a veiy short duration (i .e. , nanosecond p

w id th s ) . C ha p t e r III r ev iewed the lum pe d equ iv a l enrepresentation of the transmission line, the PFN, and it was shothat long pulse widths of hundreds of microseconds could

ach ieved w ith only a few LC sec tions . Again, however, the e xtenpulse width was gained at the expense of the pulse shape, m

specifically, the rising and trailing edges.

This chap te r in t roduces a ne twork which combines bo t

prev iously m en tion ed netw ork s. The extend ed pulse wid th of PFN is combined with the fast r ise t ime of the transmission li

The resulting pulse shape has the pulse width of a PFN and the

t im e of a tra ns m iss io n line. Th e ne tw ork is called th e hyb r

network since it is a development of two dissimilar networks (i

the distr ibuted and lumped parameter networks) .

5 0



5 1Parameters Affecting Pulse Shape

Th e hy brid netw ork is sho w n in Figure 5 .1 . The hyb ri

network consists of a transmission line in parallel with a pulforming netw ork . Both netw ork s are charge d to the sam e volta

an d th en d isch arg ed into a resistive load. In gen eral, the PFimpedance is matched to the impedance of the resistive load, R

How ever, th e impedam ce of the line is ch ose n to be sma ller t hthat of the load so that i ts discharge response is analogous to

over-damped RLC network.A typical output response of the hybrid network is shown i

F igure 5 .2 . The ou tp u t h as th ree d i s t inc t fea tu res : theinstantaneous rise time, A, the initial overshoot, B, and the init

un de rsh oo t , C. Fu rthe rm ore , the chara cter is t ic pu lse sh ap e oflumped parameter network is a lso not iceable ( i .e . , r ipple)

Therefore, the desired pulse shape is achieved.Although a s imilar pulse shape can be obtained by using

capacitor as the last stage of a PFN, the initial overshoot will be ch ar ge d voltag e of th e ca pa cito r (refer to C ha pt er IV). Up odischarge this overshoot will be twice the voltage of the pul

delivered by the PFN. By usin g a tran sm ission line, the imp edanof the l ine can be varied thus changing the init ial overshoot se

across the load.

The interaction of the distributed network and the PFN is be

des cribe d by looking at the o u tp u ts of each netw ork. A typic



PFN

-a line>

Switch

Load

Figure 5. 1. The hybrid pulseforming network.

5 2

(9C7>(0O>T3(0O

200

1 5 0 -

1 0 0 -

5 0 -

©

HYBRID DISCHARGE

0 -

-50' I • • I • • I • ' I

4 5 6 7Time in microseconds

Figu re 5.2. SPICE gen erate doutput of the hybrid network.

10





5 4

9I>

s

200

150 -

100 -

PFN DISCHARGE

4 5Tine in microse(X)nds

(a)

TLINE DISCHA RGE

<D

s3>•C3(0o

200

150 -

100 -

4 5 6Tine in microseænds

(b)

Figu re 5 .3 . Typical o u tp u tresponses for a PFN dischargeinto a matched load, (a), and at r ansmis s ion l i ne d i scha rgedinto an overmatched load, (b).



5 5

Line Decay Vs. Line Impedance200

8 >

å• o(0o

100

0.00 0.25 1.50Time in microsecon<Js

Figu re 5.4. SPICE gen eratedo u tp u t of t ra ns m iss i on l ined ischarged in to overmatchedload where Zo is the impedanceof the transmission line, and Rois the resistance of the load.

II 12

R l

Figu re 5.5 . Resistive ne two rkused to describe the need for alo w i m p e d a n c e t r a n s m i s s i o nline.



5 6voltage sources are connected in parallel to a resistive load of o h m s . Fu rth erm or e, the load is m atch ed to the im ped anc e of thsec on d voltage sou rce (i.e., R = R2). The equ ation desc ribing tcurrent through the load is given as

Tc» _ p. f R 2 R ^ N _ ^.' ^ - ^ |^R1R2 + R(R1+R2) * R1 R2 + R(R 1+R2)J- ^^ •^^

The expression inside the parentheses on the left is the term du

to II a n d th e ex pr ess ion on th e righ t is du e to 12. As theim pe da nc e of th e f irs t sou rce bec om es small , R l « R2, thecu rr en t thr ou gh the load is dom inated by the cu rre nt U. In

s imi lar manner, as the impedance of the t ransmiss ion l ine idec reas ed, th e ou tp ut vol tage is dom inated by i ts disch arge.

significant difference in the circuit of Figure 5.5 and the hybri

network is tha t the vol tage sources correspond to chargedcap ac i tor s . Therefore, the ou tp ut resp on se is governed by thtransmission l ine discharge unti l the voltage drops below th

voltage pro du ced b y the PFN. At this point, the transm issio n lihas little effect on the output response since the voltage on the litracks the voltage across the load.

There are two important effects to consider in the hybrid

ne twork :

1. Th e effects of va ria tio ns in line im pe da nc e, Z^, hav e onoverall pulse shape.

2. Th e effects of va riatio ns in line leng th hav e on the prim ar

u n de rs h o o t of the ou tp u t pu lse . Th ese two e ffec ts were



5 7de term ine d by mo del ing the netwo rk on SPICE. Ap pend ix

contains a SPICE listing of the circuit model.

Impedance Considerations For The HybridNetwork

Varia t ions in the l ine impedance di rec t ly determines theam o u n t of ini t ial overshoot in the ou tpu t pu lse. Con sider thvoltage divider a s sho w n in Figu re 5.6. Altho ugh this is a pur e

resis t ive circui t , i t is analogous to the ini t ial vol tage dropen co un ter ed by the hyb rid netw ork. The ou tp ut voltage, Vo, is function of the input voltage E by the following relation:

VoE 1 + Z^/Ro (5.2)

where Z^ is the transmission line impedance and R^ is the loa

res is tance .

Zo

A / W4

Vin Ro4

Vo

Fig ure 5.6. Sim ple resis t ivevoltage divider.

By plotting this function as a percentage of initial overshoot f

the output pulse, the init ial overshoot can be determined for an

valu e of ZQ and R^. Figure 5.7 sho w s the initial overshoo t ve rsu





5 9the im pe da nc e of the t ransm issio n l ine. As the l ine imp edan capproaches zero, the init ial overshoot approaches twice the outppu lse voltage. This scen ario is ana logo us to h aving a capac itor th e las t sta ge of a PFN. In effect, a s th e im pe da nc e of the line decreased, the l ine acts l ike a capaci tor as described by thequation for the impedance of a lossless transmission line below.

' o - V C (5.3)

w he re L is the i nd uc ta nc e p er un it length of l ine an d C is th

ca pa cita nc e per u n it leng th of line. As Z^ is dec reased , C bec omdominant in equation (5.3).

Variations in line impedance also have an effect on the initiaundershoot of the pulse as observed in the graph of Figure 5.8

This graph was generated by varying the impedance of the l ine th e SPICE m od el an d observ ing the re su lts . Th e family of cur v

are for va rio us line len gths . It is see n from th is dat a th at as the liim pe dan ce is decre ased, the ini tial un de rsh oo t is decrea sed. A

u su a l, th er e is a tr ad e off to be co ns ide red . As th e init iaundershoot is decreased, by decreasing Z^, the init ial overshoot

increased.

Line Length ConsiderationsIn the previous sect ion, two reasons were mentioned for

having a small l ine impedance relat ive to the load resis tancenam ely, pu lse sha pe and line d ischarge dom inanc e. First , i t wa



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6 1stated that the decaying pulse shape of the l ine was needed

compensate for the increasing pulse shape of the PFN dischargBy vary ing th e im pe da nc e of th e line, the rate of decay could

varied res ult ing in a variation in the overall ou tp ut pulse sh ap e. alternate way in which the rate of decay of the l ine was chang

was by changing the delay time of the transmission line (i.e^, tline leng th). Th is ch an ge in line length resu lts in a cha ng e in dec

by ch an gin g th e leng th of eac h stair step of the pu lse. Figure 5shows a plot of a transmission line output and how the rate of deis changed by altering the length of line.

Although the initial overshoot wiU not be affected by varyinthe length of the line, there is a significant change in the initi

un de rs ho ot of th e o ut p ut puls e. Figure 5.10 show s the effects vary ing th e len gth of line a s a function of th e initial un de rsho ot .

a very sh o rt line, sh o rt dela y tim e T^, relative to th e rise time the PFN, the und er sh oo t ap pro ach es 100 %. On the othe r ha ndthe PFN has a very fast rise time and is close to the delay time

the t ran sm iss io n l ine, the ini tial un de rsh oo t is very small . Tfamily of curves given in Figure 5.10 is for varying ratios of the P

to the l ine impedances.



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C H A P T E R V I

DESIGN, CONSTRUCTION, AND EVALUATION

OFTHEHYBRID NETVÔRK

Th e PFN w as a nin e-s tag e type 'E' GuiIIemin netw ork w hi

produced a pulse of 6 microseconds into a matched load of 50 Q

Th e desig n of th e PFN is given in Append ix B. Th e rise time of

pu lse w as 25 0-n an ose co nd s. The tran sm ission l ine consistedfîve 50 Q RG58-AU coaxial cables connected in parallel to form a

oh m line. Th e op era ting voltage of the system was 100 volResonant charging was used to charge both the PFN and ttran sm issio n line to 200 volts DC. A m ercury wetted relay wa s u

as th e sw itch. Figu re 6.1 sho w s th e hyb rid netw ork as i t w

constructed and a photo of the PFN.A BNC Jac k, m ou n te d on th e end of the PFN (see Figu re 6

allowed for qu ick conn ection of the switch box. The switch a

load were com bined to form an ind ep en de nt un i t . The swit

box, th e switch an d load com bination , also ha d a BNC m ou nti ng

easy connection to the PFN.

The Pulse Forming NetworkThe pulse forming network used in the experiment was a nin

sta ge GuiIIemin type 'E' PFN. A sche m ati c of the PFN is show n

64



65

(a)

BNC Conector

Solenoid .

Capacítors

GroundPlane

(b)

Fig ure 6 .1 . P ic ture ofexper imenta l pulse formingne tw ork , (a). Ske tch of PFNillustrating special features, (b).



66Figu re 6.2. Th e PFN w as designed to deliver a 6 m icroseco nd puinto a 50 -o hm load. Th e PFN w as physically com pose d of a sinsolenoid with nine 6.68-nanofarad capacitors tapped at appropriapoints . A output pulse produced by the PFN is shown in thphotograph of Figure 6.3, and the charging current of the systemshown in Figure 6.4.

PowcrSupply

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hsjsO1N4(X)4

C l

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, M . ,^rv \ rtcí\m v^so

1 M9

WÍQ

C9

Wl

Trlggcr

Gcnerator

C i _^í—N-

5 m

Fig ure 6 .2 . Sc he m at ic ofexperimental type 'E' PFN.

A 4 2- cm piece of PVC pipe w as us ed for th e PFN core. Th

core h a d a n ou tsid e ra d iu s of 1.34 cm. Eigh ty feet of 20 -g au g

in su lat ed co pp er wire w as us ed for the core w indin gs. E ac h of t

nine sect ions of the PFN core contained 28 turns, with the

exception of the ends, which had 32 turns (Gloasoe and Lebacq205) .

The element values were measured using a vector impedanc

brid ge Model H P-4 81 5. Tab les 6.1 an d 6.2 l ist all the m ea su re

va lu es of in du cta nc e an d ca pa ci ta nc e of the PFN. M utu a

in du cta nc es were calculated from the m eas ure d resu lts and ar



67


1-microsecond50 volts

Figure 6.3. Photograph of out-put pulse of the PFN.



Figure 6.4 . Ph otogr aph ofcharging current through a 3Í2viewing resistor.



Table 6.1. Values of capacitance measured at each stageof the PFN using a vector impedance bridge.

68

E l e m e n t

0 10 20 30 40 50 60 70 80 9

F r e q u e n c yí M H z ^

0.50.50.50.50.50.50.50.50.5

Magnl tucieICI)4 7 . 04 7 . 54 8 . 04 8 . 04 7 . 04 8 . 04 8 . 04 9 . 04 9 . 0

A n g l eídearees)

9 09 09 09 09 090°9 09 09 0

Capac i t anceí n F )6 . 7 76 . 7 06 .636 .636 .776 .636 .636 .506 .50

R e s l s t a n c eí m Q )0 0 0 . 00 0 0 . 00 0 0 . 00 0 0 . 00 0 0 . 00 0 0 . 00 0 0 . 00 0 0 . 00 0 0 . 0

Table 6.2. Va lues of ind ucta nce m easu red at each stageof the PFN using a vector impedance bridge.

E l e m e n t

L1L 2

L 3L 4L 5L 6L 7L 8L 9

L 1 - L 2L 2 - L 3L 3 - L 4L 4 - L 5L 5 - L 6L 6 - L 7L 7 - L 8L 8 - L 9

F r e q u e n c yí M H z )

0.50.5

0.50.50.50.50.50.50.50.50.50.50.50.50.50.50.5

M a g n i t u d eIQ)4 6 . 03 8 . 0

3 8 . 03 8 . 03 8 . 03 7 . 03 7 . 03 8 . 05 0 . 0

0 9 5 . 00 8 5 . 00 8 5 . 00 8 5 . 00 8 5 . 0

0 8 5 . 00 8 5 . 01 0 0 . 0

A n g l eídearees^

9 09 0

8 9 "90°8 9 "8 98 9 "8 98 99 09 09 09 090°

9 09 09 0

I n d u c t a n c eIvih)14 .612 .1

12 .112 .112 .11 1.811 .812 .11 5 . 93 0 . 22 7 . 12 7 . 12 7 . 12 7 . 1

2 7 . 12 7 . 13 1 . 8

R e s i s t a n c eImQ)0 0 . 00 0 . 00 0 . 70 0 . 00 0 . 70 0 . 60 0 . 60 0 . 70 0 . 90 0 . 00 0 . 00 0 . 00 0 . 00 0 . 0

0 0 . 00 0 . 00 0 . 0



69given in Table 6.3 . App endix B co ntain s additional information the PFN design.

PFN Charînpr

Resonant charging was used for ini t ial izing the PFN andtransmiss ion hne. Using an inductor as the charging e lementresonant charging. has many useful advantages over other chargim et h o d s (i.e., efficiency). Th ree im po rta nt criteria w he re m et busing the resonant charging scheme:

1. Th e sa m e am ou nt of energy was s tored in the s to rageelements for each pulse.

2. The cha rgin g ind uc tor isolated the power sup ply fromthe load during discharge of system.

3. And the re so na nt charging c i rcui t m ainta ined a h ighefficiency, > 90% (Gloasoe and Lebacqz, 365).

Table 6.3 . Calculated values of m ut ua l ind ucta nce foreach stage.

Element

M 1M 2M 3M 4M 5M 6M 7M 8

Value 1

( ^ h )14 .612.112 .112 .112 .111 .811 .812 .1

Value 2

(^th)12 .112 .112.112 .111 .811 .812 .115 .9

Sum

( H h )26 .72 4 . 22 4 . 22 4 . 223 .923 .62 3 . 92 8 . 0

V 1 . V 2

( H h )3 0 . 227 .127 .127 .127 .127 .127 .13 1 . 8

M u t u a l

( ^ h )0 1 . 80 1 . 40 1 . 40 1 . 40 1 . 60 1 . 80 1 . 60 1 . 9

Coupl ing

Coeff icen t0 .130 .120 . 1 20 . 1 20 .130 .150 .130 .14





5h

PowerSupply

rm • - '

mU •"Hybrid"Network

(a)

71



(b)

Figure 6.5 . Charging circuit (a).Photograph of charging voltageacross charging inductor.



72


>200-nanosecond50 volts

(a)


>200-nanosecond50 volts

(b)

Figure 6.6. Ch arging ind uc torwave form before (a) and after(b) the use of a RC-snubber.



7 3The Transmission Line

The transmission line for the hybrid network was constructe

by pla cin g five 5 0 n , RG58-AU coaxial cab les in para llel. E ac h liwas 20 feet long, initially, and had a one-way travel time of 3na no se co nd s. The line wa s discharged into a 51 Q load an d th

o u tp u t pu lse is sh ow n in Figu re 6.7. The line w as resistivelcharged with a 10 MQ resis tor. The charg ing time of the line wa s

approximate ly 135 ms wi th a peak charging current of 20

microamps .Comparing Figure 6.7 with Figure 5.3, it is seen that the SPIC

gene rated o utp ut of the un der m atch ed tran sm ission line discharan d the labo ratory m ea su re m en ts are con grue nt . The in it ia

overshoot of the t ransmission l ine can be determined using thgraph of Figure 5.7 for a line impedance of 2^=10 Q. an d a load

res is tance R Q = 5 1 Cl.

A small am o u n t of loop ind uc tan ce is formed betw een the

tra ns m issi on line/P FN and the load. This ind ucta nc e is du e to thgeometry of the loop formed between the PFN, switch, and th

load. The loop ind uc tan ce w as calculated to be 64 8 na no he nry s.

the ideal case, the transmission line would deliver a pulse oinstantaneous rise t ime; however, this rise t ime was l imited by t

in du ct an ce formed by the discharg e loop. This loop ind uc tan calso accounts for any minor discrepancies in the graphs given

Chapter V.



74



(a)


100-nanosecond50 volts

(b)

Figure 6.7 . Ph otog rap hs of

transmission line output.



7 5Evaluation of the Hvbrid Network

The transmission l ine and PFN previously described wer

com bine d to form the hybrid pulse forming network . In C ha pte rthe gr ap hs of the initial overshoot ve rsu s l ine im ped anc e, Figu

4.7 , and the init ial undershoot versus l ine impedance, Figure 4.8we re verifîed in th e laborato ry for th e case s given in Tab le 6.4 . T

impedance of the l ine was changed by disconnecting one of thcoaxial cables which made up the transmission line; in addition, t

delay time of the line was changed by shortening the length of linTh ere we re on ly m ino r d i sc rep an c ies in the l abo ra to ry

m ea su re m en ts and the da ta obtained with SPICE. As m entionebefore, the major reason for this disagreement was due to th

discharge loop inductance which was not accounted for in th

SPICE m od els. Overall , however, th e re su lts were with in a fepe rc en t of th e mo deled da ta and the c i rcui t performed as

expected.For a l ine impedance of 2^=10 Q and a load resistance of 50fí,

th e gra ph of Figu re 5.7 yields a 65 % oversho ot. Figure 6.8 sh owth e o u tp u t of a 10 Í2 line with a delay of 30 na no se co nd s wh ich

an equ ivale nt cas e; furth erm ore, looking at th e ph oto gra ph , it seen th at the overshoot is m eas ure d to be approxim ately 64 %.

addition to the initial overshoot of the system being predicted, tini t ial undershoot was also found to correspond to the graph oFigure 5.8.



IQObserving that the rise time, T^., of the PFN discharge. Figu

6.3 , is approximately 280 nanoseconds, and the l ine delay, T^, i30 nanoseconds , F igure 5 .8 y ie lds a fundamenta l undershoobe tw een 20 % an d 30 %. M easur ing the un de rsh oo t of Figure 6gives a value of approximately 25 % which is within the percentagiven by the graph . Da ta m easu red in the laboratoiy is summ arizin Table 6.4.

Tab le 6.4. Table show ing pa ram ete r ch an ges foreach test case and the laboratory measurements.

CaseN u m b e r

12345678910

LineImpedancc

(ohms)

10.012.516.625.010.012.516.625.010.010.0

* Based on 1

LineLength

(feet)

20.020.020.020.015.015.015.015.010.05.0

.5 ns/F L and

LineCapacitance*

(pF)

600.0600.0600.0600.0450.0450.0450^0450.0300.0150.0

30 pF/Ft. íor

DelayTime*(nS)

30.030.030.030.022.522.522.522.515.07.5

Í^6^-A/U co

Unde r shoo t(percent)

30.035.040.055.025.030.040.055.045.055.0

axial cable.

Overshoot(p)ercent)

70.055.045.030.070.060.050.035.070.040.0



77

Horizontal: 1-microsecondVertical: 50 volts

(a)



(b)

Figure 6.8 . Pho togra phs ofhybrid network output voltagefor a line delay of d=30 ns and aline impedance of Z o=10 fí.



C H A P T E R V I I

CONCLUSION

The prediction of the SPICE simulations, although similar the exper imenta l resu l t s , d id no t cor respond exac t ly. Th

differences were probably caused by unknown discharge loinductance and other strays in the system which cannot easily

ta k en in to acc ou nt in the sim ulatio ns. It is clear from th e res ultthe series arrangement that a successful combination is possib

how eve r, no ju n ct io n fil tering ha s a significant effect on ts im ula t ion . The paral lel, or hybrid. arra ng em en t is consisten

m or e su cce ssfu l . Alth ou gh no direct m etho d for com pleteeliminating the discontinuity was observed, even with the hybnetwork, i ts magnitude was reduced by changing the impedance

the l ine. Incre asing the nu m be r of stage s of the PFN redu ced initial un de rs ho ot . If th e rise time of the PFN could be m ad e eq

to the rise t ime of the transmission line, the undershoot would elimina ted; however, in this case. the tran sm ission line would

be needed.

Th ere are som e disa dv an tag es to the hybrid circuit . The re

an un de sir ab le initial overshoot; also, the im ped anc e of the l

78



7 9must be less than that of the load, which for extremely low

impedance loads, results in impractical l ine characteristics.More work is required to reduce the init ial overshoot and

un de rsh oo t. This might be achieved by placing a resistor in seriwith the transmission line, although this is not desirable because

u n w an te d pow er loss es. Addit ional calcu lat ion s involving thm ath em at ic s of the lump ed and dis t r ibuted para m eter networ

response should be performed.



R E F E R E N C E S

Cook, Ed w ard Guy, Pu lse Form ing Network Investlgation. LubbTexas Tech University, 1975.

Glaso e, G. N. an d Lebacqz, J. V., Pu lse G en er at or s. New YoDover Publications, Inc, 1984.

Jav id, M ans ou r, An alvsis. Tra nsm ission . an d Filtering of Sig naNew York: McGraw-HiII Book Company, 19 63 .

Ku, Y.H.. T ran sie nt Circuit Analysis. Princeton, New Jer sey : D. Nostrand Com pany. In c . 1 961.

Scoles. G. J.. The Reduction of Unwanted OsciIIations (RingingC h a rg i n g I n d u c t o r s a n d P ow er T r a n s f o r m e r s . lE E ECon ference R ecord s of the 12th power M odu lator Sym po sState University of New York at Buffalo. 1976.

SkiIIing. H. H. . T ra ns ie nt Electric C ur re nt s. New York: McG rHiII Book Company, 1952.

Wilson, Dale G. , Pulser Design And Performance For An ElectBe am G un . Lubb ock: Tex as Tech University, 197 7.

80



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0

2

0

1.

0

0

4

9

0

0

7

0

3

0

1.

0

0

9

0

4

0

0

9

0

0

0 0

r - ( 0 < o < D t D ( D ( o r - r ^ f « . -c o o o o c o o o q c o qU l U I U I U t U J U J U I U I U I U JO > 0 0 C J U ) ( O C J C J O ) O > ^ Ô > ' - C O ^ C O » - C M O ) O > 0 0

< o r ^ r > . ( 0 ( D r > . r . . ( 0 ( 0 < oo o o o o o o o o qU i U I U I U J U J U J U J U J U J U I• i - • * CM • * q q T- r.. u ) c j• OO CO CO 00 »- ' »-^ CJ F-*

( 0 < 0 ( 0 0 > < 0 ( 0 < 0 ( O C O < 0

o o o o o o o o o qU I U I U I U I U I U J U J U I U I U Iq r> q q æ • * q ••- æ r«.<d CM u ) T-' •<»• r i u> T-r^(0(0(0<oa>(0(0(0(0o o o o o o o o o oU l U I U J U J U t U I U I U I U J U Jq q T- r » r.. r* q u ) q u>T-* • * o> r .i CM 1-* u ) c ju ) < D r . . ( O U > u ) ( o r . . r > . < oo o o o o o o o q qU J U I U J U J U J U I U J U J U J U JT- c j c o < O T- T- « í - c j r ) 0 )T- u> T- T- u ) r « . u > c o

\n(r>(e)iO(0(OU)intr>(0o o o o c o o o o o oU J U J U J U J U J U J U J U J U J U Jo > r « . ( 0 < o r . . o o ^ u > c o u >c j c M T- ^ » a - c M r ) T- T- T- u 5

(O\e)U>\í)\nu)(oa0(Oir>o o o o o o o q q qI Î J U J U J U J U I U J U I U I U I U Ju) q ^ q co æ ^ r.; •^ c jc O T . ^ c o c o c o ^ » - ^ u ) c j r ) T- ^

^xiint^ôxíiiíiUiiíiUiie)o o o o o o o o o oU J U J U J U J U J U J U J U t U J U J••- u) •^ <o •^ •'í •^ q •^ cjU)»-^CO Cs j^ ' U ) U ) CM

• < j - ^ > - r . . T- u ) U ) r « . < o u ) U )C J C M T - T - O O O O O OO O O O ' ' ' ' ' 'O O O O U J U J l i J ^ ^ L ô o o o " . «=* T í ''? ''^d o ' d d " ^ ' - ' ' ' ' ' ' Û ) O ) 0 0 U ) O > 0 0 U > O ) T - Ô T - C M C O C O C O C O C M C J T -, , ' , 0 0 0 0 0 0 0 0 0" J o o o o o o o o o'". o o o o o o o o oo>cicicic6cic>cicici<3) r> .0 )U>u)U) r )<oo>co^ • ^ • » - o r ) 0 » - C M r ) U )O O O ,,', ,,', ,,', o o o oo o o H i J i y i y o o o oo o o ' ' ' . ' ' ' . q o o o ociôci'^<'^<^ciciôci

C 0 C M O 0 0 ( O 0 0 ^ ^ < 0 C 0 ( Or . u > ^ c o ^ ( O O U ) C J Oo > r > u ) c o ^ O ) o o ( O U ) ^T - T - T - T - T - O O O O Oo o o o o q q q q ooôdcicioôScici0 0 O ) O ) 0 0 0 0 O ) C M 0 0 0 0 ' ' -C M T - o o r ) ( D r > r « . ^ o u >C M 0 O C O O ) ^ O ) ^ O ) ^ 0 0r . . < o < o u ) u > ^ ^ ^ c o c o c jc o c o c o c o c o c o c o c o c o c oo o o o o o o o o oC M ^ ^ < O O O O C M ^ ^ < 0 0 0 0

o o o o o o o o o o



88

c s

C A

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co- J

^

r ) U ) c o c j c o u > o o c N j " ^ c o ^ c \ i c o r - . r ^ c \ i c n o ) T - T - u ) o > r « . c j ( 0^ o o c o c O ( 0 ( O c j c o c j » - ( 3 ) r ) c o u ) U ) r 5 ' < 3 - ^ ^ T í - r > T - o o u ) c o ( 0o o <o u ) + o ^ ^ ^ T - + 0 O C J T- + c\jC M<3) + r ) ( o c o + o r ) T - + r Ô T - r . . u j ' - u > T - u j O ) ^ * r ) i U ' - c j r ) L U » - < 3 > - u J t r j ' 0 _ : u J c \ i« ? * ^ ' ^ . q ' ^ " í u > q ' * u ) r . : q c s i d o ) ' « > o > d r - q r ) ' ' t ( 0 « ' . O)o o c j , - r > . u ) T - , - c j T - c o T - u ) c o < D T - o o ^ ' í ^ » - ^ ^ » - r . . ^ » - ^ i - ^ ' -< o r ) a o u ) C J C \ j ^ < 0 ( O U ) r > . < 7 ) < o r ) U ) c j r ) r ^ i n c M T - ^ r ) r ) r ^^ ^ c j r ^ c j u ) r » . r ) r > c s j ^ O ) * ^ * o r « > c o r . . r ) C J ^ < í - c j O ) O U )o o o r ^ < o c o u ) ^ ^ c 3 > " i - " ' í ' r ) o , ' r < O T - o o < D C j ^ ' j - c j » - _ : u > o o » -g î S í : ' ^ " 5 c M ' ^ « ^ ° ' - * ^ ' " ^ ^ ° í o < o ^ ' < ^ ° Î ^ C N i S d ^ r )

. " : . c o u > T . u > c M C 3 > u ) o c j c M c o " * o o c o u ) f * > c j r - . » - u > < oo o T - c 0 T - u > r . - r > c j ^ i - T - ^ ^ C M ( 0 • * c j u > u ) C M » - » - r > . ^ i -< o ^ r " * u ) T- c M U ) o o c M U ) C M T- T j - T- r > . ' - æ ^ ' í - r > o o < o < 3 ) T- a ) U )< 0 < 3 ) C M T- < D < 0 ^ ' í -( O C O O ) r > C O C M ^ ' i í -0 0 ^ ^ » - < 3 ) p ,^ 0 > ( 0 0 ' « í- 0 > T-< 3 ) r > < o o T - T - < 3 ) o o T - - ^ r « - o o ^ * r « . c j o < o ^ , - : r ) C M T - - : oS î * ^ - ' ^ - w n í 5 ® - * ^ « « * ^ o o d 9 r ) ^ 5 c j 9 < ^ C N i S < d^ ^ T - r . . T - ^ . . ' ^ < D T- 0 > T- C M < 0 T- ^ ' í - r ) < 0 < 3 ) T- C J O C M < 3 > C 0o T- r ^ u ) 0 ) r ^ »- co T- C O OOCO u > < D C M r ) » -

r ) ^ T- T- < O T- T- u ) < 0 ( O C 3 ) r ^ ( 3 > o o o o c M ( O c o c o < o c o < o u ) C M ^ < -o > » - r > . c o < 3 > o o ^ » - C M U ) o o < o ^ r . . ^ r 5 < O T - c M r > c j _ ; u ) r ) r ) ^T- c M T- T- c 3 ) o o ^ ' - c o u ) r > . " ' í O o o r ) C M _ : < o < o c j T- l Í T - " T í - r ^ c o

c 3 5 S ã o * ^ S r i - ' ^ « ' ^ - ^ - ' ^ ' ^ « ^ " ' ^ ' ^ ^ « o « ^ . - . ^ '^ ^ . ~ O c 3 > r > . ' r ' ^ T - r > c o T - u > c j < 3 > " ' t c o o ( o o < 3 ) U > u ) c o T -o o o c o T- u ) u > O ) ^ » - C M T- C J » - u ) r ) r ) i - c O T - u ) U ) T -0 > " < l " ^ C M < 0 < O ^ ^ U > U > 0 ) 0 ) ^ ' Í T - r ) C O O O T- < 0 < 0 ^ 0 0 < 3 ) < 0 < 0 0 )' - • ^ C M ^ ^ c o o < 3 ) C J U > " * c o c o o r « - < o ^ ^ o o T - ^ ^ T - r ^ r ) T - " *u ) T - ^ o o ) T - u ) ^ r > . o ) o < o c o < o ^ r « > < o o < o c o o ^ < o » - c oîr. Î : ; " ÍS :? ;T ^9Î : :S Í°°. ^ . « 0 - ^ . do;ob®'^r)°î^'<tr* ? o * : ' . W T - * " . o O o ^ ' í u ) C j < D ( o c o r ^ u > o o » - r > ^ o o <o ( 3 )o o T - O O < D T - U > U > T - U > < O C O ^ » - ' » - T- < o i n c o < D ^ < O C O

< o o ) o o ^ c o < O T - T - o > u ) r " » T — c o u ) ' ^ r ^ c o c M c o c M r - . r ^ m u ) r ^C O C M T- O C O O ) < O ^ C M < 0 ^ ^ < 3 ) C 3 ) 0 > C M C J < O C J C O C O C O r ) O C O U )O > 0 ) C J C M U ) C M T - O O ^ T - » - C O C O - ; C O T - ^ ^ C O C M + r ^ u ) ^ i - u > < 3 )< O C O ^ » - O O r ^ O ) ' C J < O U > <O T - _ / l j C 3 ) r » * ^ ^ , s . J U J m O d * ^ ' * 'c s i r ) u > q r - d ^ d « í " ' . * r ) S " ^ " « t ' u > < d r . : o > « í - " r ^ r ) U ) dO O O O C J C J T - T - U > U > O O C M C O C J T - T - C M .,- t- •^ C0(O

o o o o " < í ' c o c M ' ^ o o c M c o u ) 0 ) r ^ o > u ) r ) ^ < * ' » — o o o > u ) ' ^ c o ( 0 0 > o oc o c o o ) o o ^ » - ( 0 0 0 > ^ 0 ( O T - T - ( o o > o o c o r « . o c M C j ^ c o r )^ c o c o o > c o ^ u ) c o c o T - r « . c o o < o c o < o c o o ) o o ^ o o r ) ' j - , C M C M< O T - c j < O T - < 3 ) C M _ : o r ^ < 3 > C J r > ^ ^ _ , : - j O U ) ^ . - ^ < í < o ^ - î U jT-;C M r ) " » r q c o q d S r ) * ? * N * N d o 6 S r ^ c M r « . ' u > o c > C M T - c M r ^ c MO O O O T - C O C M T - T - ( O U ) < O T - C M C O T - C O T - T - T - C O T - C J T - U )

0 ) C s j o o r * . T — ^ T- o ) < O T- o ) r . . o > c o r ^ C M < 3 ) o o o > 0 ) C M r « . r ^ r » . ^T - o > < o O T - < o u ) o > o u ) U ) < 0 ( O O ^ o c o ^ ( O U ) r > . c j ^ ^ O )O C O C M U ) U > < 3 > ' < í - < 3 ) - < 0 < O O r . . U ) T - T - 0 _ ; " « í - < 0 ' * O C O O T -< o o > < o < 3 ) < o o > r > o r Z C M ' - c o o > ^ < o c o r ^ r f í d ' ' ' O M ^ ^ < 3 > o c oC J C M r > « * r . . r ) j ^ . ^ - : 5 ^ - q q c M q ' « i ; d < i - * . « - c o " * o > u ) u > T - r ^d d d o o T - T - c j c o o > < D U ) u > o O ' - u ) c j ' - c o T - T - T - c M r )r » . ^ o o o o o o o o r . . o > c 3 ) < 0 ( O T- o o c M O ) 0 > u ) r ) ( 0 ' - C M c o < D c o ^ ' t^ ^ • ^ < D U ) T - C 3 ) C J ' f l - 0 > C 3 > 0 ^ ' * < O C M U > U ) U > U ) 0 > C O i í r ^ T - C M< o o o o > o c M O < o ^ c o c M " c o r ) T - " » í - c M r « . o u > c O ' - - : T - q æî n " ^ S - r > - u > c M O > J u ) o r > . < o o w 2 T ^ - . « S c s i * °. 9C M C M c o c o u ) r > . ^ - T - T - Q ^ j p p j r > q q æ ^ ^ . , _ f , j < í ) . ^ C M < 3 ) ' < fci ci d d ô ci c M U ) C M C M i r ' - r » u ) u > u ) r ^ C M r - c j c j ^ ^ c jr > u > < D c o r > ^ < r ' - r > r > r > T - u ) o O T - T - u ) " « í C J ' - r > . u > æ ; « - o o o oo r î . < D c o r « . o > o o > c j c j u ) T - o ^ ^ < o o > C 3 ) < 0 ' - < 0 ' j q r ^ < D C M^ < D C 3 > u ) o r ) r ) ' - < o r ^ ' « 3 ' O U > 0 ' - r ) U ) T - T - < o o > u ) 5 o O ' -u > < o o o c j o o < D < 3 > O T - " « í - r ) u > C M _ : ^ o o o r > . o > 2 î : : 2 ^ S M í P TC M C M C M r > r ) " < í U ) o o ^ - o O p i f . : d 5 T - e M ' - : * ? ® . ' ^ ^ ^ ^ ^ ' ^ u )d d d d d d d d y- c M < O T - c j ' - r ^ u ) u > u ) U ) r « . o ) ' -r ^ c 3 ) < o r . . c o o > c o < o o o u > T - " * C M c o c o r > < o < o < o c j ' - ' - C M T - r )o o c o < 0 ' * C M r > ' « r T - o O ' - O T - C M o o o r ) 0 ) o r ) < o u ) C M ; 5 r < DC M O o c 3 > u > o o c 3 > o < o c j < D U > c J c o r * u ) r > . o c M q - » - T - < o r ) c o ou > S < D o o o r ) o o r ) ' - T - < o o O ' - 5 r - U ) 5 ; q d i J L J _ : c N ® . ^. rc j c j CM c j co co co •^ u) q r-. q co q r* ^ q o o> *R - ^- u) o ' ^d d d d d d d d d d d d y - ' T - c ^ OOCM , J T - c O ' - ' - r > .

^ o o r > . 0 ) < 0 ' * < o o > o o o > o o o o ^ ^ o o ^ ^ o O T - ^ r . . ^ o o o > r )r ^ o > r ^ T - c o ^ ^ < o c j < o c s i < o u ) 0 ) 0 > ' - r ^ c j o > r « . q c M < o c M 2 o oO C M < O C M < 3 ) 0 0 < 3 ) C O O ) 0 > C M O r ) C O C M O ^ ^ O ' - C M < 0 0 ) r - . ^ ^ U )u > u ) u ) < D < o r ^ o o o T - c o < o o ) C M < O T - r « » < D c o ^ o o T - o ) T - u ) r .C M C J C M C J C s i c M C M r ) c o r > c o c o ^ * ^ ^ u > u ) d f ^ « o q ^ c o r > T - ; r « .d d d d d d d d d d d d d d d d o o o T-T-CMCMo o c o ^ c M r « - o o r > . c o r . . o > c y > o > o o < o < o < D O ) ^ c o r « . < o c j < o o ) r )o c o r « - c o o o ) O c o r . . r ) ' - T - r > r > r ) T - T - ' * 0 ) < o < o o ) ^ C M Ô O O T - C M C J ^ U > < D 0 0 O C M ^ < 0 0 ) C M U ) 0 0 ' - U ) 0 > C 0 0 0 C 0 0 0u ) u > u > u > u > u ) U ) u > u > u ) < D < o < o < o < o r . . r ^ h . o o o o o o o > 0 ) 0 0CMCMCMCMCMCMCJCMCJCJCMCMCJCMCMCMCMCMCMCMCJCMCJCOCOd d d d d d d d d d d d d d d d d d d d o o o o oC M ' t f ' < D O O O C J ^ < D O O O C M ^ < O O O O C J ^ < O O O O C M ^ ^ < 0 0 0 0O O O O T - T - T - T - T - C M C J C M C M C J C O C O C O C O C O ^ ^ ^ ^ ^ ' Í - ^ ^ U )o o o o o o o o o o o o o o o o o o o o o o o o o



APPENDIX B

TEST SYSTEM DESIGN

8 9



9 0Tvpe 'E' PFN Design

Th e type 'E ' PFN w as designed usin g the ap pro xim ation

method (Glasoe and Lebacqz, 205) to meet the fol lowingspecifications:

Rise Time >300 n s.

Pulse W idth.T, 6 ^ s.Imp edanc e, ZQ , 50 Q .

The approximation method is based on the assumption that ath e energ y stor ed in the cap acito rs is delivered to the load. Thequations of interest are:

(B.l)

(B.2)

where T is the desired pulse width and Z^ is the PFN impedancFor a PFN with a pulse width of 6 microseconds and a impedance

50 Í2, the total capacitance, C^, was calculated to be 60 nanofaradsand the total inductance was found to be 150 microhenrys.

The type 'E' network can be reduced to a single solenoid o

tot al in d u ct an ce , L^^. The equ al valu es of cap acita nc e are th etap pe d at ap pro priate points on the solenoid. The tap s are placeso they will produce an equal inductance between each section

th e PFN. The end s, however, are m ade to hav e 20 to 30 p ercem ore ind uc tan ce (Glasoe and Lebacqz, 204 5). The indu cta nc

Cn

Ln

T2 Z o

T Z o~ 2



9 1be tw ee n e ac h stage in this arr an ge m en t is 15% of the seind uc tan ce . The total ind ucta nce of the solenoid is

L = Lg[(k -2) + 2(1 + o/oE) + 2(n-l)% M ] (B.3)

w he re n = nu m be r of stages,Lj = total inductance,

Lg = self inductance,

%E = percen t end induc tance,and %M = percent m utu al induc tance.

For a rise t ime of less than 300 nanoseconds, a nine-stagpu lse forming netwo rk wa s needed . The perce nt end in du ctan

an d m u tu a l in du c ta nc e wh ere se lec ted as 25 % and 15%resp ectiv ely . Solving for Lg ylelded a self in d u ct an ce of 12

microhenrys , an end inductance of 15.75 microhenrys , and m u tu a l in du cta nc e of 1.89 m icro he niy s. The cap acitan ce for eastag e w as fou nd by dividing th e total cap ac itan ce , Cj^, by th

n u m b er of s tag es , n , y ie ld ing a s tage cap aci ta nc e of 6 .6

nanofarads.

Element Design and PFN Construction

The stage capacitors were commercially available and had

ca pa city of 6.68 na no far ad s a nd a rat ed voltage of 60 0 volts. T

sole no id for th e type 'E' PFN w as de sig ne d to hav e a tota

inductance of 150 microhenrys and a mutual inductance of 1.



9 2m ic ro he nr ys as found p reviously. The self in du ct an ce of the co

was calculated using the formula:

r 2 n 2^ - 2 .5 4 (9 r + 10/) ^^'^^

w he re r is th e ra d iu s of the coil m ea su red in cen tim ete rs, n ith e n u m b e r of tu rn s per section, and f is the coils leng th incen time ters. The m ut ua l indu ctanc e is given as:

a A 2 ni n^ wM = 0 .00986 4 x ^ — ^^'^^

w he re w = (kj-^ + k ^ ^ + k^ 2) , ^l l oth er variab les are defined Figu re B .l E qu ati on s (B.4) an d (B.5) w here solved sim ulta ne ou sgiving a coil radius of 1.5 cm, a coil length of 4.16 cm, and 28 tu

per section.



93

coil 1

MUTUAL INDUCTANCE DESIGN

X I

D

X2

- ^ coil 2

M = {(.oo98 6M a'2)(A 2 )(nrn2)lkrkl* k3'k5* K5 'k5l/4lx) uHA - radius of coil 1a - radius of coil 2

2X = length of coil 121 - lenglh of coil 2

D = axial disiance between coilsnl - * of lurns on coil 1n2 = * of lu rns on coil 2

X I - D - XX2 - D * X

r l - l (Xr2- A '2 ) r.5r2 = l(X2-2 * A '2)l .5

* : 5 -

Kl - ( 2 / A ' 2 ) * ( ( X 2 / r 2 ) - (XI / r l ) )kl - 2 ' l

K3 - ( (XI / r l ' 5 ) - (X 2 /r 2 5)) / 2k 3 - ( A - 2 ) M i ) ' ( 3 - ( ( 4 ' r 2 ) / A ' 2))

-(A • 2 / 8) • (((XI / r l - 9) • (3 - 4 • XI -2 / A ' 2)) - X2 / n( 3 - 4 ' X 2' 2 / A 2))

k 5 - A ' 4 " l ' ( ( 5 / 2 ) - ( 1 0 '1 - 2 / A ' 2 ) * ( 4 T 4 / A * 4 )

Figure B .l . M utual inductan cebetween two coils.



APPENDIX C

VARIOUS SPICE CIRCUIT MODELS

9 4



9 5The program listings given below are the SPICE decks used as

the base model of the ser ies connected system and the hybridne twork . AII ge ne rat ed wave forms referred to t h r o u g h o u t the

thesis were constructed from these l ist ings.

Series Connection Circuit Model

** VAR. ** TYPE E - VARIATIONS IN END INDUCTANCE.* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

* *

* 9 STAGE TYPE E PULSE FORMING NETWORK IN ** SERIES WI TH A CHARGED TRANSMISSION LINE ** THI S FILE WAS DESIGNED FROM THE VALUES ** MEASURED IN THE LAB. ** W. R. CRAVEY 7/5/87 ** *

* * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * *

WIDTH IN=70 OUT=80

**** pFN STAGES ****

ClRClLlRl

C2

RC2L2R2

C3RC3L3R3

C4RC4L4R4

10101015

20202025

30303035

40404045

001520

002530

003540

004550

6.77N1E1214. 6U.155

6.70N1E1212. lU.155

6.63N1E1212. lU.155

6.63N1E1212. lU.155

IC=200

IC=200

IC=200

IC=200



96

C5RC5L5R5

C6RC6L6R6

C7RC7L7R7

C8RC8L8R8

C9RC9

50505055

60606065

70707075

80808085

9090

005560

006570

007580

008590

00

6.77N1E1212. lU

.155

6.63N1E1211.8U.155

6.63N1E1211.8U.155

6.50N1E1212. lU.155

6.50N1E12

IC=200

IC=200

IC=200

IC=200

IC=200

*** ALTERED PARAMETER **** * * * * * * * * * * * * * * * * * * * * * * * * *

L9 90 95 16U* * * * * * * * * * * * * * * * * * * * * * * * * *

R9 95 100 .155

**** MUTUAL INDUCTANCE ****

KlK2K3K4K5K6K7K8

LlL2L3L4L5L6L7L8

L2L3L4L5L6L7L8L9

.13

.12

.12

.12

.13

.15

.13

.14

**** 192 FT OF TRANSMISSION LINE ****

TLINE 100 0 101 0 Z0=50 TD=.5U 10=200,0,200,0

**** LOAD MODEL ****

RL 120 0 50



97

**** OUTPUT DECK ****

VL 101 120 0.TRAN 40N 4U UI C.PRINT TRAN V(120).END

Hybrid Network Circuit Model

TLOl- lO. PFN(3-SEC.,Z=5 0,T=6US) TLI NE(ZO=10,TDION)

*** PFN SECTIONS ***Ll 10 20 75UCl 20 0 49N I C=200V

L3C3

L505

1030

1040

300

400

75U5.4N

75U1.9N

IC=200V

IC=200V

*** TLINE ***TLI NE 100 0 10 0 Z0=10 TD=10N 10=200,0,200,0

*** LOAD ***RL 10 0 50

*** OUTPUT ***

.TRAN .075U 15 U UI C

.PLOT TRAN V(10)

.END



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