A Simplified Theory of Microwave Pulse Compression

Transcription

1 Circuit and Elctromantic Systm Dsin Nots Not 57 uust 8 Simplifid Thory of Microwav Puls Comprssion ndry D ndrv, Evrtt G Farr, and Edl Schamilolu Univrsity of Nw Mxico, ECE Dpartmnt, lbuqurqu, NM 873 Farr Rsarch, Inc, lbuqurqu, NM 873 bstract This papr dscribs a simplifid thory of th microwav puls comprssor allowin on to stimat th microwav powr ain G that is possibl to achiv insid a rsonant cavity of a sinl-mod microwav puls comprssor utilizin sinl-arm wavuid T

2 Introduction Various xprimntal schms of activ HPM puls comprssion hav bn studid durin th last 5 yars or so [] ll ths fforts ar inspird by sarchin for ways to incras radiatd microwav powr by squzin an initial lon-duration, low-powr or vn CW microwav sinal into a short-duration, hih-powr microwav puls whil pin th total radiatd microwav nry constant Th tchniqu involvs th slow xcitation of a rsonant cavity with a rathr low-powr microwav puls undr conditions whn couplin btwn stord microwav nry and th cavity output is nliibl hih Q cavity, and thn firin a fast wavuid switch to dstroy th cavity rsonanc and, in this mannr, sharply incras th couplin btwn th stord microwav nry and th cavity output low Q cavity Th stord microwav nry is thn rlasd durin tim τ that is sufficintly lss than th tim t rquird for storin th microwav nry insid th rsonant cavity; th tim t scals with th quality factor of a hih Q cavity as ~Q/ω Du to th fact that th stord microwav nry is rlasd much mor rapidly than it is stord in th rsonant cavity, τ<<t, th output microwav powr is ratr than th input powr by a factor of approximatly t/τ Thr ar basically two dsins of th sinl-mod rsonant cavity microwav puls comprssor utilizin ithr a sinl-arm wavuid T or a doubl-arm wavuid Maic T Each dsin of th rsonant cavity has input and output wavuids connctd to th input and output arm of a T, rspctivly, and a short-circuitd wavuid connctd to th sid arm of a T Th short-circuitd wavuid has a switch locatd at th position onquartr or, in th worst cas, som odd numbr of on-quartr of th wavuid wavlnth away t th stora mod of th microwav puls comprssor opration, th fild distribution insid th rsonant cavity has a minimum whr on-half of th wavuid wavlnth is positiond at th output of a T and a maximum whr on-quartr of th wavuid wavlnth is positiond at th switch position Whn th switch is fird, th microwav puls comprssor chans from th stora to th xtraction mod in such a way that th fild distribution insid th wavuid suddnly chans to hav a null at th switch position and maximum at th output of a T In othr words, whn th switch is closd, th lctrical lnth of

3 th short-circuitd wavuid is chand by on quartr of th wavuid wavlnth that rsults in th xtraction of stord microwav nry from th rsonant cavity Th prsnt papr allows on to stimat th microwav powr ain G that is possibl to achiv insid th sinl-mod rsonant cavity microwav puls comprssor utilizin a sinl-arm wavuid T

4 Simplifid thory of th microwav puls comprssor t us considr a simplifid microwav puls comprssor Fi consistin of: an input wavuid, a couplin unction iris, and 3 a rsonant cavity 3 Fi Simplifid diaram of th microwav puls comprssor: input wavuid, couplin unction iris, 3 rsonant cavity with lnth,,, ar th lctric fild componnts of lctromantic wavs travlin in opposit dirction rlativ to th diaphram on both sids of th diaphram Th iris [] may b considrd as a two-port ntwor/dvic with an input port facin th input wavuid and an output port facin th rsonant cavity s for any two-port ntwor, th scattrin matrix S [3] can b dtrmind for th iris, ivn by s s S s s [ ] If th iris is considrd to b losslss, thn th scattrin matrix of this losslss ntwor is a unitary matrix satisfyin th followin condition [3, p 78] [ * t S ] {[ S] }, and by th unitary proprty of, on can writ that [, p ] s s s s s ± s 3 5] t us dtrmin th couplin cofficint throuh th iris,, in th followin way [, p

5 s Equations 3 can b rwrittn thn as follows [, p 5] s s s s, 5 and th scattrin matrix S bcoms [, p 5] S [ ] 6 Th lctric fild amplituds of four microwav sinals travlin toward th iris and and away from th iris and ithr insid and or outsid and th rsonant cavity Fi rlat to ach othr throuh th followin matrix rprsntation [3, p 8] S [ ] 7 Substitutin 6 into 7 ivs th followin quation [5], 8 whr is th couplin cofficint btwn th input wavuid and th rsonant cavity dtrmind by th omtry of th iris Fi This cofficint can b low whn, critical, whn, or hih, whn Th rlation btwn th lctric fild amplitud of a microwav sinal scapin th output port of th iris and ntrin th rsonant cavity,, and th lctric fild amplitud of a microwav sinal ntrin th output port of th iris from th rsonant cavity,, can b writtn usin th attnuation constant, th total travlin path from to, which quals to, whr is th lnth of th rsonant cavity, and th accumulatd phas shift btwn and ovr th lnth [, p 5],

6 xp 9 Substitutin 9 into 8 ivs [, p 5], It follows from that [, p 5], [5, p 37], 3 and, and, finally, [, p 5], [5, p 37]

7 5 For a ivn total attnuation and couplin cofficint, th manitud of is maximum and assums a minimum valu whn th total phas shift bcoms [, p 5] nπ, 6 whr n,,, 3, Condition 6 turns out to b th rsonanc condition undr which and 5 bcom, rspctivly [, p 6] 7 For a ivn total attnuation, if couplin cofficint is adustabl, th maximum valu of is obtaind whn [, p 6], [5, p 373] d d 8 It follows from 8 that at optimal conditions of th microwav puls comprssor opration in th stora mod 6, th optimal couplin cofficint opt satisfis th followin condition [, p 6], [5, p 373] opt 9 or opt ± Substitutin 9 and into 7 ivs th lctric fild amplitud of a microwav sinal at optimal conditions of th microwav puls comprssor opration in th stora mod 6 rsonanc condition [, p 6], [5, p 373]

8 ± ± ± opt ± Th ain M of th lctric fild amplitud shows how much lctric fild amplitud insid th rsonator ratr than th lctric fild amplitud ntrin th rsonator Fi Th ain M is dtrmind, tain into account 5, by th followin quation [5, p 373] M 3 t optimal couplin cofficint opt 9,, which provids maximum valu of, and at optimal conditions of th microwav puls comprssor opration in th stora mod 6 rsonanc condition th ain M 3 is dtrmind, tain into account, by th followin xprssion [5, p 373] opt M ± Th maximum microwav powr P of an lctromantic wav within th rsonant cavity undr th rsonanc conditions 6 in rlations to microwav powr P of an lctromantic wav ntrin th rsonant cavity can b writtn usin as [5, p 373] M P, 5 or P P, 6 whr P is th input microwav powr ssumin that - <<, and x x whn x << Taylor's sris xpansion on can rduc 5 to th followin xprssion [5, p 373]

9 P P 7 Th amount of microwav nry W stord in a rsonant cavity durin th tim rquird for th lctromantic wav to travl within th rsonant cavity from input to output,, can b writtn usin microwav powr 6, 7 and roup vlocity υ as [, p ], [5, p 373] W P, υ 8 whr cλ ωλ υ λ πλ 9 Th microwav nry W dissipatd insid th rsonant cavity durin on priod of oscillations pr a sinl radian can b writtn as [, p ] P W ω 3 Equations 8 and 3 can now b usd to writ th quality factor of th rsonant cavity Q [, p ], [5, p 37] W P Q P, W υ ω 3 πλ ω Q P ωλ P πλ λ 3 Th attnuation constant can thn b rwrittn usin 3 as [5, p 37] πλ Qλ D Q, 33 whr Dπλ /λ is dtrmind as th omtrical factor of th rsonant cavity Substitutin 33 into and assumin that -D/Q <<, and x x whn x << ivs a rlation btwn th optimal couplin cofficint opt, quality factor Q, and omtrical

10 factor D of th rsonant cavity at optimal conditions of th microwav puls comprssor opratin in th stora mod opt D Q 3 Substitutin 3 into ivs a rlation btwn th maximum ain G of th microwav powr, th quality factor Q, and th omtrical factor D of th rsonant cavity at optimal conditions 6 of th microwav puls comprssor opratin in th stora mod λ Q Q G M D πλ 35 Substitutin 3 into 35 ivs th followin xprssion for th microwav powr ain at rsonanc 6 for an optimal couplin cofficint opt, G 36 Th microwav powr ain G 35 is what on can actually b masurd in an xprimnt by comparin input P and output P microwav powr 3 Concludin Rmars Ths rsults provid an uppr bound on th maximum cavity ain for an ida cavity rsonator, similar to that usd in puls comprssion From quation 36 w infr th maximum ain that can b ralizd, and th fact that ain varis invrsly with cavity lnth This will b usful whn intrprtin th rsults of futur xprimnts in microwav puls comprssion

11 Rfrncs [] C E aum "Comprssion of Sinusoidal Pulss for Hih-Powr Microwavs," Circuit and Elctromantic Systm Dsin Not 8, March [] C E aum "Couplin Ports in Wavuid Cavitis for Multiplyin Filds in Puls- Comprssion Schms," Circuit and Elctromantic Systm Dsin Not 5, March 6 [3] D M Pozar Microwav Eninrin Third Edition Chaptr 3 Th Scattrin Matrix/ John Wily & Sons, Inc 5, p 7 [] J ltman Microwav Circuits Chaptr 5 On-Port Cavitis: Microwav Rsonanc/ D Van Nostrand Company, Inc 96, p 3 [5] N Didno, Microwav Enrtic: Thory and pplication in Russian Chaptr Gnration of hih-powr nanoscond-duration pulss of microwav nry by tmporal comprssion mthods / Naua, Moscow, 3, p 37