Increasing Q of Waveguide PulseCompression Cavities


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1 Circuit nd Electromgnetic System Design Notes Note 61 3 July 009 Incresing Q of Wveguide PulseCompression Cvities Crl E. Bum University of New Mexico Deprtment of Electricl nd Computer Engineering Albuquerque New Mexico Abstrct A limiting fctor in microwve pulse compression is the cvity Q. For wveguide cvities of some number of wvelengths in length the skineffect losses in the conductors is limiting fctor. These cn be reduced reltive to the power in the cvity by incresing the crosssection dimensions. To void unwnted modes, techniques involving symmetry nd dding losses to these modes cn be used. ` 1
2 1. Introduction One of the problems in microwve pulse compression concerns rising the Q of the microwve cvity, s this limits the ttinble power multipliction [5]. The skineffect losses in the conducting cvity wlls re limiting fctor. A recent pper [6] considers the losses ssocited with n iris feeding into the cvity nd finds these to be unimportnt. When one switches out the energy in wveguide resonnt cvity one cn obtin pulse whose length (or number of cycles) is proportionl to the wveguide length. However, the cvity Q (nd potentil power multipliction) is inversely proportionl to this length [5]. So one will wnt to mke the number of wvelengths in the resonnt cvity not too lrge, but just lrge enough to obtin the mximum effect, depending on the ppliction. A commonly used cvity geometry is rectngulr wveguide operted in its fundmentl H 1,0 mode. A rectngulr wveguide of width nd height hs n operting bnd given by 4 8 wvelength (1.1) f c speed of light in wveguide medium (here tken s free spce) f frequency If we sty in this frequency rnge then we re limited by the crosssection re for energy propgtion with circumference of 6 on the wveguide wlls where skineffect losses tke plce. At 1 GHz, copper hs surfce resistnce of [1] Rs 8.3 m (1.) The ttenution constnt (in e z ) is proportionl to R s, nd the reciprocl of the wveguidecrosssection dimension [8]. As one increses (nd decreses the frequency ccordingly) nd keeps the length of the wveguide proportionl to (for given number of wvelengths to produce some number of cycles when switched out) the totl losses sty the sme except for the reduction in R s (which is proportionl to 1/ f ). If one keeps f fixed (sy round GHz), then one needs to decrese R s (sy by cryogenics), or increse the volumetosurfce rtio of the cvity. (The stored energy is proportionl to the volume, while the powerloss is proportionl to the surfce re of the boundry conductors.) In rectngulr wveguide this leds towrd overmoded
3 cvities (which introduce their own problems). Here we consider the second possibility. Symmetry [3] nd suppression of unwnted modes will ply importnt roles. Let us now define figure of merit for rectngulr wveguide cvities s volume for generl cvities surfce volume for wveguide cvities (1.3) perimeter For the bsic rectngulr wveguide of width nd height we hve 0 (1.4) 6 3 We cn compre vrious geometries by forming n enhncement rtio (1.5) 0. Doubling Wveguide Height Figure.1 shows wveguide with doubled height, i.e.,. This still propgtes the H 1,0 mde ( TE1,0 mode) with the electric field in the x direction (verticl). Such wveguide with squre cross section, of course, hs other modes of propgtion depending on our choice of frequency. In prticulr there is the H 0,1 mode which is 90 rottion of the H 1,0 mode (with the electric field in the y direction). For this type of wveguide the figure of merit is 4 (.1) 8 The enhncement is 3 (.) 3
4 longitudinl slots in top nd bottom to suppress ny trnsverse (x directed) currents y verticl slots in sidewlls to suppress longitudinl (z directed) currents z x Fig..1 DoubleHeight Rectngulr (Squre) W#veguide for H 1,0 Mode. To suppress this H 1,0 mode we cn put slots in the wveguide wlls s in Fig..1. These re plced prllel to the surfce current density, J s, (or equivlently perpendiculr to the mgnetic field H t the wlls) so s not to interfere with the H 1,0 mode. These slots re verticl (y directed) on the side wlls. On the top nd bottom wlls there re single longitudinl (z directed) slots centered in the wlls. The H 1,0 mode then hs slots perpendiculr to J s (prllel to H ) for suppression (with energy rdited outside the guide). One could lso plce verticl slots in the cvity ends, z = 0 nd z = L. However other things my be occurring there relted to feeding in nd extrcting power. We need to excite this H 1,0 mode without exciting the H 0,1 mode. Here we cn use symmetry s indicted in Fig... As discussed in [7 (Ch. 1)] electromgnetic fields cn be divided into two nonintercting prts, symmetric (sy) nd ntisymmetric (s), with respect to symmetry plne. Figure. hs two symmetry plnes: x =, y = (.3) The rectngulr perture of height,, is suited to feeding rectngulr wveguide of width,, nd height,. The fields re symmetric with respect to the z = plne nd ntisymmetric with respect to the y = plne. 4
5 y Possible input rectngulr wveguide E z x Fig.. Feeding Squre Wveguide With Symmetriclly Positioned Rectngulr Iris We still need to extrct the energy vi closing switch. If we were to insert switch directly in the wveguide of Fig..1 we could locte it on the x = symmetry plne. With the rc closing in the y direction there is problem mintining the y = symmetry plne. One could extend symmetricl electrodes from the y = 0 nd y = plnes so s to plce short rc closely on the y = plne to minimize the symmetry when the rc is closing. However, such short rc limits the power hndling cpbility of this wveguide cvity. This cn be improved by enclosing the switch electrodes in circulr cylindricl dielectric tube, pressurized with gs to rise the switch holdoff voltge. Another possibility is indicted in Fig..3. With the switch t g /4 from the shorted end of stndrdheight wveguide, we cn plce qurterwvetrnsformer section of wveguide (width, height ) []. Here we hve 1/ g 1 guide wvelength c c 4 cutoff wvelength (.4) With the switch recessed from the qurterwve trnsformer only the H 1,0 mode cn propgte here. Note tht the y = symmetry plne is mintined through the trnsformer nd switching section. While Fig..3 shows the input wveguide with iris feeding in from the left, it could lso feed in from the right ner the switch. 5
6 y switch input wveguide E wveguide cvity qurter Wve trnsformer z x g g 4 4 Fig..3 Wveguide Height Reduction Ner Switch After the switch fires, chnging the cvity length, one needs n output connection to extrct the power. This cn be ccomplished by connecting stndrd wveguide to the sidewll s shown in Fig..4. This is like one prt of mgic tee. It is positioned so tht during the chrging cycle it is centered on null of the wveguide electric field, giving no propgting mode in the output wveguide. Note the mintining of the y = symmetry plne. As discussed in [4] this output guide should hve hlf the height of the resonnt cvity guide to mtch the impednce of the two wves in the cvity in prllel into the output guide. Since the wveguide cvity is now high, this mkes good mtch to the stndrd output guide without reducing its height. y wveguide cvity z x Fig..4 Connection to Output Wveguide 6
7 3. Doubling Wveguide Height nd Width Going step further, let us now consider doubling the width to 4, besides the double height. Agin we utilize symmetry to select the H 1,0 mode. Now both the x = nd y = plnes re symmetry plnes. The figure of merit is now 8 (3.1) 1 3 The enhncement is now (3.) Note tht, with the incresed width from to 4, the guide wvelength g is lso incresed for given freespce wvelength,. This will lso hve some effect on the power in the mode nd the losses. With the guide width doubled the H,0 mode cn lso propgte. So it is importnt tht the iris in Fig. 3.1 be centered on x =, so s not to couple to this mode. Furthermore, the sidewll, y directed slots nd top nd bottomwll slots (now centered on x = ) cn still help in suppressing unwnted E modes, but the sidewll slots do not ffect the H 1,0 mode, while the top nd bottom slots (due to their position) do still hve some effect. y possible input rectngulr wveguide cvity E z 4 x Fig. 3.1 DoubleDimensioned Rectngulr Wveguide Cvity 7
8 We still need to compress the wve ner the switch to void introducing other modes there. The switch cn lie on the symmetry plne x = (conducting in the y direction) without introducing the H,0 mode or the H 0,1 mode (s well s the lowest E modes). As discussed in the previous section one cn center short switch rc on (x, y) = (, ) to minimize introduction of unwnted modes. Another pproch is to reduce the wveguidecrosssection dimensions ner the switch s ws done in Fig..3. Now we cn reduce both height nd width by tper s in Fig. 3., keeping every cross section centered on (x, y) = (, ), nd thereby mintining both symmetry plnes. Note tht g is chnging s the wve propgtes through the tper. If one wishes to reduce only the height, then the scheme in Fig..3 is pplicble. This leves the connection to the output wveguides. As illustrted, the scheme in Fig..4 cn be generlized to tht in Fig. 3.3 with two output wveguides, so s to mintin the x = symmetry plne. The two wveguides cn send power to two lods (such s two ntenns with proper reltive phsing), or the wveguides cn rejoin into single wveguide with n pproprite qurterwve trnsformer. Note tht the output guides re. Here is not necessrily the sme s for impednce mtching since the guide wvelength g in the output guide is not in generl the sme s the g for the H 1,0 mode in the wveguide cvity. 4. Concluding Remrks Here we hve elucidted some techniques for incresing the Q of microwve pulsecompression cvities. Fundmentlly, these involve incresing the rtio of the cvity volume to the surfce re of the conducting boundries. For wveguide cvities these become overmoded. So cre needs to be tken to void exciting nd to minimize propgtion of unwnted modes. This involves symmetry nd providing loss to unwnted modes by interfering with their surfce current ptterns. Perhps these techniques cn be extended to obtin even higher Qs of wveguide cvities. There is the lowloss H 0,1 mode of circulr wveguide which is supported by only directed surfce currents. However, this will require specil excittion nd extrction geometries for such cvitymode pttern. One cn, in principle, remove the cvity sidewlls to form FbryPerot resontor [8]. However, t frequencies round 1 GHz, such would be quite lrge nd not pproprite for some pplictions. 8
9 x = 4 switch y = x = 0 tper section g 4 A. Top view y = switch y = y = 0 tper section g 4 B. Side view Fig. 3. Tper to Switch Region y output wveguide symmetry wveguide plnes cvity output wveguide z 4 x Fig. 3.3 Connection to Output Wveguides 9
10 References 1. C. E. Bum, Terhertz Antenns nd Oscilltors Including SkinEffect Losses, Sensor nd Simultion Note 535, September C. E. Bum, Mtching Modulted Electron Bem to Wveguide, Circuit nd Electromgnetic System Design Note 39, April C. E. Bum, Compression of Sinusoidl Pulses for HighPower Microwves, Circuit nd Electromgnetic System Design Note 48, Mrch C. E. Bum, ImpednceMtched Mgic Tee, Circuit nd Electromgnetic System Design Note 51, Mrch A. D. Andreev, E. G. Frr, nd E. Schmiloglu, A Simplified Theory of Microwve Pulse Compression, Circuit nd Electromgnetic System Design Note 57, August C. E. Bum, Rising Cvity Q for MicrowvePulse Compression by Reducing Aperture SkinEffect Losses, Circuit nd Electromgnetic System Design Note 60, June C. E. Bum nd H. N. Kriticos, Electromgnetic Symmetry, Tylor & Frncis, D. M. Pozr, Microwve Engineering,nd Ed., Wiley,
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