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Cerenkov Maser: Dielectric Lined Cylindrical Waveguide Slow-Wave Structure X Z Electron Gun Dielectric Liner RF Signal, Νp Εr Collector E- E- E- E- Y

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Cerenkov Maser: Dielectric Lined Cylindrical Waveguide Slow-Wave Structure X Z Electron Gun Dielectric Liner RF Signal, Νp Εr Collector E- E- E- E- Y Metamaterial Slow-wave Structures for High-Power Microwave Devices Kubilay Sertel John. L Volakis Students: Nil Apaydin, Panos Douris & Md. Zuboraj Wave Slow-down Using Anisotropic Materials Periodic Magnetic Photonic Crystal Isotropic Dielectric Medium Periodic Isotropic Medium Unit cell F A2 A1 B B1 B2 r r2 r1 … r1 r 2 … … … r H0 B:Isotropic dielectric B :Isotropic dielectrics 1,2 A1,2:Anisotropic dielectrics Corresponding K-ω diagrams F: Biased ferrimagnetic layers w w 2nd order relation (w’=0) w 2nd order relation (w’=0) rd w w k RBE k 3 order ( ’=0, ”=0) k Slow-group velocity mode @ SIP SIP due to anisotropy Group velocity: vg k 0 c Wave slow- down(v =0) Phase velocity: v k g p 1 Field enhancement c Experimental Validation of Wave Slow-Down In Volumetric Form In Printed Form Finite 15-unit-cell Volumetric MPC Finite 9-unit-cell Printed MPC 4.4 0.44 4.40.440.1 Finite 8-unit-cell Printed MPC 3.96 0.44 3.960.440.1 Measured Group Delay (ns) SIP SIP 100 MPC MPCs Free Free Band edge Space Band edge 80 @SIP: 96.1ns Space 60 @ SIP: 7.2ns 0.18ns 0.33ns 40 Wave velocity forward backward group delay (ns) delay group reduction by a 20 factor of 286 0 2.4 2.5 2.6 2.7 2.8 2.9 Frequency (GHz) Novel Slow-wave Structures and Antenna Designs Utilizing Slow Group Velocity Modes Gain Enhanced Dipole Antenna Printed Coupled Lines Emulating Slow Modes Embedded in MPC Uncoupled Uncoupled ~Uniform Coupled |E| Aperture (V I ) 1 1 (V3 I3) Illumination L1 L3 LM C1 C3 LM CM 0 0 (V2 I2) (V4 I4) L2 L3 LM C2 C3 Inductive Capacitive 0 coupling coupling 0 High Directivity Gain Enhancement via Leaky- waves Miniaturized Antennas w/ Optimal Gain BW 2 Normalized 10log( VOC /8RIN ) 1.05” L / 20 15dB 0 1.03” 0 14 DBE Antenna dB Mode Profile at Broadside 6.5 dB Element 2.22 GHz Gain at 2.22GHz 450 Ө (in degrees) MPC Antenna Element Broadside 6.2 dB Gain at 2.35GHz Remarkably Large Bandwidth for Thin Conformal Arrays Bowtie Array with FSS in substrate Interweaved Spiral Array (ISPA) w/ •22:1 BW FSS in Substrate Infinite Unit Cell •Low profile Infinite Unit Cell •36:1 BW •Efficiciency. ≥ 69% •Low profile ε = 4 ε = 4 r •Excellent polarization r •Efficiency ≥ 63% purity (AR ≥ 43 dB) •Circular polarization 71.75mm 71. 5mm (0.06λ-1.4 λ) (0.04λ-1.5 λ) FSS in substrate: Rs = 25Ω/□ 23.25mm FSS in substrate: 23.25mm (0.02λ-0.45λ) 23.25mm Rs = 25Ω/□ (0.014λ-0.5λ) (0.02λ-0.45λ) 270-5850 MHz (22:1) 175-6350 MHz (36:1) 5 Integrated UWB Balun and Demonstrated Meta-structured Array Benefits New thin Metastructured Array is • Thinner • Much greater bandwidth • Has integrated balun and feed (several balun/feed options) • Lightweight 600-4500MHz • Military datalinks: • Link-16, DWTS, DDL, TTNT, TACAN, etc. • Almost all commercial telecom waveforms • Wideband SAR, TWRI Measured Metastructured Aperture •Much thinner integrated printed balun (trivial cost); as thin as /15 at 600MHz, lowest operational frequency. • Measured array was 8x8 and had 7.3:1 VSWR<2 bandwidth with no FSS in substrate. • Aperture: 9.4”x9.4” (89in2) • Scanning verified to 60o with no sidelobes or surface waves • Beam steering over entire band (digital or optimal beam formers required). 6 6 Nonreciprocal Leaky Wave Antenna Using Coupled Microstrip Lines Nonreciprocal Leaky-wave Antenna -1 -αy θ k θ=sin (β-1/k0) Ferrite substrate: ε =14, e k z r 0 4πM =1000 G, z s β-1 δH=10Oe, tan δε=0.0002 y x … Hi -jβ y Hi h e -1 ZL 1 2 N ZL Unit-cell Permanent magnet Dispersion Diagram l1 l2 l1 4.1 Guided Wave Leaky Wave Guided Wave w 1 H Region Region Region i 4 z x uncoupled y s coupled Hi =1600Oe 1 w 3.9 x 3 Beam-steering capability s2 w2 without frequency d 3.8 modulation due to tunable dispersion l1=110, l2=120, w1=60, 3.7 properties with bias field Frequency(GHz) H i =1450Oe w2=20, w3=30, s1=105, strength, Hi + - s =10,h=100, d=440(mils) 3.6 d -k d k d d 2 -1 o o +1 3.5 -p -0.5p 0 0.5p p Normalized wavenumber K(kd ) Nonreciprocal Transmitting and Receiving Properties • guided/slow wave: |β /k |>1 does not radiate • leaky/fast wave: |β-1/k0|<1 radiates +1 0 Traditional Slow-wave Structure for Travelling Wave Tubes Cerenkov Maser: Dielectric Lined Cylindrical Waveguide Slow-wave Structure x z electron gun dielectric liner RF signal, νp εr collector e- e- e- e- y Bunched B0, electron e- e- e- e- (static magnetic field) beam, νe- εr dielectric liner Cherenkov Radiation Condition Corresponding K-ω diagram 50 1)Microwave signal vp ≈electron velocity ve- 40 Wide BW c 30 (constant vp) p e- eV0 / m 20 eq *e and m are electron charge and mass. frequency(GHz) V0 =voltage applied to electron gun. 10 0 2)Strong longitudinal E-field at waveguide center 0 0.2p 0.4p 0.6p 0.8p p 1.2p 1.4p 1.6p Normalized wavenumber K= kd (TMz modes) for mode coupling Issues to be Addressed in Designing High-Power Microwave Devices Advantages: Shortcomings: Cerenkov Maser •Simple geometry •Limited wave slow-down •Wider bandwidth (depends on the filling ratio (a/b) •Tunable operation and r) •Several MWs of output •Dielectric charging z x microwave power •Surface breakdown y •Validated performance •Bulky design Dielectric filling ratio=a/b Goal: •Avoid •Larger amplification (G0) • Smallest configuration (L) •Wide bandwidth charging G0 G0 G0/2 G0/2 Bandwidth Gain Gain Frequency L Device Length Solution •Purely metallic slow-wave metamaterial structures Metallic construction Additional wave slow-down (L) Possible Slow-wave Structures for Travelling Wave Tubes Travelling Wave Tube with Periodic Slow-wave Liner Cherenkov Radiation in Periodic Media vp=c/n Electron ve- particle n=effective refractive index of the Limited wave slow-down 1 2 medium good for relativistic e-beams, ve-c Dielectric/Ferrite Metal Corrugations Concentric Metallic Rings Coupled Transmission Lines Corrugations on Dielectric OR Helix Double Helix Ring-Bar Structure Coupled Cavities Enormous wave slow-down (good for slower e-beams, 0.1c<ve-<0.3c) Metallic Slow Wave Structures Based on Helical Waveguide Electron gun Travelling Wave Tube V0 1/2 ve- =(eV0/m) e and m are electron charge and mass. V0 =voltage applied to electron gun. Operation Principle Advantages of Helix WG •Considerable wave slow Electron-beam bunching Field Amplification down. •Purely metallic construction. •Wide BW operation. Gain-9.54+47.3CN (dB) 2 Needs to be as EIaxial 0 large as possible to (* J. R. Pierce, Travelling Wave Tubes, NY: D.Van Nostrand C 3 Co, 1950) 2 obtain high gain. N=number of wavelengths 24 PV0 Key Performance Parameters for Helical Waveguides 2 2 1)Phase velocity of EM wave=electron velocity 2)Interaction Impedance: K0=Ez /(2β P) 1/2* -1 vp= csinψ = ve- =(eV0/m) Ψ=cot (2πa/p) (*J. R. Pierce, Travelling Wave Tubes, NY: D.Van Nostrand Co, 1950) *e and m are electron charge and mass, V0 is the voltage applied to electron gun. E : Longitudinal field z strength along z axis β:phase constant within Helix p Double- Helix p WG a P:net power flow along a helix Strong a=2.375mm transverse p=3.52mm electric field! Normalized Phase velocity Interaction Impedance K 0.5 100 0 Double-helix 0.4 ) double helix /c 0.3 p helix ( 50 0 0.2 K helix 0.1 5 10 15 0 Need Frequency(GHz) Need Larger2 K0 for4 6 8 10 12 14 stronger interaction constant vp Frequency(GHz) for wider BW with the e-beam •Double-helix allows for more energy transfer from the e-beam to the RF signal. Simplified Double-Helix : Ring-bar Structure Double-Helix Ring-bar Structure p Simpler p a a δ a=2.375mm p=3.52mm δ=0.15mm Interaction Impedance K (Ω) Normalized Phase &Group Velocity 0 0.5 100 0.4 Double Helix 80 Ring-bar WG /c slower larger ) p 0.3 60 Ring-bar WG ( 0.2 0 K 40 Double Helix 0.1 3 4 5 6 7 8 9 10 11 12 13 20 Frequency(GHz) 0 0.5 2 4 6 8 10 12 14 Frequency(GHz) 0.4 Similar dispersion /c g 0.3 Double Helix •Easier to fabricate 0.2 Ring-bar WG •Extra wave slow-down 0.1 3 4 5 6 7 8 9 10 11 12 13 •Higher K0(Ω)larger gain Frequency(GHz) Design 1: Double Ring-bar Structure for Miniaturization p Uncoupleda1=2.375mmUncoupled a2=1.9mmCoupled Ring-bar p=3.52mm (V I ) (V I ) 1 1 δ=0.15mm 3 3 δ L1 L3 LM C1 C3 LM CM 0 0 (V2 I2) (V4 I4) L2 L3 LM C2 C3 a1 Purely Inductivemetallic Capacitive construction 0 0 Connectedcoupling coupling inner and outer rings (no charging or arcs) Inner Ring (Inductive coupling) a2 Current Distribution E-field profile uncoupled coupled Inductive&capacitive coupling Strong longitudinal field stronger coupling extra wave slow-down&miniaturization between the RF signal and e-beam Performance of Double Ring-bar Structure Phase & Group Velocities Interaction Impedance 0.4 200 Larger K0 150 ) ( /c 100 slower 0 p 0.2 K 50 Ring-bar Double ring-bar 0 0 3 4 5 6 7 8 9 Frequency(GHz) 3 4 5 6 7 8 9 Ring-bar Frequency(GHz) Double ring-bar 0.4 Ring-bar Double ring-bar Extra wave slow-down /c (0.18c<v <0.32c) p g 0.2 Larger K0 over the bandwidth (90Ω<K <150 Ω) More dispersive 0 More dispersive (not desired) 0 (not desired) 3 4 5 6 7 8 9 Operates between 3-7GHz (v =0.25c±0.07c) Frequency(GHz) p Design 2: Modified Ring-bar Structure for Additional Miniaturization Modified Ring-bar Structure Concentric ring- a1=2.375mm bars increase δ a2=1.9mm the current path p=3.52mm a1 and leads to δ=0.15mm miniaturization.
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