Metamaterial-based Slow Wave Structures for Travelling Wave Tubes. Muhammed Zuboraj, Nil Apaydin, Kubilay Sertel, John. L Volakis

Transcription

1 Metamaterial-based Slow Wave Structures for Travelling Wave Tubes Muhammed Zuboraj, Nil Aaydin, Kubilay Sertel, John. L Volakis 1

2 Outlines ü Brief introduc on to Travelling Wave Tube Amlifiers ü Fundamental challenges ü Half- Ring Helix ü Cold and Hot test results ü Ring- Loaded Helix ü Cold and Hot test results ü Comarisons ü Future Direc ons and Remarks 2

3 Imortance of Microwave Power Electronics Alications that require Microwave Power Electronics Consumers Military Science Industry TV, radio, satellite communications, wireless communication, radar (weather), GPS, microwave ovens radar (search, track, missile-seeker), high-ower microwave weaons, electronic countermeasure (ECM) Fusion energy research, charged article accelerators, atmosheric radar, medical, ground enetrating radar Testing, materials rocessing, semiconductor manufacture Klystron electron gun Inut signal Travelling Wave Tube Amlified Outut signal Magnetron Focusing Magnet Collector Gyrotron 3

4 Princiles of Travelling Wave Tubes (TWTs) electron gun Inut signal TWT Amlifier Slow-wave Structure Focusing Magnet Amlified Outut signal Collector q Electron gun sulies the electron beam q Inut and Outut coulers suly the RF signal q Focusing magnets confines the electron beam to center q Slow-wave structure (i.e. helix, ring-bar structure, cerenkov maser) q Collector absorbs electrons Oeration Princile: Amlification via Cerenkov Radiation Electron-beam bunching Field Amlification v v e- v v e- Electron energy transferred to RF signal 4

5 Linearized Gain of a TWT Cherenkov Radiation Condition 1)RF signal v electron velocity v e- Electron gun ββ=2ππ/λλλλ ν ω = β ν = Small signal gain C N (db) N=number of wavelengths C=Pierce gain arameter (* J. R. Pierce, Travelling Wave Tubes, NY: D.Van Nostrand Co, 195) e 2eV m 2)Strong axial E-field at waveguide center (TM z modes) for mode couling C = 3 V v e- =(2eV /m) 1/2 e and m are electron charge and mass. V =voltage alied to electron gun. 2 Eaxial 2 2β 4 I P V Goal: Higher gain (G ) Wider bandwidth Smaller design (L ) Needs to be as large as ossible to obtain high gain. Gain G G /2 G /2 Bandwidth Gain G Frequency L Device Length 5

6 Mo va ons Ø To design a high ower TWT amlifier Ø Imrove bandwidth Ø Design a SWS coma ble with high beam current Ø Miniaturiza on of TWTA 6

7 Cold Circuit Performance of the Helix (without the electron beam) 1)Phase velocity of EM wave=electron velocity v = c sinψ = v e- =(2eV /m) 1/2* Ψ=cot -1 (2πa/)=itch angle *e and m are electron charge and mass, V is the voltage alied to electron gun. Helix δ a=4.2mm =5,8,1mm a δ=.7mm b=11mm w=1mm w ν /c Normalized Phase velocity =1mm =8mm constant v over wide BW =5mm Advantages: Simle geometry, wide bandwidth Tunable oeration 2)Pierce Imedance: K =E z2 /(2β 2 P) (*J. R. Pierce, Travelling Wave Tubes, NY: D.Van Nostrand Co, 195) K (Ω) K =E z2 /(2β 2 P)=E z2 /2β 2 Wv g v g à K E z : Longitudinal field strength along z axis β:hase constant within WG P:net ower flow along helix Strong transverse electric field! Interaction Imedance K =5mm =8mm K à TWT gain =1mm Shortcomings: Limited gain at high frequencies (K dros) Sace harmonics inhibiting amlification for v e- >.2c (smaller K for v e- >.2c) 7

8 Half-Ring Helix ü Purely Metallic structure ü Easy to fabricate Dimensions: Radius, a=4mm Pitch(Periodicity),=8mm Width w=1.45mm Thickness, δ=.74mm E-field Profile(V/m) J surface Distribution (A/m) Ø Skew symmetric current distribution Ø Better disersion and significant slowdown of wave Ø Strong E-Field at the center 8

9 Cold Circuit Performance of the Half-Ring Helix υ /c Effect of itch, Lower more slowdown =6mm =8mm =1mm v b 2a υ /c Effect of cylinder radius, b.4 b=9mm b=11mm.35 b=13mm.3.25 b v Lower b better disersion K (Ω) K at lower frequencies =6mm =8mm =1mm Lower K Design arameters: a=4mm =8mm b=11mm K (Ω) b b=9mm b=11mm b=13mm K Lower b strong couling to cylinder wall K

10 Comarison to Helix Helix Normalized Phase & Grou Velocity Half-Ring Helix Helix a=4mm =8mm w=.74mm Ø Similar disersion as helix Ø Extra slow-down of wave w Half-Ring Helix 2a υ /c.35 ü slower.3.25 Interaction Imedance K (Ω) υ g /c Half-Ring Helix Helix ü Similar Disersion K (Ω) ü Similar K (Ω) Half-Ring Helix Helix

11 Cold Test Results of Proosed Design 2a w a=4mm =8mm w=.74mm υ /c Half-Ring Helix V Vs. f Wave slow down:.28c<v <.32c.25 Almost constant V over S-band Disersion grah Wave slowdown Half-Ring Helix Light-line K (Ω) K (Ω) Vs. f Ø 8Ω>K >3 Ω Half-Ring Helix k=2πa/λ g

12 Imortant Performance Parameters- Frequency&Current Κ-ω Diagram Disersion grah -1-2 Return Loss ka> k=2πa/λ g Half-Ring Helix Light-line S11 in db Frequency in GHz TWTs oerate best for ka>.7 to handle the electron beam efficiently(f>2.25ghz) Ø Cannot oerate for I beam >.15A Ø Higher return loss comared to regular helix (limits outut ower) Ø More sensitive to velocity detuning than regular helix Small signal gain C N (db) N=number of wavelengths, C=Pierce gain arameter (* J. R. Pierce, Travelling Wave Tubes, NY: D.Van Nostrand Co, 195) 12

13 TWT Performance of Half-Ring Helix Electron article trajectory Electron velocity modulation Design Parameters Voltage V kv Current I.1 A Electron velocity.32c Magnetic Field.3T Beam radius 2 mm Interaction imedance K 55Ω Length L 8cm Gain 28dB frequency 3 GHz Frequency Sectrum of the Outut Signal Inut/outut Signals(Time Domain ) 13

14 TWT Gain versus Frequency Gain in db Half-Ring Helix Standard Helix 1dB imrovement Design Proerties Maximum Gain 28dB -3dB Gain BW.75GHz TWT length 8cm Frequency band S-band Gain Imrovement 1dB Frequency in GHz Ø Suitable for S-band satellite communications (2.5GHz-3.25GHz) Ø 1dB imrovement in the gain comared to regular helix TWT Ø Regular helix will have a similar gain with a 1.4 times longer layout. Issue: Cannot oerate for I beam>.15a 14

15 Ring-Loaded Helix with Higher Pierce Imedance 2a Uncouled Uncouled Couled Helix Ring-loaded Helix Ring Normalized Phase velocity Helix 2b a=4.2mm =8mm a1=3mm b=11mm 2a1 15 2a (V 1 I 1 ) (V 2 I 2 ) L1 L2 C1 C2 L3 L3 Ring-loaded Helix LM LM LM Inductive couling K =E z2 /(2β 2 P)=E z2 /2β 2 Wv g v g à K CM Caacitive couling Interaction Imedance K C3 C3 (V 3 I 3 ) (V 4 I 4 ) ν /c.3.28 Ring-loaded Helix K (Ω) 1 3 times larger K à TWT gain disersiveà narrow BW 5 Helix

16 Effect of Inner Ring Radius.38 Normalized Phase velocity 2 Interaction Imedance K less disersive ν /c a1=3mm a1=4mm K (Ω) 15 1 a1=3mm a1=4mm Larger K a=4.2mm =8mm b=11mm a1 à less disersiveà more BW a1 à larger K à more Gain Ø Advantage: Better erformance with smaller a1 Ø Drawback: More sensitive to sace charge effects (oerates with low current e-beams) 16

17 Disersion Reduction via Metallic WG Loading Ring-loaded Helix within Cylindrical WG 2b 2a 2a1 a=4.2mm =8mm a1=3mm b=11mm Ø Less disersiveà increased BW Ø Larger K than regular helix à higher gain Ø Smaller cross sectional area à more comact in lateral direction ν /c Normalized Phase velocity Helix (b=11mm) b=7mm Ring-loaded Helix (b=11mm) K (Ω) Interaction Imedance K Ring-loaded Helix (b=11mm) Ring-loaded Helix (b=7mm) Helix (b=11mm) Ring-loaded Helix (b=7mm) 4 2 b=7mm

18 Free sace roaga on Imortant Performance Parameters- Frequency&Current Κ-ω Diagram Small Signal Gain (db)* ka>.7 Gain(dB) I beam =.5A I beam =.25A 38 TWTs oerate best for ka>.7 to handle the electron beam efficiently(f>2.25ghz) Small signal gain C N (db) N=number of wavelengths, C=Pierce gain arameter (* J. R. Pierce, Travelling Wave Tubes, NY: D.Van Nostrand Co, 195) Doubling I beam increases the gain by 13dB. However, sace charge effects become more rominent. TWT becomes more sensitive to velocity detuning. Sace charge effects deend on the circuit and the electron charge density 18

19 TWT Performance of Ring-Loaded Helix Electron article trajectory Electron velocity modulation Inut/Outut Signals(Time Domain ) Design Parameters Voltage V 21.5 kv Current I.25 A Electron velocity.29c Magnetic Field.15T Beam radius 2 mm Couling imedance K 8 Ohm Length L 6 cm Gain 32 db frequency 2.5GHz Frequency Sectrum of the Outut Signal 19 19

20 TWT Gain versus Frequency Ring-loaded Helix with b=7mm Design Proerties Gain(dB) dB imrovement Maximum Gain -3dB Gain BW TWT length Frequency band Gain Imrovement 32dB.8GHz 6cm S-band 17dB 14 Regular Helix with b=7mm Ø Suitable for S-band satellite communications (2.1GHz-2.9GHz) Ø 17dB imrovement in the gain comared to regular helix TWT Ø Regular helix will have a similar gain with a 1.5 times longer layout. Issue: sensitive to sace charge effects due to the small ring radius, does not oerate for I beam >.25A 2

21 Design comarisons Half- Ring Helix Ring- Loaded Helix Disersion Maximum velocity devia on 5% (over the BW) Maximum velocity devia on 6%(over the BW) Interac on imedance Decreasing over the band Constant over the band and 1.5 mes higher 2 than Half- Ring Helix Ez K = 2 (suitable for high ower) 2β P Maximum Gain 28 db 32 db 3dB Bandwidth 25% 32% Beam current I beam.15a I beam.25a Miniaturiza on Less suitable More suitable Alica ons Low ower High Power Fabrica on Comara vely easier Comara vely difficult than half- Ring Helix 21

22 Concluding Remarks Half- Ring Helix Designed a Half-Ring helix that oerates with v e- >.2c Oerates with v e- =.32c. K about 4 times larger than the standard helix. Similar disersion like helix Ring- Loaded Helix Designed a ring-loaded helix that oerates with v e- >.2c Oerates with v e- =.29c. K twice as large as the regular helix. More disersive than the regular helix (limits the BW). Design a finite rototye and calculate the erformance of the high ower microwave source. Oerates with high I beam Imroves the gain by 1dB. Miniaturization by a factor 1.4 comared to a regular helix with similar gain. Suitable for S-band satellite communications. Future Direction: Increase continuous wave ower and BW by taering the circuit. Design a sever circuit to reduce reflection and increase efficiency Design a suort layout of the SWS in consideration with heat conductivity Cold and hot test of the finite 8cm TWT layout. Design a finite rototye and calculate the erformance of the high ower microwave source. Oerates with high I beam Imroves the gain by 17dB. Miniaturization by a factor 1.5 comared to a regular helix with similar gain. Suitable for S-band satellite communications. Future Direction: Disersion reduction by taering the itch of the helix. Calculating the efficiency of the overall circuit. Cold and hot test of the finite 6cm TWT layout. 22