Power amplifier beam loading and wideband feedback G
Power amplifier, beam loading and wideband feedback G. Favia, M. Paoluzzi Acknowledgements: H. Damerau, M. Morvillo, N. Nasresfahani, C. Rossi 24/01/2019 PS Landau RF System Study Group
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Outline Ø Beam loading in the Landau RF system Ø Cavity options Ø Amplifier design for a garnet and ferrite loaded cavity Ø Amplifier design for a Finemet cavity option Ø Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Beam loading Conclusions ig ΦG Φz ΦS ib I 0 V 0 it Main RF voltage 4 th harmonic ig ig = current from the power source ib = beam current it = ig+ib = YV = total current on the cavity Φz = cavity detuning angle Φg = angle between the power source and the cavity Φs = angle between the zero crossing of the Landau RF voltage and bunch center Bunch Ideally no net energy transfer between cavity and beam
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Beam loading ig ΦG Φz ΦS ib I 0 V 0 it CAVITY DETUNING ig
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions RF system options (Parameters per cavity unit) Configuration Quality factor, Q 0 Shunt impedance, R 0 Garnet tuned (mushroom-like loading) Garnet tuned (no capacitive loading) Ferrite tuned Wideband Finemet cav. Single-gap, 20 k. V Double-gap, 2 10 k. V Double gap, 2 10 k. V, 2 5 rings (2 k. V/ring) 8800 3000 340 31. 6 300 k. W 55 k. W 9. 5 k. W (19 k. W/gap) 3. 8 k. W (1. 9 k. W/gap)
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Amplifier design The design of the power source accounts for: Ø Cavity configuration q Voltage and current requirements q Beam loading q Max impedance seen by the beam Finemet cavity ‘amplifier design Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Amplifier design The design of the power source accounts for: Ø Cavity configuration q Voltage and current requirements q Beam loading q Max impedance seen by the beam Finemet cavity ‘amplifier design Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions RF system options (Parameters per cavity unit) Configuration Quality factor, Q 0 Shunt impedance, R 0 Power amplifier Garnet tuned (mushroom-like loading) Garnet tuned (no capacitive loading) Ferrite tuned Wideband Finemet cav. Single-gap, 20 k. V Double-gap, 2 10 k. V Double gap, 2 10 k. V, 2 5 rings (2 k. V/ring) 8800 3000 340 31. 6 300 k. W 55 k. W 9. 5 k. W (19 k. W/gap) 3. 8 k. W (1. 9 k. W/gap) Tube (close to cavity) Solid state (outside ring)
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions RF system options (Parameters per cavity unit) Configuration Quality factor, Q 0 Shunt impedance, R Power amplifier Garnet tuned (mushroom-like loading) Garnet tuned (no capacitive loading) Ferrite tuned Wideband Finemet cav. Single-gap, 20 k. V Double-gap, 2 10 k. V Double gap, 2 10 k. V, 2 5 rings (2 k. V/ring) 8800 3000 340 31. 6 300 k. W 55 k. W 8. 5 k. W (19 k. W/gap) 3. 8 k. W (1. 9 k. W/gap) Tube (close to cavity) Solid state (outside ring)
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Amplifier design The design of the power source accounts for: Ø Cavity configuration q Voltage and current requirements q Beam loading q Max impedance seen by the beam Finemet cavity ‘amplifier design Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions RF tube choice The power stage has to be able to provide the total current and withstand the required gap voltage RS 1084 CJ Max frequency Known characteristics: f 250 MHz Anode voltage (dc) Va 12 k. V Anode dissipation Pa 70 k. W Efficiency η 65% • gm=0. 0822 A/V • RA~3 kΩ • Verified performance at Va=10 k. V (PSC 10 and PSC 20) • Anode current up to 40 A
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions RF system options Configuration Quality factor, Q 0 Shunt impedance, R 0 Power amplifier Garnet tuned (mushroom-like loading) Garnet tuned (no capacitive loading) Ferrite tuned Wideband Finemet cav. Single-gap, 20 k. V Double-gap, 2 10 k. V Double gap, 2 10 k. V, 2 5 rings (2 k. V/ring) 8800 3000 340 31. 6 300 k. W 55 k. W Tube Coupler between amplifier and cavity foreseen (N=2) 8. 5 k. W (19 k. W/gap) 3. 8 k. W (1. 9 k. W/gap) Tube Solid state (outside ring) Direct connection between amplifier and cavity (N=1)
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Amplifier design The design of the power source accounts for: Ø Cavity configuration q Voltage and current requirements q Beam loading q Max impedance seen by the beam Finemet cavity ‘amplifier design Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Garnets tuned cavity
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Double gap ferrite cavity The beam sees the two gaps in series
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design RF system options (Parameters per cavity unit) Garnet tuned (mushroom-like loading) Garnet tuned (no capacitive loading) Ferrite tuned Single-gap, 20 k. V Single-gap, 20 k. V Double-gap, 2 10 k. V 8800 3000 340 Shunt impedance, R 0 300 k. W 55 k. W 9. 5 k. W (19 k. W/gap) Loaded shunt impedance, RL 11. 5 k. W 9. 9 k. W 2. 3 k. W 1. 7 A (IA=3. 4 A) 2 A (IA=4 A) 4. 3 A 3. 2 A (IA=6. 4 A) 3. 5 A (IA=7 A) 7. 3 A Required RF power, P, at 0° 18 k. W 20 k. W 22 k. W Required RF power, P, at 30° 33 k. W 35 k. W 37 k. W Tube (RS 1084 CJ) Configuration Quality factor, Q 0 Required current, Ig , at 0° at 30° Power amplifier Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions RF system options (Parameters per cavity unit) Garnet tuned (mushroom-like loading) Garnet tuned (no capacitive loading) Ferrite tuned Single-gap, 20 k. V Single-gap, 20 k. V Double-gap, 2 10 k. V 8800 3000 340 Shunt impedance, R 0 300 k. W 55 k. W 9. 5 k. W (19 k. W/gap) Loaded shunt impedance, RL 11. 5 k. W 9. 9 k. W 2. 3 k. W 1. 7 A (IA=3. 4 A) 2 A (IA=4 A) 4. 3 A 3. 2 A (IA=6. 4 A) 3. 5 A (IA=7 A) 7. 3 A Required RF power, P, at 0° 18 k. W 20 k. W 22 k. W Required RF power, P, at 30° 33 k. W 35 k. W 37 k. W Tube (RS 1084 CJ) Configuration Quality factor, Q 0 Required current, Ig , at 0° at 30° Power amplifier x 4 as seen by the beam
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Amplifier design The design of the power source accounts for: Ø Cavity configuration q Voltage and current requirements q Beam loading q Max impedance seen by the beam Finemet cavity ‘amplifier design Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Amplification chain Af CAVITY
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Amplification chain Grounded cathode Ø higher power gain Ø higher input capacitance Ø Miller effect at 40 MHz Grounded grid Ø lower power gain Ø lower input capacitance Ø Miller effect negligible Af CAVITY
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Amplification chain Grounded cathode Ø higher power gain Ø higher input capacitance Ø Miller effect at 40 MHz Grounded grid Ø lower power gain Ø lower input capacitance Ø Miller effect negligible The advantages of the higher power gain of the grounded grid configuration are undermined by the huge and harmless Af CAVITY
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Amplification chain Af Solid - state ~1 k. W Low input impedance CAVITY
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Fast RF-feedback Finemet cavity ‘amplifier design Conclusions β Af RF IN ~1 k. W Solid - state Low input impedance 1. 5 kΩ CAVITY
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design RF system options (Parameters per cavity unit) Garnet tuned (mushroom-like loading) Garnet tuned (no capacitive loading) Ferrite tuned Single-gap, 20 k. V Single-gap, 20 k. V Double-gap, 2 10 k. V 8800 3000 340 Shunt impedance, R 0 300 k. W 55 k. W 9. 5 k. W (19 k. W/gap) Loaded shunt impedance, RL 11. 5 k. W 9. 9 k. W 2. 3 k. W 500 250 84 Required RF power, P, at 0° 18 k. W 20 k. W 22 k. W Required RF power, P, at 30° 33 k. W 35 k. W 37 k. W Power amplifier Tube (RS 1084 CJ) Beam impedance < 1. 5 k. W, direct feedback ~400 ns ~240 ns ~86 ns Configuration Quality factor, Q 0 Loaded quality factor, QL Group Delay How far from the cavity can we install the amplifier ? Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions RF system options (Parameters per cavity unit) Configuration Quality factor, Q 0 Shunt impedance, R 0 Power amplifier Garnet tuned (mushroom-like loading) Garnet tuned (no capacitive loading) Ferrite tuned Wideband Finemet cav. Single-gap, 20 k. V Double-gap, 2 10 k. V Double gap, 2 10 k. V, 2 5 rings (2 k. V/ring) 8800 3000 340 31. 6 300 k. W 55 k. W 19 k. W 3. 8 k. W (1. 9 k. W/gap) Tube Solid state (outside ring)
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Finement cavity option Three possible amplifier configurations to drive a Finemet based cavity: • Tube based amplifier provides required current directly to the gap ① • Solid-state amplifier N. of cores=N. of SSA modules: each core is fed by a module ② More cores can be paralleled and fed by a single module ③ ① ② ③ 29
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Tube drive Finemet cavity ‘amplifier design Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Amplifier design The design of the power source accounts for: Ø Cavity configuration q Voltage and current requirements q Beam loading q Max impedance seen by the beam Finemet cavity ‘amplifier design Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Solid state drive Due to the inherent shunt impedance and large bandwidth of the cavity, the amplifier can be located outside the tunnel, hence choosing solid state technology Cavity configuration: • 2 gaps • 5 rings 5 x 210 Ω According to measurements results, the cores’ impedance summing shows a transformation factor N=1. 36 due to electrical coupling: Zgap=N 2·(5 x 210 ) ~2 kΩ Vgap=N· (5 x 1. 45 k. V)~10 k. V Each individual core driven by a 5 k. W solid-state amplifier through a 1 to n 2=4 impedance transformer. It provides: • IA 0= n · N · Ig = 2 · 1. 36 · 5 A ~ 14 A • Beam adds RF current
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Amplifier design The design of the power source accounts for: Ø Cavity configuration q Voltage and current requirements q Beam loading q Max impedance seen by the beam Finemet cavity ‘amplifier design Conclusions
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Beam impedance Realistic delay values for 5 k. W amplifier and the loop are 30 ns to 50 ns ( factor 2 -3 in impedance reduction)
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions RF system options (Parameters per cavity unit) Garnet tuned (mushroom-like loading) Garnet tuned (no capacitive loading) Ferrite tuned Wideband Finemet cav. Single-gap, 20 k. V Single-gap, 20 k. V Double-gap, 2 10 k. V Double gap, 2 10 k. V, 2 5 rings (2 k. V/ring) 8800 3000 340 8. 5 Shunt impedance, R 0 300 k. W 55 k. W 8. 5 k. W (19 k. W/gap) 1. 9 k. W/gap Loaded shunt impedance, RL 11. 5 k. W 9. 9 k. W 2. 3 k. W 1. 9 k. W (0. 95 k. W/gap) 1. 7 A (IA=3. 4 A) 2 A (IA=4 A) 4. 3 A 2 x 5 A (10 x IA=14 A ) 3. 2 A (IA=6. 4 A) 3. 5 A (IA=7 A) 7. 3 A 2 x 6. 6 A (10 x IA=18 A) Required RF power, P, at 0° 18 k. W 20 k. W 22 k. W 50 k. W Required RF power, P, at 30° 33 k. W 35 k. W 37 k. W 66 k. W Power amplifier Tube (RS 1084 CJ) Solid state (outside ring) Beam impedance < 1. 5 k. W, direct feedback 1. 9 k. W (2 x 0. 95 k. W/gap) Configuration Quality factor, Q 0 Required current, Ig , at 0° at 30°
Outline Beam Loading Cavity options Garnet and Ferrite cavities’ amplifier design Finemet cavity ‘amplifier design Conclusions Ø A preliminary design for an amplifier driving the three Landau system options has been developed, based on a preliminary design of the cavity Ø A possible power source design foreseeing a vacuum tube with validated performance has been demonstrated for garnets and ferrite options § An impedance reduction can be provided with safe margins in terms of delay § A pre-amplification stage based on SSA can be foreseen Ø A SSA is the most suitable for a Finement cavity to cover a large bandwidth § RF feedback not possible if locating the amplifier far from the cavity § If close to the cavity the reduction would be negligible
Input power CLASS AB - half RF cycle conduction - IA vs. Vgrid non linearity -230
Power amplifier configuration • Grounded cathode Ø higher power gain Ø higher input capacitance • Grounded grid anode Ø lower power gain Ø lower input capacitance anode RF OUT RF IN grid Y IN cathode Y IN RF IN
Grounded cathode parameters • Grounded cathode Ø higher gain Ø higher input capacitance Positive feedback: risk of oscillations RF OUT Miller effect: RF IN Y IN Stability condition • gm=0. 0822 A/V • RA~3 kΩ • Av=230=47 d. B
Grounded grid parameters • Grounded grid Ø lower power gain Ø lower input capacitance Negative feedback: -prevents oscillations -lowers the input capacity RF OUT Miller effect: Y IN RF IN • gm=0. 0822 A/V • RA~3 kΩ • Av=230=47 d. B
Smaller tube option RS 2012 C Frequency f 110 MHz Anode voltage (dc) Va 7. 5 k. V Anode dissipation Pa 12 k. W Efficiency η 63% Transconductance gm 0. 05 A/V Anode resistance RA 3 kΩ PA= 7. 5 k. W
Smaller tube option Max tolerable current PA=11 k. W PA diss =5 k. W< 12 k. W
Landau cavity options (Parameters per cavity unit) Garnet tuned (mushroomlike loading) Garnet tuned (no capacitive loading) Ferrite tuned Wideband Finmet cav. Single-gap, 20 k. V Double-gap, 2 10 k. V Double gap, 2 10 k. V, 2 5 rings (2 k. V/ring) 8800 3000 340 15. 8 300 k. W 55 k. W 19 k. W 3. 8 k. W Loaded quality factor, QL 500 250 ~42 <10 Loaded Shunt impedance, RL 500 250 ~42 <10 Required RF power, P, at 0° 18 k. W 20 k. W 22 k. W 53 k. W Required RF power, P, at 30° 33 k. W 35 k. W 37 k. W 67 k. W Power amplifier Tube (RS 1084 CJ) Solid state (outside ring) Beam impedance < 1. 5 k. W, direct feedback 1. 9 k. W (no feedback) Configuration Quality factor, Q 0 Shunt impedance, R 0
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