A PFN consists of a series of high-voltage energy-storage capacitors and inductors. These components are interconnected as a "ladder network" that behaves similarly to a length of transmission line. For this reason, a PFN is sometimes called an "artificial, or synthetic, transmission line". Electrical energy is initially stored within the charged capacitors of the PFN by a high-voltage DC power supply. When the PFN is discharged, the capacitors discharge in sequence, producing an approximately rectangular pulse. The pulse is conducted to the load through a transmission line. The PFN must be impedance-matched to the load to prevent the energy reflecting back toward the PFN.
Transmission-line PFNs
Simple charged transmission-line pulse generator
A length of transmission line can be used as a pulse-forming network.[1][2] This can give substantially flat-topped pulses at the inconvenience of using of a large length of cable.
In a simple charged transmission-line pulse generator (animation, right) a length of transmission line such as a coaxial cable is connected through a switch to a matched load RL at one end, and at the other end to a DC voltage source V through a resistor RS, which is large compared to the characteristic impedance Z0 of the line.[1] When the power supply is connected, it slowly charges up the capacitance of the line through RS. When the switch is closed, a voltage equal to V/2 is applied to the load, the charge stored in the line begins to discharge through the load with a current of V/2Z0, and a voltage step travels up the line toward the source.[2] The source end of the line is approximately an open circuit due to the high RS,[1] so the step is reflected uninverted and travels back down the line toward the load. The result is that a pulse of voltage is applied to the load with a duration equal to 2D/c, where D is the length of the line, and c is the propagation velocity of the pulse in the line.[1] The propagation velocity in typical transmission lines is within 50% of the speed of light. For example, in most types of coaxial cable the propagation velocity is approximately 2/3 the speed of light, or 20 cm/ns.
High-power PFNs generally use specialized transmission lines consisting of pipes filled with oil or deionized water as a dielectric to handle the high power dissipation.[2]
A disadvantage of simple PFN pulse generators is that because the transmission line must be matched to the load resistance RL to prevent reflections, the voltage stored on the line is divided equally between the load resistance and the characteristic impedance of the line, so the voltage pulse applied to the load is only one-half the power-supply voltage.[1][2]
Simple charged transmission-line pulse generator
A length of transmission line can be used as a pulse-forming network.[1][2] This can give substantially flat-topped pulses at the inconvenience of using of a large length of cable.
In a simple charged transmission-line pulse generator (animation, right) a length of transmission line such as a coaxial cable is connected through a switch to a matched load RL at one end, and at the other end to a DC voltage source V through a resistor RS, which is large compared to the characteristic impedance Z0 of the line.[1] When the power supply is connected, it slowly charges up the capacitance of the line through RS. When the switch is closed, a voltage equal to V/2 is applied to the load, the charge stored in the line begins to discharge through the load with a current of V/2Z0, and a voltage step travels up the line toward the source.[2] The source end of the line is approximately an open circuit due to the high RS,[1] so the step is reflected uninverted and travels back down the line toward the load. The result is that a pulse of voltage is applied to the load with a duration equal to 2D/c, where D is the length of the line, and c is the propagation velocity of the pulse in the line.[1] The propagation velocity in typical transmission lines is within 50% of the speed of light. For example, in most types of coaxial cable the propagation velocity is approximately 2/3 the speed of light, or 20 cm/ns.
High-power PFNs generally use specialized transmission lines consisting of pipes filled with oil or deionized water as a dielectric to handle the high power dissipation.[2]
A disadvantage of simple PFN pulse generators is that because the transmission line must be matched to the load resistance RL to prevent reflections, the voltage stored on the line is divided equally between the load resistance and the characteristic impedance of the line, so the voltage pulse applied to the load is only one-half the power-supply voltage.[1][2]
Technical References on Scalar Waves:
9. "Flux-normalised versus field-normalised decomposition of the scalar wave equation;" Dr
Kees Wapenaar, Department of Geoscience and Engineering, Delft University of
Technology, 2600 GA Delft, The Netherlands; 2019.
10. "A new perspective on the Ermakov-Pinney and scalar wave equations;" Giampiero
Esposito ORCID: 0000-0001-5930-8366; Istituto Nazionale di Fisica Nucleare,
Sezione di Napoli,Complesso Universitario di Monte S. Angelo,Via Cintia Edificio 6, 80126
Napoli, Italy; Marica Minucci, Dipartimento di Fisica “Ettore Pancini,” Universit`a Federico
II,Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126 Napoli, Italy; 2019.
11. “GLOBAL EXISTENCE FOR SYSTEMS OF QUASILINEAR WAVE EQUATIONS IN(1 +
4)-DIMENSIONS” Dr Jason Metcalfe and Dr Katrina Morgan; Department of Mathematics,
University of North Carolina, Chapel Hill.
12. “WAVE ASYMPTOTICS AT A COSMOLOGICAL TIME-SINGULARITY:CLASSICAL AND
QUANTUM SCALAR FIELDS,” Alain Bachelot Universite de Bordeaux, Institut de
Mathematiques, UMR CNRS 5251, F-33405 Talence Cedex.
13. “Exact gravitational plane waves and two-dimensional gravity;" Jorge G. Russo
*Institucio Catalana de Recerca i Estudis Avan cats; Lluis Companys, 23, 08010 Barcelona,
Spain. Department de Fisica Cuantica Astrofisica and Institut de Ciencies del Cosmos,
Universitat de Barcelona, Marti Franques, Barcelona, Spain.
14. "D=3: Singularities in gravitational scattering of scalar waves;" C. Klimcik, Nuclear
Centre, Charles University, Prague, Czechoslovakia and, P. Kolnik, Department of Theoretical
Physics, Charles University, Prague, 1992.
15. “Spectral methods for the wave equation in second-order form,” Taylor, Nicholas W. and
Kidder, Lawrence E. and Teukolsky, Saul A. (2010) Caltech; Physical Review D, 82 (2). Art.
No. 024037 . ISSN 1550-7998.
16. “Transmission Through a Scalar WaveThree-Dimensional Electromagnetic Metamaterial
and the Implication for Polarization Control,” Jonghwa Shin, Jung-Tsung Shen, and Shanhui
Fan, Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon
305-701, Korea, Ginzton Lab and Department of Electrical Engineering, Stanford University,
Stanford, California.
9. "Flux-normalised versus field-normalised decomposition of the scalar wave equation;" Dr
Kees Wapenaar, Department of Geoscience and Engineering, Delft University of
Technology, 2600 GA Delft, The Netherlands; 2019.
10. "A new perspective on the Ermakov-Pinney and scalar wave equations;" Giampiero
Esposito ORCID: 0000-0001-5930-8366; Istituto Nazionale di Fisica Nucleare,
Sezione di Napoli,Complesso Universitario di Monte S. Angelo,Via Cintia Edificio 6, 80126
Napoli, Italy; Marica Minucci, Dipartimento di Fisica “Ettore Pancini,” Universit`a Federico
II,Complesso Universitario di Monte S. Angelo, Via Cintia Edificio 6, 80126 Napoli, Italy; 2019.
11. “GLOBAL EXISTENCE FOR SYSTEMS OF QUASILINEAR WAVE EQUATIONS IN(1 +
4)-DIMENSIONS” Dr Jason Metcalfe and Dr Katrina Morgan; Department of Mathematics,
University of North Carolina, Chapel Hill.
12. “WAVE ASYMPTOTICS AT A COSMOLOGICAL TIME-SINGULARITY:CLASSICAL AND
QUANTUM SCALAR FIELDS,” Alain Bachelot Universite de Bordeaux, Institut de
Mathematiques, UMR CNRS 5251, F-33405 Talence Cedex.
13. “Exact gravitational plane waves and two-dimensional gravity;" Jorge G. Russo
*Institucio Catalana de Recerca i Estudis Avan cats; Lluis Companys, 23, 08010 Barcelona,
Spain. Department de Fisica Cuantica Astrofisica and Institut de Ciencies del Cosmos,
Universitat de Barcelona, Marti Franques, Barcelona, Spain.
14. "D=3: Singularities in gravitational scattering of scalar waves;" C. Klimcik, Nuclear
Centre, Charles University, Prague, Czechoslovakia and, P. Kolnik, Department of Theoretical
Physics, Charles University, Prague, 1992.
15. “Spectral methods for the wave equation in second-order form,” Taylor, Nicholas W. and
Kidder, Lawrence E. and Teukolsky, Saul A. (2010) Caltech; Physical Review D, 82 (2). Art.
No. 024037 . ISSN 1550-7998.
16. “Transmission Through a Scalar WaveThree-Dimensional Electromagnetic Metamaterial
and the Implication for Polarization Control,” Jonghwa Shin, Jung-Tsung Shen, and Shanhui
Fan, Department of Physics, Korea Advanced Institute of Science and Technology, Daejeon
305-701, Korea, Ginzton Lab and Department of Electrical Engineering, Stanford University,
Stanford, California.
Forwarded from LA QUINTA COLUMNA TV
IMÁGENES MEJORADAS DEL CONTENIDO DE VACUNA PFIZER. R. Delgado 2022