![]() |
electric & magnetic fields ??
As I understand it a shielded loop (non-magnetic shield) favors the
magnetic field. If I wanted to measure the difference between the 2 fields how would I measure the electric field? A loop shielded with magnetic material would probably reject both fields. The 3.5 foot loop for my old HP comparator for WWVB is totally non-magnetic. Can I generate and transmit each field separately? If so how would I do it? tnx -- 73 Hank WD5JFR |
"Henry Kolesnik" wrote in message
... As I understand it a shielded loop (non-magnetic shield) favors the magnetic field. Correct. If I wanted to measure the difference between the 2 fields how would I measure the electric field? Any antennna can measure the electric field, you simply have to know the antenna factor. Antenna factors can be calculated for various structures; for example the aperture of a half wave dipole is given by: 0.13*lambda^2. Simple calculations can then provide the antenna factor, and relate the E field (in V/m) to the received signal. The electric and magnetic fields are related by a constant -- the impedance of free space, 377 ohms. i.e. E/H = 377. In the vicinty of an antenna (the near field) the impedance of free space becomes a complex number. A loop shielded with magnetic material would probably reject both fields. Probably true, but have never experimented with such antennas. The 3.5 foot loop for my old HP comparator for WWVB is totally non-magnetic. Can I generate and transmit each field separately? If so how would I do it? No. The E field cannot exist without the H field. See the relationship above. Some people claim to have invented antennas that seperately generate E and H fields. Such antennas are known as "EH" and "Crossed-field", and have largely been rejected by the engineering comunity as bogus. The designers claim that they do not conform to Maxwell's Equations, but some other indefinable mathematics. Regards, Frank tnx -- 73 Hank WD5JFR |
Frank
If I have two parallel plates seperated by an air space and the plates are connect to a batttery I have a capacitor with an E field between the plates and squeezing out the sides. In steady state there's no current flow so I have no H field. If I have a coil or a solenoid and connect it to a battery I have a current flow with a strong H field but I'm not certainabout the E field. Can this be taken to the next step to answer my original question? tnx -- 73 Hank WD5JFR "Frank" wrote in message news:4Pyie.68625$tg1.4151@edtnps84... "Henry Kolesnik" wrote in message ... As I understand it a shielded loop (non-magnetic shield) favors the magnetic field. Correct. If I wanted to measure the difference between the 2 fields how would I measure the electric field? Any antennna can measure the electric field, you simply have to know the antenna factor. Antenna factors can be calculated for various structures; for example the aperture of a half wave dipole is given by: 0.13*lambda^2. Simple calculations can then provide the antenna factor, and relate the E field (in V/m) to the received signal. The electric and magnetic fields are related by a constant -- the impedance of free space, 377 ohms. i.e. E/H = 377. In the vicinty of an antenna (the near field) the impedance of free space becomes a complex number. A loop shielded with magnetic material would probably reject both fields. Probably true, but have never experimented with such antennas. The 3.5 foot loop for my old HP comparator for WWVB is totally non-magnetic. Can I generate and transmit each field separately? If so how would I do it? No. The E field cannot exist without the H field. See the relationship above. Some people claim to have invented antennas that seperately generate E and H fields. Such antennas are known as "EH" and "Crossed-field", and have largely been rejected by the engineering comunity as bogus. The designers claim that they do not conform to Maxwell's Equations, but some other indefinable mathematics. Regards, Frank tnx -- 73 Hank WD5JFR |
Henry Kolesnik wrote:
"If I wanted to measure the difference between the two fields how would I measure the electric field?" If this is the radiation field, not the reactive field, it would make no difference if you measured the electric field or the magnetic field, as they contain the same quantity of energy. In fact, the energy is identical as one field begets the other field. That`s "The Secret of Propagation". That does not mean the fieldfs can`t be separated. It is easy. Enclose your loop in an effective Faraday screen. This screen prohibits electrostatic coupling to the loop, but freely allows magnetic coupling. Faraday screens are not rare. Nearly every medium wave broadcast station uses a Faraday screen at every tower between the primary and secondary of an air-core coupling transformer. Because, without the screen, capacitive coupling to the tower would favor harmonics of the broadcast frequency over its fundamental frequency and make compliance with FCC rules difficult. The Faraday screen is also an excellent lightning protector. It`s just as easy to allow only capacitive coupling. Simply put a circuit to be kept from magnetic coupling in an enclosure which is completely enclosed in a metal structure (sealed like an expensive signal generator except for one small hole). Use a capacitor through the small hole to couple to the outside world. Only the electric field via the capacitor will influence the circuit in the box. R-F will not penetrate a metal shield, unless it`s special like the sliced-up Faraday screen. Then, it`s only the magnetic field which penetrates. Skin effect requires r-f to flow only on the surface of good conductors to any appreciable depth. Best regards, Richard Harrison, KB5WZI |
Henry Kolesnik wrote:
"If I have a coil or solenoid and connect it to a battery I have a current flow with a strong H field but I`m not certain about the E field." Resistance somewhere is limiting the current. The E field accompanies the resistive voltage drop. Static fields don`t make waves. Only the rate of change makes a disturbance which propagates in waves, E&M, which generate each other. Best regards, Richard Harrison, KB5WZI |
Hank, and Richard, For a good explanation of this subject I always liked the
book: "Introduction to Electromagnetic Fields" by Paul and Nasar. The first two chapters of mathematical review are excellent. I see barnesandnoble.com has the 3rd edition, used, for as low as $66. John D. Kraus' book; "Electromagnetics" is also a very good text. 73, Frank |
Isn't Kraus "Electromagnetics" a little heavy on the math for the
average Ham ?? Frank wrote: Hank, and Richard, For a good explanation of this subject I always liked the book: "Introduction to Electromagnetic Fields" by Paul and Nasar. The first two chapters of mathematical review are excellent. I see barnesandnoble.com has the 3rd edition, used, for as low as $66. John D. Kraus' book; "Electromagnetics" is also a very good text. 73, Frank |
"Richard Harrison" wrote
Nearly every medium wave broadcast station uses a Faraday screen at every tower between the primary and secondary of an air-core coupling transformer... Because, without the screen, capacitive coupling to the tower would favor harmonics of the broadcast frequency over its fundamental frequency and make compliance with FCC rules difficult. ____________ Must politely disagree with that last part -- and probably the first part as well, at least for modern ACU (Antenna Coupling Unit) designs used in MW broadcasting. As a condition of the FCC or other qualification needed legally to offer the tx for sale, MW broadcast transmitters must meet their harmonic suppression specs by themselves. They are not permitted to use ACU Faraday screens or other external means in doing so. A MW ACU is optimised for maximum power transfer between the transmission line and the tower for the carrier and its sidebands, however it almost never uses coupled coils to do that. It uses T, L or Pi networks. But with or without a Faraday screen, an ACU can couple no more harmonic energy to the radiator than exists, with respect to the carrier, at the input of the ACU -- which already meets harmonic suppression specs. RF |
Richard Fry wrote:
"As a condition of the FCC or other qualification needed to legally offer the tx for sale, MW broadcast transmitters must meet their harmonic suppression specs by themselves." It`s true. They are type accepted and don`t produce excess harmonics at their outputs. The coupling system does not suppress the fundamental but may further suppress the harmonics. I`m sorry to misspeak. Never the less, a capacitor`s impedance is inversely proportional to frequency. Its elimination as a coupling to the antenna eliminates a preference for higher frequencies in the coupling system. A pi or T network with shunt capacitance and series inductance favors the fundamental frequency over its harmonics. These aren`t required to meet specs but they further reduce harmonic radiation from the radio station. The Faraday screen is common in radio stations. It was put there not to affect the antenna match but only to eliminate capacitive coupling to the antenna. It also serves as a path to earth for many antenna lightning strikes as evidenced by numerous pits and metal hrom them splashed about the enclosure. Best regards, Richard Harrison, KB5WZI |
"Ham op" wrote in message ... Isn't Kraus "Electromagnetics" a little heavy on the math for the average Ham ?? I guess it depends on how interested they are. A good grounding in advanced calculus is certainly a prequesit for either of those texts. Even elementary calculus, combined with chapters 1 and 2, of Paul and Nasar, should be sufficient. 73, Frank Frank wrote: Hank, and Richard, For a good explanation of this subject I always liked the book: "Introduction to Electromagnetic Fields" by Paul and Nasar. The first two chapters of mathematical review are excellent. I see barnesandnoble.com has the 3rd edition, used, for as low as $66. John D. Kraus' book; "Electromagnetics" is also a very good text. 73, Frank |
"Richard Harrison" wrote
The Faraday screen is common in radio stations. It was put there not to affect the antenna match but only to eliminate capacitive coupling to the antenna. It also serves as a path to earth for many antenna lightning strikes as evidenced by numerous pits and metal hrom them splashed about the enclosure. ______________ This must be a very dated observation. In my experience, and as confirmed to me this morning by colleagues and consultants who design such networks, MW broadcast Antenna Coupling Units commonly do not contain Faraday screens. Lightning protection for most MW broadcast antenna systems is provided by some combination of a small inductance in series with the tower feed (copper tubing with a helical loop or two in it to connect the ACU output to the tower feedpoint), an arc gap across the tower base to ground adjusted to flash over at the lowest practical peak voltage, and a static drain choke (path with high Z for RF, but low DC resistance to ground). RF |
Richard Hry wrote:
"---MW broadcast Antenna Coupling Units commonly do not contain Faraday screens." My observation is from a previous century. Faraday screens were used in stations in which I worked. My response was to the question: Can the E and H fields be separated? Yes they can, and the Faraday screen is a way to eliminate coupling the E field while coupling the H field. On the decoupled side of the shield, induced magnetic lines immediately produce electric potential differences and E fields. Little changes and nothing has been lost except for capacitive coupling between circuits on opposite sides of the Faraday screen. Breaks in the screen prevent circulating current which would generate opposition to magnetic coupling. This is demonstrated as effective since ancient times in electricity. Electric lines find a ground return in the Faraday screen and go no further. A shield without breaks allows current circulation which generates an opposing force (Lenz`s law) and nullifies the induction. The continuous conducting screen also provides a grounded termination for the electric lines and blocks their passage too. Capacitive coupling through a hole in a continuous shield can allow the E field to be coupled while eliminating magnetic coupling. This does not say there is any merit to the E/H Antenna, about wehich I am ignorant. Best regards, Richard Harrison, KB5WZI |
"Richard Harrison" wrote
Richard Fry wrote: "---MW broadcast Antenna Coupling Units commonly do not contain Faraday screens." My observation is from a previous century. Faraday screens were used in stations in which I worked. My response was to the question: Can the E and H fields be separated? Yes they can, (etc) _____________ No dispute about the nature and effectiveness of Faraday screens where appropriately used -- only about your statements that "Nearly every medium wave broadcast station uses a Faraday screen," and as to the virtual requirement that they MUST be used in MW ACUs to suppress harmonics to legal levels and to prevent lightning damage. None of that is accurate. RF |
Ham Op:
Yes, it is... mostly, people who are NOT gifted in explanations that the "layman" can understand--gravitate to such extreme mathematics (and turn them off, effectively silencing them).... let me give you my views... .... it is somewhat obvious that when a wave sent forth from our antennas encounters a metallic object that is close to resonate freq, and a very good to EXCELLENT conductor, that a LARGE current flows in the metallic structure encountered--what E and what H wave are then products are debatable (the energy absorbed is re-radiated)--however--probably of a very different nature than that of wave which encountered the metallic object in question--and here is where this debate is ongoing... at an extreme is a "tesla coil", ultimate voltage and virtually NO current (very minimal current to generate the nice purple coronas)--yet an excellent transmitting "antenna"--and that is ALL "E-wave." (well, mostly...) Warmest regards, John "Ham op" wrote in message ... Isn't Kraus "Electromagnetics" a little heavy on the math for the average Ham ?? Frank wrote: Hank, and Richard, For a good explanation of this subject I always liked the book: "Introduction to Electromagnetic Fields" by Paul and Nasar. The first two chapters of mathematical review are excellent. I see barnesandnoble.com has the 3rd edition, used, for as low as $66. John D. Kraus' book; "Electromagnetics" is also a very good text. 73, Frank |
Excellent logic Richard, I applaud you....
Warmest regards, John "Richard Harrison" wrote in message ... Richard Hry wrote: "---MW broadcast Antenna Coupling Units commonly do not contain Faraday screens." My observation is from a previous century. Faraday screens were used in stations in which I worked. My response was to the question: Can the E and H fields be separated? Yes they can, and the Faraday screen is a way to eliminate coupling the E field while coupling the H field. On the decoupled side of the shield, induced magnetic lines immediately produce electric potential differences and E fields. Little changes and nothing has been lost except for capacitive coupling between circuits on opposite sides of the Faraday screen. Breaks in the screen prevent circulating current which would generate opposition to magnetic coupling. This is demonstrated as effective since ancient times in electricity. Electric lines find a ground return in the Faraday screen and go no further. A shield without breaks allows current circulation which generates an opposing force (Lenz`s law) and nullifies the induction. The continuous conducting screen also provides a grounded termination for the electric lines and blocks their passage too. Capacitive coupling through a hole in a continuous shield can allow the E field to be coupled while eliminating magnetic coupling. This does not say there is any merit to the E/H Antenna, about wehich I am ignorant. Best regards, Richard Harrison, KB5WZI |
"John Smith" wrote in message ... Ham Op: Yes, it is... mostly, people who are NOT gifted in explanations that the "layman" can understand--gravitate to such extreme mathematics (and turn them off, effectively silencing them).... let me give you my views... I thought that my explanations were very non-mathematical, requiring only minimal use of very simple calculations. My response was not complete as I did not want to go overboard, but try to give very easy examples that could be expanded on if any interest was shown. Perhaps you could be more specific as to where I went wrong in my response. My mention of a couple of textbooks was only to provide references for those interested in trying to understand concepts in more detail. While it is true that some people are capable of rigorous mathematical analysis, they cannot explain it in non-mathematical terms. Those people, then, do not really understand their subject. It is also true that such complex subjects cannot be fully understood without in-depth math (Which is something I wish I had). .. ... it is somewhat obvious that when a wave sent forth from our antennas encounters a metallic object that is close to resonate freq, Not sure that resonance is important. and a very good to EXCELLENT conductor, that a LARGE current flows in the metallic structure encountered-- Current will flow in the surface. what E and what H wave are then products are debatable (the energy absorbed is re-radiated)--however--probably of a very different nature than that of wave which encountered the metallic object in question--and here is where this debate is ongoing... If the conducting surface is perfect, no absorbtion takes place. The reflected EM wave is planar, and identical to the incident plane wave -- with the exception of direction of propagation, and a phase reversal. A (spatial) standing wave pattern is set up, and the analysis is identical to that of a shorted transmission line. at an extreme is a "tesla coil", ultimate voltage and virtually NO current (very minimal current to generate the nice purple coronas)--yet an excellent transmitting "antenna"--and that is ALL "E-wave." (well, mostly...) A Tesla coil is not an antenna, although some radiation will take place from its conductors -- which will probably be damped sinusoidal pulses similar to a spark transmitter. The radiation will not be all "E", but will have the same E/H ratio of any radiated signal. i.e. E/H = 377 (ohms) in the far field. 73, Frank Warmest regards, John "Ham op" wrote in message ... Isn't Kraus "Electromagnetics" a little heavy on the math for the average Ham ?? Frank wrote: Hank, and Richard, For a good explanation of this subject I always liked the book: "Introduction to Electromagnetic Fields" by Paul and Nasar. The first two chapters of mathematical review are excellent. I see barnesandnoble.com has the 3rd edition, used, for as low as $66. John D. Kraus' book; "Electromagnetics" is also a very good text. 73, Frank |
A Tesla coil is not an antenna, although some radiation will take place
from its conductors -- which will probably be damped sinusoidal pulses similar to a spark transmitter. The radiation will not be all "E", but will have the same E/H ratio of any radiated signal. i.e. E/H = 377 (ohms) in the far field. 73, Frank Just checked http://home.wtal.de/herbs_teslapage/theory.html The Tesla coil is a spark transmitter without an antenna connected. Frank |
Shield the coil, the coronas effect is still as powerful on florescents,
vtvms detecting voltage... that voltage may well be inducing a magnetic field as it is conducted by air/ether/ground... but it looks to me like the voltage is the main force... rfi will tear up a neighborhood too... Warmest regards, John "Frank" wrote in message news:GVbje.7002$wr.3522@clgrps12... "John Smith" wrote in message ... Ham Op: Yes, it is... mostly, people who are NOT gifted in explanations that the "layman" can understand--gravitate to such extreme mathematics (and turn them off, effectively silencing them).... let me give you my views... I thought that my explanations were very non-mathematical, requiring only minimal use of very simple calculations. My response was not complete as I did not want to go overboard, but try to give very easy examples that could be expanded on if any interest was shown. Perhaps you could be more specific as to where I went wrong in my response. My mention of a couple of textbooks was only to provide references for those interested in trying to understand concepts in more detail. While it is true that some people are capable of rigorous mathematical analysis, they cannot explain it in non-mathematical terms. Those people, then, do not really understand their subject. It is also true that such complex subjects cannot be fully understood without in-depth math (Which is something I wish I had). . ... it is somewhat obvious that when a wave sent forth from our antennas encounters a metallic object that is close to resonate freq, Not sure that resonance is important. and a very good to EXCELLENT conductor, that a LARGE current flows in the metallic structure encountered-- Current will flow in the surface. what E and what H wave are then products are debatable (the energy absorbed is re-radiated)--however--probably of a very different nature than that of wave which encountered the metallic object in question--and here is where this debate is ongoing... If the conducting surface is perfect, no absorbtion takes place. The reflected EM wave is planar, and identical to the incident plane wave -- with the exception of direction of propagation, and a phase reversal. A (spatial) standing wave pattern is set up, and the analysis is identical to that of a shorted transmission line. at an extreme is a "tesla coil", ultimate voltage and virtually NO current (very minimal current to generate the nice purple coronas)--yet an excellent transmitting "antenna"--and that is ALL "E-wave." (well, mostly...) A Tesla coil is not an antenna, although some radiation will take place from its conductors -- which will probably be damped sinusoidal pulses similar to a spark transmitter. The radiation will not be all "E", but will have the same E/H ratio of any radiated signal. i.e. E/H = 377 (ohms) in the far field. 73, Frank Warmest regards, John "Ham op" wrote in message ... Isn't Kraus "Electromagnetics" a little heavy on the math for the average Ham ?? Frank wrote: Hank, and Richard, For a good explanation of this subject I always liked the book: "Introduction to Electromagnetic Fields" by Paul and Nasar. The first two chapters of mathematical review are excellent. I see barnesandnoble.com has the 3rd edition, used, for as low as $66. John D. Kraus' book; "Electromagnetics" is also a very good text. 73, Frank |
"John Smith" wrote in message ... Shield the coil, the coronas effect is still as powerful on florescents, vtvms detecting voltage... that voltage may well be inducing a magnetic field as it is conducted by air/ether/ground... but it looks to me like the voltage is the main force... rfi will tear up a neighborhood too... Warmest regards, John Since I have never had experience with a Tesla coil, this is all relatively new to me. After a little research I found the following information, which may be of interest. The Tesla coil design reference at http://home.wtal.de/herbs_teslapage/design.html provides an Excel spread sheet showing all the appropriate parameters. The spread sheet example shows a single gap spark transmitter, of input power 375 W at a frequency of 322 kHz. Since the wavelength is relatively long, at 932 m, the near field/far field transition is very close to the radiating structure, which will include the conductive arc plasma. Near field/far field transition is approximated as (2D^2)/lambda, where D is the largest dimension of the radiating structure, and lambda is the wavelength. The observable effects you mention are therefore most likely due to far field effects. The E/H ratio is still a constant at 377 ohms. From the above formula you can see that you would have to be very close to the souce for any inductive or capacative coupling to occur. Having heard of Tesla coils I never realized they were only simple spark gap transmitters. 73, Frank |
First tesla coils I ever made were spark gaps using a 15,000 volt neon sign
transformer, large caps out of aluminum foil, xfrmr oil and polyethylene sheeting... later on friends and I built units around 50Khz-150Khz which used push-pull circuits to drive the primary coil of the tesla (no noise from the spark gap which is almost deafening!)--I think the first used 811 (825's?) tubes from old gov't surplus equip (I remember the tubes were about the size of coke bottles).... Warmest regards, John "Frank" wrote in message news:EWkje.7026$wr.338@clgrps12... "John Smith" wrote in message ... Shield the coil, the coronas effect is still as powerful on florescents, vtvms detecting voltage... that voltage may well be inducing a magnetic field as it is conducted by air/ether/ground... but it looks to me like the voltage is the main force... rfi will tear up a neighborhood too... Warmest regards, John Since I have never had experience with a Tesla coil, this is all relatively new to me. After a little research I found the following information, which may be of interest. The Tesla coil design reference at http://home.wtal.de/herbs_teslapage/design.html provides an Excel spread sheet showing all the appropriate parameters. The spread sheet example shows a single gap spark transmitter, of input power 375 W at a frequency of 322 kHz. Since the wavelength is relatively long, at 932 m, the near field/far field transition is very close to the radiating structure, which will include the conductive arc plasma. Near field/far field transition is approximated as (2D^2)/lambda, where D is the largest dimension of the radiating structure, and lambda is the wavelength. The observable effects you mention are therefore most likely due to far field effects. The E/H ratio is still a constant at 377 ohms. From the above formula you can see that you would have to be very close to the souce for any inductive or capacative coupling to occur. Having heard of Tesla coils I never realized they were only simple spark gap transmitters. 73, Frank |
On Fri, 20 May 2005 02:26:46 GMT, "Frank"
wrote: "John Smith" wrote in message ... Ham Op: Yes, it is... mostly, people who are NOT gifted in explanations that the "layman" can understand--gravitate to such extreme mathematics (and turn them off, effectively silencing them).... let me give you my views... I thought that my explanations were very non-mathematical, requiring only minimal use of very simple calculations. My response was not complete as I did not want to go overboard, but try to give very easy examples that could be expanded on if any interest was shown. Perhaps you could be more specific as to where I went wrong in my response. My mention of a couple of textbooks was only to provide references for those interested in trying to understand concepts in more detail. While it is true that some people are capable of rigorous mathematical analysis, they cannot explain it in non-mathematical terms. Those people, then, do not really understand their subject. So they can discover some knowledge and use it to make products or predictions, but if they cannot explain it in non-mathematical terms to your satisfaction, then, by your lights, they do not understand it? As a counter example, consider the comments of Richard Feynman. When he was awarded a Nobel prize for his work in (I believe) quantum electrodynamics, he was honored at a luncheon provided by the faculty wives at his university. During the proceedings, he was asked, "Doctor Feynman, could you let us know, in simple terms, what your work was about?" He answered, "Madam, if I could explain it in simple terms, they wouldn't have given me the Nobel prize for it." Will you contend he didn't understand his subject? In addition, you fail to understand that discovering knowledge and teaching it are entirely separate gifts. Some who understand deeply are incapable of teaching. Others, with less than complete understanding, can teach effectively, while being incapable of coming up with the knowledge in the first place. One of our most poisonous (and arrogant) sayings is the one which states, "Those who can, do; those who can't, teach." It's not all that common to find people who can do both well. It is also true that such complex subjects cannot be fully understood without in-depth math (Which is something I wish I had). Wherein you contradict yourself. You can't contend at the samer time that a knowledge of mathematics on the part of the learner is a necessity at the same time that you indict the one who can explain only in mathematical terms for lack of understanding. Heads or tails? . ... it is somewhat obvious that when a wave sent forth from our antennas encounters a metallic object that is close to resonate freq, Not sure that resonance is important. and a very good to EXCELLENT conductor, that a LARGE current flows in the metallic structure encountered-- Current will flow in the surface. what E and what H wave are then products are debatable (the energy absorbed is re-radiated)--however--probably of a very different nature than that of wave which encountered the metallic object in question--and here is where this debate is ongoing... If the conducting surface is perfect, no absorbtion takes place. The reflected EM wave is planar, and identical to the incident plane wave -- with the exception of direction of propagation, and a phase reversal. A (spatial) standing wave pattern is set up, and the analysis is identical to that of a shorted transmission line. at an extreme is a "tesla coil", ultimate voltage and virtually NO current (very minimal current to generate the nice purple coronas)--yet an excellent transmitting "antenna"--and that is ALL "E-wave." (well, mostly...) A Tesla coil is not an antenna, although some radiation will take place from its conductors -- which will probably be damped sinusoidal pulses similar to a spark transmitter. The radiation will not be all "E", but will have the same E/H ratio of any radiated signal. i.e. E/H = 377 (ohms) in the far field. 73, Frank Warmest regards, John "Ham op" wrote in message ... Isn't Kraus "Electromagnetics" a little heavy on the math for the average Ham ?? Frank wrote: Hank, and Richard, For a good explanation of this subject I always liked the book: "Introduction to Electromagnetic Fields" by Paul and Nasar. The first two chapters of mathematical review are excellent. I see barnesandnoble.com has the 3rd edition, used, for as low as $66. John D. Kraus' book; "Electromagnetics" is also a very good text. 73, Frank |
All times are GMT +1. The time now is 01:34 AM. |
Powered by vBulletin® Copyright ©2000 - 2025, Jelsoft Enterprises Ltd.
RadioBanter.com