Re: Very low cost 20 bit 125 MSa/s 64kB AWG
If you want to avoid monotonicity errors, resistor tolerance (actually matching) has to be within 2**(-n), which would be 0.1% for a 10-bit converter, and 1 ppm for 20 bits. This is achieved in integrated DACs through the nearly perfect matching obtained with lithography. Non-monotonic DACs are really interesting to watch on a spectrum analyzer as you vary the amplitude of a sine wave, and even more interesting if you add a bit of dc offset to the digital waveform.
Still, it’s a fun and cheap way to build a DAC of modest resolution and you will learn a lot along the way!
Gary NA6O
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Re: Very low cost 20 bit 125 MSa/s 64kB AWG?
A common version of the ~$125 60 MHz Chinese AWGs uses an R-2R network instead of a DAC.
The Pico can write the sample values to as many R-2R ladders as are needed to let all the ladders settle before switching them to the output via an analog multipexer. SMD resistors are very cheap. Constant impedance length matching each trace in the ladders is a significant chore, but that only has to be done once and will go a very long way in reducing settling times which are inverse to the bandwidth.
The key is in being able to write a sine wave to the DAC and then measure it with a PC sound card, determine the errors of each resistor and store that in a table. Any PC downloading a waveform via USB ASCII text will have it predistorted to produce the correct output by the Pico. That makes using random resistors viable and cost negligible.
Replacing the Pico clock with an Si5351 referenced to a $3 CTI OSC5A03B2 should produce a < 1 ps jitter. For 250 MSa/s use the Si5351 to multiplex a pair of Picos on alternate phases of the master clock.
Put a 100 MHz voltage follower supplying 10 dBm into 50 ohms on the output and call it done.
User generates a waveform file and writes it to a USB serial port. The file is predistorted by the Pico(s) and stored. After the entire file has been transferred it plays in a loop at 125 MSa/s when the user presses the start/stop button. That's one step above blinky light and button embedded programming.
I don't have the PCB design tool to do this. I'm hoping to pay someone to take up the challenge. I'll supply Picos and JLCPCB preassembled PCBs. If you're interested please contact me off line.
Have Fun!
Reg On Thursday, November 30, 2023 at 08:40:16 AM CST, Ed Marciniak <edr10000@...> wrote:
Good luck with making the R-2R work with that many bits. Even if you did, you still have the problem of buffering and the settling time on the outputs(ringing and ripple might be insignificant at low frequencies but not at high frequencies).
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Re: Very low cost 20 bit 125 MSa/s 64kB AWG?
Good luck with making the R-2R work with that many bits. Even if you did, you still have the problem of buffering and the settling time on the outputs(ringing and ripple might be insignificant at low frequencies but not at high frequencies).
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Very low cost 20 bit 125 MSa/s 64kB AWG?
This popped up on HackaDay:
After looking at the datasheet for the Pico I decided to splurge and buy 25 of them from Digikey for the princely sum of $4 each.
There are 23 GPIOs so in principle it can do a 23 bit R2R network at up to 133 MHz. That sets Nyquist at 67 MHz and would allow a very high dynamic range RF source of great flexibility. Use ordinary resistors to build the ladder then connect it to the input of a soundcard and adjust the signal until it matches the desired value at the output of the DAC. Store the calculated constants in the Pico.
Then whenever a waveform is loaded, during the loading process, the Pico pre-distorts the waverform. To store data to it you feed it an ASCII waveform file.
Comments? I really like the possibility of a $20 AWG DAC module. Still needs analog output section and a control interface.
Have Fun!
Reg
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--
Prof. Thomas H. Lee
Faculty Co-Director, SystemX Alliance
Director, Stanford-Samsung Research Initiative
Allen Ctr., Rm. 205
420 Via Palou Mall
Stanford University
Stanford, CA 94305-4070
|
For information - Low cost bought in SMA attenuator construction
I have been using a number of low cost SMA attenuators of Chinese origin for 4-5 years, sold with a 2W 6GHz rating.? The match is not great (quoted as <1.25:1), but they are good enough for general purposes at lower frequencies.? I recently had two fail to very high attenuation in fairly quick succession so decided to look at their construction.? The pi attenuator board is connected to the pins and the body with conductive glue, and the outer cover is pressed on (not very tightly).? In each case, the pin connection was open circuit and was not very tight in the insulator which would have exacerbated the stresses of minor misalignment when mating with other low-cost SMA connectors.? The glue seemed to be in good condition. They still cost less than ?10 apiece and they preserve my better quality attenuators as calibration references.? PeterS?? G8EZE 
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From the age of 12 I'd always asked 'but what are radio waves'. The closest i have ever got to an answer is from Fleisch's book cited here. It is worth reading and re-reading.
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Jeff,
Thanks for taking the time to write an excellent essay.
I am a geoscientist, not an EE. In my view the major problem with EE education is the course loads don't allow students enough time to master the course material.
I took a BA in English lit before going back to school for an MS in geology. So I only had a 12 hr load when I took Cal I and didn't take Physics I until the following semester. So I was concurrently taking Cal III and E&M and could afford to spend 4 hours on a single problem.
The upshot of this was on the E&M final I had the highest score, 89, which was 1 point short of twice the class average. I'm pretty sure the next highest score, 79, was the class hotshot from my Cal I class. We ran into each other one day waiting for the TA to show and it turned out we were both there after having spent 4 hours beating our heads against the same E&M problem.
Mathematics is like playing a musical instrument. If you don't practice a lot you just never get very good.
In the geoscience world a BS is a technician degree. The MS has been the traditional professional degree for 100 years or so. I personally think the attempt to cram an MSEE curriculum into a BS time frame in engineering is a major source of both misery for students and marginal abilities after graduation. By the time someone becomes competent in DSP they need 30+ hours of mathematics. As an example, I recently posted to EEVblog asking if anyone had experience with multichannel signal processing. There were no responses. In light of the extreme importance of the topic I found this a bit distressing.
Medicine and law used to be single degree professions. Now they are 2 degree professions.
I think it time for engineering and EE in particular to go the same way.
Have Fun!
Reg
On Friday, November 10, 2023 at 09:37:17 AM CST, Jeff Kruth via groups.io <kmec@...> wrote:
Hello All!
Don't misunderstand me - I am not saying you need to solve field theory math to be able to do microwave work (it is nice though). But, you should understand the basics if you want to be as accurate as possible. Computers can solve the math (do the heavy lifting!) for you now if you can afford the software.
I do a brief review of Maxwell in my Microwave Systems class for the students (who all hate Calc 3 - Vector math, and didn't learn much in Physics II) and my explanation is that there are two source equations and two linkage equations. They provide insight into what is going on: the fact that a time changing E or H field caused by circuit quantities (like current) can give rise to a SPATIALLY distributed vector field of the other quantity. Time changing E gives rise to spatially distributed H, etc. In other words, the magic by which a time changing current in an antenna can make energy "leap out" into space and propagate away to a structure (another antenna) with the correct properties at some distance, inducing a current in that structure.
The source equations just tell you where the energy is coming from (no magnetic monopoles!), and the constituent equations link E & H to D & B thru material properties (permittivity and permeability). The latter is VERY important as it shows how materials effect E-M waves, something we use a lot in our work.
Oliver Heaviside is a much overlooked genius who (IIRC) took Maxwell's almost opaque work of 20 equations in 20 unknowns (very few who read it, sadly, could understand it, even though Maxwell was also a genius)? and reduced it to the familiar 4 equations we call Maxwell's equations today. From about 1890 to the end of the 1920's, we called them the "Maxwell-Heaviside" equations because Heavyside made them accessible to the common practitioner. Albert Einstein was somewhat lazy in his writings and dropped Heavisides name from Maxwell, dooming Heavyside to obscurity. That was OK with the physicists, because they didn't like Heavyside anyway. This was due to Heavyside creating the study of Electrical Engineering ("electricity was too important to leave to the physicists alone") and thus diminishing the involvement of physicists (in their eyes, at least) in this important field. After all,the 19th century WAS the century of electricity!
Heaviside created so much we use - The telegrapher equation for characteristic impedance of transmission lines, coax cable, early studies on the ionosphere (the "Heavyside Layer"), echo cancelling in telephone circuits and so. A great book on his life is from the IEEE press called "Sage in Solitude" and worth a read. He also wrote a (IIRC) three volume set which was a collection of his letters and writings which (as I understand it) is a much more readable explanation of the M-H equations and their implications. Maybe after I retire, I will locate and read these.
If you do want a little deeper understanding of E-M in microwaves, concentrate of boundary conditions - how waves interact when encountering the boundary between two materials. That's where the magic occurs (shorts, opens, losses, phase delay, etc.)
Regards,
Jeff Kruth
|
Can't say I disagree with the way that the HR droids work.
On the other hand, I might be able to take a stab at the refrigerator door.
answer #1:? Badly unless it's magnetic
answer #2:
It seems to me that magnetic fields are stress fields, and their lowest energy state is collapsed, i.e. North pole on top of South Pole.
Bringing a magnet close to a metal distorts the magnetic field in the metal (assuming the metal is not magnetized).? That magnetic stress field is a mirror of the one in the magnet pole, and therefore wants to collapse.? The pull is the magnetic field wanting to collapse.? Since magnetic fields are stress fields (bipolar rather than unipolar), there's likely an opposite pole on the other side of the refrigerator door.
Having gone out this far on a limb, I'll continue sawing between myself and the tree.....
The electric field in the EM radiation causes the electrons in the antenna to drift.? (Imagine a long tube half filled with water and the EM radiation is rocking it)
Antennas are always differential, (even a vertical antenna has a "mirror" in the ground, below the ground plane).? So with the right wavelength, a dipole left side is going (say negative) and a dipole right side is therefore going positive, your job is to have that water sloshing through a feed line, causing a current/voltage drop, and amplifying that.
Longer antennas have a better capture area.? Rubber ducks (coiled wire) antennas may have an electrical length that precisely matches the input frequency requirements, but being coiled up, can catch less of it.
Larger antennas can intercept more of the wave coming in. Collinear (5/8 wave) antennas stack two antennas end to end with a matching section, and the larger size gives more capture area.
Hope that helps, and let's see how much I got right.
Harvey
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Show quoted text
On 11/10/2023 11:48 AM, n8fgv wrote: I never took a course in Vector Calculus, I learned what I know of it by
studying Maxwell's equations. I learned most of my mathematics in physics and
engineering classes. Math professors are obsessed with proving things, as they
should be, but have no concept of any physical meaning that the equations
might be describing.
One book that was recommended to me (45 years ago) was "Div, Grad, Curl, and
All That: An Informal Text on Vector Calculus" by H. M. Schey. It seems to
still be in print and available on Amazon.
If the students in my school would have preferred euthanasia to Maxwell's
equations, they didn't show it. Many of them had T-shirts that said "And God
said [Maxwell's equations] and there was light..."
We don't do a very good job of teaching scientific history, we present the
material to students in its present day understanding as if it was handed down
from heaven on stone tablets, with no background of how humanity came to
understand such things.
Today there seems to be a notion in engineering schools that students don't
need to learn the equations because modern computer software can crank out an
answer for you. Your ability to find a job is solely dependent on which
software keywords you list on your resume, and you better list the "Industry
Standard" commercial software, not the lower cost open source alternatives
(e.g. Matlab, not Octave, etc). Professors also tell physics majors that "with
a physics degree you can do any job" but when the Human Resources droids at a
company are told to hire engineers, they won't look at any resume that doesn't
list an engineering degree with the proper software keywords.
Two things I would like to understand (intuitively not mathematically) before
I die are:
1. How exactly do magnets stick to a refrigerator door?
2. How does a dipole antenna convert electromagnetic waves to electric
current, and why do longer ones work better?
Dan Schultz
|
I never took a course in Vector Calculus, I learned what I know of it by
studying Maxwell's equations. I learned most of my mathematics in physics and
engineering classes. Math professors are obsessed with proving things, as they
should be, but have no concept of any physical meaning that the equations
might be describing.
One book that was recommended to me (45 years ago) was "Div, Grad, Curl, and
All That: An Informal Text on Vector Calculus" by H. M. Schey. It seems to
still be in print and available on Amazon.
If the students in my school would have preferred euthanasia to Maxwell's
equations, they didn't show it. Many of them had T-shirts that said "And God
said [Maxwell's equations] and there was light..."
We don't do a very good job of teaching scientific history, we present the
material to students in its present day understanding as if it was handed down
from heaven on stone tablets, with no background of how humanity came to
understand such things.
Today there seems to be a notion in engineering schools that students don't
need to learn the equations because modern computer software can crank out an
answer for you. Your ability to find a job is solely dependent on which
software keywords you list on your resume, and you better list the "Industry
Standard" commercial software, not the lower cost open source alternatives
(e.g. Matlab, not Octave, etc). Professors also tell physics majors that "with
a physics degree you can do any job" but when the Human Resources droids at a
company are told to hire engineers, they won't look at any resume that doesn't
list an engineering degree with the proper software keywords.
Two things I would like to understand (intuitively not mathematically) before
I die are:
1. How exactly do magnets stick to a refrigerator door?
2. How does a dipole antenna convert electromagnetic waves to electric
current, and why do longer ones work better?
Dan Schultz
|
One last suggestion:
Check out the YouTube channel Machining and Microwaves. Neil has a lot of really cool stuff happening there. You will spend hours there I am sure!
Sam Reaves
Electronics and Mechanical Hardware Design Engineering Manager
Staff Scientist Andritz Rolls Global Research Center (RETIRED)
On Fri, Nov 10, 2023 at 10:51?AM Sam Reaves via <sam.reaves= [email protected]> wrote: Wow Jeff I was waiting to see if you would chime in on this.?
Kathy Joseph of Kathy Loves Physics YouTube channel does a great talk on this. She is a fascinating?person whom I first became acquainted with as the keynote speaker at last year's PCB Carolina trade show. She wrote a great book titled "The Lightning Tamers" which covers in great detail the history of electricity and the masters thereof.
I highly recommend anyone with an interest?in this watch her videos and buy her book.
See you at the Berryville Hamfest next year!
Sam
Electronics and Mechanical Hardware Design Engineering Manager
Staff Scientist Andritz Rolls Global Research Center (RETIRED)
Hello All!
Don't misunderstand me - I am not saying you need to solve field theory math to be able to do microwave work (it is nice though). But, you should understand the basics if you want to be as accurate as possible. Computers can solve the math (do the heavy lifting!) for you now if you can afford the software.
I do a brief review of Maxwell in my Microwave Systems class for the students (who all hate Calc 3 - Vector math, and didn't learn much in Physics II) and my explanation is that there are two source equations and two linkage equations. They provide insight into what is going on: the fact that a time changing E or H field caused by circuit quantities (like current) can give rise to a SPATIALLY distributed vector field of the other quantity. Time changing E gives rise to spatially distributed H, etc. In other words, the magic by which a time changing current in an antenna can make energy "leap out" into space and propagate away to a structure (another antenna) with the correct properties at some distance, inducing a current in that structure.
The source equations just tell you where the energy is coming from (no magnetic monopoles!), and the constituent equations link E & H to D & B thru material properties (permittivity and permeability). The latter is VERY important as it shows how materials effect E-M waves, something we use a lot in our work.
Oliver Heaviside is a much overlooked genius who (IIRC) took Maxwell's almost opaque work of 20 equations in 20 unknowns (very few who read it, sadly, could understand it, even though Maxwell was also a genius)? and reduced it to the familiar 4 equations we call Maxwell's equations today. From about 1890 to the end of the 1920's, we called them the "Maxwell-Heaviside" equations because Heavyside made them accessible to the common practitioner. Albert Einstein was somewhat lazy in his writings and dropped Heavisides name from Maxwell, dooming Heavyside to obscurity. That was OK with the physicists, because they didn't like Heavyside anyway. This was due to Heavyside creating the study of Electrical Engineering ("electricity was too important to leave to the physicists alone") and thus diminishing the involvement of physicists (in their eyes, at least) in this important field. After all,the 19th century WAS the century of electricity!
Heaviside created so much we use - The telegrapher equation for characteristic impedance of transmission lines, coax cable, early studies on the ionosphere (the "Heavyside Layer"), echo cancelling in telephone circuits and so. A great book on his life is from the IEEE press called "Sage in Solitude" and worth a read. He also wrote a (IIRC) three volume set which was a collection of his letters and writings which (as I understand it) is a much more readable explanation of the M-H equations and their implications. Maybe after I retire, I will locate and read these.
If you do want a little deeper understanding of E-M in microwaves, concentrate of boundary conditions - how waves interact when encountering the boundary between two materials. That's where the magic occurs (shorts, opens, losses, phase delay, etc.)
Regards,
Jeff Kruth
|
Oh, yeah, didn't comment here:
Yes, you are entirely correct. Now the phase shift of the wave through the part (or off the surface of a parabola, BTW) is significant enough to cause errors.
Usually, 1/8 wave (45 degrees) was the limit used in E-M texts but engineers like 1/10 which is fine!
Jeff Kruth?
?
| 1b.? |
Re: VNAs - Microwaves?
From:?Hugh Gilbert
Date: Tue, 07 Nov 2023 09:02:57 PST
?
I was taught that when the circuit size exceeds about 1/10 wavelength, Kirchoff's voltage and current laws as they are near DC representations of Maxwell's equations no longer hold, and you need to resort to Maxwell's equations.
?
Hugh Gilbert
|
|
|
|
Wow Jeff I was waiting to see if you would chime in on this.?
Kathy Joseph of Kathy Loves Physics YouTube channel does a great talk on this. She is a fascinating?person whom I first became acquainted with as the keynote speaker at last year's PCB Carolina trade show. She wrote a great book titled "The Lightning Tamers" which covers in great detail the history of electricity and the masters thereof.
I highly recommend anyone with an interest?in this watch her videos and buy her book.
See you at the Berryville Hamfest next year!
Sam
Electronics and Mechanical Hardware Design Engineering Manager
Staff Scientist Andritz Rolls Global Research Center (RETIRED)
Hello All!
Don't misunderstand me - I am not saying you need to solve field theory math to be able to do microwave work (it is nice though). But, you should understand the basics if you want to be as accurate as possible. Computers can solve the math (do the heavy lifting!) for you now if you can afford the software.
I do a brief review of Maxwell in my Microwave Systems class for the students (who all hate Calc 3 - Vector math, and didn't learn much in Physics II) and my explanation is that there are two source equations and two linkage equations. They provide insight into what is going on: the fact that a time changing E or H field caused by circuit quantities (like current) can give rise to a SPATIALLY distributed vector field of the other quantity. Time changing E gives rise to spatially distributed H, etc. In other words, the magic by which a time changing current in an antenna can make energy "leap out" into space and propagate away to a structure (another antenna) with the correct properties at some distance, inducing a current in that structure.
The source equations just tell you where the energy is coming from (no magnetic monopoles!), and the constituent equations link E & H to D & B thru material properties (permittivity and permeability). The latter is VERY important as it shows how materials effect E-M waves, something we use a lot in our work.
Oliver Heaviside is a much overlooked genius who (IIRC) took Maxwell's almost opaque work of 20 equations in 20 unknowns (very few who read it, sadly, could understand it, even though Maxwell was also a genius)? and reduced it to the familiar 4 equations we call Maxwell's equations today. From about 1890 to the end of the 1920's, we called them the "Maxwell-Heaviside" equations because Heavyside made them accessible to the common practitioner. Albert Einstein was somewhat lazy in his writings and dropped Heavisides name from Maxwell, dooming Heavyside to obscurity. That was OK with the physicists, because they didn't like Heavyside anyway. This was due to Heavyside creating the study of Electrical Engineering ("electricity was too important to leave to the physicists alone") and thus diminishing the involvement of physicists (in their eyes, at least) in this important field. After all,the 19th century WAS the century of electricity!
Heaviside created so much we use - The telegrapher equation for characteristic impedance of transmission lines, coax cable, early studies on the ionosphere (the "Heavyside Layer"), echo cancelling in telephone circuits and so. A great book on his life is from the IEEE press called "Sage in Solitude" and worth a read. He also wrote a (IIRC) three volume set which was a collection of his letters and writings which (as I understand it) is a much more readable explanation of the M-H equations and their implications. Maybe after I retire, I will locate and read these.
If you do want a little deeper understanding of E-M in microwaves, concentrate of boundary conditions - how waves interact when encountering the boundary between two materials. That's where the magic occurs (shorts, opens, losses, phase delay, etc.)
Regards,
Jeff Kruth
|
Hello All!
Don't misunderstand me - I am not saying you need to solve field theory math to be able to do microwave work (it is nice though). But, you should understand the basics if you want to be as accurate as possible. Computers can solve the math (do the heavy lifting!) for you now if you can afford the software.
I do a brief review of Maxwell in my Microwave Systems class for the students (who all hate Calc 3 - Vector math, and didn't learn much in Physics II) and my explanation is that there are two source equations and two linkage equations. They provide insight into what is going on: the fact that a time changing E or H field caused by circuit quantities (like current) can give rise to a SPATIALLY distributed vector field of the other quantity. Time changing E gives rise to spatially distributed H, etc. In other words, the magic by which a time changing current in an antenna can make energy "leap out" into space and propagate away to a structure (another antenna) with the correct properties at some distance, inducing a current in that structure.
The source equations just tell you where the energy is coming from (no magnetic monopoles!), and the constituent equations link E & H to D & B thru material properties (permittivity and permeability). The latter is VERY important as it shows how materials effect E-M waves, something we use a lot in our work.
Oliver Heaviside is a much overlooked genius who (IIRC) took Maxwell's almost opaque work of 20 equations in 20 unknowns (very few who read it, sadly, could understand it, even though Maxwell was also a genius) and reduced it to the familiar 4 equations we call Maxwell's equations today. From about 1890 to the end of the 1920's, we called them the "Maxwell-Heaviside" equations because Heavyside made them accessible to the common practitioner. Albert Einstein was somewhat lazy in his writings and dropped Heavisides name from Maxwell, dooming Heavyside to obscurity. That was OK with the physicists, because they didn't like Heavyside anyway. This was due to Heavyside creating the study of Electrical Engineering ("electricity was too important to leave to the physicists alone") and thus diminishing the involvement of physicists (in their eyes, at least) in this important field. After all,the 19th century WAS the century of electricity!
Heaviside created so much we use - The telegrapher equation for characteristic impedance of transmission lines, coax cable, early studies on the ionosphere (the "Heavyside Layer"), echo cancelling in telephone circuits and so. A great book on his life is from the IEEE press called "Sage in Solitude" and worth a read. He also wrote a (IIRC) three volume set which was a collection of his letters and writings which (as I understand it) is a much more readable explanation of the M-H equations and their implications. Maybe after I retire, I will locate and read these.
If you do want a little deeper understanding of E-M in microwaves, concentrate of boundary conditions - how waves interact when encountering the boundary between two materials. That's where the magic occurs (shorts, opens, losses, phase delay, etc.)
Regards,
Jeff Kruth
|
There are a great video course from MIT , Walter Lewin was the profesor . Sadly he was fired from MIT. They clases were very fun and complete ending with Maxwell equations . The course is 8.02x.? This is the basis.? S parameters is more like circuit theory on permanent regime , one application of Maxwell theory. ?These vectors are harmonic phasors , these amplitudes and phases represents the permanent responde of the system. This is only a part of Maxwell solutions that also provides the vectors of fields on device for example a waveguide. On S parameter you only measure wave relations , incident and reflected phasors ratios … this is an abstraction to phisical model. The classical quadrupole theory.? I’m not very good in English I hope ir result clear.? Don’t mix Field (E,D,H,B… ) vectors (3 dimensions ) with a permanent regime solution based on harmonic phasors . This is the amplitude of vectors only . And is a part of complete solution that result enough to put the device on a black box and these S parameters are complete for most applications.
Ing. Patricio A. GrecoTaller Aeronáutico de Reparación 1B-349Organización de Mantenimiento Aeronáutico de la Defensa OMAD-001Gral. Martín Rodríguez 2159San Miguel (1663)Buenos AiresT:?+5411-4455-2557F:?+5411-4032-0072
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On 9 Nov 2023, at 20:32, Mike M <groups@...> wrote:
?Here is a website with some explanation:
This book is good. It includes explanations of the vector calculus operators:
|
In college I had a calculus professor from Czechoslovakia. When we did not understand a concept he used to sigh and say "every child in my old country knows this"
I was proficient in the circuit theory classes but struggled in the E&M class. We had a student from Greece that was proficient in vector calculus and he soaked up the concepts like a sponge. He went on to design Microwave Antennas.
That was a long time ago.
Mike N2MS
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On 11/09/2023 5:56 PM EST Tom Lee <tomlee@...> wrote:
I think many students feel as you do. Part of the reason, I suspect, is
that most students don't study vector calculus first. Without that
background, Maxwell's equations seem to be written in hieroglyphics. And
if you aren't in the priestly class, then it all seems abstract and
arbitrary.
But if you start with the fundamental experiments of, say, Faraday and
Ampere and see how it all got started, then the intuition precedes the
math(s) and the beauty (and utility) of Maxwell's formulation (the
modern textbook version of which is actually more due to Heaviside and
Gibbs) emerges more naturally. Unfortunately, many E&M (S&M?) courses
present little or none of the history and jump straight to the equations.
Too bad, really.
--Tom
|
Here is a website with some explanation:
This book is good. It includes explanations of the vector calculus operators:
|
Maxwell's Treatise is worth a read (he was a genius; lesser mortals
have built careers on his throwaway margin notes -- the
switched-capacitor filter comes to mind), but only after you've
mastered the now-standard vector calculus version of the equations.
Maxwell himself went through an evolution of thinking, starting with
writing out the vector relations term by term, and then adopting
quaternions as a more elegant way of showing off the symmetries.
Heaviside was the superior engineer, and so re-wrote the equations
in a way that he thought would inform engineering better, rather
than optimize for the happiness of mathematicians.
But before tackling the Treatise in its original form, it's very
helpful to read up on the experiments and struggles of both Ampere
and Faraday (the correspondence between these two is also extremely
revealing; these gents disagreed on quite fundamental matters at
times, and the arguments are hugely educational). In particular, the
geometric images that Faraday invented are very appealing,
intuitively speaking. For reasons that I don't fully understand,
textbooks dumped his pictures starting around WWII, and kept only
the equations. But earlier texts preserved Faraday's explanation of
his law of induction, for example, by talking about so many "lines
of force" "cutting some area" per unit time. The vector calculus
equations express precisely the same idea, but often without the
pictures. And when pictures are provided, the field lines are
deliberately treated as quite abstract, virtually guaranteeing that
students tune out at some point. I always liked Faraday's mental
pictures (that's how I first learned the stuff). I don't know why
modern authors have disdain for them.
--Tom
--
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
420 Via Palou Mall
Stanford University
Stanford, CA 94305-4070
On 11/9/2023 3:09 PM, ebrucehunter via
groups.io wrote:
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Tom,
As a student, following
a recommendation of the professor to the class, I
tried to read Maxwell's Treatise but gave up, as I recall,
because his use of quatrions? instead of vectors made it hard
to follow.? I guess it was the genius Oliver Heaviside who
sorted out the four equations we now know.
Bruce, KG6OJI
|
Tom,
As a student, following a recommendation of the professor to the class, I tried to read Maxwell's Treatise but gave up, as I recall, because his use of quatrions? instead of vectors made it hard to follow.? I guess it was the genius Oliver Heaviside who sorted out the four equations we now know.
Bruce, KG6OJI
On Thursday, November 9, 2023 at 02:56:37 PM PST, Tom Lee <tomlee@...> wrote:
I think many students feel as you do. Part of the reason, I suspect, is
that most students don't study vector calculus first. Without that
background, Maxwell's equations seem to be written in hieroglyphics. And
if you aren't in the priestly class, then it all seems abstract and
arbitrary.
But if you start with the fundamental experiments of, say, Faraday and
Ampere and see how it all got started, then the intuition precedes the
math(s) and the beauty (and utility) of Maxwell's formulation (the
modern textbook version of which is actually more due to Heaviside and
Gibbs) emerges more naturally. Unfortunately, many E&M (S&M?) courses
present little or none of the history and jump straight to the equations.
Too bad, really.
--Tom
--
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
420 Via Palou Mall
Stanford University
Stanford, CA 94305-4070
On 11/9/2023 1:58 PM, Jinxie wrote:
> Personally, I'd sooner resort to voluntary euthanasia than Maxwell's
> equations.
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I think many students feel as you do. Part of the reason, I suspect, is that most students don't study vector calculus first. Without that background, Maxwell's equations seem to be written in hieroglyphics. And if you aren't in the priestly class, then it all seems abstract and arbitrary.
But if you start with the fundamental experiments of, say, Faraday and Ampere and see how it all got started, then the intuition precedes the math(s) and the beauty (and utility) of Maxwell's formulation (the modern textbook version of which is actually more due to Heaviside and Gibbs) emerges more naturally. Unfortunately, many E&M (S&M?) courses present little or none of the history and jump straight to the equations.
Too bad, really.
--Tom
--
Prof. Thomas H. Lee
Allen Ctr., Rm. 205
420 Via Palou Mall
Stanford University
Stanford, CA 94305-4070
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On 11/9/2023 1:58 PM, Jinxie wrote: Personally, I'd sooner resort to voluntary euthanasia than Maxwell's equations.
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