From like 48:06 the "/ dz" is missing in the update terms. It is fixed in the lecture notes on the website already. Just so people know when watching this. And also there are some other changes for the boundary conditions, which I also wondered about (so it goes only up to e2 and h2). So worth checking it out.
@empossible15779 ай бұрын
Thank you for pointing this out!
@pedrovagos821710 жыл бұрын
Audio at min 26 is missing during ~1 minute.
@comment8767 Жыл бұрын
@slide no 26-38, audio is missing. Please provide the audio! I just bought the book, but the lecture is too good to have in incomplete form!
@comment8767 Жыл бұрын
Hmmm.... looks like I need to pay $600 for the on-line course. Will have to check my piggybank.
@empossible1577 Жыл бұрын
@@comment8767 The 1D FDTD course is $295. Also, the first half of that course is entirely free to see if you like the teaching style. I think you will learn a lot just from that free content.
@empossible1577 Жыл бұрын
Sorry for the missing audio. It is on my very long to-do list to fix that. When I do, I will update the course website with the latest link. Here is the course website: empossible.net/academics/emp5304/
@PadmaRamaiya5 ай бұрын
Hello sir , thank you for tour videos, i am doing under this topic. Sir here at 8:29 chapter "adding soft source". At iteration 90/700 , we are getting one type of wave. And ay 700/700 , we are getting one type of wave. My prediction is this must be the equal one. But it is not equal. Is my prediction correct sir? Or any mistake is there?
@empossible15775 ай бұрын
Very sorry, but I don't understand your question. I "think" you are asking why there seems to be two types of waves later in the simulation. That is because I am visualizing both the electric (blue) and magnetic (red) fields. At first, they overlap so closely you cannot tell them apart. After scattering from the boundaries, they get a different phase shift and they invert from each other. Hopefully this is what you were asking!
@PadmaRamaiya5 ай бұрын
@@empossible1577 tq sir
@Makedonomaxos883 жыл бұрын
Thank you again for your great lectures, Professor! In slides 32-35, you imply that S
@khaledalhorani79655 жыл бұрын
I encourage you to write a book regrading Computational Electromagnetics. If so, I believe it would be one of the best of its kind. Best wishes ...
@empossible15773 жыл бұрын
Not too long after you wrote this message, I did start writing a book. It will be released Jan 1, 2022. Here is the book website... empossible.net/fdfdbook/
@khaledalhorani79653 жыл бұрын
@@empossible1577 Can't wait to read it from A to Z! So grateful and thankful...
@huonghuongnuquy72722 жыл бұрын
@@empossible1577 hello, i'm currently in a research project and i'm very interested in your book. Juste before buying this book, i have a question about the content of your book. I almost understand in theory about the FDTD thank to your videos (I already watch it several time). However, I need more in detail about how i can write the matlab code steps by steps with the examples to really understand and to be able to write the code by myself. So could you telle me if your book could help me for this point ? I'm still student who live in a poor familly, I wanna to know if it is possible to have a reduction for the book ? Thank you very much.
@empossible15772 жыл бұрын
@@huonghuongnuquy7272 You might be confusing finite-difference frequency-domain (FDFD) with finite-difference time-domain (FDTD). Mathematically, these methods are strongly related, but their implementation is very different. The book teaches FDFD, not FDTD. Here is a link to the book website: empossible.net/fdfdbook/ Unfortunately, the book belongs to Artech House and I have no control over sales and pricing. In fact, I have to buy my own copy if I want one! Have you considered asking your university library to buy the book? Do you have an advisor or department head that might also buy the book? If you want to try to learn FDFD with completely free materials, I recommend first working through Topics 6 and 7 at the link below to learn the finite-difference method. empossible.net/academics/emp4301_5301/ From there, FDFD is taught in Topic 4 here: empossible.net/academics/emp5337/ These are the notes I use for my face-to-face classes so I am uncertain how effective they are without having me there to teach them and demonstrate codes. The book was developed specifically to be a complete learning resource and I think it is really good. If you can at all get the book, I highly recommend it. It teaches how to use FDFD to do many things. Another option is FDTD. I provide the notes and videos for free that go with my face-to-face class. Here is the link: empossible.net/academics/emp5304/ Again, this may be difficult if you are not taking the class face-to-face with me. For FDTD, I have also developed an online course that is specifically meant to be for beginners and is complete with MATLAB codes. It is actually a pretty awesome course that you can work through on your own time. Here is a link to a video that showcases the content of the course: kzbin.info/www/bejne/q3PMoaV_g52anLs Here is a direct link the FDTD courses. The entire first half of the first course is free and you may find it very helpful and enough to get you through the free material I gave above. empossible.thinkific.com/collections?category=FDTD-in-MATLAB Hope something here helps!
@huonghuongnuquy72722 жыл бұрын
Hello i'm not understand the implementation of PEC in 53:14. I did exactly the same code in the video, but in fact H2,H1, E2 and E1 need to be defined. Anyone could help me to figure out this issue please ?
@empossible15772 жыл бұрын
This is not the perfect electric conductor (PEC) boundary condition. Instead, it is the perfectly absorbing boundary condition. Yes, H2, H1, E2 and E1 need to be initialized to zero before the main loop. Unfortunately, I do not have room to show the entire code so this was left out. Also, let me point you to the official course website. I have links to the latest version of the notes, videos, and other learning resources. You will see that the notes have been considerably revised and include error corrections and other things that have not made it into the videos yet. empossible.net/academics/emp5304/
@ShekoufehAbdollahi Жыл бұрын
Thank you for this amazing course! Slide 35 is muted. Can you explain how n_bc involved in the equation? Why n_min is replaced by n_bc? And how should we consider different materials in each side (BC) of problem?
@empossible1577 Жыл бұрын
Sorry for the video problem! n_bc is the refractive index at the very edge (i.e. boundary) of your grid. The time step delta_t is calculated such that the wave travels one grid cell in EXACTLY two time steps. n_min is no longer needed when calculated this way. As formulated, you cannot have a different refractive index on either side. If you want to, you need to do one of two things: 1. Use a different boundary condition, such as a perfectly matched layer. This is taught in the 2D section of this course. 2. You will need to store the field value over enough time steps that you can interpolate the field at the edge from this array. For example, you may need to know the value of the field at the edge of the grid after 2.3 time steps. You would record the field for three time steps and then interpolate the field at 2.3. I personally recommend approach 1. In the end, you will have a more capable code because it can also do 2D. A 2D code if written correctly can still simulate 1D problems. I wanted to make you aware of a couple of things. Right now you are going through my free FDTD course: empossible.net/emp5304/ These are the notes that I use for my in-person class. If you are just getting started, you may be interested in the online FDTD course I put together. It is next level awesome in terms of simplicity and is written specifically for the complete beginner. It also teaches an improved and more powerful FDTD and includes all of the MATLAB codes. Here is a link to a video showcasing the course: kzbin.info/www/bejne/q3PMoaV_g52anLs Here is a link directly to the FDTD courses: empossible.thinkific.com/collections/FDTD-in-MATLAB Also, I recently wrote a book to help the complete beginner get started in computational electromagnetics (CEM). It teaches the art of CEM using finite-difference frequency-domain (FDFD), which is the frequency-domain equivalent to FDTD that you are learning. Here is a link to the book's website: empossible.net/fdfdbook/ Hope this helps!!
@winnis888 жыл бұрын
(50:00) Inject source block is placed at the end of the udate equations. However, is it not more appropriate to place it "in-between" the Update E from H block?
@empossible15778 жыл бұрын
Yes, I think it could be done that way and perhaps even more efficiently. My main purpose here to teach FDTD so I like to organize the code so that a particular section is only doing one thing. If two things are happening at once, it may become more confusing.
@winnis888 жыл бұрын
Okay, thank you again.
@winnis888 жыл бұрын
(38:32) and in homework 4, that the E field and normalized H fields are in-phase (plots overlap) in -z-direction and out of phase in +z-direction. Is it correct to understand this as a consequence of orthogonality, right-hand rule between the E, H and wave-vector?
@empossible15778 жыл бұрын
This is correct. I tend not think to think of them as out of phase. I think of them in terms of keeping ExH=P. Both ways of thinking are saying the same thing.
@uvaiskhan99263 жыл бұрын
Where's the code for plotting Reflectance and transmittance? It was only till update equations.
@empossible15773 жыл бұрын
Unfortunately, I have already provided more MATLAB code in this video than I probably should. In my experience, providing code shuts down students' thinking and they go into a "code hacking" mode that is hard to pull them out of. While it can be frustrating, it is MUCH better to write the code yourself. If you are desperate, I have created fully online courses on FDTD that cover all of the code and multiple device examples. The code is typed and explained line-by-line in addition to all of the theory. Further, the online courses teach a more powerful version of FDTD. The entire first half of the 1D FDTD course is completely free so see if you like the format. empossible.thinkific.com/collections?category=FDTD-in-MATLAB
@zhyfn97732 жыл бұрын
Thank you for the lecture! I have one question though, why is energy not strictly adding up to one during the simulation for some frequencies?
@empossible15772 жыл бұрын
There are a variety of reasons this can happen. There is numerical error that is typically well less than 1%. There is the case where field energy is still in the simulation and not yet escaped to be counted as transmitted or reflected. There is also the case near a diffraction order cutoff where waves are propagating nearly parallel absorbing boundaries. Depending on what you are doing, there could be other reasons.
@debasishraymohapatra21776 жыл бұрын
I divided the whole grid into three mediums: UR=1(leftmost), UR=4, UR=2(rightmost). And then run the FDTD engine with a TF/SF soft source. I have implemented the perfect 1D boundary condition. My understanding is the wave will bounce back and forth in the mid-slab for specific times, but it will be absorbed entirely on both sides. But during simulation, I found out like the wave was absorbed on the leftmost side. But there was a reflection from the right side boundary. And when I set the ER/UR to 1 for the rightmost medium, the wave was absorbed on both sides. So, my understanding is incorrect, or I might have an issue with my code? Appreciate your help.
@wenxiuli62348 жыл бұрын
Hi sir, Thank you for the quality of your lectures.I have a question about how to use the FDTD realize the coupling of two straight waveguide ,which one is gain waveguide and another is loss waveguide.How did I use the FDTD to set the gain coefficient and loss coefficient ? Please help...
@pearltorto7 жыл бұрын
Hi! This is great thanks! With your description of periodic boundary conditions, does that mean PEC boundary conditions are a special type of PBC where the field is just zero at either side of the unit cell?
@empossible15777 жыл бұрын
While both are simple boundary conditions, I see them as very different. A periodic boundary condition allows waves exit one side of the grid and reenter on the other. A PEC blocks the wave altogether and it reflects.
@pearltorto7 жыл бұрын
Ahh ok but to achieve the PBC the fields on the left must be same as those on the other side of the unit cell - which is what you also do for the PEC its just they are well zero lol so completely reflect. Also say if you assume to have a dipole above a PEC then to solve for the fields do you not have a virtual dipole on the other side of the PEC so in a way the sources are being repeated i.e. it is periodic?
@empossible15777 жыл бұрын
I think I see the way you are thinking. If your dipole source was not centered in the grid, the PBC and PEC would behave much differently. Second, you would have a virtual dipole on the other side of the PEC, the PEC essentially ends the problem there. The PBC would force the problem to repeat indefinitely.
@pearltorto7 жыл бұрын
Of course and that is why you don't put the source in the center to see this effect! Ok thanks so much thats clarified it for me!
@sreeramaravind94954 жыл бұрын
sir, even after adding boundary condition small part of the waves are reflected back. I have used a gaussian source. What should i do?
@empossible15774 жыл бұрын
What do you mean by small? Depending on the resolution of your grid, you can expect your reflection to be at least six orders or magnitude smaller than the original pulse. This is normal. If you really want this much smaller, you will need higher grid resolution or you will need to compensate for dispersion on your grid. If your wave is more like 0.1 of your original pulse, then something is wrong. Did you calculate your grid resolution and time step correctly?
@AnubhabHaldarChronum7 жыл бұрын
At around minute 8, when you show us the field updates of the moving pulse, we see that the fields slowly dealign. Is this numerical dispersion?
@empossible15777 жыл бұрын
I am not sure if there is any misalignment since E and H are coupled. You may be observing numerical dispersion where different frequencies travel at different speeds simply due to the numerical approximations made. This can deform the pulses.
@AnubhabHaldarChronum7 жыл бұрын
Yes, that explains it. Many thanks!
@winnis888 жыл бұрын
18:00 We force fields at the boundaries to be zero, which causes reflections. You say that forcing the E field to 0 likens PEC, and forcing H field to 0 likens PMC. However given any perfect conductor (either electric or magnetic), both E field and H-field is 0. Example, inside perfect conductor electric field is 0 (cause otherwise there would be infinite current inside the conductor), and hence even time varying magnetic field is 0 because of Maxwells eqns. Comments?
@empossible15778 жыл бұрын
There are two things to consider. First, there is a difference between PMC and PEC. Tangential E fields tend toward zero as they approach a PEC, but they do not have to tend toward zero approaching a PMC. Same argument for H fields. Second, a magnetic field can exist inside of a PEC, it just has to be a static magnetic field. Likewise, there can be an electric field inside of a PMC, albeit a static E field.
@winnis888 жыл бұрын
So by forcing E fields (tangential to XY plane) to 0 on one side of the grid and H field (tangential to XY plane) to 0 on other side of grid, we get PEC and PMC. This was the asymmetry you talked about. Thank you.
@akhilagouda55603 жыл бұрын
Thank you, sir, your every video inspire and help me to make corrections in my code. I have a small doubt at 23-24, that you mentioned metallic structure ( PEC ) converges at N=40-60. most of the time, I feel PEC converges quickly and it's sufficient with N=20. so I'm confused here. could you help me with that? Also on doing all these simulations time will increse.
@empossible15773 жыл бұрын
For 1D simulations, you likely will not notice this. I observe that for 2D simulations. For 3D simulations, I have observed that metallic structures sometimes do not converge until around N=100. There are techniques that can help in these cases like nonuniform or unstructured grids. Fundamentally this is happening because the fields vary rapidly in most metallic structures and it takes higher resolution to resolve the rapid fluctuations. Hope this helps!
@akhilagouda55603 жыл бұрын
@@empossible1577 Thank you, sir, one small doubt, want to know the thumb rule for calculating the number of free space cells between the boundary and the target object. I usually take 1lambda, is it sufficient.
@empossible15773 жыл бұрын
@@akhilagouda5560 One lambda is probably not sufficient. Usually 3 to 5 wavelengths large. It is best determined through convergence. Try making it larger and larger under your answer does not change any more. You can also look at the modes and make sure the evanescent fields decay to zero and stay zero for a little bit before encountering the edges.
@raghavdhingra54174 жыл бұрын
Sir, how do I visualize my gaussian wave? I notice there's a function called draw1d.p on your website. But the input parameters for the same are not mentioned.
@empossible15774 жыл бұрын
Great question. You have motivated me to add the function headers (what you would see if you typed help at the command prompt) to see a brief summary of how to use the functions. Below is a link to the official course website. The Help Headers is not the very last link on the course page. empossible.net/academics/emp5304/ Hope this helps! Perhaps I should also include demo files. Hmmm... Maybe in the future.
@raghavdhingra54174 жыл бұрын
@@empossible1577 Thank you so much. It worked well for me. Your lectures are really comprehensive and were the ultimate resource for someone looking to pick up TMM and FDTD within a week.
@raghavdhingra54174 жыл бұрын
I can't seem to wrap my head around why the REF/TRN spectra often crosses the unit value before all of the energy has left the system. You mentioned it in a comment somewhere, but I couldn't understand. Could you elaborate?
@empossible15774 жыл бұрын
@@raghavdhingra5417 One week? Very nice! I am jealous. It took me way longer than that! Nice job!
@raghavdhingra54174 жыл бұрын
@@empossible1577 It's all thanks to you, sir. I just managed to get some expected results with a DBR stacked on a dispersive layer. Even though I had studied the Drude Model, I was in a bit of a fix to apply it to my FDTD code. All solved! Thank you!
@gangaruwandi31534 жыл бұрын
Hi sir... Can you help me to model a thin wire (radius < cell width) on yee grid using MATLAB?
@empossible15774 жыл бұрын
Suppose the wire runs in a y direction. I think the easiest thing you can do is just set ERyy to a very large number like 1e6 at all points on the wire. Technically the width of the wire will be half a grid cell, but it is an easy thing to do and will get you close.
@gangaruwandi31534 жыл бұрын
@@empossible1577 Thank you for the response sir. ERyy - does this mean the conductivity?
@empossible15774 жыл бұрын
@@gangaruwandi3153 No, ERyy is my notation for the yy element of the dielectric tensor. It is the permittivity at the points of Ey and Dy. Incorporating conductivity is a little more involved. Setting ERyy to something very large is a great place to start.
@gangaruwandi31534 жыл бұрын
@@empossible1577 It's clear now. Thanks again.
@empossible15774 жыл бұрын
@@gangaruwandi3153 Awesome!
@ommslab9 жыл бұрын
Hi, Thank you for your tutorials, they are really helpful. Just a small question, if I want the device to be a piece of steel, how do I set the parameters. What permittivity value do i set. As far as I know permittivity of metal is infinity. Please help..
@empossible15779 жыл бұрын
ommslab This topic is discussed in Lecture 18. Work through that and let me know if you are still need help.
@ommslab9 жыл бұрын
Hi, I am trying to add a metal device using conductivity term. So I have to update coefficient as: %%%%%% sigma = 1e7; % conductivity of iron mHx = (c0*dt)./UR; %%magnetic field update coefficient mEy1 = ((2*e0.*ER)-(dt*sigma))./((2*e0.*ER)+(dt*sigma)); mEy2 = (2*e0*c0*dt)./((2*e0.*ER)+(dt*sigma)); %%%% and my main loop is %% %initialize fields Ey = zeros(1,Nz); %electric field initial value Hx = zeros(1,Nz); %magnetic field initial value %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% FDTD Code %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Main loop for T = 1:STEPS %update H from E for nz = 1:Nz-1 Hx(nz) = Hx(nz) + mHx(nz)*( Ey(nz+1)-Ey(nz) )/dz; end Hx(Nz) = Hx(Nz) + mHx(Nz)*( E3 -Ey(Nz) )/dz; % add H-field source Hx(nz_src-1) = Hx(nz_src-1) - mHx(nz_src-1)*Esrc(T)/dz; %record H-field at the boundary H3 = H2; H2 = H1; H1 = Hx(1); %update E from H Ey(1) = mEy1(1)*Ey(1) + mEy2(1)*(Hx(1)- H3)/dz; for nz = 2:Nz Ey(nz) = mEy1(nz)*Ey(nz) + mEy2(nz)*(Hx(nz)- Hx(nz-1))/dz; end %add E-field source Ey(nz_src) = mEy1(nz_src)*Ey(nz_src) - mEy2(nz_src)*Hsrc(T)/dz; %record E-field at the boundary E3 = E2; E2 = E1; E1 = Ey(Nz); if ~mod(T,10) %show all the fields draw1D(ER,Ey,Hx,dz); xlim([dz Nz*dz]); ylim([-3 3]); xlabel('FDTD Fields'); title(['Field at step ' num2str(T) ' of ' num2str(STEPS)]); %draw graphics drawnow; end end %%%%%% I do get animation but the source does not move from its origin. However, if I put sigma=0, then then the animation shows perfect result as a dielectric object just as you said. But as sigma is increased to 1 and so on, the source does not move any more. I have checked the E and H field update equation with your lecture and believe there is no mistake. Think the issue is the with E and H field source. Would you be kind enough to have a look please.
@szaman71005 жыл бұрын
Sir, I've a question to know. I've faced this one in 1D FDTD simulation. I think my code is right. Case 1: When Source (Ex) is unit gaussian pulse, CFL= 0.5 the normalized value of Ex and Hz also become unit pulse. Case 2: CFL= 0.25, the normalized value of Ex and Hz become twice of unit pulse. Case 3: CFL= 1, the normalized value of Ex and Hz become (1/2) of unit pulse. My question is why E and H field magnitude depends on CFL value? Doesn't it should be independent of CFL?
@empossible15775 жыл бұрын
Is your 1D grid along the y-axis? By CLF, you are talking about the Courant stability condition, correct? The magnitudes should only depend on material impedance, not the stability condition. Perhaps if you chose a value that made the code unstable weird things could happen. I never played with that. Check what else changes in your code when you change CFL. If nothing else changes but your time step, I will be confused.
@szaman71005 жыл бұрын
@@empossible1577 Fields magnitude vary with stability criterion but no problem with stability. Can I show you my 1D code? I cant find out the error. I will be really graetful.
@ShivrajNaorem3 жыл бұрын
the part i wanted to see has its audio disabled
@empossible15773 жыл бұрын
Hmmm...which part? I did not mean to disable anything!
@ajaykochar95806 жыл бұрын
Did anybody understand the implementation of PBC? Due to missing audio, i couldn't get that. Can anyone help? How is the disturbance felt after 2 time steps ? what about h3=h2, h2=h1, h1=H(1)? How is this implemetation tackling the things? Please help.
@empossible15776 жыл бұрын
For the PBC, the time step is chosen so that waves will travel a distance of one Yee cell in exactly two time steps. To make a PBC, the values at the grid boundaries are saved for two time steps and these delayed values are used as the field values just outside of the grid.
@ajaykochar95806 жыл бұрын
Thanks for replying sir. Does that mean the intermediate number which we are getting during T=2 is a field value at the mid of the cell. Because, we observe 1 in the next cell at T=3.
@empossible15776 жыл бұрын
There is sort of one unused delay term, that is only used to produce the delay. Is this what you were asking?
@ajaykochar95806 жыл бұрын
@@empossible1577 Yes sir. That is only the issue now. Other issues do not exist now. Thank you.
@ProfeARios3 жыл бұрын
@@empossible1577 in 31:10 you said we have to implement h3=h2, h2=h1 and h1=H(1), but in the PDF file of the course materials empossible.net/wp-content/uploads/2020/01/Lecture-Implementation-of-1D-FDTD.pdf it shows only h2=h1, h1=H(1) on slide 43. Is that incorrect?
@atsul.79437 жыл бұрын
Hello sir, thank you so much for these materials. For me who is a beginner in this very exciting field, these videos of yours are about the best resources available here on earth. However, about 26 mins into the video, the audio was missing. I miss out on the perfectly absorbing boundary condition even when u came back to it later in the video. Since no corrected videos are out yet, could you kindly point me to some resources that explains the perfectly absorbing boundary condition just like you did around that portion of the video.
@empossible15777 жыл бұрын
Happy to help. Let me point you to the official course website that contains links to these videos, the course notes, and many other resources to help you. The notes have seen some revisions and improvements so they may differ from the videos a bit. emlab.utep.edu/ee5390fdtd.htm Once on the course website, take a look at Lecture 5. Hope this helps!!
@atsul.79437 жыл бұрын
Okay. Thank you very much
@prakashranjan66758 жыл бұрын
Thanks for such a wonderful tutorials. @slide no 26-38, audio is missing. plz upload new video with audio because those were very important slides.
@empossible15778 жыл бұрын
Strange. Thank you. I will fix this as soon as I can.
@youtobebug7 жыл бұрын
any further results? the new video with audio??? (it is a really great online lecture, thank u for ur effort ^__^)
@gagggari6 жыл бұрын
Is there a new video with audio ??You are the boss :)
@empossible15776 жыл бұрын
Is the audio not working?
@deepaksangwan17216 жыл бұрын
yes it is not working for a minute starting from 26.02 to 27.06. In this time period videos covers 11 slides from 27 to 39 and all of them are very important.
@gagggari6 жыл бұрын
yeah but you can figure what he is saying from the slides
@oussamagassab32827 жыл бұрын
it is very amazing lectures, i m really enjoying during watching this amazing lectures. thank you so much for this lectures. there is one thing : in 34.30 i think you mean tau >1/(pi*fmax) isn't it ?
@empossible15777 жыл бұрын
No. tau can be made smaller (shorter pulse), but not longer. A longer pulse would have more limited bandwidth and thus not produce much power at the frequencies you are interested in. Does this make sense?
@oussamagassab32827 жыл бұрын
thank you so much for your reply professor, in your condition which claims B
@empossible15777 жыл бұрын
In the latest version of the notes, I removed B from the discussion entirely. B and fmax seemed to cause too much confusion with everyone. fmax is the cutoff frequency of the source. The frequency content of the source decays smoothly so there is still power in frequencies above fmax, but fmax is a convenient metric to use as the cutoff frequency of the source, above which there is too little power to get accurate simulation results. B is the bandwidth you are interested in simulating your device over. Thus, you must keep B < fmax for accurate simulations. The confusion arose because there is an important difference between bandwidth of a signal that extends from 0 Hz up to B and a signal that extends from f1 to f2 where B = f2 - f1. I fixed this confusion by eliminating B from the discussion entirely. Now a source with duration tau will cover all frequencies from 0 Hz up to fmax.
@oussamagassab32827 жыл бұрын
since we need to cover all the range 0 Hz to fmax, the necessary condition is tau
@cssaziado5 жыл бұрын
Hi, I think I am missing something. I don't have perfect boundary reflection ...but almost. I think I am doing everything ok... for ti in range(1,len(t)): #mainloop print(ti) for nz in range(0,len(z)-1): Hx[nz] = Hx[nz] + mHx[nz]*(Ey[nz+1]-Ey[nz])/dz Hx[sourceindex-1]=Hx[sourceindex-1] -mHx[sourceindex-1]/dz *EyT[ti] #Total field/scatter field Hx[Nz] = Hx[Nz] + mHx[Nz]*(e3-Ey[Nz])/dz #condições perfect boundary h3=h2 #condições perfect boundary h2=h1 #condições perfect boundary h1=Hx[0] #condições perfect boundary for nz in range(1,len(z)): Ey[nz] = Ey[nz] + mEy[nz]*(Hx[nz]-Hx[nz-1])/dz Ey[sourceindex]= Ey[sourceindex] -mEy[sourceindex]/dz *HxT[ti] #Total field/scatter field Ey[0] = Ey[0] + mEy[0]*(Hx[0]-h3)/dz #condições perfect boundary e3=e2 #condições perfect boundary e2=e1 #condições perfect boundary e1=Ey[Nz] #INJECT SOURCE Ey[sourceindex]+=EyT[ti] Hx[sourceindex]+=HxT[ti]
@empossible15775 жыл бұрын
I have revised this section of the notes, but have not yet rerecorded the videos. Take a look at the revised notes and see what you can figure out. empossible.net/wp-content/uploads/2019/08/Lecture-6-Implementation-of-1D-FDTD.pdf It looks like you are trying to implement the the perfect BC. In this case, there should be very low reflection, not 100% reflection. If you are plotting in MATLAB and letting it autoscale the amplitude axis, it may look like significant waves are reflecting. Check their amplitude, they should be many orders of magnitude smaller than 1.