What Every PCB Designer Should Know - Crosstalk Explained (with Eric Bogatin)

  Рет қаралды 101,115

Robert Feranec

Robert Feranec

Күн бұрын

Пікірлер: 221
@foobarables
@foobarables 3 жыл бұрын
For those who became hungry: Signal and Power Integrity - Simplified by Eric Bogatin. An excellent book.
@ekarter1981
@ekarter1981 3 жыл бұрын
Recently Rick Hartley and now Eric Bogatin... Wow! That's the real deal!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
:)
@OrsHunorDetre
@OrsHunorDetre 3 жыл бұрын
@@RobertFeranec Next one Henry W. Ott?
@Tech2k25
@Tech2k25 3 жыл бұрын
The last slide has answer to crosstalk. 1- Keep the transmission lines shorter than the rise time of the high speed signal into consideration. 2- Keep a reasonable distance between the two high speed signals e.g 2 time of width of the trace 3- Use stripline configuration i.e. use the high speed transmission lines between the dielectric material i.e. use a separate signal layer for high speed signals that has on top and bottom the dielectric material layer. Then on top of top dielectric the low speed signal layers or any other interconnect and on the bottom of the bottom dielectric use a solid copper ground plane
@ats89117
@ats89117 3 жыл бұрын
The technical term for that situation is, you're screwed... Eric Bogatin
@mixguru9669
@mixguru9669 3 жыл бұрын
Eric handles the host very well in addition to the amazing explanation. 😎
@bennybrown4342
@bennybrown4342 3 жыл бұрын
Thank you, Robert, for creating these excellent videos! Books are good, too, but nothing beats a real conversation on a complex topic. And thanks to Dr. Eric for the clear and enlightening explanations! Please please keep making more of these videos, esp. with Dr. Eric :D Some questions/requests I have for you: 1. Can you please discuss termination resistors? What do the signals look like with and without them? Best placement of them? Do most ICs requiring controlled impedances have them built-in, or are they always required externally? 2. What do I do about high-density ICs? When I have something unavoidable like multiple GHz MIPI traces converging into a tight area under a BGA, are there design techniques I can use to mitigate cross-talk? 3. I have seen a number of designs in real products that have high-speed traces on the surface layers that have good SI and EMI performance. But the difference described in this video between microstrip and stripline cross-talk makes me think microstrips should be more problematic. Is it really possible to have good SI/EMI with microstrips? 4. How do these cross-talk concepts apply to differential signals that are tightly coupled with each other?
@thisoldjeepcj5
@thisoldjeepcj5 3 жыл бұрын
A clear understanding of the basics is your best tool.
@derstrom8
@derstrom8 3 жыл бұрын
I ran into an issue recently with a digital video board I designed. I kept getting very thin (1px thick) vertical pink lines across the entire screen. I am fairly certain it has to do with the extremely tight coupling of tracks I had on an internal layer. This video definitely helped me visualize it much better, and has inspired me to revisit the board design and try to improve it. Thanks!
@karthikmaheshrao6021
@karthikmaheshrao6021 3 жыл бұрын
As a serdes engineer i come across so many issues of crosstalk on boards and packages. This video was on point and helpful. Thanks.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Karthik
@rogerfurer2273
@rogerfurer2273 3 жыл бұрын
I know that technical term: "You're screwed!" Thank you both. Question 1: Is ringing result of reflections? Question 2: How do guard traces affect the results?
@krisjk999
@krisjk999 3 жыл бұрын
Qn:1, Indeed the ringing is due to not terminating with characteristic impedance. There will be reflections (Calculated using reflection coefficient). Qn:2, the guard traces can have interesting effects. If it is not grounded, it builds up a charge due to capacitive coupling and there is no shileding effect. If it is grounded, then the field is confined more towards the guard trace. In effect a similar effect of the ground plane. If guard trace is grounded, would expect inductive coupling to treat it as a ground path while those induced currents in the guard trace can still couple to the victim line. I would say that is an "it depends" situation based on my limited understanding
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Roger, thank you Jayakrishnan
@alexpioner
@alexpioner 3 жыл бұрын
25 years ago one electronics teacher has said me: "Alex, the more you study the more you understand you know almost nothing" :) Robert, thanks a lot for proving this to me :) Like your videos very much! I've discovered your channel a couple of months ago, and I'm trying to see as many of your videos as possible, and recommend them to colleagues. I can even say, that after about of 20 years of experience I'm starting to understand something in board design :) Since you've asked for our opinion regarding your sessions with the experts, it can be cute to join some engineers from different industries having some real questions and problems, so the experts can try to help, and then show the results. Best wishes to you and your channel!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you very much Alexander for your words. PS: Number of people suggested to make a video with more than 1 guest .... so I keep playing with the idea, I am just not sure how it would turn out.
@emredincol
@emredincol 2 жыл бұрын
Thanks for this excellent video. When thinking about electromagnetic effects there is always three types of currents to consider: 1.Conduction current 2.Displacement current 3.Convection current
@montvydasklumbys7584
@montvydasklumbys7584 3 жыл бұрын
Really liked the whole video, really useful content! Actually, correct me if you can, but I actually like to think about crosstalk like to what happens in the generator, just on a smaller scale: 1. When we move a magnet next to a coil, we mechanically create a changing magnetic field, which induces current in the coil. We use a coil to induce a lot of current, however we can identically use a single wire, it will only induce less current. 2. Similarly, electricity traveling in the coil acts as an electromagnet. If we replace a coil with a single wire, we will still create an electromagnet, just many times smaller in size. 3. Now we put this all onto a PCB, where a signal travels down one line (electromagnet) and there is an adjacent line (generator coil). We do not continuously move one line against another, but instead we generate changing current (di/dt), which creates a changing magnetic field... 4. The generator coil (victim line) picks up the changing field, which results in induced displacement current!
@sigfreed11
@sigfreed11 3 жыл бұрын
Yes please continue the crosstalk discussion. Now that we better understand WHAT it is, let’s discuss how to mitigate crosstalk issues as well as understanding NEXT/FEXT plots, and how do we know if we have a crosstalk issue or something else?
@RobertFeranec
@RobertFeranec 3 жыл бұрын
I asked Eric.
@Retinatronics
@Retinatronics 3 жыл бұрын
When somebody knows something in depth; he will be able to explain it very clearly. Thank you for the video.
@mohammadkarimi8359
@mohammadkarimi8359 3 жыл бұрын
Thanks really for your online interview with Eric and expert engineers like him. Please do like this again. My suggestion is, please at the end of each question , you mention the vital points like that you do for two layers pcb and its crosstalk till we get the exact meaning of their talking.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Mohammad
@stephendeese97
@stephendeese97 2 жыл бұрын
This is such excellent content. I would love to see a followup where you give practical tips for avoiding cross-talk (by applying what we have learned here).
@ElectricNimPedalsPhilippines
@ElectricNimPedalsPhilippines 8 ай бұрын
I cant believe im getting all these insights for free :) Thank you guys!
@IXSigmaXI
@IXSigmaXI 2 жыл бұрын
mindblowing. If i understand what Eric was saying, doesn't that mean that for a microstrip, which had the magnetic coupling outweigh the electric coupling, increasing the impedance would lower the magnetic component in order to restore the cancellation? Please bring Eric back!
@MaxWattage
@MaxWattage 3 жыл бұрын
Another fantastic video, greatly appreciated. I say this as someone whose restless brain keeps them awake at night with bad memories of a horrendous crosstalk issue I had 26 years ago! It was a system with a 40-bit parallel data bus communicated between two equipment racks over several metres of ribbon cable. It had cross-talk in the ribbon cable, ground-loops, EMI, ground-bounce, simultaneous-switching-noise issues, you name-it.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Nicholas. PS: I am very happy, that I am not the only one with really bad experience with crosstalk
@jorgemunoz5678
@jorgemunoz5678 3 жыл бұрын
Great video! Please, create another one about this topic it is both interesting and extremely useful.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you very much Jorge
@maheshu3938
@maheshu3938 3 жыл бұрын
Finally i got clarity on crosstalk. Thanks Robert for your wonderful video...
@magdabalazs5598
@magdabalazs5598 3 жыл бұрын
I finally got to understand better the crosstalk! Eric Bogatin explains it so good and you are asking the best questions! Thank you very much for these videos!
@santhoshk8703
@santhoshk8703 7 ай бұрын
🎯 Key Takeaways for quick navigation: 25:11 *🔋 Energy from aggressor. * 26:35 *💡 Inductive coupling subtleties. * 31:06 *⚡ Capacitive & inductive noise. * 34:24 *📏 Near-end & microstrip crosstalk. * 36:44 *🔄 Crosstalk scaling factors. * 43:41 *🔀 Reflections and crosstalk.* Made with HARPA AI
@鄭峻杰-i2k
@鄭峻杰-i2k 3 жыл бұрын
Thanks. It's much clear on Crosstalk. The cause and responsible solution. Thanks again.
@abhishekupadhyay3419
@abhishekupadhyay3419 3 жыл бұрын
Good going, thanks for bringing the Eric Bogatin here... more power to you keep going. :)
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Abhishek
@marvin19966
@marvin19966 3 жыл бұрын
So that's what guard traces are used for, very interesting and well explained video
@whiterabbitangel
@whiterabbitangel 3 жыл бұрын
Guard traces decrease the capacitor coupling. A simple, not entirely accurate, way to think about it is imagine two capacitors in series between the aggressive and the victim.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you marvin19966
@amoghjain
@amoghjain 3 жыл бұрын
woww!!! thankyouuu soo much!!! another great in-depth and highly conceptual yet simple to understand video!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you very much Amogh
@harishrao2952
@harishrao2952 3 жыл бұрын
Thank you very much Robert for this video. Words are not sufficient to explain but the way eric makes every topic interesting is really good.
@Ghost572
@Ghost572 2 жыл бұрын
This video was really good. I Learned a lot in 50 minutes.
@MatthewHoworko
@MatthewHoworko 3 жыл бұрын
Such an informative and useful video! It really demystified crosstalk for me. Thank you Robert and Eric!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Matthew for leaving your feedback
@uccoskun
@uccoskun 3 жыл бұрын
Very informative. I like when you stop the video and explain things also.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you
@ThomasBomber
@ThomasBomber 2 жыл бұрын
I am just starting to get in the field of PCB design and your videos are full of very useful information that helps me growing my knowledge. I hope can use that in my career in the future. Thank you!
@gharbisalem1254
@gharbisalem1254 3 жыл бұрын
Hey Robert thank you for sharing , we hope you can provide more of these videos
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you gharbi
@superciliousdude
@superciliousdude 3 жыл бұрын
Another fantastic video! So much easier to understand from the visualisations in your video. Back in the day when I learned this stuff, the best we had was the Howard Johnson & Martin Graham book on high speed digital design. Love it!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you PS: I agree, we only had transparent foils at University - not the best tool for animation :D How lucky are today's students :)
@yel1110
@yel1110 3 жыл бұрын
The learning never ends, really interesting!
@thenoisyelectron
@thenoisyelectron 3 жыл бұрын
these videos are priceless thank you for your time and effort. I am going through a re-spin of multiple boards and I'm trying to soak up as much information as I can to make this the final revision
@anuradhapatel6021
@anuradhapatel6021 10 ай бұрын
BEST Video I have ever seen.
@michaelk.1108
@michaelk.1108 3 жыл бұрын
Great video, Robert! Thank you! The last slide was very important for me, because it really showed some values. This gives me a better feeling of how much distance of traces is required. I would really like to see another video with 2 or 3 examples showing something like a good situation and one where it is really screwed up be crosstalk. And maybe a difference between stripline and microstrip situation. This is a really interesting topic. And also thanks to Eric for his great explanations!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Michael. PS: I have already contacted Eric if he would be interested to continue talking about this topic.
@brokenicry
@brokenicry 3 жыл бұрын
PLEASE... You should definitely have more videos about this topic
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you
@hichemsetif1741
@hichemsetif1741 3 жыл бұрын
You are welcome. It was a pleasure.
@jeanclgcayer8259
@jeanclgcayer8259 3 жыл бұрын
Thank you Robert (and Eric) I just found many solutions to my problems here !!!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Jeanclg
@burievsardor76
@burievsardor76 3 жыл бұрын
Great work, Robert. I never thought that someone would make such kind of videos on youtube. This is what i wanted and it's amazing. I also never thought that a two layer pcb with solid ground plane would make crosstalk problems. Soon i will be your student on academy.fedevel. You are doing great work and keep on.
@giannisasp1208
@giannisasp1208 3 жыл бұрын
Fantastic explanation from mr Bogatin! Thank you Robert! It would be really interesting to speak a little bit more about how can we estimate or calculate a maximum coupled length for our signals (based on RT, track separations, e.t.c.) with some examples like we saw in the last slide. Also how would we estimate or calculate at what separation distance are our tracks “safe” and are not considered coupled any more, something like a “threshold”.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you. It's on my list ...
@sandeepkumartutiki851
@sandeepkumartutiki851 3 жыл бұрын
Wow Robert! really appreciate your work! Bring more topics with Eric and Rick..
@sergeyivanov3453
@sergeyivanov3453 3 жыл бұрын
Please continue this series
@duttabikash0013
@duttabikash0013 3 жыл бұрын
These Video sessions with Eric Bogatin are exceptionally informational. Thanks Robert. GROUND BOUNCE/ RETURN BOUNCE would be another topic which Eric explains extremely well. Please do a video on this too.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Bikash
@haribabuk850
@haribabuk850 3 жыл бұрын
Thanks for this video, This type of videos are really interesting, this video really helps lot of engineers to get clear understanding on cross talk, really love the animation 😀, we were also happy when guessing that capacitive and inductive coupling will cancel out, there our Eric explained a complications about microstrip 😀 again it's worst for people who design 2 layer and 4 layer Pcbs, you are doing such a wonderful job by sharing this type of content with free of cost, this channel deserves alot 👌 Kindly make one video on how the tabbed routing helps to control impedance and cross talk( if you found it is interesting)
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you very much Haribabu
@dimtsk838
@dimtsk838 3 жыл бұрын
Thanks Robert! Keep up this great contribution!
@XxfieryfirexX
@XxfieryfirexX 3 жыл бұрын
A Video of pro tips on how to avoid crosstalk would be really great please!!! :D
@CasualInventor
@CasualInventor 3 жыл бұрын
Fantastic video. Helps me understand a problem I'm dealing with at work. I'm looking at 5 ns rise-time at 200 VDC! Over 100 signals that need to be routed with minimal crosstalk AND all length matched! I like a challenge though :)
@samihawasli7408
@samihawasli7408 3 жыл бұрын
Eric's answer to "why is the maximum coupling only 50%?" was pretty wishy washy. The fields just "equilibrate over time"? In my opinion, a more mathematical answer is to think of the "aggressor" as a signal source with its own impedance, if the impedance of the source and load are matched, the maximum power transfer is 50%. Love the videos you all produce, great stuff!
@timpeng1269
@timpeng1269 3 жыл бұрын
Great interview. Could you please have Eric again for some power integrity topic and simulation in hyperlynx?
@ColinMacKenzieRobots
@ColinMacKenzieRobots 2 жыл бұрын
Very informative. Agreed, great animation! Thanks Robert & Eric
@chromatec-video
@chromatec-video 3 жыл бұрын
Very interesting and great explanation of crosstalk between traces. Can I now suggest that Eric returns in future to analyse the effect caused between differential pairs when the edges are not phase matched - presumably this will result in crosstalk and is even more dangerous since the traces will be closely coupled over most of their length. Robert can you also please consider this problem with regard to package flight-times which mean that the signals are not in phase at the source before any tracking has even begun.
@placiduzzu
@placiduzzu 3 жыл бұрын
Congrats for the nice discussion and the material presented. Engineering feast.
@tsusec
@tsusec 3 жыл бұрын
If i may ask, im new to this... What is the difference between ground and power plane? As far as i can remember AC current doesn't care ether of them because ie. battery is always represented as short when you calculate the impedance. And we always take GND as reference.
@TD-er
@TD-er 3 жыл бұрын
This really is a great and informative video. One thing I would like to know is to have some kind of rules of thumb to know when we enter the very scientifically defined "you're screwed". For example, what kind of ratio of length vs frequency can be used for 2 parallel traces over their full length at 1*w separation on a 2-layer board ? (somewhat of a worst case scenario) I do realize the rise time plays a very big factor in the "it depends", but let's assume it is 1/4th of the period.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Gijs. PS: I may do some experiments with this and then a video, but you can find some answers if you play with a crostalk calculator. E.g. this may help: kzbin.info/www/bejne/hWW3aqyVlq58qqM
@guillep2k
@guillep2k 3 жыл бұрын
Excellent video, Robert, thank you!!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you guillep2k
@THEQueeferSutherland
@THEQueeferSutherland 2 жыл бұрын
I think I learned a lot from this, but I'm also still sort of trying to wrap my head around what this actually means in practice, like what are some general guidelines to follow to avoid crosstalk in PCB design
@LucasFernandesAndrade
@LucasFernandesAndrade Жыл бұрын
Awesome video, thank you very much Robert and Eric!
@BeMuslimOnly
@BeMuslimOnly 2 жыл бұрын
Thank you very much both of you. 💕💕
@rvrtnn1121
@rvrtnn1121 3 жыл бұрын
The picture at 14 minutes in has a scale at the bottom showing the lenght in the picture of 100 mm. Something tells me it should have been µm. 100 mm is 10 cm, which is about 3" :-D
@Elektrotechnik-einfach
@Elektrotechnik-einfach 3 жыл бұрын
Excellent explanations and great talk (Y)!
@anuradhapatel6021
@anuradhapatel6021 10 ай бұрын
Hii Robert, Could you please make this type of video for RETURN LOSS and INSERTION LOSS with ERIC. Thanks
@Gengh13
@Gengh13 3 жыл бұрын
Awesome video, I'm starting to get an intuitive understanding of crosstalk. Keep up the great work.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you very much
@lalitverma6833
@lalitverma6833 3 жыл бұрын
Nice video Robert. One request: Will it be possible for you to share the PPT which Eric has shown
@amigo2x
@amigo2x 3 жыл бұрын
Thanks guys! Very interesting and useful!!. And if possible yes would be nice to watch second part
@gsuberland
@gsuberland 3 жыл бұрын
Fantastic video, and yet another great guest!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Graham
@diogoviegas.
@diogoviegas. 3 жыл бұрын
Robert, a return path don´t have to be necessary a GND plane, it could be a VCC plane. But normaly GND is better.. it depends on design...
@mdchethan
@mdchethan 3 жыл бұрын
Hi Robert, Excellent information. Waiting for more of these. Also its been a while we have seen your videos related to PCB design, missing those.
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Chethan PS: Yes, during Christmas I used different topics
@manideepdunna827
@manideepdunna827 3 жыл бұрын
Thanks Robert for the amazing video with lot of good information. Can you please make a video with Eric Bogatin to understand the effects of Microstrip vs co-planar waveguide traces?
@edouardmalot51
@edouardmalot51 3 жыл бұрын
Very good teacher
@madhuriwawale4297
@madhuriwawale4297 3 жыл бұрын
Great video but I want more information on crosstalk how we can reduce it because increase rise time may be the solution for avoiding crosstalk but I feel it may cause some other problems
@khangau4844
@khangau4844 3 жыл бұрын
thanks for such an informative lecture vid!!! It d be great if you can share w us the simulation software that Eric used in the video, those sims are sooooo on point!!
@KamleshGadhvana
@KamleshGadhvana 3 жыл бұрын
so how do we reduce cross talk in double layers pcb ?,thanks for the great video
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Kamlesh. PS: How to reduce crosstalk in 2 layer PCB? Honestly, after my very bad experience with crosstalk on multiple 2 layer PCBs, my best recommendation would be do not use 2 layer PCB. The 4 layer PCBs are not expensive anymore and that is what I would use instead.
@saravanankv823
@saravanankv823 2 жыл бұрын
I have a couple of Questions Why does the Crosstalk increase in magnitude on far end alone? And why does the Crosstalk on Rear end not uniformly distributed when the coupling region increases( why Cross talk on Rear end does not increase in magnitude)? How does the increase in Rise time decrease the Crosstalk?
@DiegoColl44
@DiegoColl44 3 жыл бұрын
Really nice video..!! Thanks Robert and Eric..!!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Diego
@evolutionaryelectronics6787
@evolutionaryelectronics6787 3 жыл бұрын
Amazing vedio on cross talk .....
@Anaxroche
@Anaxroche 3 жыл бұрын
thanks for your videos Robert
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you özhan
@66impala34
@66impala34 3 жыл бұрын
Very well presented. Great work
@arsalansyed4709
@arsalansyed4709 3 жыл бұрын
Thank you so much for making this video! This was super informative!
@yunusYT7
@yunusYT7 3 жыл бұрын
Awesome explanation!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Yunus
@JeffreyBoye
@JeffreyBoye 3 жыл бұрын
Awesome video, is there a link to the simulator Eric demonstrated? If you are looking for ideas for other topics, how about rounding out the "Big 4" with videos on loss, impedance and delay (timing budget)? You may have done this already, I apologize if so
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Jeffrey PS: I do not have link to the animation.
@simonndungu1196
@simonndungu1196 3 жыл бұрын
Thanks Robert!!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Simon
@ayrtonestrella
@ayrtonestrella 3 жыл бұрын
Could you please add bookmarks of your video in the comments with the specific video times for each section of your video? This would greatly help navigate your video to the sections of interest without having to watch 1+ hour video. Thanks, Robert!
@SerafinoConvertini
@SerafinoConvertini 3 жыл бұрын
Great as usual
@sailtogether3236
@sailtogether3236 8 ай бұрын
Really interesting details. Thank you!
@j121212100
@j121212100 2 жыл бұрын
Why not use FEM to explain this phenomenon instead of the coupled capacitor and inductor approximation. Simulating Maxwell's equations for the circuit layout seems to be the optimal way to minimize the crosstalk issue.
@venkannachimata6946
@venkannachimata6946 2 жыл бұрын
Thank you very much for the great video
@Ech01378
@Ech01378 3 жыл бұрын
Question: Is it better to insert analog signals into striplines or microstrips? Consider many other digital signals running over a board.
@painchaud49
@painchaud49 3 жыл бұрын
This was amazing, thank you !
@barismetin1014
@barismetin1014 3 жыл бұрын
Very good video. Thank you very much!
@22icyo
@22icyo 3 жыл бұрын
please more! very interesting and well explained. Thanks!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you very much 22icyo
@hugoboyce9648
@hugoboyce9648 2 жыл бұрын
Thanks for the video! It was very informative!
@sajinm7625
@sajinm7625 3 жыл бұрын
Please add another video for this topic.. i really appreciate your help
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Sajin
@MyMcMichael
@MyMcMichael 3 жыл бұрын
Thank you a lot!
@RobertFeranec
@RobertFeranec 3 жыл бұрын
Thank you Michael for leaving feedback
@michaellove7912
@michaellove7912 2 жыл бұрын
this is good stuff, thank you both
@pendalink
@pendalink 2 жыл бұрын
Loved it. Learn your physics!
@studynotes4835
@studynotes4835 2 ай бұрын
thank you so much
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