#257

แชร์
ฝัง
  • เผยแพร่เมื่อ 23 ต.ค. 2024
  • This video talks about the different roles that the various power supply decoupling and filter capacitors serve on a circuit board. While the video doesn't cover how to select the values, it does illustrate and demonstrate why both "bulk" electrolytic caps and high frequency (usually ceramic) caps are used, and why they are placed where they are. There is a lot written about the topic of selecting values - google is your friend. Here is one good example which includes some good general guidelines:
    pdfs.semantics...
    Here is a good extensive paper from Murata:
    www.murata.com/...
    Nice app note from Maxim:
    www.maximinteg...
    Really good resource from Texas Instruments:
    www.ti.com/lit/...

ความคิดเห็น • 411

  • @mariusbogdan9036
    @mariusbogdan9036 20 วันที่ผ่านมา +1

    Very good video! I agree with you! I'm already 70 years old, I can't stop this profession. (It's also my hobby) I also worked as a sound engineer and I also worked with impulse technology (analog video) circuits. This "impedance" approach has also worked for me. I used to design audio power amplifiers with a bandwidth of several megahertz, without loop feedback. They had very good voices. I wish you more success and good health from Hungary.

  • @grumpysailor8132
    @grumpysailor8132 7 ปีที่แล้ว +102

    Probably one of the best explanations I've witnessed in 30 years of electronic work. Thank you.

  • @sylvaind9086
    @sylvaind9086 3 หลายเดือนก่อน +1

    Thanks! This is the first time I see a "real world" representation of the effects of bypass caps, although I have used this method for decades.👍

  • @BEdmonson85
    @BEdmonson85 7 ปีที่แล้ว +9

    This is a brilliant explanation of why we use decoupling caps. I think most people know that they "should", but most don't know exactly why. You have a gift to be able to explain concepts so clearly and with practical examples. Thank you.

  • @joshua.hintze
    @joshua.hintze ปีที่แล้ว

    Just wanted to say thank you. I like your theoretical explanations but nothing beats a demonstration which you pull off flawlessly. Thank you.

  • @markwebcraft
    @markwebcraft 7 ปีที่แล้ว +60

    I absolutely love your videos because you are such a wonderful teacher. Your ability to simplify complex subjects and then create easily understandable examples to demonstrate them is second to no one on TH-cam. Thank you so much for the time and effort you put into these video, you really are helping.

    • @robh1908
      @robh1908 6 ปีที่แล้ว

      Yeah he's a natural when it comes to teaching. He has a very calming voice too which is a negative because I keep falling asleep watching his videos.

  • @fkungms
    @fkungms ปีที่แล้ว +1

    Probably one of the best explanation and demonstration of bulk and local decoupling capacitors

  • @NoorHafeez
    @NoorHafeez 7 ปีที่แล้ว +3

    so now i actually Know the Purpose of using the Cap near to my TLP250 Mosfet Gate Driver IC ... Thanks Alot ur channel is the best for Learning Things which books wont teach pretty well ... cheers!

  • @lucasng3330
    @lucasng3330 3 ปีที่แล้ว

    That world record smallest scope is absolutely adorable! Nice quality video, Alan. Thanks

  • @parochial2356
    @parochial2356 3 ปีที่แล้ว +1

    Excellent presentation and spot on. The TH-cam PC repair channels that simply remove and discard shorted decoupling caps and not replace them with equivalent parts and then state "it's not needed" should reconsider their advice and start replacing them rather than stating "it's fixed" because the short is gone. There is a reason why the engineers put them there, as W2AEW makes abundantly clear.

  • @dominicgoodwin1147
    @dominicgoodwin1147 3 ปีที่แล้ว +2

    This is the best practical teaching video I have seen on decoupling capacitors. The demonstration layout with the copper board and actually moving the caps to different locations to see the reuslting traces is so good. Thank you.

  • @masoudhosseinzade9621
    @masoudhosseinzade9621 7 ปีที่แล้ว +1

    Probably the only channel that really teaches something, really great!

  • @pnjunction5689
    @pnjunction5689 7 ปีที่แล้ว +31

    Absolutely brilliant explanation and demonstration! Much better than what you'll find in some books or lectures.

  • @hubertbonnisseur-de-la-bat4858
    @hubertbonnisseur-de-la-bat4858 2 ปีที่แล้ว +1

    Shortest inductance path ! Very powerful concept ! thanks a lot

  • @mikesradiorepair
    @mikesradiorepair 7 ปีที่แล้ว +2

    Great demonstration of how important placement of decoupling caps is. Thanks for sharing.

  • @windward2818
    @windward2818 2 ปีที่แล้ว +1

    I like your videos. The challenge in supplying high frequency current is the load may be dynamic. In other words, not just a set repeatable current step as with your demo board. Although it is an excellent place to start.
    A microcontroller is a good example where current demand is really dependent on the code that is running (ports turning on and off). How to address decoupling with a dynamic load which may only occasionally exhibit a worse case current draw (special exception through the code)?
    We have to look at supplying current in the magnitude that is required (with some margin) without limitations due to inductance in a worse case estimate. So a low ESR bulk-ish cap (like a tant) may be very close to the processor depending on the overall supply impedance at chip. For the very high frequencies the lowest inductance decoupling cap is actually the interplane capacitance. This is one of the reasons we use adjacent power planes in multilayer PCBs.
    Essentially, different capacitors are used in parallel to compliment each other for lowest impedance or overlapping lowest Z self resonance. These together form a Power Distribution Network (PDN). From a high level standpoint power is consumed over a broad band of frequencies. For lowest EMI supply impedance must filter (satisfy) currents such that the power from an outside source (AC supply for example) is of a very low frequency content. Ideally a steady supply or average current without high frequency content. The video you did on E and H near field probes ties into identifying problems with the PDN.

  • @tolgasen2419
    @tolgasen2419 5 ปีที่แล้ว +1

    This channel needs a gold medal

  • @Robert-hr6sh
    @Robert-hr6sh ปีที่แล้ว +1

    Good demonstration, nice video so people can see the importance and thus learn to better themselves as for circuit board layout as well. And why decoupling caps are used.

  • @PapasDino
    @PapasDino 7 ปีที่แล้ว +3

    Great to have you back, hope the ankle is healing or back to normal...been there, done that two times myself! Off to recommend this video to our local club's e-mail reflector. 73 - Dino KL0S

    • @w2aew
      @w2aew  7 ปีที่แล้ว +8

      Not normal yet, but getting closer. Still on one crutch. Hopefully will begin physical therapy later this month.

  • @Eletronicacasa
    @Eletronicacasa 4 ปีที่แล้ว +1

    I'm Brazilian and i work in an EMC lab. Your explanations are helping me a Lot to clarify some issues.

  • @lcradan24
    @lcradan24 7 ปีที่แล้ว

    The absolute best bite size tutorials. I wish you many many years of great health to continue seeing your tutorials. Thank you!

  • @12012004
    @12012004 6 ปีที่แล้ว

    I can not understand how this channel has only 88k subscribers. It is the best one covering the topic electronics in youtube. Thank you very much!!!

    • @w2aew
      @w2aew  6 ปีที่แล้ว

      I guess its because I don't have an associated forum or blog like EEVBlog, or any corporate sponsorship or partnership. It's really just all word-of-mouth.... So, spread the word!!

  • @philipdonovan6510
    @philipdonovan6510 2 ปีที่แล้ว +1

    That was really good. I've been building guitar pedals and tube amps for some years now and never had a clear picture about why different caps were placed as they were. And with the very high frequency devices where I work, that is ever more deliberate. Thank you!

  • @jasonlaverty76
    @jasonlaverty76 7 ปีที่แล้ว +3

    You really help me brush up on the principles that have managed to evaporate in my memory due not applying them much anymore.Thanks for an excellent clear explanation.

  • @ashishderhgawen
    @ashishderhgawen 7 ปีที่แล้ว +5

    You seem to be reading my mind. A few days ago I was thinking about the different types of capacitors, and you made a video about it. Yesterday I was thinking about power supply filtering with capacitors, and you made a video about it! Thanks so much. Your videos are very helpful.

    • @w2aew
      @w2aew  7 ปีที่แล้ว +20

      Do me a favor... Start thinking about winning the lottery!

    • @vinceibeachum5048
      @vinceibeachum5048 7 ปีที่แล้ว

      lol

    • @entoletao
      @entoletao 7 ปีที่แล้ว

      No Lottery for you! Otherwise you run away and stop teaching us new things..

  • @frankpitochelli6786
    @frankpitochelli6786 5 ปีที่แล้ว

    This just came up in my feed, I've been an electronics tech for 40 yrs (tv service etc)
    You're very knowledgeable and are well spoken in your explanations of technology.
    Well done.!!

  • @StreuB1
    @StreuB1 7 ปีที่แล้ว +7

    Alan, I learn so much from your videos. You are such a great teacher and your knowledge is just amazing. Thank you so much! I am more of a mechanical engineer that dabbles in electrical but my electronics knowledge is where I really fall short. Your videos have opened up my understanding far more than it ever would have on its own.

  • @Harbingerx81
    @Harbingerx81 7 ปีที่แล้ว +1

    Awesome video! As a hobbyist, I knew these caps needed to be there and had a very basic understanding of why, but this definitely gave the 'why' some real substance.

  • @timthompson468
    @timthompson468 7 ปีที่แล้ว +8

    Great explanation. I'm amazed how many BSEEs I've worked with who do not understand this, and design circuits with no local bulk capacitors or bypass caps.

    • @w2aew
      @w2aew  7 ปีที่แล้ว +7

      I know! Well, at least *this* BSEE tries to do it right ;-)

  • @donnymac575
    @donnymac575 7 ปีที่แล้ว +3

    This is an outstanding quick and dirty explanation on PS decoupling and high frequency filtering. Thank you!

  • @JackZimmermann
    @JackZimmermann 7 ปีที่แล้ว +10

    You sir, are a godsend! Great to see that you ramped up the output of videos. I learned a lot from you.

  • @dell177
    @dell177 7 ปีที่แล้ว +1

    Great tutorial!
    I worked in the custom power supply industry for most of my life. In the early days of switch mode power supplies I remember combining a 555 with a 709 to replicate what was later known as a 3524. We got to learn all about the need for proper decoupling the hard way!

  • @konturgestalter
    @konturgestalter 3 ปีที่แล้ว

    This is literally the best expanation on this topic I have seen.

  • @benish0r
    @benish0r 7 ปีที่แล้ว +8

    Thank you, Alan! You have awesome teaching skills and are able to explain complex things in a simple manner. The hands-on approach is wonderful since seeing is believing. I would love to see more videos like this one.
    73!
    Adrian, YO6SSW

  • @antonionisini6677
    @antonionisini6677 5 ปีที่แล้ว

    In few minutes, you made this obscure matter crystal clear with a perfectly designed experiment.
    Great lesson, thank you so much.

  • @maxxsmaxx1901
    @maxxsmaxx1901 6 ปีที่แล้ว +4

    When things become clear, my heart thanks you ! I love all your videos

  • @aduedc
    @aduedc 2 ปีที่แล้ว

    Great work of explaining decoupling caps. I learned why it is not important to place large caps near the active devices.
    Of course you could improve it by placing a smaller cap, say 150pF, next to 1.5 nF to get rid of self resonant frequency of 1.5nF cap.
    They , also, use beads for RF circuit isolation.

  • @UnexpectedMaker
    @UnexpectedMaker 6 ปีที่แล้ว

    Late to this video... but wow, what a clear and amazing breakdown of how and why we use low and high freq caps for decoupling. I've been using them without truly understanding why for ages, and now I have a much better insight. Thanks heaps!

  • @avichalid5604
    @avichalid5604 2 ปีที่แล้ว +1

    Thank you for all the shared knowledge I appreciate great teacher. Keep up the great work.

  • @victornpb
    @victornpb 7 ปีที่แล้ว +78

    Can you do a follow-up video on decoupling vs bypassing, and how chokes and ferrite beads play together. I had problems with Bluetooth audio modules coupling noise on their audio output. Solved by trial and error with different combinations of capacitors with a low pass filter on the power rail. But I will not pretend to understand what I was doing even thou I got it working...

  • @deryckschnee6376
    @deryckschnee6376 7 ปีที่แล้ว +1

    Thanks for this video. I've been struggling to understand this high-frequency ground return path issue, and you've just made it click in my brain! Appreciate your work and look forward to more in the future.

  • @florinssl
    @florinssl 7 ปีที่แล้ว +2

    Excelent way of explaining, a real pleasure to watch and learn from this videos. Please continue making this kind of tutorials and presentations

    • @DaSmik101
      @DaSmik101 2 ปีที่แล้ว

      Florineleeeeeee

  • @TonyButchT
    @TonyButchT 2 ปีที่แล้ว

    Amazing demonstration with visual confirmation, along with an excellent explanation! Thank You!

  • @ivib570
    @ivib570 7 ปีที่แล้ว +3

    This is part of my thesis. When the current goes Back under the trace is called IMAGE PLANE. In short you can say: Maxed well equation for high frequency and Ohms equation for low frequency. Greeting from Sweden :).

  • @mikolaj8776
    @mikolaj8776 6 ปีที่แล้ว

    At last after a year of trying to understand why ceramic caps have to be close to uC - because everybody talks about this and noone was explaining it - I have found this video. G R E A T ! ! !

  • @hongpan0507
    @hongpan0507 7 ปีที่แล้ว +4

    Great Video. I have been reading quite a few articles about this topic. Your video is the most practical example by far. Here are a couple questions:
    1. Are those high frequency noise on the scope caused by the fast switching or you manually inject into the power supply rail? Please excuse my question, just have to confirm. It makes more sense that the HF noise is from the switching because we wouldn't be able to the noise when you placed the ceramic cap close to the input of the power supply if you were to inject the HF noise on purpose.
    2. And how high is your high frequency switching? I have never seen a HF noise so noticeable on a scope before.
    3. I would love to see if you can demonstrate filtering high frequency noise in the power supply rail with your current setup. That would require manual HF noise injection. It's a good example because HF frequency noise does get into the power supply rail.
    4. I found a couple people are confused by the current path with your explanation. I was a little confused at the beginning. But one of your comments made it clear. I am going to repeat it here with my own words (correct me if I am wrong.). It is easier to think about your ceramic cap as a local storage cap that is capable of discharging its charge at a very high frequency, therefore, it is easier to think about the ceramic cap as a power supply that is capable of providing high frequency current demand due to fast switching. Then it will be clear that the high frequency current is returning back to the ceramic cap and not returning to the input of the actual power supply.
    Thanks for the great demonstration.

  • @omgkingdano
    @omgkingdano 7 ปีที่แล้ว +1

    Great practical demonstration of a very complex topic with very real consequences if you don't do it right

  • @chrisgorman816
    @chrisgorman816 7 ปีที่แล้ว

    This is a really great practical experiment. Insufficient decoupling is usually learned the hard expensive way.

  • @cpopte
    @cpopte 5 ปีที่แล้ว

    Great asa always Alan ! Love that little Tek mockup that you have in the lower left corner of your scope. Thankyou for your work again ! Truly apreciated.

  • @adilmalik7066
    @adilmalik7066 7 ปีที่แล้ว +2

    Alan, thankyou so much for such insightful examples. Amazing as always. I hope you actually write a book one day.

  • @FF7824
    @FF7824 4 ปีที่แล้ว

    Very informative. While I kind of knew this, your demonstration made it much clearer. Thanks.

  • @antonio406193
    @antonio406193 7 ปีที่แล้ว +1

    I like most of your videos. This one was great. Very well explained, thank you for making the demo board to show the performance of the different caps in different positions along the rail!

  • @rissole7229
    @rissole7229 4 ปีที่แล้ว

    Thank uou for another informative tutorial.
    I have found all your presentations extremely clear, concise and easily understood.
    Keep up the great work!

  • @racecarrr
    @racecarrr 5 ปีที่แล้ว

    Subscribed! You speak very clearly. I like your balance of info density & video length

  • @pradeepselvam
    @pradeepselvam 6 ปีที่แล้ว +2

    Thanks a lot brother you are the best teacher for me

  • @loberd09
    @loberd09 7 ปีที่แล้ว +3

    really helpful and great demo. Would love to see more of this "style" where there is a simple demo and explanation for things that are generally "assumed knowledge"

  • @PelDaddy
    @PelDaddy 7 ปีที่แล้ว

    Excellent demonstration! Thanks for sharing. I like the way your video simplify things and encourage viewers to experiment themselves.

  • @davidf8749
    @davidf8749 7 ปีที่แล้ว +1

    I've often wondered why a small ceramic is placed in parallel to an electrolytic for power supply decoupling. Great info - esp in that the ceramic cap needs to be close to the active element whereas the electrolytic doesn't.

  • @VDDThomas
    @VDDThomas 7 ปีที่แล้ว +6

    Very nice explanation! Way better than the professor who tried explaining the same thing at university :P

  • @josephwarren849
    @josephwarren849 7 ปีที่แล้ว +6

    I do like your back to basics videos they are very helpful

  • @krish2nasa
    @krish2nasa 6 ปีที่แล้ว

    Excellent explanation, this will greatly enhance in designing reliable circuits.

  • @OctavMandru
    @OctavMandru 7 ปีที่แล้ว

    Such teaching skills are exceptional, sir

  • @Michael-lo3ht
    @Michael-lo3ht 6 ปีที่แล้ว

    Excellent video. I see a lot of people in the maker community designing circuit boards and leaving out this critical part of the design. Usually in an all-digital design you might get lucky and not be an issue or might be a major one. A lot of my interests lately have been a mixture of rf and digital. Then it almost becomes absolutely imperative. To me it should be a standard feature of every design to decouple every IC. One such case is a radio kit that everyone can build. It has digital circuitry, rf, and audio. You can imagine that a lot of the complaints have been noise in the audio, rf distortion, and all sorts of interactions. Largely because the design is built around solving the main problem of getting a job done, but not over basic design features you need to include as well.

  • @TheMadMagician87
    @TheMadMagician87 4 ปีที่แล้ว

    This is an excellent demonstration, thank you very much for the effort that went into thinking this video through and producing it!

  • @redemptusrenatus5336
    @redemptusrenatus5336 7 ปีที่แล้ว +2

    I really appreciate the mock-up to help bring the idea down to the topic at hand. My question is what sort of symptoms might be experienced if these types of coupling caps are not existing in a circuit that would require them? I could see the noise on the scope but I'm curious as to what sorts of problems might arise from that extra noise. I do realize it probably varies from circuit to circuit but if there's a specific application you might be able to present or know of off-hand I'd love to hear about it or see it if possible in a demonstration like you did here. Thanks for sharing.

    • @w2aew
      @w2aew  7 ปีที่แล้ว +4

      The negative effects are highly dependent on the particular circuit of course. But, some of the most common problems from inadequate decoupling are:
      - circuit oscillation
      - unwanted logic transitions
      - unstable circuit operation
      - excessive EMI (RF radiation)
      - excessive RF susceptibility
      - all kinds of logic, state machine and uProcessor problems from logic glitches
      - distortion in signals
      -etc.

    • @akhtaralimalik989
      @akhtaralimalik989 5 ปีที่แล้ว

      w2aew thanks 🙏

  • @edwilliams9914
    @edwilliams9914 6 ปีที่แล้ว +1

    Very clear discussion. Great use of the demo-example board -- really helps simplify / clarify what's going on on the scope. I'm only half-mystified by it now! :-)

  • @yurikslalom
    @yurikslalom 7 ปีที่แล้ว +3

    Thank you, Sir! Very well explained. Looking forward for more excellent videos.

  • @Duckariffic
    @Duckariffic 2 ปีที่แล้ว

    I've been wondering why my 2.2uf cap keeps dying in my HP3312A...It's probably the transistor next to it!!!
    !!!GENIOUS!!!
    Thank you for this video and sending me on the right troubleshooting path!!!
    I'll post if it works!!!
    -Anoob

  • @dumouchelclermont4982
    @dumouchelclermont4982 7 ปีที่แล้ว +3

    Welcome back again .. Love it... great demo..

  • @LlNDEN
    @LlNDEN 7 ปีที่แล้ว

    I just found your channel, and the way you're able to explain everything so clearly is fantastic. Instantly subbed and I'm excited to start watching your vast collection of videos.
    Keep it up

  • @av6966
    @av6966 7 ปีที่แล้ว

    Thank you, for a great explanation that has answered one of long time standing questions I wasn't smart enough to know to ask. Awesome upload!

  • @brucetouzel6484
    @brucetouzel6484 4 ปีที่แล้ว

    excellent teaching video and distinguishing the different purposes of decoupling and filtering

  • @felixchen946
    @felixchen946 7 ปีที่แล้ว +1

    Thank you so much. This is so helpful for my senior design project!

  • @kmonyt
    @kmonyt 7 ปีที่แล้ว

    Great explanation. Simple presentation and illustrated well! Great job!

  • @lawrencemiller3829
    @lawrencemiller3829 7 ปีที่แล้ว +1

    Thanks for discussing and showing how the loop area affects high frequency return currents.

  • @WaltonPete
    @WaltonPete 7 ปีที่แล้ว +1

    Informative and interesting video with great practical demonstration of the subject in question. Thanks.

  • @owensboromunicipalcommissi4945
    @owensboromunicipalcommissi4945 7 ปีที่แล้ว +3

    Excellent video - thanks so much for this explanation !

  • @neethus3294
    @neethus3294 8 หลายเดือนก่อน

    Excellent demonstration. Thank you!

  • @stevegelnett4469
    @stevegelnett4469 3 ปีที่แล้ว

    So that’s what ground loops are.
    I’ve heard of them but never understood them.
    Thanks, man.

  • @DirtyEngineer
    @DirtyEngineer 7 ปีที่แล้ว

    Thanks for the wonderful and informative videos. I learn so much each time.

  • @petti78
    @petti78 7 ปีที่แล้ว +1

    Brilliant explanation and not too long either! Definitely deserved the like :)

  • @jimmy2drinks
    @jimmy2drinks 7 ปีที่แล้ว

    Thanks very much, will definitely share this with the students where I work.

  • @silvergmc
    @silvergmc 7 ปีที่แล้ว +3

    Another excellent video, thanks!

  • @simonyoungglostog
    @simonyoungglostog 2 ปีที่แล้ว +1

    Excellent. Enjoy the coffee.

    • @w2aew
      @w2aew  2 ปีที่แล้ว

      Thank you - much appreciated!!

  • @georgetroulis
    @georgetroulis 6 ปีที่แล้ว +2

    I always hear about decoupling caps but never have I seen a visual demonstration of why they are useful. Very well done, keep up the good work :)

  • @KeesHessels
    @KeesHessels 5 ปีที่แล้ว

    Thank you. you made it a lot more insightful and still keeping it simple enough for a noob (that would be me) to understand..

  • @jix177
    @jix177 7 ปีที่แล้ว +2

    Very well explained. Thanks!

  • @moiseslopez4446
    @moiseslopez4446 7 ปีที่แล้ว

    Learning a lot from your videos, keep it up they are enjoyable.

  • @mustafamuhammed9066
    @mustafamuhammed9066 6 ปีที่แล้ว +1

    You are a genius! Keep making those videos.

  • @byronwatkins2565
    @byronwatkins2565 3 ปีที่แล้ว

    As things are moved about, as boards expand and contract differently with temperature, etc. the power connections slip and generate us and ms having no power connection. Bulk capacitors near power connections absorb these transients and the board's circuitry continues to function. Less voltage transients across connectors make them last longer as well. This is all in addition to the benefits you mention.
    If an IC or transistor has only one high current output (or you are utilizing only one), you can reduce the transient even more by grounding the cap as close to that current's return as possible and by placing the power end as close to the power pin as possible while enclosing as little area as possible. For hand assembly, a small axial cap directly across the chip yields optimum performance.

  • @hoodaly
    @hoodaly 7 ปีที่แล้ว +3

    Very instructive, well done!

  • @jasoneyes01
    @jasoneyes01 7 ปีที่แล้ว

    Clear and Easy to understand. Thanks!

  • @warwolt
    @warwolt 9 หลายเดือนก่อน +1

    Fantastic!

  • @ericgee6585
    @ericgee6585 7 ปีที่แล้ว

    Very well explained and demonstrated. Thanks

  • @xDevscom_EE
    @xDevscom_EE 7 ปีที่แล้ว

    Good vid showing decoupling work in simple way. Now for part 2 you could show difference of using multiple values cap for local decoupling, such as why 0.1uF + 1uF + 10uF better than just 2 x 10uF :). Or that can be part 3, and part 2 can cover how to determine how much capacitance for bulk you need to have good power delivery. :)

  • @VeryMuchBlessed
    @VeryMuchBlessed 7 ปีที่แล้ว

    Super good lesson! Examples very helpful. Thanks for helping with my learning.

  • @adrianjohnson555
    @adrianjohnson555 7 ปีที่แล้ว +3

    Great video, thanks very much.

  • @bertronixtv
    @bertronixtv 7 ปีที่แล้ว +1

    simply amazing. i admire you for sharing your knowledge.

  • @donaldfilbert4832
    @donaldfilbert4832 7 ปีที่แล้ว +3

    Yes !! Very well explained !! Thanks.

  • @andycristea
    @andycristea 7 ปีที่แล้ว +2

    Extremely interesting! Thank you!