Thanks so much for making these! They are the first RF videos I've found where I've managed to follow everything. You are a great teacher -- very concise and logical.
@MegawattKS3 жыл бұрын
You're so welcome! I'm especially happy you posted this comment on part 2. I recently re-watched the Episode 1 stuff and thought part 1 was pretty decent, but wasn't as happy with part 2. Glad the concepts came though well :-)
@DavePKW7 ай бұрын
I just now happened to see your channel. I love RF circuits and radios. I always wanted to learn how to design them. But I never could really understand some of the books I have looked at. Especially impedance matching and filters. Thank you so much for this series of videos. You make an excellent presentation that is easy to follow. It is exactly the kind of instruction I have been looking for. Please do more of them if you can. 73
@MegawattKS7 ай бұрын
Welcome aboard. Glad it resonated (pun intended ;-) ).
@nick1f Жыл бұрын
Thank you for the explanations, they are clear. The homework - for the bandwidth of 20 MHz, center freq of 98 MHz, Rp = 1500 ohm, we get L = 497 nH and C = 5.3 pF
@MegawattKS Жыл бұрын
Yes - very good ! I got 480nH and 5.5pF through some quick scaling calculations. I think yours is more exact though. But it all has to be adjusted anyway after its built due to other parasitics not included in the calculation :-) Another option might be to decrease Rc (and re-do the matching network) - but that would give up too much gain...
@user-su5sq5ib3i3 жыл бұрын
Wow I am so happy I found your channel. Thank you!
@MegawattKS3 жыл бұрын
You are so welcome! The videos will be kinda slow coming, but hoping to keep it going. :-)
@fjs11112 жыл бұрын
Awesome! Those RF inductor IC's are something!
@MegawattKS2 жыл бұрын
Thanks. They're fairly low frequency, so the inductors were nice and big :-)
@minazulkhan8287 Жыл бұрын
Great videos. Learning a lot
@asc1653 жыл бұрын
Great videos, please keep them comming!
@MegawattKS3 жыл бұрын
Thanks, will do. Working on impedance matching one now :-)
@CannonballCircuit2 жыл бұрын
at 24:45 when you're looking at the equivalent impedance seen from the load, why aren't C5, L1, R4 included as part of the circuit?
@MegawattKS2 жыл бұрын
For the full circuit, they should be. But here, we're breaking the circuit into two parts where one part is what's circled in red and the other part is everything else. If we can reduce what's circled in red to a simpler circuit (a single resistor, when operating at fo), then we can come back to analyzing the full circuit more easily. The slide and discussion at 24:45 is just trying to find a simpler 'equivalent' circuit to replace Lm, Cm, and Rs (the 50 Ohm load) with. That equivalent circuit is the Rp and turns out to be 3.2K in this example. When this is used in the full amplifier at the output, the collector just sees R4 in parallel with 3.2K (since C5, L1 resonate-out, as doe the Lm,Cm parts. Hope that helps.
@eebasement45302 жыл бұрын
Hi , thanx for the video. Q: how do you calculate the resistance value for the inductor from Q in the parasitic analysis ? 4.12 is probably the Xo fro previous equation, but the 0.405 from where it come ?
@MegawattKS2 жыл бұрын
The 0.405 (or 0.406) is the series resistance at the operating frequency (while 4.12 is the series reactive part). See the NanoVNA readout at 14:00 in the video. It says 406m + 4.12j for the measured impedance - though I confess it's blurry and really hard to read. Sorry about that.
@MegawattKS2 жыл бұрын
So to add to that, please note that there are two different models for an inductor in general. The VNA reads out the impedance in the series-equivalent form (R+jX), whereas here we're using the parallel-equivalent form. See this site for how the conversion is made between the two in general (Fig 1). aaronscher.com/Circuit_a_Day/Impedance_matching/series_parallel/series_parallel.html
@minazulkhan8287 Жыл бұрын
@@MegawattKS thanks for making it clear . I had same question, I thought it was from datasheet.
@cholan21003 жыл бұрын
Built a wideband Image filter to accommodate the FM band frequency range, but looks like two BPF's couple to form a ripple on the peak with a 6dB trough in the middle. With such wideband, input impedence and SWR measurements go for a toss. So yeah for any serious product quality design would need a tracking filter. Would be interesting to sync track along with electronic tuning of LO. I think with vintage radios it was done using LC with gang capacitors.
@NathanAlpern Жыл бұрын
Hi. thank you for the videos. I didnt's understand in the example why is there both parallel and series circuit. and if the load is 50 what is exactly the RP?
@MegawattKS Жыл бұрын
You're welcome. I'm not sure which part of the video you are asking about. There are two examples at 8:40 and 18:40, plus the matching network discussion at 23:06 and a commercial radio schematic at 25:50 . I think maybe we're talking about the last one. If so, then they used a series LC followed by a shunt LC in order to make a higher-order filter that attenuates more outside the passband. If we assume the input Z or the CB amplifier Q1 is roughly 50 Ohms resistive, then for the tank circuit L2,C2, Rp would be 25 Ohms, assuming the antenna is also roughly 50 Ohms. That's because at the center frequency, the series leg L1,C1 looks like a very low impedance (ideally zero) connection from Q1e to the antenna. So looking to the left we see the 50 Ohm antenna, and looking to the right we see the 50 Ohm Rin of Q1. Off-resonance, at higher or lower frequencies, the impedance of L1,C1 increases rapidly while the impedence of L2,C2 decreases rapidly, making a strong voltage division. Hence the higher attenuation than using the shunt leg L2,C2 only. Hope that helps. Is this the part of the video you're asking about?
@NathanAlpern Жыл бұрын
@@MegawattKS Hi. thank you for the response. I actually meant from ~23:50. I didnt understand the calculation method? Why from the load side do we have a series LC network? The inductor seems to be parallel. When you calculate the Rp in the parallel circuit why do you ignore the 50 Ohm resistor? sorry for my late replay. I am from Israel so we are in a war with Isis Gaza so the times are a bit tough.
@MegawattKS Жыл бұрын
@@NathanAlpern I probably should have started the discussion by stating that we're just "looking to the right" of the LCR circuit at the collector. The goal is to pick matching network (MN) components that transform 50 to 3.2K. That is, build the MN so that looking to the right, we see 3.2K resistive at fo. With that said, the goal of the discussion is to understand how the MN does this. The 'proof' is based on power conservation (Q can actually be defined in physics by 2 pi (peak energy stored during a cycle) / (energy lost per cycle due to resistance). When we're just looking to the right (and not working with the LCR 'tank' circuit at the collector), we have a series resonator, with a Q of 8 in this case because the loss resistance that dispenses energy each cycle is 50 Ohms. But we can also imagine it as a parallel RLC circuit and assess what the parallel loss resistance would have to be if it were a parallel resonator. The Q would be the same, by power conservation, so we calculate 3.2K. At resonance, the MN LC plus the 50 Ohm load looks like a 3.2K resistor to the rest of the circuit. Hope that helps.
@MegawattKS Жыл бұрын
@NathanAlpern So sorry about the war. It is hard and very sad. Please stay safe.
@MegawattKS Жыл бұрын
For another treatment, here are the class notes from the university course. It is more mathematical, and doesn't give a physics feeling for what's actually happening. That's why I took a different approach in the video. But this set of notes also covers series/parallel equivalent circuits - which has it's own value... ecefiles.org/rf-circuits-course-section-6/
@rjordans3 жыл бұрын
Great explanation, thanks!
@rjordans3 жыл бұрын
For the take home part, a quick guess bandwidth *3 gives inductance *3 and capacitor / 3. How about changing the q of the inductor to get higher bandwidth? Of would that impact the matching of loss too much?
@MegawattKS3 жыл бұрын
Excellent idea (the scaling of the values to match the scaling of the bandwidth) ! Scaling is a very powerful technique. Changing the inductor Q however would unfortunately destroy most if not all the amplifier gain (effectively the same as lowering R4 value), and mess up the output match S22. But absolutely, yes, scale L and C as you said !
@rjordans3 жыл бұрын
@@MegawattKS another thing I noted, in calculating the matching network you put the new inductor parallel to the output tank, if you replace both with a single inductor of lower value that might help getting back to an easier to make inductor value right?
@rjordans3 жыл бұрын
I think that may work indeed, L1 would be 270nH, taking both the original scaled capacitor from the tank 5pF and the 4pF from the matching circuit in parallel to calculate resonance still gets a center frequency of 101MHz
@MegawattKS3 жыл бұрын
@@rjordans Awesome. Merging the MN inductor with the tank one should definitely help decrease the size too. The 4pF in the output match however will need to stay in series (can't be put in the tank). But it can serve as the DC block happily :-)
@cholan21003 жыл бұрын
With through hole component(soldered as surface mount with shortest possible lead length), the center frequency of BPF was almost achievable, but Q was terrible at 3. Lets see what happens when i have the SMD 0805 sample book delivered, i guess i should have gone with even small ones.
@cholan21003 жыл бұрын
and VSWR is at ~5, with insertion loss at -3.6dB.
@davistroy3 жыл бұрын
Awesome videos. Can’t wait for the next one! What was the class you taught?
@MegawattKS3 жыл бұрын
Thanks! I did various courses, including Electronics 2, Design of Communication Circuits, Antennas and Microwaves, and Digital Radio Design (plus intro EE, and some others). This material is mainly from Design of Comm Circuits which was a senior design elective with lecture and lab components (always a good combination IMO :-) .
@cholan21003 жыл бұрын
Does PCB design constraints matter at 100Mhz band? I think the trace length wouldn't be much of a problem considering the longer wavelength, but should the trace width for 50 ohm impedance be considered? I had good performing filter tested on NanoVNA testboard kit, but the custom made PCB(phenolic single layer, with coplanar ground plane) with wide trace width, had huge offset in center frequency(98 Mhz vs 75 Mhz) for the same components filter.
@cholan21003 жыл бұрын
NanoVNA TestBoard has decent via stiching wave guide and all.
@MegawattKS3 жыл бұрын
It does matter for some circuits. Depends on the resistance and reactance levels of the different parts of the circuit/components. How spread out are the components on the CPW board relative to those on the NanoVNA board? My guess is that you have extra parasitic inductance at play maybe? See this video if you haven't already: (I keyed it up to the parasitics discussion) kzbin.info/www/bejne/iGHQg4efnL6tmdE
@cholan21003 жыл бұрын
@@MegawattKS i redid the pcb on double sided glass epoxy with ground plane+cpw and the 50ohm impedence controlled transmission line trace, that got it better. Although home etched pcb didn't get it perfect. But what got it on target is your suggestion on spread out. I moved the inductor literally on top of capacitor, to get 100.xxMhz - 19db bandwidth, Q=5.1 and insertion loss -0.9db. But adds more worry 😟 what levels of pcb planning should i use when i cascade these along with amplifiers and mixer and more filters.
@cholan21003 жыл бұрын
@@MegawattKS i used 330pf+8.2nh tank configuration
@cholan21003 жыл бұрын
@@MegawattKS yeah it looks like parasitics of footprint added to the problem, which resolved when i reworked and soldered the components right on the transmission trace. So "Keep it all short and close", should reduce the parasitics away.
@ernestb.237710 ай бұрын
Finally started to build the first band-select filter, as I now have a lot little UFL connectors... Enormous insertion loss of about -50dB 🙂It looked like a bandpass filter but totally useless. Probably my capacitors are useless at higher frequencies. The inductor didn't even had a lot influence. I have used 1206 MLCC X7R (cheap CN sample Book). Next thing I am going to do is do some testing of the C's I have. I read now I should use the SLC type instead of MLCC. But this is very good to learn. If it worked first time build I would learn less 😉 Anyway great series, but very specific work: as well as specific knowledge as components used and the way built!
@MegawattKS10 ай бұрын
Absolutely - if it works the first time, half the learning opportunity is missed 🙂 Epilogue 2 in the series even goes into some troubleshooting methods, as I had some problems when I was trying to improve the IF amp after the first build. I suspect the components in the filter are OK. Except for damage to caps from excessive heat in a few cases, we rarely saw hard failures from the components. But cables and ground connections (and other connections made with solder) were sometimes a problem. A few things to try maybe: (you may have done much of this already): A careful visual check with good optical aids. Ohmmeter check from cable to board ground and from cable center-lead to component on board to verify connection. Ohm from center to ground to check for cable/connector short to ground. Any other connections that look potentially iffy in the visual. Another thing that often works with the VNA is to look at S11 and see if it looks open or shorted, rather than somewhere in the middle of the chart at the resonant frequency. A lot of info can be collected that way - including cable issues. Sometimes its quicker than Ohming it out. (S22 can be checked by turning the board around - looking for the same issues). Hope the detective work goes well :-) kzbin.info/www/bejne/aWKwmXxph7iEe6s
@ernestb.237710 ай бұрын
@MegawattKS Thanks a lot for the tips. As said, RF is a challenging specialty. I have checked with an Ohm meter, as it is all quite small. Grounding is also black magic 😀 Looking forward to explore more, as it is all educational and no pressure.
@ernestb.237710 ай бұрын
@@MegawattKS I figured out what I am doing wrong. I have obviously not checked good enough.. I had some shortage under the UFL connector. Problem is, I don't have the dedicated experiment PCB for that special UFL-SMD-PCB-pattern, so this is not going to work. Now trying to find some experiment PCB where you can mount the UFL's ... Any help is welcome 🙂
@ernestb.237710 ай бұрын
@@MegawattKS work in progress here. I am kind of abandon the ufl (as I don't have adequate PCB-pads) and started to build with a piece of PCB with SMA mounted. Got the first results at much lower f0 at about 70MHz. Then calculated that I had twice the L and instead of 2 windings used just 1. That got the f0 almost right at 100Mhz, then I shortened it a few mm and it was at 100. But still have quite an insertion loss of -4dB! So need to work on that... Previously, with ufl I was able to make one filter with 0.5dB insertion loss, but I had also peak f0 at about 70MHz. Those ufl would be okay if I had specific PCB to mount on, otherwise not easy... Some transistors are on the way and looking forward to go further with LNA 🙂
@ernestb.2377 Жыл бұрын
Sorry to bother you. I was wandering if there would be the list of materials (and/or schematics) used for the Projects 1 through 4, so I can collect those beforehand, and can build as I go through the series. If not, no problem I will discover as I go...
@MegawattKS Жыл бұрын
The only thing similar to that is here on the companion website: ecefiles.org/rf-circuits-course-notes/ BUT - the parts list shown in the first link on that page is _not_ the set of parts used in the videos (except for a few items like the transistors). The Radio Design 101 series is an 'abstract' of the course it was derived from, and I made several changes to make it more reasonable for KZbin. So it is scaled down a lot. Still - the website and links are relevant, and all the lectures from the actual course are there (without any narration, and hand-written - so they're probably a bit hard to work through). Sorry I don't have anything more directly fitting for the videos.
@ernestb.2377 Жыл бұрын
@MegawattKS it's okay, I will see as I go along. I think I will order some handy materials like those ufl connectors. I want also to build modular and try to get the whole to work as expected. But I also realize that RF building techniques are specific, gnd-plane, via's to gnd etc. I will search for those handy RF experiment boards, like vna test boards....
@MegawattKS Жыл бұрын
@@ernestb.2377 Sounds good! I'm not sure if you have seen this yet, but a viewer has created a Github site so that boards can be easily made though a place like JLCPCB or ExpressPCB. Details on his boards and associated things can be found here: github.com/maelh/radio-frequency-prototype-boards/blob/main/README.md and on the ECEFILES.ORG site here: ecefiles.org/rf-circuit-prototyping/
@spottedgeckgo6 ай бұрын
Probably a dumb question and not sure if you are still answering comments. Why on the amplifier circuit are you feeding into the emitter instead of the base with signal in? I'm very new to RF but I've been making some amplifier circuits and for common emitters I've been feeding to the base.
@MegawattKS6 ай бұрын
Good question. Yes - for common-emitter amps, we feed at the base and put a bypass cap to ground the emitter. The intent is to vary the base-emitter voltage with the signal, which is the first step in the amplification process. Here we chose to feed the signal in at the emitter and bypass the base. - so the base-to-emitter voltage is still varied and the amount of voltage amplification can still be the same (though the input resistance is less). This is called a common-base configuration. Details can be found in Episode 3 ("RF Amplifiers"). And even a deeper dive is presented in Appendix A. kzbin.info/www/bejne/i4bPoopjq7ikb68 and kzbin.info/www/bejne/o2q7YaCcnMRrorM
@jchatterton21133 ай бұрын
I'm struggling to figure out how to get a 20 MHz bandwidth out of the filter(s) + amp + matching network. I use the equations, come up with the values, but for some reason the simulations are showing that at best I can get maybe 10 MHz. I even tried off-tuning the bandpass filters on the front and back end, but still no luck. Any hints? Maybe I'm not accounting for something in my simulations that would help me out a little? I'm obviously missing a step here, because simulating just the bandpass filter by itself seems to give the desired BW. But then when I combine that filter on the output on the amp with the matching networks and pre-select filter, my BW drops significantly. Thanks for any advice you can provide!
@MegawattKS3 ай бұрын
This is an excellent question. Thanks for bringing it up. There are many things that could be the cause, so this is going to be part 1 of an answer. In this part I would offer that RF design often is (or should be) an exercise in tradeoffs and compromise, and that 10 MHz is actually fine for the FM broadcast application - especially if it keeps the cost of the radio low. It may actually be good if you know which end of the band has the weakest signals - just center there and let the other frequencies not have full gain. There is so much "margin" in the FM transmission 'link' that a few dB doesn't hurt at all. Maybe just center the filter at 98MHz and take a minor hit at the low and high frequency ends of the band. I'll follow-up with some circuit thoughts in "Part 2" of this answer 🙂
@MegawattKS3 ай бұрын
Here's part 2 of an answer... At the circuit level, there could be effects such as feedback through the transistor parasitic capacitances/etc that could be at play in 'sharpening-up' the response from 20 MHz to 10 MHz. The simulator may be modeling the transistor's parasitics more closely than we do in the initial analysis. But don't put too much emphasis on that - once the circuit is built, parasitic L,C, couplings can make even the simulator's results 'off'. BUT it could be something more simple that we're not thinking about. I assume you've looked over the simulation schematic extra carefully for minor errors? The idea of off-tuning front and back end filtering is a good one. If that didn't work, then maybe there's something odd in the sim setup. What simulator and transistor models are you using? Is there a good bypass cap on the base of the CB amp? Typically I would expect the bandwidth to widen up, not narrow up.
@jchatterton21133 ай бұрын
@@MegawattKS I keep trying to reply but KZbin deletes it. Thanks for your insight and suggestions! I am using QucsStudio for my simulation. I am tuning the inductors for the input/output networks and will then confirm performance. I will say that it's good to know that 10 Mhz would be OK, and I will soon be able to measure actual performance. And thanks for your video on how to measure S21 with a Nano VNA, because I will be performing just that procedure!
@babeimichen38919 ай бұрын
Hi, thanks for your video. I really learned a lot from your content. But I got confused over 23: 15 did you mean that the 50 ohm load with the LC matching network is in parallel with R4? So this means the Av=gm*R4 without the negative sign in front? And is it normal since in my impression the load is usually connected to the really 0 voltage ground instead of Vcc? Thanks
@MegawattKS9 ай бұрын
Hi. Yes and no. Yes - the 50 Ohm load with the matching network is in parallel with R4. That means the 50 Ohm load R is changed to 3.2K Ohms by the matching network and that 3.2K Ohm is in parallel with R4. So we don't think about it being 50 Ohms now. It has been changed to 3.2K. Note that Vcc is an "AC ground" due to the bypass capacitor C3. So while it looks visually like R4 is to Vcc, we treat it as if it's to ground in the analysis. Hence it's in parallel with the 3.2K transformed load R. But no on the Av question. The actual voltage gain is gm*(R4 || 3.2K). If R4 is 3.2K (I think its 3K in a previous slide, but that's close enough), this means the gain from the emitter to the collector is now approximately gm*1/2*3.2K. The fact that it is a positive gain rather than a negative gain is due to a different issue. This is a Common-Base amplifier. The input signal comes in on the emitter and goes out on the collector, with the base 'common'. This common-base or CB design is a non-inverting type amplifier - unlike the more familiar Common-Emitter type which would have the formula Av = -gm*R (or -gm*R/2 if it has a matched load on it). Hope that helps.
@MegawattKS9 ай бұрын
For more on these issues, the formulas for the different amps (CB vs CE) are given in Episode 3 here: kzbin.info/www/bejne/i4bPoopjq7ikb68 , and also in an "Appendix" here: kzbin.info/www/bejne/o2q7YaCcnMRrorM . These episodes will hopefully also elaborate the definition of AC grounds (which comes from splitting the amplifier analysis into the DC bias analysis and the AC analysis.
@babeimichen38919 ай бұрын
Thank you so much! I realized that with C3(the bypass capacitor,) all AC signals go through it, so it's just like the ground (hopefully, I got it right this time.) And about the common base type of transistor, I just found it out! Now I'm so glad and here I want to recommend a book that I've been using for RF learning and found really useful, especially for self-learners. @@MegawattKS
@hectorbarrera9496 Жыл бұрын
Hi, thanks for your video, I have a question, I just made a bandpass filter for 60 Mhz, but the nano VNA measure give -10 db at center frequency, that's ok or how can i improve?
@MegawattKS Жыл бұрын
Assuming -10 dB is the S21 reading at the center frequency, the Q of the resonator is the first place to look. And the overall resonator Q is typically limited by the inductors, as noted in the video starting around time 13:16 . But it could be one or more of many other things. Ultimately it is a mystery to be solved through collection of clues and trying different solutions. That's what makes RF tricky (and fun ?) sometimes. Thankfully a VNA allows us to get good measurements to help guide the search and do less guessing. I always advise students to take S11 (and S22) measurements in addition to S21. That way we can collect more clues, postulate what could cause those readings, and that can guide us in tracking down the issue 🙂 Hope that helps.
@hectorbarrera9496 Жыл бұрын
@@MegawattKS Thank you for your answer, I will follow your recommendation and do the measurements that you mention
@coffeecuppepsi Жыл бұрын
Is the course work available for purchase? I have been trying without success for many many many years to build a receiver, also I'm in a remote place where it is not possible to meet people or attend lectures. I think the course work will help me immensely, perhaps you yourself have published books in the subject?
@MegawattKS Жыл бұрын
No - BUT - there is an associated website ( ecefiles.org ) where all the slides can be downloaded in PDF form. AND - there's also a section of that site that has the entire course notes and assignments from a representative semester. Unfortunately, it is harder to work through than the videos because the assignments were for different circuits than in the videos and the notes are hand-written. They were just the ones I used when presenting in class to make sure I covered everything I planned, and in a logical order/presentation. When I did the video series, I abstracted out some material (and expanded other topics in the Epilogs at the end of the series :-) ) See the syllabus in the course material for recommended book(s). Hope that helps !
@coffeecuppepsi Жыл бұрын
@@MegawattKS thank you so much for your reply and link ))
@athuldas446 ай бұрын
Why suddenly jumped to Rf amplifier didn't even explained the Circuit please explain the RF amplifier
@MegawattKS6 ай бұрын
Hi. Here's the full Playlist. RF (small signal) amplifiers are covered in Episode 3. kzbin.info/aero/PL9Ox3wpnB0kqekAyz6blg4YdvoEMoJNJY and here's a link into that third episode where I've queued it up to the walkthrough of that amplifier. kzbin.info/www/bejne/i4bPoopjq7ikb68 The rest of the video covers lots of other background and variations - and there's a "Part 2" (called Appendix A) in the playlist for anyone who wants a deeper treatment.
@steelinhank2 жыл бұрын
Is there a reason that the AGC isn't Discussed?
@MegawattKS2 жыл бұрын
Good question. I should maybe talk about that in one of the Epilogue episodes. The reason it didn't come up here is that the project was built around an FM broadcast receiver. For FM, non-linear amplification is OK (and even preferred). The IF amp is a "limiting" amp. It is OK for it to saturate and for the signal to become something resembling a squarewave (because the information is contained in the frequency which is unaffected by overloading). FM is great in that sense, and no AGC is generally needed. But as you point out, AGC is needed in other systems (like QAM digital/etc.), and maybe a modified version of it could be useful for dealing with strong off-channel interference...
@tcarney573 жыл бұрын
Excellent presentation, though it's the kind that has to be seen a number of times for the content to sink in. That's okay, but even if it wasn't there's really no way around it--for either the presenter (who can't spend twelve hours going over and over the same material) or the learner (who can't _really_ focus more than thirty minutes at one sitting anyway). People who complain that YT presenters "go too fast" forget they can pause, rewind, and replay as often as they need to. YT isn't just a new way to _deliver_ the same content (a traditional lecture, for instance), it's a new way to _use_ it as well.
@MegawattKS3 жыл бұрын
Excellent points ! Thanks for pointing out these things. I actually had a 'take-1' version of this video that mentioned the need to go back and review in order to learn the material well, but cut it out in take 2 (among other elaborations) to keep the video to 30 minutes. Thanks also for pointing out the pause/replay thing too. I personally don't like Powerpoint slides and virtually never use them in class, but for YT, with this capability as you said, they're there for leisurely study as desired :-)