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nanoVNA - Measuring Inductors and Capacitors (Vers. 3) 

Gregg Messenger - VE6WO
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This method is not for higher frequency characterization of components. It simply allows a person to determine the basic low frequency values of inductors and capacitors to identify or confirm their values.
0:15 - explanation of the test setup reference: www.electronics-notes.com/art...
2:30 - calibrating the nanoVNA
3:23 - looking at an inductor
6:24 - shunt configuration accuracy reference: www.signalintegrityjournal.co...
9:20 - looking at a capacitor
Reference regarding shunt method accuracy and why I chose to make measurements at 50 ohms or 90 degrees S11 phase: www.mwrf.com/technologies/tes...
Aug 2021 - For clarity, I would like to address the fact that measuring the reactive device under test at 50 ohms is not done because it “matches” the source impedance in the traditional sense that this concept would be understood by amateur radio operators with regards to maximum power transfer theory. This is not the intent at all. Rather, as has been stated in the video and supporting documentation, 50 ohms is used primarily because it lies within the shunt method’s best accuracy region. Secondary reasons include: it’s at 90 degrees on the smith chart (the top or bottom depending on what you’re measuring), is easy to remember, makes measurements consistent, keeps people away from going too low in frequency, avoids the self resonant frequency of the device and test fixture.

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2 июн 2024

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Комментарии : 116   
@rfjgfude
@rfjgfude 7 месяцев назад
Best tutorial on measuring inductors and capacitors on a Nano VNA I've seen yet. Thank you.
@lmantuano6986
@lmantuano6986 9 месяцев назад
GM, I keep on coming back to your videos for the value of the information and the clear and calm way you deliver it.. you are good! 73 de vk3ola
@intotheblue50
@intotheblue50 6 месяцев назад
Showing how you do this has really enabled me to see how I can use a VNA to tackle my projects thank you very much.
@dondonaldson1684
@dondonaldson1684 5 месяцев назад
Hi Gregg, this RF Engineer didn't "cringe". When I looked at your test setup I thought "those leads are going to be resonant" because there is parallel capacitance induced. This is shown exactly in the sweep trace of the vector network analyser. 15uH is small, as are the few pico Farads across the alligator clips at the reference plane. If the resonant frequency is 10 MHz, one can easily calculate the amount of intra-lead capacitance. Inductive reactance is 2 pi f L and capacitive reactance is 1/2 pi f C. At resonance the magnitude of XL is equal to the magnitude of XC and they are 180 degrees out of phase. Your method is excellent, by the way and shows exactly why there is focus in the amateur radio exam regarding series and parallel tank circuits!!! Well done. Don, VE3NAP
@ve6wo
@ve6wo 5 месяцев назад
Thank you.
@benutzernamenichtverfugbar4977
@benutzernamenichtverfugbar4977 3 месяца назад
Hi there, power electronics engineer here. I don't know that much about VNAs and RF stuff, but I stumbled across this topic a few days ago when I was wondering about how to measure small parasitic inductances. Thinking about buying a nanoVNA and trying it out, looks like a nice tool especially when considering how cheap it is. But I wonder: Which VNA measurement method would be suitable for measuring very low impedances? My main focus would be measuring stray inductances of commutation loops on copper busbars and PCBs with typical inductance values of 1...100 nH. Due to parasitic capacitance, I don't think I can use super high frequencies, maybe up to ~20 MHz. Since you said in this video, that the shunt method is good for 20...200 Ohms, I suppose it's not really suited in my case, right?
@ve6wo
@ve6wo 3 месяца назад
You would use a shunt-thru measurement for very low impedances. I have never used this configuration nor have I made measurements of very low impedances, so I’m not much help on this. Sorry :-(
@benutzernamenichtverfugbar4977
@benutzernamenichtverfugbar4977 3 месяца назад
@@ve6woNo problem, now I know what I have to search for at least. Thank you for the hint.
@richardchambers256
@richardchambers256 2 месяца назад
​@@benutzernamenichtverfugbar4977Now you have me curious. please let us know what you find. 😀
@K8RFT
@K8RFT 2 года назад
This is really helpful! Thanks so much for passing along the method - and the rationale behind it! It will be very helpful in my component testing.
@Steve-GM0HUU
@Steve-GM0HUU 2 года назад
Thanks for posting - very useful. No doubt about it, the NanoVNA is an amazing tool for the radio ham or any RF hobbyist.
@richardphillips2405
@richardphillips2405 3 года назад
Thank you. I've learned a lot from this video. This video serves as an inspiration to learn more about rf transmission.
@acestudioscouk-Ace-G0ACE
@acestudioscouk-Ace-G0ACE 2 года назад
Clearly explained and understood by this beginner. Thank you.
@gerd3136
@gerd3136 Год назад
I‘m new to NanoVNA and your video helped me a lot to understand the way things work. Thanks a lot!
@ve6wo
@ve6wo Год назад
Glad it helped!
@bobgarrett7036
@bobgarrett7036 Год назад
Thanks for posting. Was struggling with measuring an inductor and this should work!
@homeralbufera7068
@homeralbufera7068 Год назад
Thanks for sharing! I have just bought a NanoVNA from China that will be arriving next week. It's helpful to me and other hams around the world to determine the value of inductor which could not be read by available multimeter. I will use this knowledge to design a telescopic antenna 1.3 meter long to resonate at 10 meter band using a tank circuit.
@richardchambers256
@richardchambers256 2 месяца назад
Great information! You andwered my questions in the first 3 minuits. Thx. W6rch
@barrykery1175
@barrykery1175 2 года назад
I always wondered why my readings were not constant so I never used my VNA to check those values. I do have an LCR meter but now I know how to use my VNA. Great video. Thanks for posting. Barry, KU3X
@ve6wo
@ve6wo Год назад
Glad to help!
@RobLudwick
@RobLudwick 2 года назад
This is really excellent. Thank you.
@rickmckee6698
@rickmckee6698 Год назад
It would be nice if you show how to get to that screen and markers you are using for us beginners of the VNA!
@K13F3Rx22
@K13F3Rx22 2 года назад
Just what I needed to know. Ty!
@SpinStar1956
@SpinStar1956 8 месяцев назад
Just ran across your channel and really like your explanations so SUBSCRIBED! So, hope you keep doing videos, and looking forward to looking backward in your catalog! 73 & thanks for doing these! 😊
@ve6wo
@ve6wo 8 месяцев назад
Thank you.
@billcheung65
@billcheung65 3 года назад
Thanks so much for this - have been trying to figure this out on my NanoVNA and this was very helpful, including zooming in to see how your traces were set up! 73 DE VE7WYC.
@ve6wo
@ve6wo 3 года назад
You’re welcome. Glad I was able to help :-)
@asc165
@asc165 2 года назад
Outstanding video!
@hubercats
@hubercats Год назад
Nicely done, thank you!
@richytug7612
@richytug7612 Месяц назад
Thanks a lot for detailed description! 73!
@johnwest7993
@johnwest7993 2 года назад
I don't know if it's 'right', (or if it matters,) but I was taught on the color code for resistors and inductors that the 'multiplier' band started with black being 'zero', and the band itself indicating how many zeros to add to the number obtained by the previous bands. In practice, I don't think it matters. It's just a matter of point of view, but it might cause some confusion among those who have learned the color code described the other way.
@ve6wo
@ve6wo 2 года назад
A valid observation. www.te.com/usa-en/products/passive-components/resistors/intersection/resistor-color-codes.html This is how I learned it :-)
@dougbas3980
@dougbas3980 4 месяца назад
New tool in my box. Thank you.
@emailuser3869
@emailuser3869 2 года назад
Thanks for posting this, Gregg. Appreciate you taking the time to share.
@geokuf9679
@geokuf9679 3 года назад
Excellent, thank you very much. Another video on that very useful subject. 73, Jerzy SP6CAL
@tegra5971
@tegra5971 2 года назад
Beautiful explanation of not only “how to” but also the right amount of context! I feel just a little bit smarter! (VA7TQB)
@ve6wo
@ve6wo 2 года назад
Thanks, I appreciate that :-)
@BobMellor1954
@BobMellor1954 2 года назад
Very helpful, thank you 73's
@cbnation1
@cbnation1 10 месяцев назад
Regarding the "strange" measurements you have at the beginning of the video with the inductor, they are probably right and the most useful thing you measured. You found the self-resonance point of the component. Beyond that, the inductor behaves as a capacitor and is not useful anymore for those frequencies. 73 de ON4CKM
@leroybuller7087
@leroybuller7087 6 месяцев назад
Great job. Heading to te shack to try it out
@andrewkurtz6280
@andrewkurtz6280 2 года назад
Thanks, very helpful! Where do you get, and how do you define, the part that converts from an SMA coax to 2 alligator clips?
@ve6wo
@ve6wo 2 года назад
You’ll need an SMA to BNC adapter, at which point a standard 50 ohm test cable with BNC on one end and alligator clips on the other can be used. Go to Amazon and punch “BNC to Aligator” in the search bar..
@danielboulet964
@danielboulet964 2 года назад
Thanks Gregg. Very helpful. I have a couple of toroids whose characteristics are unknown. I'll should be able to turn them into inductors, measure the value and calculate permeability. -73 VA3GLB
@ozioldman4720
@ozioldman4720 Год назад
Thank you for the video. Was struggling with the NanoVNA. This demistified the magic somewhat
@jorgerive7335
@jorgerive7335 2 года назад
Nice video. Thank you! What would the VNA's response look like if you did the same measurement with inductor and the capacitor connected together in series and in parallel?
@ve6wo
@ve6wo 2 года назад
I just published another video where I do that exact thing.. I placed the capacitor and inductor measured in parallel and looked at the circuit using port 2 of my nanoVNA. Go take a look :-)
@hamradioeconomystyle48
@hamradioeconomystyle48 2 года назад
Thank you for the info. on measuring Capacitors and Inductors. Also, I wondered if it was ok to calibrate in the fasion you did, without using the three standards that came with the VNA. Thanks for verifying that method.
@ve6wo
@ve6wo Год назад
At these low frequencies, you won’t see a difference in the readings. At higher frequencies, you definitely need to be more formal when calibrating or the results will be way out to lunch.
@williamokrasinski9840
@williamokrasinski9840 3 года назад
Thank you for this. Much of the NVNA is beyond my ability to understand, however, for me a simple and practical method of using it to take measurements is very helpful. Can you tell me where to buy the coax that accommodates your test leads ? 73
@ve6wo
@ve6wo 3 года назад
Hi William. I think a lot of the issue with VNA concepts seeming to be out of reach for many is due to the fact that until very recently this kind of instrument cost a phenomenal amount of money and was only accessible to engineers and universities. With the advent of the nanoVNA which now makes this instrument available to almost anyone who wishes to own one, we now have to work towards translating the concepts and methods across in terms that most of us can understand. That is the general goal of my videos, and I hope the information presented helps you :-)
@ve6wo
@ve6wo 3 года назад
The test leads I use are simply BNC to 50 ohm coax with alligator clips attached to the end. I think I got mine from my local electronics supplier, however, here is a link to one on Amazon. Pack of 2Pcs BNC Q9 to Dual Alligator Clip Oscilloscope Test Probe Leads www.amazon.ca/dp/B0713V844H/ref=cm_sw_r_cp_api_i_SN12XMXGGDWQ8G1K4PNY
@TheRetiredtech
@TheRetiredtech 2 года назад
Great video
@VorpalForceField
@VorpalForceField 8 месяцев назад
Good Stuff .. Thank You for sharing .. Cheers :)
@tcarney57
@tcarney57 2 года назад
This was a pretty-good demonstration. i couldn't help notice, though, that the VNA was reading between 8 and 16pF with just the clip leads (no component in place _but_ after you calibrated them as "open"), and that the different readings depended on slight movements of the cable and its unshielded clip leads. I'm not a cringing engineer--just another amateur--but I've seen myself the kind of parasitic capacitance and inductance such leads can produce depending on how they're placed--how close the clips are, how close the 15cm leads are, whether they cross or not, how big a loop area they form when measuring inductance, etc. I think the method you demonstrated is a good one, but the cable and test leads you used cannot produce a stable reference plane for the VNA. A simple test fixture built on a small perfboard screwed to a piece or wood or plastic with a hard-wired 50 ohm cable and some pin sockets would be a stable-enough reference plane, and frankly it would be easier and less fiddly to use as well. As Einstein said, “Everything should be made as simple as possible, but no simpler.”
@ve6wo
@ve6wo 2 года назад
Yes, I agree. In fact, I ordered one of those test board kits with the SMA connectors and sockets off of AliExpress… The test clip leads I used originally ‘worked’.. but if a person needs a bit better / more stable or reproducible readings then I think an upgrade in the test fixture is needed.
@Leo-pd8ww
@Leo-pd8ww 3 года назад
Very nice. I've ordered one after watching this. I'm curious to see how accurate this is compared to my LCR meter. The NanoVNA only costs a fraction of a LCR meter too! Looking forward to messing around with it.
@ve6wo
@ve6wo 3 года назад
Please report back and let us know your findings. I do not own an LCR meter to compare the results, so I am quite curious :-)
@RP4UXO
@RP4UXO 3 года назад
@@ve6wo I made some comparisons with a cheap Chinese LC meter and the results are quite close. I would probable trust the NanoVNA as more accurate, wouldn't you say ?.
@w5cdt
@w5cdt 2 года назад
Parasitic inductance for a wire is approximately 10 nano-Henries per inch.
@ES-iv6wb
@ES-iv6wb Год назад
Wow. Incredible video. Liked and subscribed! I have a quick question, if I wanted to measure the mH of the inductor or pF of a cap in circuit with other components do you think the VNA would give ballpark figures to be able to decide if an inductor or capacitor is good or way off?
@ve6wo
@ve6wo Год назад
I have never tried it, however, in my minds eye I see all kinds of possible issues with this as far as being able to trust the result. For in circuit testing of capacitors and inductors, when I worked as a bench tech at a general electronics repair shop, we used a “curve tracer” and an oscilloscope for this. Even then, we sometimes still had to remove components from the circuit for testing. It completely depends on what circuit your components are part of as to how test gear will react when trying to test in circuit.
@ve6wo
@ve6wo Год назад
Thank you for the complement.
@ES-iv6wb
@ES-iv6wb Год назад
Amazing. Do you think you can make a video with curve tracer and an oscilloscope to find a faulty cap or inductor? I bet it will get a lot of views.
@ve6wo
@ve6wo Год назад
@@ES-iv6wb I think I may still have my old curve tracer attachment that I built for my scope back in the 90’s somewhere…
@908hanhouni
@908hanhouni 2 года назад
Great video thanks for sharing! What is this cable you are using? Any link/model name? Appreciate it!
@ve6wo
@ve6wo 2 года назад
Any BNC to alligator clip test lead set will work. It needs to be 50 ohm characteristic impedance though. Here is a random example off Amazon.. Elenco Electronics TL-17 BNC to Alligator Test Lead Set www.amazon.ca/dp/B0002JJU4G/ref=cm_sw_r_cp_api_glt_i_T4MRK1SWWMXY4T468GNY
@bparker86
@bparker86 Год назад
Good stuff man thank you
@briansschubox2942
@briansschubox2942 3 года назад
Thanks for the Video! Brian - N9NAZ here. VERY Shade Tree approach to KIS and to git it done! I do have the Nano VNA H4 that I just got a couple of days ago, so I can see a few differences in the display, but looking at traces 1 (yellow) & 2 (blue) - respectively I see [ S11 X 2.00k/......] & [ S11 REAL 1.00/ .... ] and am wondering why after I set the formats of my traces to match yours, mine shows [ CH1 X 100/......] & [ CH1 REAL 250m/ .... ] (The S11 & CH1 difference is not the issue ) the X 100/ & 250m/ is my interest. Is that some scaling or offset feature I need to apply to each trace? I have scanned through several docs so still trying to absorb the info and uses of the VNA. If you could point me to the right direction I would appreciate it.
@ve6wo
@ve6wo 2 года назад
Try this document, page 7 and see if this information helps. www.nemarc.org/Absolute_Beginner_Guide_NanoVNA.pdf
@la7yka
@la7yka 3 года назад
Great info on how to use my NanoVNA :) Best 73's de LA7YKA Einar.
@robertralston2395
@robertralston2395 2 года назад
Thank you for this video. Using this method probably depends on which nanoVNA you have and its specific firmware. I have tried to duplicate your experiment and cannot. My NanoVNA - H 4 has FW 0.5.0. I'm using a Crystal CCSMACL-MC-24 cable, SMA to clips. I calibrated at stop = 5 MHz and used a 1% 51Ω resistor for the load. I set the 4 traces up like yours, I think, with the reactance scaled to 2.00k. I can dial into about 50 ohms reactance at 89.6 degrees phase but then read only changing microfarads on the smith trace. This inductor measures as 13.6 microH on a Peak LCR45, so I don't really need to measure on my VNA. But, leaves me wondering, why the difference. A different problem with a 100PF silver mica attached, cannot dial in 90 degrees
@ve6wo
@ve6wo 2 года назад
Hmmm… it’s hard to know what’s going on without being able to actually physically be present with you to view what you’re seeing. Do you have the ability to try a different VNA, or maybe try the experiment with someone you know locally who also has a nanoVNA?
@robertralston2395
@robertralston2395 2 года назад
@@ve6wo No, no access to another VNA. I will try again but probably much later in this year as I'm now immersed in studying an ESP32 chip. Thank you for your reply. Probably an error on my part
@robertralston2395
@robertralston2395 2 года назад
OK, probably user error on my part. I originally set up my VNA traces to look like this video. But, if I make trace CH0 (yellow) as the Smith Chart, then dialing in the phase to 90 degrees shows 13.0 nH at 600 kHz. At 5 MHz the Smith says 3.4 nH at phase 13.5 degrees. And using CH0 as Smith, it now identifies the silver mice as about 100 pF. So I'm now thinking that CH0 on this particular VNA with this FW has to be set as Smith although it would seem like you should be able to set any trace to any format. ??
@acestudioscouk-Ace-G0ACE
@acestudioscouk-Ace-G0ACE Год назад
I've just watched your video again and wonder if it would be OK to measure electrolytic capacitors... provided they had been properly discharged first of course!?
@ve6wo
@ve6wo Год назад
I’m not sure if this will work with capacitors of such large values. Perhaps give it a try and see what happens!
@MasterIvo
@MasterIvo Год назад
I am tempted to parallel connect my (bifilar pancake) coil like that. My worry is at resonance it can develop a too high voltage for the VNA and destroying it. How do you know if your inductor is safe enough, for measuring it this way?
@luisg6000
@luisg6000 2 года назад
Very interesting!!! I have a simple question for you: where do I get the cable with the alligator clips? They are very practical. Thanks in advance for the clue.
@ve6wo
@ve6wo 2 года назад
I got mine from Amazon. Any will do. Here is an example: Elenco Electronics TL-17 BNC to Alligator Test Lead Set www.amazon.ca/dp/B0002JJU4G/ref=cm_sw_r_cp_api_i_BJHX8VRV23K63XYXRN6K
@luisg6000
@luisg6000 2 года назад
Thank you!
@riadhalgamaty8844
@riadhalgamaty8844 8 дней назад
Thank you very much for your detailed explanation. May I know how to get same cable that you used? From wich srore
@bassdowg
@bassdowg 2 года назад
Outstanding 73s grt help
@ve6wo
@ve6wo 2 года назад
Thank you. Glad it was helpful.
@jonathanrobertson3406
@jonathanrobertson3406 Год назад
Question: What is the item that connects between your TinySA and what you are testing? I have the kit to make it work, but whatever you are using in this video seems far more useful in that is it smaller and more streamlined.
@ve6wo
@ve6wo Год назад
You mean the BNC connector and aligator clip leads?
@jonathanrobertson3406
@jonathanrobertson3406 Год назад
@@ve6wo Thanks for return reply. Specifically the small two port that hosts two ( positive and negative) alligator clips and then, I assume, terminates in a bnc on the other end to interface with the nano. Thanks!
@ve6wo
@ve6wo Год назад
@@jonathanrobertson3406 yes, I purchased this on Amazon. It has 50 ohm cable with BNC and on the other end it has alligator clips.
@jonathanrobertson3406
@jonathanrobertson3406 Год назад
@@ve6wo Thank you Gregg! I have yet to scratch the surface of what this device can do (I use it for SWR testing on antennas) so looking forward to a new project now. Thanks for the video and your response. 73 KMH4OC
@edwardwilliams7213
@edwardwilliams7213 Год назад
Do you think this might work for finding a ballpark value of a super capacitor?
@ve6wo
@ve6wo Год назад
No. Super capacitors are typically very large values and the frequencies that the nanoVNA is designed to work at are much too high for this. I would take and build a high power resistive load bank and measure the RC time constant of the discharging super capacitor and then take and do the math to find the capacitor’s value based on the result.
@osmargarnica
@osmargarnica Год назад
Does this VNA outputs the impedance in the R+jX form?
@gustavowkaiser
@gustavowkaiser 2 года назад
Very nice approach. You got the point. Too low or too high impedances related to 50 ohm, makes difficult for the instrument to calculate the values which will be displayed. I use to preset 7 calibrated frequency bands, for instance, the first ranging from 50KHz to 5MHz, the second from 5MHz to 50MHz and so on, up to 3GHz, so the full range of the instrument is covered. As there are 7 memory slots to save the calibrated bands, one can easily switch to the band of interest, by means "recall" function.
@ve6wo
@ve6wo 6 месяцев назад
Great idea! Thanks for sharing :-)
@waterforfuel
@waterforfuel Год назад
Thanks!
@davidh1187
@davidh1187 Год назад
Hmmm. I have the NanoVNA-F V2 and I am only getting 1/2 the actual value using this method for inductors (exactly 1/2)
@sudiptaghose5247
@sudiptaghose5247 2 года назад
Can I measure inductance of transformer windings?
@ve6wo
@ve6wo 2 года назад
I’ve never tried it, but I would have to say yes! If I had more time I would delve into it and make a video.
@haroldskinner1783
@haroldskinner1783 5 месяцев назад
Would love to see a video on how to measure the inductance of a coil for a vertical antenna- like the wolf river coil for example sporty forty
@watcharapongchuginda842
@watcharapongchuginda842 2 года назад
No say trace setup?
@clems6989
@clems6989 Год назад
Great video, good job .73 N8QZH
@h.sapienstechnologicus8865
@h.sapienstechnologicus8865 3 года назад
I like the _"how I do it and it works"_ attitude, w/o becoming too anal about the precision here.
@ve6wo
@ve6wo 3 года назад
Haha! Yes, there seem to be quite a few ‘engineers’ out there who insist on being super anal about using these $50 instruments as through they are $25,000 pieces of lab grade test gear. In most cases, I have found minuscule differences between results when I try to use more formal test jigs and practices.. the bottom line, however, is for most amateurs the quick and dirty approach gets us the answers we need.
@johnstephens7414
@johnstephens7414 2 года назад
Efficient and simple
@rickeaston3228
@rickeaston3228 Год назад
The measure is accurate at the frequency you measure it. Inductance and capacitance can change with frequency and it is still measuring accurate. The camera is far from the nano. I can't read anything. You could have used nano saver, but you didn't bother to do that either.
@protuber4925
@protuber4925 3 года назад
3:30
@frankamato8886
@frankamato8886 Год назад
How did you set up the nanoVNA?
@vladskrypnyk6881
@vladskrypnyk6881 4 месяца назад
Code 102 means 1000 pF, not 100 pF
@ve6wo
@ve6wo 4 месяца назад
Hmmmm, where in the video did I say 100 pF? I went to 10:15 in the video and checked.. I said 1000 pF 🤷‍♂️
@bruceblosser384
@bruceblosser384 11 месяцев назад
Too many traces on the screen! To much info! But I did get some helpful tips anyway! :)
@aduedc
@aduedc 2 года назад
Your transmission line is not rigid enough, so your calibration is not valid. You need resonant frequency of capacitor and inductor alone, and not with added lose wires.
@thurmanmerman3643
@thurmanmerman3643 3 года назад
Dude. I sense this video _might_ contain the knowledge I need, but you are just babbling all over the place! Could you remake this video 6x shorter and more directive? Like: do this, do that, click here untill you see this.. I've been re-watching this video like 5 times and still can't follow thru. You into long winded calibration an "brief" how NanoVNA works and when it comes to the meat of the video, you loose your train of thought and clarity.
@ve6wo
@ve6wo 3 года назад
Thanks for the feedback. This is version 3 of this video.. hahaha! You should have seen the first two tries! I’ll keep your thoughts in mind and if I have some more time off work I’ll maybe try again.
@tcarney57
@tcarney57 2 года назад
Thurman Merman: I had no trouble at all following everything he said. There was no "babbling," and it doesn't need to be any shorter. For a video like this, you have to bring some knowledge yourself, and if you couldn't follow what Gregg said then you didn't bring enough. You didn't bring any tact or decent manners at all. In any event, expecting a paint-by-numbers, check-box list of steps with no explanations or elaborations is pathetic--particularly when you seem to expect it for free.
@tcarney57
@tcarney57 2 года назад
@@ve6wo You have nothing to apologize for. Your presentation was clear and brief enough. Anyway, you don't owe anybody anything.
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