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- เผยแพร่เมื่อ 13 พ.ค. 2024
- The most often requested video! In this tutorial Dave explains what Operational Amplifiers (OpAmps) are and how they work. The concepts of negative feedback, open loop gain, virtual grounds and opamp action. The comparator, the buffer, the inverting and non-inverting amplifiers, the differential amplifier, and the integrator circuit configurations are also explained.
Then a practical breadboard circuit to demonstrate a virtual ground and the effect of voltage rail limitations.
All EEVblog Opamp related videos are here:
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I know this will probably get lost in the comments but I have to say it. I absolutely have a high respect for people like you who share knowledge so freely and willingly. People like you are a godsend. Thank you sincerely.
it didn't get lost in the comments!!!!!!
@@user-uq4ly2lk1n We're all lost my friend.
I totally agree dude…. we’re so fortunate to have people like this dude
Came up as the first comment... 🙂 The mysterious ways of the youtube algorithm will never be comprehensible for us "ordinary people" 😎
This guy is DATA from Startrek ];-D.
Nine years later, this is still the best and most understandable intro to Op Amps ever.
one of the very best
Fully agree!
this video got me my first electronic job i watched this video before my interview and they quizzed me on op amps! the luck!
Wow good for you! :) That's so weird. Reminds me of a line from the movie predestination, "luck, is the residue of planning." It's so true. When you work hard for something, luck helps you along the way, more often than not in bad situations. Was that the case with you? Btw I'm in my 3rd year in EE, my school isn't so glorious if u know what I mean. So It's hard trying to become an autodidact, especially with complex matters which don't always have the clear specific explaination on the internet... Sorry for rambling lol
So, do you still have your job Jaguar paw?
@@microdesigns2000 The job this video helped me get was a great place to start I had an excellent mentor there and i worked there for 2 years.
I have since changed employer with a more embedded and programming focus I have been at this subsequent job for 2 years and 2 months now!
Although it was over 4 years ago i still remember the night before the interview trying to cover everyrhing they might ask and watching great videos like this.
@@jaguarpaw1638 That's awesome. I'd love to hear what kind of designs you are working on, without posting anything proprietary.
@@microdesigns2000 I work mainly on low power IoT projects now . I also do home projects too . id like to start my own electronics design business one day!
"The gain is almost infinite"
spoken like a true engineer!
A power speaker guidance glee Iowa amp it up yeah
48:40
Can anybody please tell me the reason of this ?
@@youtubegoogle4163 I just gave this reaction below, but i think it's the sink current working very close to the maximum rating:
the sink current for Vout=200mV is only 50uA, and goes quickly up to 20mA at Vo=2V. Because of the 10k resitor for R2 it's working very close to it's maximum ratings at the lower end. 0.5V out is 50uA sink current. And (apparently) in practice this results in the weird ground spike that fck ups the output.
@@youtubegoogle4163 Looks like crossover distortion, the switch from sinking to sourcing current... and at the point when this happens the opamp is neither sinking nor sourcing correctly, so the negative feedback stops working properly and the input voltage is allowed to spike momentarily.
and the open loop bandwidth is darn near zero Hz.
I Learned more in 10 min of your video than 1 month of my Power Control Electronics class. Thank you!!!!!
+RRClassicman Glad to hear! (well, kinda...)
+RRClassicman Well 50 minutes in my case. It changed my biased "OMG an OpAmp" to "OpAmps, I love'em"
+Kenneth Tan blew my mind when I finally figured out why they use a buffer on an inverting op-amp. It's the simple things that others take for granted. These videos are chucked full of informational tid bits one should store away
my understanding of circuit design is getting better with each eevblog
+RRClassicman This is true fact about formal education, mostly in schools you learn almost nothing! That is situacion in Croatia, just a lot of unnecessary material with zero interactivity with the student
+Blade Runner Well, in a TH-cam video, there's also 0 interactivity with the student ;) Other than that, you're 100% right.
In my whole electronics major shit , I have never seen a person who explains virtual ground like this.
#RESPECT
This term makes no sense
@@StEvUgnIn Abolutely no sense.
He’s amazing love it,,I’ll figure it out virtual ground oupps
It’s spiritual
@@StEvUgnIn Does the "virtual ground" means 0V ?? If so then it really doesn't make any sense 🤦♂️🤦♂️
5.300 students are very grateful you uploaded this video
+95berre count me in!
You can't have 5.3 students.
As a retired Senior Applications Engineer at Burr-Brown and Texas Instruments, I must compliment you on this presentation! It is very similar to the "factory" technical presentations that we used to give to audiences around the globe. The technical level is just right, not to basic and not too advanced. Good job! To be a good teacher it takes far more than just knowledge of the subject. A teacher's job is to impart knowledge to his student; if the student doesn't understand, the teacher is not doing his job. Some PhDs can teach, others can't- Richard Feynman was an example of a fellow who not only thoroughly understood his subject but who could teach it as well.... and do it in an interesting and entertaining manner.
How i can get a job in TI ?😅😅😅i mean its awkward to ask this way but yeah
Sorry beforehand 😅😅
@@naveengupta5588 The best way is to send in a copy of your resume. Good luck- the world needs more analog engineers.
@@neilalbaugh4793 could you please suggest best book for Analog electronics for beginners
I find myself revisiting this tutorial as a refresher every time I need to incorporate an OpAmp into one of my projects. Thanks Dave! 👍🏻
I have been watching this as a kid and now it feels so nostalgic after i have passed my electronics engineering school , it really so nostalgic
what makes you a gorgeous teacher is that you not only talk about what is going on but also about what the follower might think is going on but actually is not and why. i had so many frustrating experiences in the past because of teachers that did'nt care about that. i truly love your lessons.
Mirko Mueller it's also great to see someone enthusiastic about what he does.
Mirko Mueller So are you enthralled?
A good teacher.
48:40
Can anybody please tell me the reason of this ?
Interestingly I just recently recommended someone to look into using an opamp for their project...
EEVblog never disappoints.
Been a tech for 43 years and I have never seen it explained so concise. Thanks and I am turning the junior techs onto this video. Cheers!
You have left a legacy on TH-cam for the coming generations. You are immortal. Salutes.
Regarding the puzzle at the end, the low resistance effect is an increased current at the OA output. the OA at approximately Vout= -0.5V should sink 50uA which is higher than the value in the datasheet/figure13 of 30uA max. so the virtual ground voltage fluctuates and so does the output at approx. -0.5V.
baby...
Thank you.
in the new datasheet, i think its figure 47, that explains this.
@@cireekratz2017
Above explanation said.
at Vout = -0.5V
I sink = 50uA (> 30uA)
Can you please explain me,
What special thing happens at -0.5 V,
Which doesn't happens at other output voltages ?
@@youtubegoogle4163 Hi, the thing is, that this IC has limited current sinking capabilities at low negative output voltages.
In the -0.5V case the sinked current should be (-0.5V/10kOhm) 50 uA. But the IC is not capable to sink that much current at this V_out. Figure 47 in the datasheet shows that it only can handle ~40mA.
Now there are 2 cases:
- slightly higher V_out (like -0.25V): the sink current lowers to 25 uA and that is just in the limit that can be provided (when the supply V difference is at 30V, grey curve) After that the virtual GND can begin to deteriorate.
- lower V_out (like -0.75V): the current sink capability of the IC rises rapidly (after the kink in the curve). It lands around 1.15mA which is sufficient by far.
In the end Dave chose a really nice corner case, where there is only 1 output voltage, where this problem arises. If you lower the R values further, the problem should expand and should arise shortly after V_out = 0V and stretch to around -0.6V.
Hope this helps.
The fact we can learn this and not have to go into debt... your a gift to engineering Dave!
Forget the debt. Being water boarded everyday is not what i would call learning.
@@kevin42 agreed and they inject way too much to do with political issues at times to
One of the most sensible ways of explaining the basics of op amps. Great work Dave
i always catch myself smiling while watching this guy
Hi dave I've been watching your channel a lot for the last couple years now and it's fantastic! I'm currently doing my honors in electronics engineering and my University here in hamilton New Zealand has instructed my class to watch this video on the current section we are covering on op-amps. You have finally made it to university level teaching my friend!
48:40
Can anybody please tell me the reason of this ?
Yes for an op-amp terminating video.
7 years on and your videos are still helping new technicians. I really appreciate this, thank you.
I have watched this umpteen times. Best tutorial EVER. Thank you.
Thumbs-up for the vid on properly terminating op-amps please Dave ;)
i agree too!
e2e.ti.com/blogs_/archives/b/thesignal/archive/2012/11/27/the-unused-op-amp-what-to-do - found this today on TI's website
What the hell just happened? I felt like I had watched a 10 min video. By the time I looked at the time line, 49 minutes had already passed. Magic OOOOoooooo. XD
FINALLY!!!! A video that ACTUALLY EXPLAINS HOW IT WORKS!!!!!
Dave, this video was a godsend.
Some people really got the "art of sincere teaching". This is the best I've seen so far regarding Op amp basics. God bless you Sir.
If anyone is interested the gain of the non-inverting config can be derived from the voltage divider equation:
Vin = Vout*R1/(R1+Rf)
Vin/Vout = R1/(R1+Rf)
Vout/Vin = (R1+Rf)/R1
Vout/Vin = 1+Rf/R1
And the gain of the inverting config can be found from the currents:
I(Rf) = Vout/Rf
I(R1) = -Vin/R1
-> Current through both resistors is equal so...
-Vin/R1 = Vout/Rf
Vout/Vin = -Rf/R1
:)
Amazing how simple the above is when you can assume that the internal gain of the opamp is infinite. Everyone going through EE should be able to demonstrate the above in the time it takes to write it down. Well done.
Here Vin1=Vin2 due to the virtual short between the input terminals, if anyone had a doubt
Thank you so much for this! Not as bad as I thought coming into this! Matter-in-fact, really fun!!!!!!!!!!!! :DDDDDDDDDDD ♡
This is my new favorite TH-cam channel!!! I am a marine engineer by trade, but I started getting bored, so I signed up for an online electronic engineering programme at my local university, to put my spare time into good use.
I have never gained much from sitting in a classroom listening to a lecturer bleating for two hours at a blackboard, so I was thrilled, when I got the opportunity to work at getting a degree, working by myself at home. These videos are an absolutely excellent supplement to all the videos available from my university.
Thank you!!!
as an electrical engineering student, this channel is priceless. thank you for this channel and to so many other folks who do the same...
Read this after 12:23 and listen to buffer amplifier again.
The primary objective of buffer circuit is to boost the current in any circuit at any stage. Buffer circuits are mainly used where a signal has very low current input(high input impedance) which needs to be increased maintaining the same voltage levels. So, this buffer circuits draws current from power source and adds it to the signal.
Buffer amp is also called as voltage follower or unity gain amplifier . Hope this makes sense now !
Very helpful. I'm an electronics technician and you see this stuff when you're doing repairs or troubleshooting but you never get down to the nitty gritty details especially after 30+ or so years goes by from your initial electronics training so it was really nice of you to explain this especially on layman's terms. Someone else mentioned in this blog about cutting and pasting working circuits into projects and calculating as you went along to fit your needs which is pretty much what I've done in the past so this has really been a BIG help in the memory refresh department. Thank you ten times over and may the "electro" Gods shine good fortune down upon you sir!
I had electronics like a hobby in the secondary school and also the time I was in the university even I've studied mechanics. Great presentation !!
electronic technicians nowdays repair FLAT TVs, monitors, cell phones, install and repair satellite installations, alarm systems, fire detection systems, CCTV installation, PLC programming and maintenance in industrial applications, and a variety of other applications ...
Nowadays, even the electrical appliances of a hotel kitchen may have electronic control boards with fiber optic and internet connectivity.
And in some countries it is not always "throw the old board away and put the new one"
this is the easy way that even a 10 yo child can do.
What if a new electronic board is too expensive ?
When I learned how to use Op-Amps, the 741 was the state of the art at the time. Yes, had to learn them the hard way back in those days. What a great refresher course for this young man born 9-11-1946. Great job Dave and thank you. Respectfully, Steve
On behalf of every each one of electronics students thank
You are saving my university career 🙏🙏🙏🙏
Thanks a lot you really saved me
5 years later
The concept of virtual ground was delivered precisely.
Thank you Dave!!!!
yep. he nailed it
Truly one of the best reviews of OP Amps. This validates everything I have learned about OP Amps.
-Thanks
It's so great to see fellow Australians showing up on TH-cam. Especially for something like explaining electricity. Bringing fame and reputation to our country!
Back in May of 1978 I started work at an aerospace company that made the engine controllers for a military jet aircraft. The engine controller was a low frequency (less than 10 KHz) precision analogue computer that had amplifier gains & offsets calibrated to +/- 2 mV with select on test 1% tolerance resistors. Some critical circuits in the controller used 0.1% tolerance resistors. Positive 10 V and negative 10 V references were used throughout, and as well as the usual feedback loop components there were two 10.6 V Zener diodes in each loop. All of the virtual earths were connected to a virtual earth monitor that used a high gain amplifier to indicate any opamp failures. After a few years the engine controller was redesigned around 12 MHz 16 bit microprocessors and was considered to be not as good as the analogue version because at full speed the aircraft would travel about 50 feet before the software loop was reiterated.
Some of the circuitry in the analogue version was very unusual and complex and I learned a lot about circuit design with opamps. It was a great place to work because there were occasions when batches of high grade components were thrown into a skip, and the company didn't care where they went. To this day I have a huge stock of mostly obsolete but still useful components that I use for making projects and stuff that can't be purchased off the shelf.
Thanks for the video.
so was the processor just running at too low frequency? also what did the engine controller do/was used for?
Hi Dave,
Please do a video on how to terminate OP-AMP, it's an important topic as well.
Good job, thank you.
Yeah!
perfect explanation about virtual ground.
Thanks Dave!
Patrick Franco Bello Thanks, glad you liked it.
@@EEVblog Thanks
This explanation is superb! It is THE best I've ever seen from any book or professor. Truly, a gold nugget.
Your video is gold. I modeled both inv amp and non-inv amp in LTspice with MAX4352 op-amp. Input voltage: [0,0.5] volts. Vcc:+5v, Vee: GND. Worked perfect. Thanks for your work!
Happy 600th EEVBlog Dave!
Wow, huge thanks for a crystal clear explaination! I have watched several other videos where others tried to show how awesome opamps are and after those videos I became more confused. At last, thanks to your awesome video I understand what it is and how I can use them. Awesome Dave, it´s like christmas following your videos.
If only I had the opportunity to watch this when I was learning about OpAmps some decades ago ! So much simpler to understand with you, Dave !
Nice explanation. Opamps were a mystery back in college, but one youtube movie explains it very clearly.
This video made everyone think I'm a genius when we were taught this in class!
Simply 💯 percent on target
And here I am looking at it at 5am when I have a quiz over ideal and non ideal opamps at 9am
👍
It's amazing how bored teachers can make something not that complicated look like a mountain.. I never ever understood opamps at school, and after a fews minutes in now, i'm like... How the hell did they manage to overcomplicate that???
@@usoppbarbosa981 is it because they don't have practical design experience??...
I spent few years in school to learn this (hundreds of years ago) but no teacher was able to present it so clearly like you did - thank you bro
Dude, best explanation of opamps I've ever heard! My professor in college back in the day was an asshole, making this so complicated.
Thanks, Dave - at last! an understandable demonstration of the OpAmp c/w bells and whistles. Good one! Thanks a mill.
Dave, this is amazing. Thank you for these mini classes, honestly it’s worth more than any electronics class I ever paid for.
Negative feedback op-amps just clicked into place for me about 10 minutes in. I had been struggling with this concept for days. Thank you so much.
Never gave money to a TH-camr ever, until now. Started this hobby six months ago. Tried to make a little lab myself but made mistakes. Then I watched your video on how to start an electronics lab. Followed your advice and now everything is set up and working perfectly. makes it so much easier! My learning curve has advanced leaps and bounds. Cant thank you enough.
One of your best tutorials for me. Thanks Dave!
Love these. More, please. I've been using Op Amps and Comparators for decades and still learned a couple tricks watching this video!
I am in my senior year for EE and we had a whole 8 weeks in one of my circuit theory classes dedicated solely to op amps. We got to delve deep into these and do some really fun design problems and lab experiments. This video really is a great refresher and good start for anyone new to them.
I wish we had the time for that... I'm in my second year and we spent two days on op amps. This video helped me quite a bit.
I guess we'll return to the op amps later on..
@@TheDaniel85 I am in my junior year, If anything interesting starts, it's going to be in 3rd, 4th year. First two years is just a dull foundation, during a third year pieces of puzzle will be coming together.
This was the Video that made me fall in love with electronics!
What an awesome tutorial !!
I love this guy.. Very savvy, but breaks it down for the general population.
8 yrs passed till now , I never had seen such an video anywhere , It's Awesome really cool.
Hey Dave, can your next video be on the stuff you crossed out? I wanted to cry there for a sec. There are tons and tons of resources about the basics of op amps, there a dime a dozen. However, there are very very few complete videos on op amp internals. Finding videos on the basics is utterly simple but finding well presented videos on more advance material such as op amp internals is painfully difficult.
Agreed! It (almost) always helps, after learning the basics, to learn how they physically work inside to really cement the concepts in your brain!
And now we need a second part, where you show us the non-common circuits, as let say...Gyrator-stuff, Log-converters, average/peak rectifiers, and "interferences" when using OpAmps in RF circuits (like input pin reversion)....;)
"You can turn it into a summa which is just an adda!" 😄 I LOVE Oz... Thanks for a great vid!
This brings back memories. I learned all this in studying for by BSEE degree that I got in 1976.
I have no idea why TH-cam sent me here. The last video I watched was on modeling an MOV surge protector in LTSpice. I dozed off and wound up here.
Back in 1976 we had a saying:
*_”Four years ago I couldn’t spell ‘injuneer’ and now I are one!”_*
Thanks for doing teaching vids, Dave! I took many electrical engineering courses in college and we did a lot with op-amps, but I'm embarrassed to admit I've completely forgotten everything about them since then. These practical introduction videos are perfect for people like me who want to reconnect to something we learned in the past. Thanks again!
Excellent discussion. Takes me back 35 years to my intro to op-amps. My professor explained what was to us an amazing and confusion subject just as you did and within a day or so we couldn't wait for the lab. I'm now hooked on your channel. atb Opal
tonight i learned 10x more about op-amps, and with a deeper understanding, than
i did in a whole semester in a suffocating classroom. Thank you for your time.
Your videos are simply outstanding. I love learning about things and messing with electronics is one of my hobbies. Thanks for taking the time to make this and all your other videos.
I love you. You should have been my EE professor for every class at my uni
+Edith Mejia wow. i would have thought that your school had good professors!
+Edith Mejia what would be the fun in that? Don't you enjoy not understanding something and then spending hours online looking for information...for free? I know I do! (that's a lie)
aww wook at the wittle fluffy headed female. it's thinks it knows how electronics works
You have to be kidding mate.
Joseph Beasley Mmmm deep male insecurity, pretty embarrassing comment there. I'm not sure you understand how insecure this makes you look.
This is the best explanation I've seen on the virtual ground. Nice!
P.S: Next time, please consider giving an intro to DSPs, would be awesome!
Best OP AMP tutorial ever! Thanx Dave!
Majestic explanation. I'm always amazed how things can become clear after your videos. Unbelievable.
You are really great at this. I'm in a 3rd semester EET student and I learned a thing or two about op-amps from you. I should be paying you tuition!
your enthusiasm is awesome! You remind me so much of my high school science teacher. He made it exciting and fun. As you would say “good on ya mate!”
This is probably the best video about OpAmps on TH-cam.
Hi Dave! I just want to say thank you so much for sharing your knowledge with us! And providing us with great content which not only educate but also inspire! I finally understood op amps by watching your video! The textbooks I have read don't do justice and make it so hard for beginners to understand op amps.
Excellent video Dave!
Concerning the puzzle on the end. I think it's the reduced current sinking capabilities of the LM358 when Vout is small in respect to ground. If look up the "Output Characteristics Current Sinking" graph in the datasheet you can see that the LM358 can sink very little current at low output voltages. As you have a 1k R1 and 2Vpp input voltage you have 2mApp of current, which is still too much to sink for the LM358 at low output voltages. So the LM358 can't keep the virtual ground equal with the "real" ground trough it's FB network. Therefore you get those spikes and the sagging and rising of the virtual ground in between.
Nice work! I noticed that all datasheets doesnt show this. The Motorola version did not so that might be an extra "trap for young players"
That´s it, exatcly :)
You are right, just a small clarification. the OA at Vout= -0.5V should sink 50uA which is higher than the value in the datasheet/figure13 of 30uA max. so the virtual ground voltage fluctuates and so does the output at approx. -0.5V.
+TheElectr0nicus but why does it jump like that? And why is there such a weird knee in the sink around that voltage (i.e. the physical reason for the fact that it goes closer to linear at even lower voltages)
Well, I secured more marks than my friends in our exam just by watching this video 2 hour prior to my exam. Thanks Dave.
Brilliant! No one can explain it better. Thank you so much for the lesson
Someone in my class has been spreading around this video to everyone and they're all raving about how useful your video is.
i'm literally crying, thank you so much. my physics midterm is tomorrow and i truly thought i was screwed. but now i think i can save my grade, subscribed x
How did you do on your midterm?? This stuff is not easy so don't give up!
You just solved my question for a project.. there we go.. another step forward.
+EEVblog Best Educators mostly are in the wrong position
watching your videos just keeps motivation high ! subscribed.
You are single handedly getting me through my digital electronics class!!
Great explanation, you just took the best OP-Amp explanation until now from:YT- John Santiago Op Amp Design Basics - Inverting Amplifier - Part 3
(i was actually wondering when you will do that 8-).
While you mentioned ohm's law you might add Kirchhoff circuit law in the part where you "wonder" about where current goes and that lack of minus in inv. OP gain formula was bugging me until you corrected it...
For the end, you put smaller resistor which drives 10x larger current form output trough feedback resistor to "match/counter" input current (100uAmpsp rise into 1mAp) so output stage switches into B class (whole chip with 2xOPAmps has less then 1mA quiescent current and output stage probably uses about 70% of that) and you see clear crossover distortion on the output waveform (where OP-Amp loses control hence the spikes on the input, you can represent that as vehicle steering wheel dead play for mechanical types)
Great video, just took best opamp explanation title,cant wait for #2,3,....
Great explanations. I used OpAmps before, but more copy-and-paste style, just using the standard circuits without thinking about it. Now it makes sense why it works, and with the two rules I might even create equations to analyze more complex circuits, like the differential amplifier, where you've lost me a bit.
Yeah, I did gloss over the differential amplifier a bit, sorry about that.
Gloss? Yeah I totally missed Diff Amp totally. You probably used initials DA and it just didn't register in my mind.
He's always smiling, and sharing useful knowledge. EV and Rosman are my fav. channels.
Wasted hours reading lots of "introduction to OPAMP" books, spent almost an hour on this video and understood more than anything those books tried to teach, Thank you....
I spent 10 minutes waiting to see a correction for the inverting op amp, didn't want to comment too soon but finally my mind is at rest :)
Would you believe me if I said it was a deliberate test?
Probably not, but hearYe hearYe, spoiler alert.
I wish you could do one like this for transistors!
Bipolar transistor explanation:
The base-emitter junction behaves like a diode. In NPN transistors, it goes from base to emitter, and in PNP transistors, it goes from emitter to base.
The current flowing between the emitter and the collector is limited to some gain (>100 for small-signal transistors, 20-100 for power transistors) times the base-emitter current. This current is only allowed in one direction (from collector to emitter in NPN transistors, from emitter to collector in PNP transistors).
Field-effect transistor explanation:
¯\_(ツ)_/¯
Transistors are even simpler
Thanks Dave. I watched this as a refresher for an Engineer II technical interview. They asked all Op Amp questions! Passed it!
Thanks Dave. Watched a load of videos that were doing my head in. Very well explained. Cheers.
This guy taught me what I couldn't understand in my class even after discussing with 3 professors😂😂
Same bro
I was just thinking the same thinking I wish my college professor explained it like this...or maybe I was just too hung over to understand :-)
That's because he has designed so much own circuits
Was a professional electronic designer
Invented 32 channel logic analyser in the 80s
Played with lot of op amps and some professors have never used a 741
Your professors probably don't understand it either, so tell them to watch this video ;)
Thank you Dave! This video has saved me headaches on multiple occasions. Everything is so well explained. I keep coming back to it for reference.
This is an excellent intro to Op Amps. Great work!
Just great, a topic I always left apart until you discover it to me. I suppose there are LOTS of applications but it's great to learn that way. A lot of things I discovered! Thank you so much!
OMG THANKS SO MUCH!! T^T You just saved my exams:')
The things that were written on the board at the starting is exactly what my university wants me to learn
Dave is really passionate about electronics that's why he took all the explanation to a whole new level! Thank you!
Thanks for taking the time to do this... I'm learning electronics on my own and this really helps...
For the love of Tesla, I was so friggin' nervous when you forgot the 'negative' of inverting gain!